From 0dc9e0996aa0210b04fff9fa908b2d7ec579417c Mon Sep 17 00:00:00 2001 From: Gianluca Guida Date: Fri, 18 Mar 2011 15:52:16 +0000 Subject: [PATCH] Import unmodified NetBSD's libm for compiling with new libc. As the current libc includes a libm implementation, with the new libc this is needed. Unneeded (for the moment) archs have been removed. --- lib/nbsd_libm/Makefile | 280 ++++++++ lib/nbsd_libm/arch/i387/.depend | 2 + lib/nbsd_libm/arch/i387/Makefile | 10 + lib/nbsd_libm/arch/i387/abi.h | 77 +++ lib/nbsd_libm/arch/i387/e_acos.S | 24 + lib/nbsd_libm/arch/i387/e_asin.S | 23 + lib/nbsd_libm/arch/i387/e_atan2.S | 18 + lib/nbsd_libm/arch/i387/e_atan2f.S | 18 + lib/nbsd_libm/arch/i387/e_exp.S | 108 +++ lib/nbsd_libm/arch/i387/e_expf.S | 55 ++ lib/nbsd_libm/arch/i387/e_fmod.S | 23 + lib/nbsd_libm/arch/i387/e_log.S | 18 + lib/nbsd_libm/arch/i387/e_log10.S | 18 + lib/nbsd_libm/arch/i387/e_log10f.S | 18 + lib/nbsd_libm/arch/i387/e_log2.S | 18 + lib/nbsd_libm/arch/i387/e_log2f.S | 18 + lib/nbsd_libm/arch/i387/e_logf.S | 18 + lib/nbsd_libm/arch/i387/e_remainder.S | 22 + lib/nbsd_libm/arch/i387/e_remainderf.S | 22 + lib/nbsd_libm/arch/i387/e_scalb.S | 19 + lib/nbsd_libm/arch/i387/e_scalbf.S | 18 + lib/nbsd_libm/arch/i387/e_sqrt.S | 17 + lib/nbsd_libm/arch/i387/e_sqrtf.S | 17 + lib/nbsd_libm/arch/i387/empty.S | 1 + lib/nbsd_libm/arch/i387/fenv.c | 514 ++++++++++++++ lib/nbsd_libm/arch/i387/lrint.S | 23 + lib/nbsd_libm/arch/i387/s_atan.S | 18 + lib/nbsd_libm/arch/i387/s_atanf.S | 18 + lib/nbsd_libm/arch/i387/s_ceil.S | 45 ++ lib/nbsd_libm/arch/i387/s_ceilf.S | 43 ++ lib/nbsd_libm/arch/i387/s_copysign.S | 53 ++ lib/nbsd_libm/arch/i387/s_copysignf.S | 53 ++ lib/nbsd_libm/arch/i387/s_cos.S | 31 + lib/nbsd_libm/arch/i387/s_cosf.S | 18 + lib/nbsd_libm/arch/i387/s_finite.S | 26 + lib/nbsd_libm/arch/i387/s_finitef.S | 25 + lib/nbsd_libm/arch/i387/s_floor.S | 43 ++ lib/nbsd_libm/arch/i387/s_floorf.S | 43 ++ lib/nbsd_libm/arch/i387/s_ilogb.S | 32 + lib/nbsd_libm/arch/i387/s_ilogbf.S | 32 + lib/nbsd_libm/arch/i387/s_log1p.S | 76 +++ lib/nbsd_libm/arch/i387/s_log1pf.S | 76 +++ lib/nbsd_libm/arch/i387/s_logb.S | 18 + lib/nbsd_libm/arch/i387/s_logbf.S | 18 + lib/nbsd_libm/arch/i387/s_modf.S | 106 +++ lib/nbsd_libm/arch/i387/s_rint.S | 17 + lib/nbsd_libm/arch/i387/s_rintf.S | 17 + lib/nbsd_libm/arch/i387/s_scalbn.S | 30 + lib/nbsd_libm/arch/i387/s_scalbnf.S | 30 + lib/nbsd_libm/arch/i387/s_significand.S | 18 + lib/nbsd_libm/arch/i387/s_significandf.S | 18 + lib/nbsd_libm/arch/i387/s_sin.S | 31 + lib/nbsd_libm/arch/i387/s_sinf.S | 18 + lib/nbsd_libm/arch/i387/s_tan.S | 33 + lib/nbsd_libm/arch/i387/s_tanf.S | 19 + lib/nbsd_libm/arch/i387/shlib_version | 5 + lib/nbsd_libm/arch/x86_64/fenv.c | 524 +++++++++++++++ lib/nbsd_libm/compat/compat_cabs.c | 29 + lib/nbsd_libm/compat/compat_cabsf.c | 29 + lib/nbsd_libm/complex/Makefile.inc | 28 + lib/nbsd_libm/complex/cabs.3 | 53 ++ lib/nbsd_libm/complex/cabs.c | 17 + lib/nbsd_libm/complex/cabsf.c | 17 + lib/nbsd_libm/complex/cacos.3 | 57 ++ lib/nbsd_libm/complex/cacos.c | 44 ++ lib/nbsd_libm/complex/cacosf.c | 44 ++ lib/nbsd_libm/complex/cacosh.3 | 58 ++ lib/nbsd_libm/complex/cacosh.c | 45 ++ lib/nbsd_libm/complex/cacoshf.c | 45 ++ lib/nbsd_libm/complex/carg.3 | 56 ++ lib/nbsd_libm/complex/carg.c | 17 + lib/nbsd_libm/complex/cargf.c | 17 + lib/nbsd_libm/complex/casin.3 | 58 ++ lib/nbsd_libm/complex/casin.c | 120 ++++ lib/nbsd_libm/complex/casinf.c | 120 ++++ lib/nbsd_libm/complex/casinh.3 | 58 ++ lib/nbsd_libm/complex/casinh.c | 42 ++ lib/nbsd_libm/complex/casinhf.c | 42 ++ lib/nbsd_libm/complex/catan.3 | 58 ++ lib/nbsd_libm/complex/catan.c | 79 +++ lib/nbsd_libm/complex/catanf.c | 79 +++ lib/nbsd_libm/complex/catanh.3 | 58 ++ lib/nbsd_libm/complex/catanh.c | 42 ++ lib/nbsd_libm/complex/catanhf.c | 42 ++ lib/nbsd_libm/complex/ccos.3 | 53 ++ lib/nbsd_libm/complex/ccos.c | 46 ++ lib/nbsd_libm/complex/ccosf.c | 46 ++ lib/nbsd_libm/complex/ccosh.3 | 53 ++ lib/nbsd_libm/complex/ccosh.c | 46 ++ lib/nbsd_libm/complex/ccoshf.c | 46 ++ lib/nbsd_libm/complex/cephes_subr.c | 124 ++++ lib/nbsd_libm/complex/cephes_subr.h | 5 + lib/nbsd_libm/complex/cephes_subrf.c | 123 ++++ lib/nbsd_libm/complex/cephes_subrf.h | 5 + lib/nbsd_libm/complex/cexp.3 | 54 ++ lib/nbsd_libm/complex/cexp.c | 47 ++ lib/nbsd_libm/complex/cexpf.c | 47 ++ lib/nbsd_libm/complex/cimag.3 | 63 ++ lib/nbsd_libm/complex/cimag.c | 17 + lib/nbsd_libm/complex/cimagf.c | 17 + lib/nbsd_libm/complex/cimagl.c | 44 ++ lib/nbsd_libm/complex/clog.3 | 58 ++ lib/nbsd_libm/complex/clog.c | 47 ++ lib/nbsd_libm/complex/clogf.c | 47 ++ lib/nbsd_libm/complex/conj.3 | 56 ++ lib/nbsd_libm/complex/conj.c | 19 + lib/nbsd_libm/complex/conjf.c | 19 + lib/nbsd_libm/complex/conjl.c | 48 ++ lib/nbsd_libm/complex/cpow.3 | 57 ++ lib/nbsd_libm/complex/cpow.c | 57 ++ lib/nbsd_libm/complex/cpowf.c | 57 ++ lib/nbsd_libm/complex/cproj.3 | 59 ++ lib/nbsd_libm/complex/cproj.c | 63 ++ lib/nbsd_libm/complex/cprojf.c | 64 ++ lib/nbsd_libm/complex/cprojl.c | 63 ++ lib/nbsd_libm/complex/creal.3 | 63 ++ lib/nbsd_libm/complex/creal.c | 17 + lib/nbsd_libm/complex/crealf.c | 17 + lib/nbsd_libm/complex/creall.c | 44 ++ lib/nbsd_libm/complex/csin.3 | 53 ++ lib/nbsd_libm/complex/csin.c | 46 ++ lib/nbsd_libm/complex/csinf.c | 46 ++ lib/nbsd_libm/complex/csinh.3 | 53 ++ lib/nbsd_libm/complex/csinh.c | 46 ++ lib/nbsd_libm/complex/csinhf.c | 46 ++ lib/nbsd_libm/complex/csqrt.3 | 56 ++ lib/nbsd_libm/complex/csqrt.c | 99 +++ lib/nbsd_libm/complex/csqrtf.c | 99 +++ lib/nbsd_libm/complex/ctan.3 | 53 ++ lib/nbsd_libm/complex/ctan.c | 58 ++ lib/nbsd_libm/complex/ctanf.c | 58 ++ lib/nbsd_libm/complex/ctanh.3 | 53 ++ lib/nbsd_libm/complex/ctanh.c | 48 ++ lib/nbsd_libm/complex/ctanhf.c | 48 ++ lib/nbsd_libm/gen/Makefile.inc | 12 + lib/nbsd_libm/gen/nan.3 | 95 +++ lib/nbsd_libm/gen/nan.c | 85 +++ lib/nbsd_libm/gen/nanf.c | 41 ++ lib/nbsd_libm/gen/nanl.c | 41 ++ lib/nbsd_libm/man/acos.3 | 83 +++ lib/nbsd_libm/man/acosh.3 | 77 +++ lib/nbsd_libm/man/asin.3 | 85 +++ lib/nbsd_libm/man/asinh.3 | 75 +++ lib/nbsd_libm/man/atan.3 | 77 +++ lib/nbsd_libm/man/atan2.3 | 192 ++++++ lib/nbsd_libm/man/atanh.3 | 77 +++ lib/nbsd_libm/man/ceil.3 | 65 ++ lib/nbsd_libm/man/cos.3 | 77 +++ lib/nbsd_libm/man/cosh.3 | 81 +++ lib/nbsd_libm/man/erf.3 | 87 +++ lib/nbsd_libm/man/exp.3 | 385 +++++++++++ lib/nbsd_libm/man/fabs.3 | 69 ++ lib/nbsd_libm/man/fdim.3 | 89 +++ lib/nbsd_libm/man/feclearexcept.3 | 139 ++++ lib/nbsd_libm/man/feenableexcept.3 | 97 +++ lib/nbsd_libm/man/fegetenv.3 | 114 ++++ lib/nbsd_libm/man/fegetround.3 | 84 +++ lib/nbsd_libm/man/fenv.3 | 283 ++++++++ lib/nbsd_libm/man/floor.3 | 65 ++ lib/nbsd_libm/man/fmax.3 | 100 +++ lib/nbsd_libm/man/fmod.3 | 79 +++ lib/nbsd_libm/man/frexp.3 | 85 +++ lib/nbsd_libm/man/hypot.3 | 124 ++++ lib/nbsd_libm/man/ieee.3 | 189 ++++++ lib/nbsd_libm/man/ieee_test.3 | 96 +++ lib/nbsd_libm/man/isinff.3 | 76 +++ lib/nbsd_libm/man/j0.3 | 153 +++++ lib/nbsd_libm/man/ldexp.3 | 89 +++ lib/nbsd_libm/man/lgamma.3 | 123 ++++ lib/nbsd_libm/man/lrint.3 | 103 +++ lib/nbsd_libm/man/math.3 | 682 +++++++++++++++++++ lib/nbsd_libm/man/modf.3 | 74 ++ lib/nbsd_libm/man/rint.3 | 64 ++ lib/nbsd_libm/man/round.3 | 76 +++ lib/nbsd_libm/man/sin.3 | 73 ++ lib/nbsd_libm/man/sinh.3 | 75 +++ lib/nbsd_libm/man/sqrt.3 | 91 +++ lib/nbsd_libm/man/tan.3 | 77 +++ lib/nbsd_libm/man/tanh.3 | 74 ++ lib/nbsd_libm/man/trunc.3 | 79 +++ lib/nbsd_libm/noieee_src/mathimpl.h | 114 ++++ lib/nbsd_libm/noieee_src/n_acosh.c | 102 +++ lib/nbsd_libm/noieee_src/n_asincos.c | 170 +++++ lib/nbsd_libm/noieee_src/n_asinh.c | 101 +++ lib/nbsd_libm/noieee_src/n_atan.c | 87 +++ lib/nbsd_libm/noieee_src/n_atan2.c | 279 ++++++++ lib/nbsd_libm/noieee_src/n_atanh.c | 82 +++ lib/nbsd_libm/noieee_src/n_cabs.c | 227 +++++++ lib/nbsd_libm/noieee_src/n_cbrt.c | 117 ++++ lib/nbsd_libm/noieee_src/n_cosh.c | 146 ++++ lib/nbsd_libm/noieee_src/n_erf.c | 398 +++++++++++ lib/nbsd_libm/noieee_src/n_exp.c | 215 ++++++ lib/nbsd_libm/noieee_src/n_exp__E.c | 136 ++++ lib/nbsd_libm/noieee_src/n_expm1.c | 168 +++++ lib/nbsd_libm/noieee_src/n_floor.c | 218 ++++++ lib/nbsd_libm/noieee_src/n_fmax.c | 38 ++ lib/nbsd_libm/noieee_src/n_fmaxf.c | 38 ++ lib/nbsd_libm/noieee_src/n_fmin.c | 38 ++ lib/nbsd_libm/noieee_src/n_fminf.c | 38 ++ lib/nbsd_libm/noieee_src/n_fmod.c | 154 +++++ lib/nbsd_libm/noieee_src/n_gamma.c | 333 +++++++++ lib/nbsd_libm/noieee_src/n_j0.c | 444 ++++++++++++ lib/nbsd_libm/noieee_src/n_j1.c | 448 +++++++++++++ lib/nbsd_libm/noieee_src/n_jn.c | 311 +++++++++ lib/nbsd_libm/noieee_src/n_lgamma.c | 308 +++++++++ lib/nbsd_libm/noieee_src/n_log.c | 491 ++++++++++++++ lib/nbsd_libm/noieee_src/n_log10.c | 95 +++ lib/nbsd_libm/noieee_src/n_log1p.c | 170 +++++ lib/nbsd_libm/noieee_src/n_log__L.c | 110 +++ lib/nbsd_libm/noieee_src/n_lround.c | 53 ++ lib/nbsd_libm/noieee_src/n_lroundf.c | 53 ++ lib/nbsd_libm/noieee_src/n_pow.c | 220 ++++++ lib/nbsd_libm/noieee_src/n_round.c | 53 ++ lib/nbsd_libm/noieee_src/n_roundf.c | 53 ++ lib/nbsd_libm/noieee_src/n_sincos.c | 110 +++ lib/nbsd_libm/noieee_src/n_sinh.c | 133 ++++ lib/nbsd_libm/noieee_src/n_support.c | 520 +++++++++++++++ lib/nbsd_libm/noieee_src/n_tan.c | 73 ++ lib/nbsd_libm/noieee_src/n_tanh.c | 99 +++ lib/nbsd_libm/noieee_src/trig.h | 223 +++++++ lib/nbsd_libm/shlib_version | 5 + lib/nbsd_libm/src/e_acos.c | 104 +++ lib/nbsd_libm/src/e_acosf.c | 82 +++ lib/nbsd_libm/src/e_acosh.c | 62 ++ lib/nbsd_libm/src/e_acoshf.c | 50 ++ lib/nbsd_libm/src/e_asin.c | 115 ++++ lib/nbsd_libm/src/e_asinf.c | 87 +++ lib/nbsd_libm/src/e_atan2.c | 123 ++++ lib/nbsd_libm/src/e_atan2f.c | 98 +++ lib/nbsd_libm/src/e_atanh.c | 63 ++ lib/nbsd_libm/src/e_atanhf.c | 47 ++ lib/nbsd_libm/src/e_cosh.c | 86 +++ lib/nbsd_libm/src/e_coshf.c | 65 ++ lib/nbsd_libm/src/e_exp.c | 162 +++++ lib/nbsd_libm/src/e_expf.c | 99 +++ lib/nbsd_libm/src/e_fmod.c | 133 ++++ lib/nbsd_libm/src/e_fmodf.c | 106 +++ lib/nbsd_libm/src/e_hypot.c | 125 ++++ lib/nbsd_libm/src/e_hypotf.c | 84 +++ lib/nbsd_libm/src/e_j0.c | 389 +++++++++++ lib/nbsd_libm/src/e_j0f.c | 352 ++++++++++ lib/nbsd_libm/src/e_j1.c | 384 +++++++++++ lib/nbsd_libm/src/e_j1f.c | 349 ++++++++++ lib/nbsd_libm/src/e_jn.c | 274 ++++++++ lib/nbsd_libm/src/e_jnf.c | 204 ++++++ lib/nbsd_libm/src/e_lgamma_r.c | 298 +++++++++ lib/nbsd_libm/src/e_lgammaf_r.c | 234 +++++++ lib/nbsd_libm/src/e_log.c | 136 ++++ lib/nbsd_libm/src/e_log10.c | 87 +++ lib/nbsd_libm/src/e_log10f.c | 56 ++ lib/nbsd_libm/src/e_log2.c | 80 +++ lib/nbsd_libm/src/e_log2f.c | 81 +++ lib/nbsd_libm/src/e_logf.c | 87 +++ lib/nbsd_libm/src/e_pow.c | 303 +++++++++ lib/nbsd_libm/src/e_powf.c | 247 +++++++ lib/nbsd_libm/src/e_rem_pio2.c | 169 +++++ lib/nbsd_libm/src/e_rem_pio2f.c | 181 +++++ lib/nbsd_libm/src/e_remainder.c | 73 ++ lib/nbsd_libm/src/e_remainderf.c | 66 ++ lib/nbsd_libm/src/e_scalb.c | 49 ++ lib/nbsd_libm/src/e_scalbf.c | 46 ++ lib/nbsd_libm/src/e_sinh.c | 79 +++ lib/nbsd_libm/src/e_sinhf.c | 61 ++ lib/nbsd_libm/src/e_sqrt.c | 446 +++++++++++++ lib/nbsd_libm/src/e_sqrtf.c | 90 +++ lib/nbsd_libm/src/k_cos.c | 89 +++ lib/nbsd_libm/src/k_cosf.c | 57 ++ lib/nbsd_libm/src/k_rem_pio2.c | 306 +++++++++ lib/nbsd_libm/src/k_rem_pio2f.c | 199 ++++++ lib/nbsd_libm/src/k_sin.c | 72 ++ lib/nbsd_libm/src/k_sinf.c | 47 ++ lib/nbsd_libm/src/k_standard.c | 815 +++++++++++++++++++++++ lib/nbsd_libm/src/k_tan.c | 156 +++++ lib/nbsd_libm/src/k_tanf.c | 94 +++ lib/nbsd_libm/src/llrint.c | 13 + lib/nbsd_libm/src/llrintf.c | 13 + lib/nbsd_libm/src/llround.c | 13 + lib/nbsd_libm/src/llroundf.c | 13 + lib/nbsd_libm/src/lrint.c | 92 +++ lib/nbsd_libm/src/lrintf.c | 91 +++ lib/nbsd_libm/src/lround.c | 85 +++ lib/nbsd_libm/src/lroundf.c | 80 +++ lib/nbsd_libm/src/math_private.h | 278 ++++++++ lib/nbsd_libm/src/namespace.h | 34 + lib/nbsd_libm/src/s_asinh.c | 58 ++ lib/nbsd_libm/src/s_asinhf.c | 50 ++ lib/nbsd_libm/src/s_atan.c | 120 ++++ lib/nbsd_libm/src/s_atanf.c | 100 +++ lib/nbsd_libm/src/s_cbrt.c | 82 +++ lib/nbsd_libm/src/s_cbrtf.c | 72 ++ lib/nbsd_libm/src/s_ceil.c | 73 ++ lib/nbsd_libm/src/s_ceilf.c | 54 ++ lib/nbsd_libm/src/s_copysign.c | 35 + lib/nbsd_libm/src/s_copysignf.c | 38 ++ lib/nbsd_libm/src/s_copysignl.c | 51 ++ lib/nbsd_libm/src/s_cos.c | 86 +++ lib/nbsd_libm/src/s_cosf.c | 61 ++ lib/nbsd_libm/src/s_erf.c | 303 +++++++++ lib/nbsd_libm/src/s_erff.c | 212 ++++++ lib/nbsd_libm/src/s_exp2.c | 401 +++++++++++ lib/nbsd_libm/src/s_exp2f.c | 139 ++++ lib/nbsd_libm/src/s_expm1.c | 223 +++++++ lib/nbsd_libm/src/s_expm1f.c | 128 ++++ lib/nbsd_libm/src/s_fabs.c | 32 + lib/nbsd_libm/src/s_fabsf.c | 35 + lib/nbsd_libm/src/s_fabsl.c | 49 ++ lib/nbsd_libm/src/s_fdim.c | 49 ++ lib/nbsd_libm/src/s_finite.c | 32 + lib/nbsd_libm/src/s_finitef.c | 35 + lib/nbsd_libm/src/s_floor.c | 74 ++ lib/nbsd_libm/src/s_floorf.c | 63 ++ lib/nbsd_libm/src/s_fmax.c | 58 ++ lib/nbsd_libm/src/s_fmaxf.c | 58 ++ lib/nbsd_libm/src/s_fmaxl.c | 61 ++ lib/nbsd_libm/src/s_fmin.c | 58 ++ lib/nbsd_libm/src/s_fminf.c | 58 ++ lib/nbsd_libm/src/s_fminl.c | 61 ++ lib/nbsd_libm/src/s_frexp.c | 52 ++ lib/nbsd_libm/src/s_frexpf.c | 45 ++ lib/nbsd_libm/src/s_ilogb.c | 48 ++ lib/nbsd_libm/src/s_ilogbf.c | 40 ++ lib/nbsd_libm/src/s_infinity.c | 14 + lib/nbsd_libm/src/s_isinf.c | 28 + lib/nbsd_libm/src/s_isinff.c | 27 + lib/nbsd_libm/src/s_isnan.c | 35 + lib/nbsd_libm/src/s_isnanf.c | 37 + lib/nbsd_libm/src/s_ldexp.c | 30 + lib/nbsd_libm/src/s_ldexpf.c | 33 + lib/nbsd_libm/src/s_lib_version.c | 40 ++ lib/nbsd_libm/src/s_log1p.c | 165 +++++ lib/nbsd_libm/src/s_log1pf.c | 104 +++ lib/nbsd_libm/src/s_logb.c | 39 ++ lib/nbsd_libm/src/s_logbf.c | 36 + lib/nbsd_libm/src/s_matherr.c | 27 + lib/nbsd_libm/src/s_modf.c | 78 +++ lib/nbsd_libm/src/s_modff.c | 59 ++ lib/nbsd_libm/src/s_nextafter.c | 76 +++ lib/nbsd_libm/src/s_nextafterf.c | 67 ++ lib/nbsd_libm/src/s_nextafterl.c | 94 +++ lib/nbsd_libm/src/s_nexttoward.c | 89 +++ lib/nbsd_libm/src/s_rint.c | 79 +++ lib/nbsd_libm/src/s_rintf.c | 68 ++ lib/nbsd_libm/src/s_round.c | 59 ++ lib/nbsd_libm/src/s_roundf.c | 59 ++ lib/nbsd_libm/src/s_scalbn.c | 65 ++ lib/nbsd_libm/src/s_scalbnf.c | 61 ++ lib/nbsd_libm/src/s_signgam.c | 5 + lib/nbsd_libm/src/s_significand.c | 31 + lib/nbsd_libm/src/s_significandf.c | 28 + lib/nbsd_libm/src/s_sin.c | 86 +++ lib/nbsd_libm/src/s_sinf.c | 57 ++ lib/nbsd_libm/src/s_tan.c | 73 ++ lib/nbsd_libm/src/s_tanf.c | 45 ++ lib/nbsd_libm/src/s_tanh.c | 79 +++ lib/nbsd_libm/src/s_tanhf.c | 57 ++ lib/nbsd_libm/src/s_trunc.c | 66 ++ lib/nbsd_libm/src/s_truncf.c | 58 ++ lib/nbsd_libm/src/w_acos.c | 40 ++ lib/nbsd_libm/src/w_acosf.c | 44 ++ lib/nbsd_libm/src/w_acosh.c | 39 ++ lib/nbsd_libm/src/w_acoshf.c | 44 ++ lib/nbsd_libm/src/w_asin.c | 44 ++ lib/nbsd_libm/src/w_asinf.c | 48 ++ lib/nbsd_libm/src/w_atan2.c | 44 ++ lib/nbsd_libm/src/w_atan2f.c | 48 ++ lib/nbsd_libm/src/w_atanh.c | 44 ++ lib/nbsd_libm/src/w_atanhf.c | 49 ++ lib/nbsd_libm/src/w_cosh.c | 44 ++ lib/nbsd_libm/src/w_coshf.c | 48 ++ lib/nbsd_libm/src/w_drem.c | 19 + lib/nbsd_libm/src/w_dremf.c | 20 + lib/nbsd_libm/src/w_exp.c | 51 ++ lib/nbsd_libm/src/w_expf.c | 56 ++ lib/nbsd_libm/src/w_fmod.c | 40 ++ lib/nbsd_libm/src/w_fmodf.c | 44 ++ lib/nbsd_libm/src/w_gamma.c | 44 ++ lib/nbsd_libm/src/w_gamma_r.c | 42 ++ lib/nbsd_libm/src/w_gammaf.c | 43 ++ lib/nbsd_libm/src/w_gammaf_r.c | 47 ++ lib/nbsd_libm/src/w_hypot.c | 44 ++ lib/nbsd_libm/src/w_hypotf.c | 48 ++ lib/nbsd_libm/src/w_j0.c | 62 ++ lib/nbsd_libm/src/w_j0f.c | 67 ++ lib/nbsd_libm/src/w_j1.c | 63 ++ lib/nbsd_libm/src/w_j1f.c | 68 ++ lib/nbsd_libm/src/w_jn.c | 85 +++ lib/nbsd_libm/src/w_jnf.c | 64 ++ lib/nbsd_libm/src/w_lgamma.c | 44 ++ lib/nbsd_libm/src/w_lgamma_r.c | 42 ++ lib/nbsd_libm/src/w_lgammaf.c | 43 ++ lib/nbsd_libm/src/w_lgammaf_r.c | 47 ++ lib/nbsd_libm/src/w_log.c | 44 ++ lib/nbsd_libm/src/w_log10.c | 43 ++ lib/nbsd_libm/src/w_log10f.c | 48 ++ lib/nbsd_libm/src/w_log2.c | 43 ++ lib/nbsd_libm/src/w_log2f.c | 48 ++ lib/nbsd_libm/src/w_logf.c | 49 ++ lib/nbsd_libm/src/w_pow.c | 62 ++ lib/nbsd_libm/src/w_powf.c | 69 ++ lib/nbsd_libm/src/w_remainder.c | 39 ++ lib/nbsd_libm/src/w_remainderf.c | 43 ++ lib/nbsd_libm/src/w_scalb.c | 54 ++ lib/nbsd_libm/src/w_scalbf.c | 59 ++ lib/nbsd_libm/src/w_sinh.c | 44 ++ lib/nbsd_libm/src/w_sinhf.c | 48 ++ lib/nbsd_libm/src/w_sqrt.c | 39 ++ lib/nbsd_libm/src/w_sqrtf.c | 43 ++ 407 files changed, 35869 insertions(+) create mode 100644 lib/nbsd_libm/Makefile create mode 100644 lib/nbsd_libm/arch/i387/.depend create mode 100644 lib/nbsd_libm/arch/i387/Makefile create mode 100644 lib/nbsd_libm/arch/i387/abi.h create mode 100644 lib/nbsd_libm/arch/i387/e_acos.S create mode 100644 lib/nbsd_libm/arch/i387/e_asin.S create mode 100644 lib/nbsd_libm/arch/i387/e_atan2.S create mode 100644 lib/nbsd_libm/arch/i387/e_atan2f.S create mode 100644 lib/nbsd_libm/arch/i387/e_exp.S create mode 100644 lib/nbsd_libm/arch/i387/e_expf.S create mode 100644 lib/nbsd_libm/arch/i387/e_fmod.S create mode 100644 lib/nbsd_libm/arch/i387/e_log.S create mode 100644 lib/nbsd_libm/arch/i387/e_log10.S create mode 100644 lib/nbsd_libm/arch/i387/e_log10f.S create mode 100644 lib/nbsd_libm/arch/i387/e_log2.S create mode 100644 lib/nbsd_libm/arch/i387/e_log2f.S create mode 100644 lib/nbsd_libm/arch/i387/e_logf.S create mode 100644 lib/nbsd_libm/arch/i387/e_remainder.S create mode 100644 lib/nbsd_libm/arch/i387/e_remainderf.S create mode 100644 lib/nbsd_libm/arch/i387/e_scalb.S create mode 100644 lib/nbsd_libm/arch/i387/e_scalbf.S create mode 100644 lib/nbsd_libm/arch/i387/e_sqrt.S create mode 100644 lib/nbsd_libm/arch/i387/e_sqrtf.S create mode 100644 lib/nbsd_libm/arch/i387/empty.S create mode 100644 lib/nbsd_libm/arch/i387/fenv.c create mode 100644 lib/nbsd_libm/arch/i387/lrint.S create mode 100644 lib/nbsd_libm/arch/i387/s_atan.S create mode 100644 lib/nbsd_libm/arch/i387/s_atanf.S create mode 100644 lib/nbsd_libm/arch/i387/s_ceil.S create mode 100644 lib/nbsd_libm/arch/i387/s_ceilf.S create mode 100644 lib/nbsd_libm/arch/i387/s_copysign.S create mode 100644 lib/nbsd_libm/arch/i387/s_copysignf.S create mode 100644 lib/nbsd_libm/arch/i387/s_cos.S create mode 100644 lib/nbsd_libm/arch/i387/s_cosf.S create mode 100644 lib/nbsd_libm/arch/i387/s_finite.S create mode 100644 lib/nbsd_libm/arch/i387/s_finitef.S create mode 100644 lib/nbsd_libm/arch/i387/s_floor.S create mode 100644 lib/nbsd_libm/arch/i387/s_floorf.S create mode 100644 lib/nbsd_libm/arch/i387/s_ilogb.S create mode 100644 lib/nbsd_libm/arch/i387/s_ilogbf.S create mode 100644 lib/nbsd_libm/arch/i387/s_log1p.S create mode 100644 lib/nbsd_libm/arch/i387/s_log1pf.S create mode 100644 lib/nbsd_libm/arch/i387/s_logb.S create mode 100644 lib/nbsd_libm/arch/i387/s_logbf.S create mode 100644 lib/nbsd_libm/arch/i387/s_modf.S create mode 100644 lib/nbsd_libm/arch/i387/s_rint.S create mode 100644 lib/nbsd_libm/arch/i387/s_rintf.S create mode 100644 lib/nbsd_libm/arch/i387/s_scalbn.S create mode 100644 lib/nbsd_libm/arch/i387/s_scalbnf.S create mode 100644 lib/nbsd_libm/arch/i387/s_significand.S create mode 100644 lib/nbsd_libm/arch/i387/s_significandf.S create mode 100644 lib/nbsd_libm/arch/i387/s_sin.S create mode 100644 lib/nbsd_libm/arch/i387/s_sinf.S create mode 100644 lib/nbsd_libm/arch/i387/s_tan.S create mode 100644 lib/nbsd_libm/arch/i387/s_tanf.S create mode 100644 lib/nbsd_libm/arch/i387/shlib_version create mode 100644 lib/nbsd_libm/arch/x86_64/fenv.c create mode 100644 lib/nbsd_libm/compat/compat_cabs.c create mode 100644 lib/nbsd_libm/compat/compat_cabsf.c create mode 100644 lib/nbsd_libm/complex/Makefile.inc create mode 100644 lib/nbsd_libm/complex/cabs.3 create mode 100644 lib/nbsd_libm/complex/cabs.c create mode 100644 lib/nbsd_libm/complex/cabsf.c create mode 100644 lib/nbsd_libm/complex/cacos.3 create mode 100644 lib/nbsd_libm/complex/cacos.c create mode 100644 lib/nbsd_libm/complex/cacosf.c create mode 100644 lib/nbsd_libm/complex/cacosh.3 create mode 100644 lib/nbsd_libm/complex/cacosh.c create mode 100644 lib/nbsd_libm/complex/cacoshf.c create mode 100644 lib/nbsd_libm/complex/carg.3 create mode 100644 lib/nbsd_libm/complex/carg.c create mode 100644 lib/nbsd_libm/complex/cargf.c create mode 100644 lib/nbsd_libm/complex/casin.3 create mode 100644 lib/nbsd_libm/complex/casin.c create mode 100644 lib/nbsd_libm/complex/casinf.c create mode 100644 lib/nbsd_libm/complex/casinh.3 create mode 100644 lib/nbsd_libm/complex/casinh.c create mode 100644 lib/nbsd_libm/complex/casinhf.c create mode 100644 lib/nbsd_libm/complex/catan.3 create mode 100644 lib/nbsd_libm/complex/catan.c create mode 100644 lib/nbsd_libm/complex/catanf.c create mode 100644 lib/nbsd_libm/complex/catanh.3 create mode 100644 lib/nbsd_libm/complex/catanh.c create mode 100644 lib/nbsd_libm/complex/catanhf.c create mode 100644 lib/nbsd_libm/complex/ccos.3 create mode 100644 lib/nbsd_libm/complex/ccos.c create mode 100644 lib/nbsd_libm/complex/ccosf.c create mode 100644 lib/nbsd_libm/complex/ccosh.3 create mode 100644 lib/nbsd_libm/complex/ccosh.c create mode 100644 lib/nbsd_libm/complex/ccoshf.c create mode 100644 lib/nbsd_libm/complex/cephes_subr.c create mode 100644 lib/nbsd_libm/complex/cephes_subr.h create mode 100644 lib/nbsd_libm/complex/cephes_subrf.c create mode 100644 lib/nbsd_libm/complex/cephes_subrf.h create mode 100644 lib/nbsd_libm/complex/cexp.3 create mode 100644 lib/nbsd_libm/complex/cexp.c create mode 100644 lib/nbsd_libm/complex/cexpf.c create mode 100644 lib/nbsd_libm/complex/cimag.3 create mode 100644 lib/nbsd_libm/complex/cimag.c create mode 100644 lib/nbsd_libm/complex/cimagf.c create mode 100644 lib/nbsd_libm/complex/cimagl.c create mode 100644 lib/nbsd_libm/complex/clog.3 create mode 100644 lib/nbsd_libm/complex/clog.c create mode 100644 lib/nbsd_libm/complex/clogf.c create mode 100644 lib/nbsd_libm/complex/conj.3 create mode 100644 lib/nbsd_libm/complex/conj.c create mode 100644 lib/nbsd_libm/complex/conjf.c create mode 100644 lib/nbsd_libm/complex/conjl.c create mode 100644 lib/nbsd_libm/complex/cpow.3 create mode 100644 lib/nbsd_libm/complex/cpow.c create mode 100644 lib/nbsd_libm/complex/cpowf.c create mode 100644 lib/nbsd_libm/complex/cproj.3 create mode 100644 lib/nbsd_libm/complex/cproj.c create mode 100644 lib/nbsd_libm/complex/cprojf.c create mode 100644 lib/nbsd_libm/complex/cprojl.c create mode 100644 lib/nbsd_libm/complex/creal.3 create mode 100644 lib/nbsd_libm/complex/creal.c create mode 100644 lib/nbsd_libm/complex/crealf.c create mode 100644 lib/nbsd_libm/complex/creall.c create mode 100644 lib/nbsd_libm/complex/csin.3 create mode 100644 lib/nbsd_libm/complex/csin.c create mode 100644 lib/nbsd_libm/complex/csinf.c create mode 100644 lib/nbsd_libm/complex/csinh.3 create mode 100644 lib/nbsd_libm/complex/csinh.c create mode 100644 lib/nbsd_libm/complex/csinhf.c create mode 100644 lib/nbsd_libm/complex/csqrt.3 create mode 100644 lib/nbsd_libm/complex/csqrt.c create mode 100644 lib/nbsd_libm/complex/csqrtf.c create mode 100644 lib/nbsd_libm/complex/ctan.3 create mode 100644 lib/nbsd_libm/complex/ctan.c create mode 100644 lib/nbsd_libm/complex/ctanf.c create mode 100644 lib/nbsd_libm/complex/ctanh.3 create mode 100644 lib/nbsd_libm/complex/ctanh.c create mode 100644 lib/nbsd_libm/complex/ctanhf.c create mode 100644 lib/nbsd_libm/gen/Makefile.inc create mode 100644 lib/nbsd_libm/gen/nan.3 create mode 100644 lib/nbsd_libm/gen/nan.c create mode 100644 lib/nbsd_libm/gen/nanf.c create mode 100644 lib/nbsd_libm/gen/nanl.c create mode 100644 lib/nbsd_libm/man/acos.3 create mode 100644 lib/nbsd_libm/man/acosh.3 create mode 100644 lib/nbsd_libm/man/asin.3 create mode 100644 lib/nbsd_libm/man/asinh.3 create mode 100644 lib/nbsd_libm/man/atan.3 create mode 100644 lib/nbsd_libm/man/atan2.3 create mode 100644 lib/nbsd_libm/man/atanh.3 create mode 100644 lib/nbsd_libm/man/ceil.3 create mode 100644 lib/nbsd_libm/man/cos.3 create mode 100644 lib/nbsd_libm/man/cosh.3 create mode 100644 lib/nbsd_libm/man/erf.3 create mode 100644 lib/nbsd_libm/man/exp.3 create mode 100644 lib/nbsd_libm/man/fabs.3 create mode 100644 lib/nbsd_libm/man/fdim.3 create mode 100644 lib/nbsd_libm/man/feclearexcept.3 create mode 100644 lib/nbsd_libm/man/feenableexcept.3 create mode 100644 lib/nbsd_libm/man/fegetenv.3 create mode 100644 lib/nbsd_libm/man/fegetround.3 create mode 100644 lib/nbsd_libm/man/fenv.3 create mode 100644 lib/nbsd_libm/man/floor.3 create mode 100644 lib/nbsd_libm/man/fmax.3 create mode 100644 lib/nbsd_libm/man/fmod.3 create mode 100644 lib/nbsd_libm/man/frexp.3 create mode 100644 lib/nbsd_libm/man/hypot.3 create mode 100644 lib/nbsd_libm/man/ieee.3 create mode 100644 lib/nbsd_libm/man/ieee_test.3 create mode 100644 lib/nbsd_libm/man/isinff.3 create mode 100644 lib/nbsd_libm/man/j0.3 create mode 100644 lib/nbsd_libm/man/ldexp.3 create mode 100644 lib/nbsd_libm/man/lgamma.3 create mode 100644 lib/nbsd_libm/man/lrint.3 create mode 100644 lib/nbsd_libm/man/math.3 create mode 100644 lib/nbsd_libm/man/modf.3 create mode 100644 lib/nbsd_libm/man/rint.3 create mode 100644 lib/nbsd_libm/man/round.3 create mode 100644 lib/nbsd_libm/man/sin.3 create mode 100644 lib/nbsd_libm/man/sinh.3 create mode 100644 lib/nbsd_libm/man/sqrt.3 create mode 100644 lib/nbsd_libm/man/tan.3 create mode 100644 lib/nbsd_libm/man/tanh.3 create mode 100644 lib/nbsd_libm/man/trunc.3 create mode 100644 lib/nbsd_libm/noieee_src/mathimpl.h create mode 100644 lib/nbsd_libm/noieee_src/n_acosh.c create mode 100644 lib/nbsd_libm/noieee_src/n_asincos.c create mode 100644 lib/nbsd_libm/noieee_src/n_asinh.c create mode 100644 lib/nbsd_libm/noieee_src/n_atan.c create mode 100644 lib/nbsd_libm/noieee_src/n_atan2.c create mode 100644 lib/nbsd_libm/noieee_src/n_atanh.c create mode 100644 lib/nbsd_libm/noieee_src/n_cabs.c create mode 100644 lib/nbsd_libm/noieee_src/n_cbrt.c create mode 100644 lib/nbsd_libm/noieee_src/n_cosh.c create mode 100644 lib/nbsd_libm/noieee_src/n_erf.c create mode 100644 lib/nbsd_libm/noieee_src/n_exp.c create mode 100644 lib/nbsd_libm/noieee_src/n_exp__E.c create mode 100644 lib/nbsd_libm/noieee_src/n_expm1.c create mode 100644 lib/nbsd_libm/noieee_src/n_floor.c create mode 100644 lib/nbsd_libm/noieee_src/n_fmax.c create mode 100644 lib/nbsd_libm/noieee_src/n_fmaxf.c create mode 100644 lib/nbsd_libm/noieee_src/n_fmin.c create mode 100644 lib/nbsd_libm/noieee_src/n_fminf.c create mode 100644 lib/nbsd_libm/noieee_src/n_fmod.c create mode 100644 lib/nbsd_libm/noieee_src/n_gamma.c create mode 100644 lib/nbsd_libm/noieee_src/n_j0.c create mode 100644 lib/nbsd_libm/noieee_src/n_j1.c create mode 100644 lib/nbsd_libm/noieee_src/n_jn.c create mode 100644 lib/nbsd_libm/noieee_src/n_lgamma.c create mode 100644 lib/nbsd_libm/noieee_src/n_log.c create mode 100644 lib/nbsd_libm/noieee_src/n_log10.c create mode 100644 lib/nbsd_libm/noieee_src/n_log1p.c create mode 100644 lib/nbsd_libm/noieee_src/n_log__L.c create mode 100644 lib/nbsd_libm/noieee_src/n_lround.c create mode 100644 lib/nbsd_libm/noieee_src/n_lroundf.c create mode 100644 lib/nbsd_libm/noieee_src/n_pow.c create mode 100644 lib/nbsd_libm/noieee_src/n_round.c create mode 100644 lib/nbsd_libm/noieee_src/n_roundf.c create mode 100644 lib/nbsd_libm/noieee_src/n_sincos.c create mode 100644 lib/nbsd_libm/noieee_src/n_sinh.c create mode 100644 lib/nbsd_libm/noieee_src/n_support.c create mode 100644 lib/nbsd_libm/noieee_src/n_tan.c create mode 100644 lib/nbsd_libm/noieee_src/n_tanh.c create mode 100644 lib/nbsd_libm/noieee_src/trig.h create mode 100644 lib/nbsd_libm/shlib_version create mode 100644 lib/nbsd_libm/src/e_acos.c create mode 100644 lib/nbsd_libm/src/e_acosf.c create mode 100644 lib/nbsd_libm/src/e_acosh.c create mode 100644 lib/nbsd_libm/src/e_acoshf.c create mode 100644 lib/nbsd_libm/src/e_asin.c create mode 100644 lib/nbsd_libm/src/e_asinf.c create mode 100644 lib/nbsd_libm/src/e_atan2.c create mode 100644 lib/nbsd_libm/src/e_atan2f.c create mode 100644 lib/nbsd_libm/src/e_atanh.c create mode 100644 lib/nbsd_libm/src/e_atanhf.c create mode 100644 lib/nbsd_libm/src/e_cosh.c create mode 100644 lib/nbsd_libm/src/e_coshf.c create mode 100644 lib/nbsd_libm/src/e_exp.c create mode 100644 lib/nbsd_libm/src/e_expf.c create mode 100644 lib/nbsd_libm/src/e_fmod.c create mode 100644 lib/nbsd_libm/src/e_fmodf.c create mode 100644 lib/nbsd_libm/src/e_hypot.c create mode 100644 lib/nbsd_libm/src/e_hypotf.c create mode 100644 lib/nbsd_libm/src/e_j0.c create mode 100644 lib/nbsd_libm/src/e_j0f.c create mode 100644 lib/nbsd_libm/src/e_j1.c create mode 100644 lib/nbsd_libm/src/e_j1f.c create mode 100644 lib/nbsd_libm/src/e_jn.c create mode 100644 lib/nbsd_libm/src/e_jnf.c create mode 100644 lib/nbsd_libm/src/e_lgamma_r.c create mode 100644 lib/nbsd_libm/src/e_lgammaf_r.c create mode 100644 lib/nbsd_libm/src/e_log.c create mode 100644 lib/nbsd_libm/src/e_log10.c create mode 100644 lib/nbsd_libm/src/e_log10f.c create mode 100644 lib/nbsd_libm/src/e_log2.c create mode 100644 lib/nbsd_libm/src/e_log2f.c create mode 100644 lib/nbsd_libm/src/e_logf.c create mode 100644 lib/nbsd_libm/src/e_pow.c create mode 100644 lib/nbsd_libm/src/e_powf.c create mode 100644 lib/nbsd_libm/src/e_rem_pio2.c create mode 100644 lib/nbsd_libm/src/e_rem_pio2f.c create mode 100644 lib/nbsd_libm/src/e_remainder.c create mode 100644 lib/nbsd_libm/src/e_remainderf.c create mode 100644 lib/nbsd_libm/src/e_scalb.c create mode 100644 lib/nbsd_libm/src/e_scalbf.c create mode 100644 lib/nbsd_libm/src/e_sinh.c create mode 100644 lib/nbsd_libm/src/e_sinhf.c create mode 100644 lib/nbsd_libm/src/e_sqrt.c create mode 100644 lib/nbsd_libm/src/e_sqrtf.c create mode 100644 lib/nbsd_libm/src/k_cos.c create mode 100644 lib/nbsd_libm/src/k_cosf.c create mode 100644 lib/nbsd_libm/src/k_rem_pio2.c create mode 100644 lib/nbsd_libm/src/k_rem_pio2f.c create mode 100644 lib/nbsd_libm/src/k_sin.c create mode 100644 lib/nbsd_libm/src/k_sinf.c create mode 100644 lib/nbsd_libm/src/k_standard.c create mode 100644 lib/nbsd_libm/src/k_tan.c create mode 100644 lib/nbsd_libm/src/k_tanf.c create mode 100644 lib/nbsd_libm/src/llrint.c create mode 100644 lib/nbsd_libm/src/llrintf.c create mode 100644 lib/nbsd_libm/src/llround.c create mode 100644 lib/nbsd_libm/src/llroundf.c create mode 100644 lib/nbsd_libm/src/lrint.c create mode 100644 lib/nbsd_libm/src/lrintf.c create mode 100644 lib/nbsd_libm/src/lround.c create mode 100644 lib/nbsd_libm/src/lroundf.c create mode 100644 lib/nbsd_libm/src/math_private.h create mode 100644 lib/nbsd_libm/src/namespace.h create mode 100644 lib/nbsd_libm/src/s_asinh.c create mode 100644 lib/nbsd_libm/src/s_asinhf.c create mode 100644 lib/nbsd_libm/src/s_atan.c create mode 100644 lib/nbsd_libm/src/s_atanf.c create mode 100644 lib/nbsd_libm/src/s_cbrt.c create mode 100644 lib/nbsd_libm/src/s_cbrtf.c create mode 100644 lib/nbsd_libm/src/s_ceil.c create mode 100644 lib/nbsd_libm/src/s_ceilf.c create mode 100644 lib/nbsd_libm/src/s_copysign.c create mode 100644 lib/nbsd_libm/src/s_copysignf.c create mode 100644 lib/nbsd_libm/src/s_copysignl.c create mode 100644 lib/nbsd_libm/src/s_cos.c create mode 100644 lib/nbsd_libm/src/s_cosf.c create mode 100644 lib/nbsd_libm/src/s_erf.c create mode 100644 lib/nbsd_libm/src/s_erff.c create mode 100644 lib/nbsd_libm/src/s_exp2.c create mode 100644 lib/nbsd_libm/src/s_exp2f.c create mode 100644 lib/nbsd_libm/src/s_expm1.c create mode 100644 lib/nbsd_libm/src/s_expm1f.c create mode 100644 lib/nbsd_libm/src/s_fabs.c create mode 100644 lib/nbsd_libm/src/s_fabsf.c create mode 100644 lib/nbsd_libm/src/s_fabsl.c create mode 100644 lib/nbsd_libm/src/s_fdim.c create mode 100644 lib/nbsd_libm/src/s_finite.c create mode 100644 lib/nbsd_libm/src/s_finitef.c create mode 100644 lib/nbsd_libm/src/s_floor.c create mode 100644 lib/nbsd_libm/src/s_floorf.c create mode 100644 lib/nbsd_libm/src/s_fmax.c create mode 100644 lib/nbsd_libm/src/s_fmaxf.c create mode 100644 lib/nbsd_libm/src/s_fmaxl.c create mode 100644 lib/nbsd_libm/src/s_fmin.c create mode 100644 lib/nbsd_libm/src/s_fminf.c create mode 100644 lib/nbsd_libm/src/s_fminl.c create mode 100644 lib/nbsd_libm/src/s_frexp.c create mode 100644 lib/nbsd_libm/src/s_frexpf.c create mode 100644 lib/nbsd_libm/src/s_ilogb.c create mode 100644 lib/nbsd_libm/src/s_ilogbf.c create mode 100644 lib/nbsd_libm/src/s_infinity.c create mode 100644 lib/nbsd_libm/src/s_isinf.c create mode 100644 lib/nbsd_libm/src/s_isinff.c create mode 100644 lib/nbsd_libm/src/s_isnan.c create mode 100644 lib/nbsd_libm/src/s_isnanf.c create mode 100644 lib/nbsd_libm/src/s_ldexp.c create mode 100644 lib/nbsd_libm/src/s_ldexpf.c create mode 100644 lib/nbsd_libm/src/s_lib_version.c create mode 100644 lib/nbsd_libm/src/s_log1p.c create mode 100644 lib/nbsd_libm/src/s_log1pf.c create mode 100644 lib/nbsd_libm/src/s_logb.c create mode 100644 lib/nbsd_libm/src/s_logbf.c create mode 100644 lib/nbsd_libm/src/s_matherr.c create mode 100644 lib/nbsd_libm/src/s_modf.c create mode 100644 lib/nbsd_libm/src/s_modff.c create mode 100644 lib/nbsd_libm/src/s_nextafter.c create mode 100644 lib/nbsd_libm/src/s_nextafterf.c create mode 100644 lib/nbsd_libm/src/s_nextafterl.c create mode 100644 lib/nbsd_libm/src/s_nexttoward.c create mode 100644 lib/nbsd_libm/src/s_rint.c create mode 100644 lib/nbsd_libm/src/s_rintf.c create mode 100644 lib/nbsd_libm/src/s_round.c create mode 100644 lib/nbsd_libm/src/s_roundf.c create mode 100644 lib/nbsd_libm/src/s_scalbn.c create mode 100644 lib/nbsd_libm/src/s_scalbnf.c create mode 100644 lib/nbsd_libm/src/s_signgam.c create mode 100644 lib/nbsd_libm/src/s_significand.c create mode 100644 lib/nbsd_libm/src/s_significandf.c create mode 100644 lib/nbsd_libm/src/s_sin.c create mode 100644 lib/nbsd_libm/src/s_sinf.c create mode 100644 lib/nbsd_libm/src/s_tan.c create mode 100644 lib/nbsd_libm/src/s_tanf.c create mode 100644 lib/nbsd_libm/src/s_tanh.c create mode 100644 lib/nbsd_libm/src/s_tanhf.c create mode 100644 lib/nbsd_libm/src/s_trunc.c create mode 100644 lib/nbsd_libm/src/s_truncf.c create mode 100644 lib/nbsd_libm/src/w_acos.c create mode 100644 lib/nbsd_libm/src/w_acosf.c create mode 100644 lib/nbsd_libm/src/w_acosh.c create mode 100644 lib/nbsd_libm/src/w_acoshf.c create mode 100644 lib/nbsd_libm/src/w_asin.c create mode 100644 lib/nbsd_libm/src/w_asinf.c create mode 100644 lib/nbsd_libm/src/w_atan2.c create mode 100644 lib/nbsd_libm/src/w_atan2f.c create mode 100644 lib/nbsd_libm/src/w_atanh.c create mode 100644 lib/nbsd_libm/src/w_atanhf.c create mode 100644 lib/nbsd_libm/src/w_cosh.c create mode 100644 lib/nbsd_libm/src/w_coshf.c create mode 100644 lib/nbsd_libm/src/w_drem.c create mode 100644 lib/nbsd_libm/src/w_dremf.c create mode 100644 lib/nbsd_libm/src/w_exp.c create mode 100644 lib/nbsd_libm/src/w_expf.c create mode 100644 lib/nbsd_libm/src/w_fmod.c create mode 100644 lib/nbsd_libm/src/w_fmodf.c create mode 100644 lib/nbsd_libm/src/w_gamma.c create mode 100644 lib/nbsd_libm/src/w_gamma_r.c create mode 100644 lib/nbsd_libm/src/w_gammaf.c create mode 100644 lib/nbsd_libm/src/w_gammaf_r.c create mode 100644 lib/nbsd_libm/src/w_hypot.c create mode 100644 lib/nbsd_libm/src/w_hypotf.c create mode 100644 lib/nbsd_libm/src/w_j0.c create mode 100644 lib/nbsd_libm/src/w_j0f.c create mode 100644 lib/nbsd_libm/src/w_j1.c create mode 100644 lib/nbsd_libm/src/w_j1f.c create mode 100644 lib/nbsd_libm/src/w_jn.c create mode 100644 lib/nbsd_libm/src/w_jnf.c create mode 100644 lib/nbsd_libm/src/w_lgamma.c create mode 100644 lib/nbsd_libm/src/w_lgamma_r.c create mode 100644 lib/nbsd_libm/src/w_lgammaf.c create mode 100644 lib/nbsd_libm/src/w_lgammaf_r.c create mode 100644 lib/nbsd_libm/src/w_log.c create mode 100644 lib/nbsd_libm/src/w_log10.c create mode 100644 lib/nbsd_libm/src/w_log10f.c create mode 100644 lib/nbsd_libm/src/w_log2.c create mode 100644 lib/nbsd_libm/src/w_log2f.c create mode 100644 lib/nbsd_libm/src/w_logf.c create mode 100644 lib/nbsd_libm/src/w_pow.c create mode 100644 lib/nbsd_libm/src/w_powf.c create mode 100644 lib/nbsd_libm/src/w_remainder.c create mode 100644 lib/nbsd_libm/src/w_remainderf.c create mode 100644 lib/nbsd_libm/src/w_scalb.c create mode 100644 lib/nbsd_libm/src/w_scalbf.c create mode 100644 lib/nbsd_libm/src/w_sinh.c create mode 100644 lib/nbsd_libm/src/w_sinhf.c create mode 100644 lib/nbsd_libm/src/w_sqrt.c create mode 100644 lib/nbsd_libm/src/w_sqrtf.c diff --git a/lib/nbsd_libm/Makefile b/lib/nbsd_libm/Makefile new file mode 100644 index 000000000..3c3de53b9 --- /dev/null +++ b/lib/nbsd_libm/Makefile @@ -0,0 +1,280 @@ +# $NetBSD: Makefile,v 1.101 2011/01/12 23:03:56 joerg Exp $ +# +# @(#)Makefile 5.1beta 93/09/24 +# +# ==================================================== +# Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. +# +# Developed at SunPro, a Sun Microsystems, Inc. business. +# Permission to use, copy, modify, and distribute this +# software is freely granted, provided that this notice +# is preserved. +# ==================================================== +# +# + +# +# There are two options in making libm at fdlibm compile time: +# _IEEE_LIBM --- IEEE libm; smaller, and somewhat faster +# _MULTI_LIBM --- Support multi-standard at runtime by +# imposing wrapper functions defined in +# fdlibm.h: +# _IEEE_MODE -- IEEE +# _XOPEN_MODE -- X/OPEN +# _POSIX_MODE -- POSIX/ANSI +# _SVID3_MODE -- SVID +# +# Here is how to set up CPPFLAGS to create the desired libm at +# compile time: +# +# CPPFLAGS = -D_IEEE_LIBM ... IEEE libm (recommended) +# CPPFLAGS = -D_SVID3_MODE ... Multi-standard supported +# libm with SVID as the +# default standard +# CPPFLAGS = -D_XOPEN_MODE ... Multi-standard supported +# libm with XOPEN as the +# default standard +# CPPFLAGS = -D_POSIX_MODE ... Multi-standard supported +# libm with POSIX as the +# default standard +# CPPFLAGS = ... Multi-standard supported +# libm with IEEE as the +# default standard +# + +USE_SHLIBDIR= yes + +# require this for the value of I387_LIBM from mk.conf, if set. +.include + +.if (${MACHINE_ARCH} == "alpha") +.PATH: ${.CURDIR}/arch/alpha +ARCH_SRCS = s_copysign.S s_copysignf.S lrint.S +.elif ((${MACHINE_ARCH} == "i386") || (${MACHINE_ARCH} == "x86_64")) + +.if (${MACHINE_ARCH} == "x86_64") +.PATH: ${.CURDIR}/arch/x86_64 +.endif +.PATH: ${.CURDIR}/arch/i387 + +COMMON_SRCS+= fenv.c s_nextafterl.c s_nexttoward.c +ARCH_SRCS = e_acos.S e_asin.S e_atan2.S e_exp.S e_expf.S e_fmod.S e_log.S \ + e_logf.S e_log10.S e_log10f.S e_log2.S e_log2f.S e_remainder.S \ + e_remainderf.S e_scalb.S e_scalbf.S e_sqrt.S e_sqrtf.S s_atan.S \ + s_atanf.S s_ceil.S s_ceilf.S s_copysign.S s_copysignf.S s_cos.S \ + s_cosf.S s_finite.S s_finitef.S s_floor.S s_floorf.S s_ilogb.S \ + s_ilogbf.S s_log1p.S s_log1pf.S s_logb.S s_logbf.S s_rint.S \ + s_rintf.S s_scalbn.S s_scalbnf.S s_significand.S \ + s_significandf.S s_sin.S s_sinf.S s_tan.S s_tanf.S lrint.S +# do not pick up the i387 asm version, it is incorrect +s_modf.o s_modf.pico s_modf.po s_modf.d: s_modf.c + +.if (${MACHINE_ARCH} == "i386") +SUBDIR=arch/i387 +.endif +.elif (${MACHINE_ARCH} == "m68k") +.if defined(M68060) +.PATH: ${.CURDIR}/arch/m68060 +.include "${.CURDIR}/arch/m68060/Makefile.list" +COPTS+=-m68060 +.PATH: ${.CURDIR}/arch/m68k +ARCH_SRCS += s_ceil.S s_copysign.S s_finite.S s_floor.S s_rint.S +.elif defined(M68040) +.PATH: ${.CURDIR}/arch/m68k +COPTS+=-m68040 +ARCH_SRCS = s_copysign.S s_finite.S +.else +.if (${MKSOFTFLOAT} != "yes") +.PATH: ${.CURDIR}/arch/mc68881 ${.CURDIR}/arch/m68k +ARCH_SRCS = e_acos.S e_asin.S e_atanh.S e_cosh.S e_exp.S e_fmod.S e_log.S \ + e_log10.S e_remainder.S e_scalb.S e_sinh.S e_sqrt.S s_atan.S \ + s_ceil.S s_copysign.S s_cos.S s_expm1.S s_finite.S s_floor.S \ + s_log1p.S s_logb.S s_rint.S s_scalbn.S s_sin.S s_tan.S s_tanh.S +.endif +.endif +# end of m68k +.elif (${MACHINE_ARCH} == "vax") +#.PATH: ${.CURDIR}/arch/vax + +#NOIEEE_ARCH= n_infnan.S n_argred.S n_sqrt.S +#ARCH_SRCS = n_atan2.S n_cabs.S n_cbrt.S n_support.S n_sincos.S n_tan.S +# XXX - ripped out due to lack of the insn polyd in the Mariah chip, +# and emulation code isn't written yet. +WARNS?=4 +.endif + +WARNS?=4 + +.PATH: ${.CURDIR}/man +.PATH: ${.CURDIR}/src +.PATH: ${.CURDIR}/noieee_src + +.if (${MACHINE_ARCH} != "vax") +CPPFLAGS+= -D_MULTI_LIBM -D_POSIX_MODE +# XXX noieee libm is gross +COPTS+= -fno-strict-aliasing +.endif +CPPFLAGS+=-DLIBM_SCCS + +LIB= m +COMMON_SRCS+= e_acos.c e_acosf.c e_acosh.c e_acoshf.c e_asin.c e_asinf.c \ + e_atan2.c e_atan2f.c e_atanh.c e_atanhf.c e_cosh.c e_coshf.c e_exp.c \ + e_expf.c e_fmod.c e_fmodf.c e_hypot.c e_hypotf.c e_j0.c e_j0f.c \ + e_j1.c e_j1f.c e_jn.c e_jnf.c e_lgamma_r.c e_lgammaf_r.c e_log.c \ + e_log2.c e_log10.c e_log10f.c e_log2f.c e_logf.c e_pow.c e_powf.c \ + e_rem_pio2.c e_rem_pio2f.c e_remainder.c e_remainderf.c e_scalb.c \ + e_scalbf.c e_sinh.c e_sinhf.c e_sqrt.c e_sqrtf.c \ + k_cos.c k_cosf.c k_rem_pio2.c k_rem_pio2f.c k_sin.c k_sinf.c \ + k_standard.c k_tan.c k_tanf.c \ + s_asinh.c s_asinhf.c s_atan.c s_atanf.c s_cbrt.c s_cbrtf.c s_ceil.c \ + s_ceilf.c s_copysign.c s_copysignf.c s_copysignl.c s_cos.c s_cosf.c s_erf.c \ + s_erff.c s_exp2.c s_exp2f.c s_expm1.c s_expm1f.c s_fabsf.c s_fabsl.c \ + s_finite.c s_finitef.c \ + s_floor.c s_floorf.c s_frexpf.c s_ilogb.c s_ilogbf.c \ + s_isinff.c s_isnanf.c s_ldexpf.c s_lib_version.c s_log1p.c \ + s_log1pf.c s_logb.c s_logbf.c s_matherr.c s_modff.c s_nextafter.c \ + s_nextafterf.c s_rint.c s_rintf.c s_round.c s_roundf.c s_scalbn.c \ + s_scalbnf.c s_signgam.c s_significand.c s_significandf.c s_sin.c \ + s_sinf.c s_tan.c s_tanf.c s_tanh.c s_tanhf.c s_trunc.c s_truncf.c \ + w_acos.c w_acosf.c w_acosh.c w_acoshf.c w_asin.c w_asinf.c w_atan2.c \ + w_atan2f.c w_atanh.c w_atanhf.c w_cosh.c w_coshf.c \ + w_drem.c w_dremf.c w_exp.c w_expf.c w_fmod.c w_fmodf.c w_gamma.c \ + w_gamma_r.c w_gammaf.c w_gammaf_r.c w_hypot.c w_hypotf.c w_j0.c \ + w_j0f.c w_j1.c w_j1f.c w_jn.c w_jnf.c w_lgamma.c w_lgamma_r.c \ + w_lgammaf.c w_lgammaf_r.c w_log.c w_log10.c w_log10f.c w_log2.c \ + w_log2f.c w_logf.c \ + w_pow.c w_powf.c w_remainder.c w_remainderf.c w_scalb.c w_scalbf.c \ + w_sinh.c w_sinhf.c w_sqrt.c w_sqrtf.c \ + lrint.c lrintf.c llrint.c llrintf.c lround.c lroundf.c llround.c \ + llroundf.c s_frexp.c s_ldexp.c s_modf.c \ + s_fmax.c s_fmaxf.c s_fmaxl.c s_fmin.c s_fminf.c s_fminl.c s_fdim.c + +.PATH: ${.CURDIR}/compat +COMMON_SRCS+= compat_cabs.c compat_cabsf.c +# XXX our compatibility cabs() is different! +.if defined(HAVE_GCC) && ${HAVE_GCC} == 4 +COPTS.compat_cabs.c= -fno-builtin-cabs +COPTS.compat_cabsf.c= -fno-builtin-cabsf +.endif + +# math routines for non-IEEE architectures. +NOIEEE_SRCS = n_asincos.c n_acosh.c n_asinh.c n_atan.c n_atanh.c n_cosh.c \ + n_erf.c n_exp.c n_exp__E.c n_expm1.c n_floor.c n_fmod.c n_gamma.c \ + n_lgamma.c n_j0.c n_j1.c n_jn.c n_log.c n_log10.c n_log1p.c \ + n_log__L.c n_pow.c n_sinh.c n_tanh.c \ + n_sincos.c n_tan.c \ + n_round.c n_roundf.c n_lround.c n_lroundf.c \ + n_fmax.c n_fmaxf.c n_fmin.c n_fminf.c +# n_sqrt.c n_argred.c n_infnan.c n_atan2.c n_cabs.c n_cbrt.c n_support.c + + +# NetBSD's C library supplies these functions: +#COMMON_SRCS+= s_fabs.c s_frexp.c s_isinf.c s_isnan.c s_ldexp.c s_modf.c + +.if (${MACHINE_ARCH} == "vax") +SRCS= ${NOIEEE_SRCS} ${NOIEEE_ARCH} +.else +SRCS= ${COMMON_SRCS} +.endif + +.ifdef ARCH_ADDS +SRCS+= ${ARCH_ADDS} +.endif + +# Substitute common sources with any arch specific sources +.for i in ${ARCH_SRCS} ${NOIEEE_ARCH} + SRCS:=${SRCS:S/^${i:S/.S/.c/}/$i/} +.endfor + +.if (${MACHINE_ARCH} == "vax") # XXX until POLYD is written. +.PATH: ${.CURDIR}/arch/vax +SRCS:=${SRCS} n_sqrt.S n_argred.S n_infnan.S n_atan2.S n_cabs.S n_cbrt.S \ + n_support.S +.endif + +.if (${MACHINE_ARCH} == "i386") +# XXX this gets miscompiled. There should be a better fix. +COPTS.s_tanh.c+= -O0 +.endif + +MAN+= acos.3 acosh.3 asin.3 asinh.3 atan.3 atan2.3 atanh.3 ceil.3 \ + cos.3 cosh.3 erf.3 exp.3 fabs.3 floor.3 fmod.3 frexp.3 hypot.3 ieee.3 \ + ieee_test.3 isinff.3 j0.3 ldexp.3 lgamma.3 lrint.3 \ + math.3 modf.3 rint.3 round.3 sin.3 sinh.3 \ + sqrt.3 tan.3 tanh.3 trunc.3 fmax.3 fdim.3 + +# fenv.h interface +MAN+= feclearexcept.3 feenableexcept.3 fegetenv.3 fegetround.3 fenv.3 +MLINKS+=feclearexcept.3 fegetexceptflag.3 \ + feclearexcept.3 feraiseexcept.3 \ + feclearexcept.3 fesetexceptflag.3 \ + feclearexcept.3 fetestexcept.3 +MLINKS+=feenableexcept.3 fedisableexcept.3 \ + feenableexcept.3 fegetexcept.3 +MLINKS+=fegetenv.3 feholdexcept.3 \ + fegetenv.3 fesetenv.3 \ + fegetenv.3 feupdateenv.3 +MLINKS+=fegetround.3 fesetround.3 + +MLINKS+=acos.3 acosf.3 +MLINKS+=acosh.3 acoshf.3 +MLINKS+=asin.3 asinf.3 +MLINKS+=asinh.3 asinhf.3 +MLINKS+=atan.3 atanf.3 +MLINKS+=atan2.3 atan2f.3 +MLINKS+=atanh.3 atanhf.3 +MLINKS+=ceil.3 ceilf.3 +MLINKS+=cos.3 cosf.3 +MLINKS+=cosh.3 coshf.3 +MLINKS+=erf.3 erff.3 erf.3 erfc.3 erf.3 erfcf.3 +MLINKS+=exp.3 expf.3 exp.3 expm1.3 exp.3 expm1f.3 \ + exp.3 exp2.3 exp.3 exp2f.3 \ + exp.3 log.3 exp.3 logf.3 \ + exp.3 log10.3 exp.3 log10f.3 \ + exp.3 log1p.3 exp.3 log1pf.3 \ + exp.3 pow.3 exp.3 powf.3 \ + exp.3 log2.3 exp.3 log2f.3 +MLINKS+=fabs.3 fabsf.3 +MLINKS+=floor.3 floorf.3 +MLINKS+=fmod.3 fmodf.3 +MLINKS+=hypot.3 hypotf.3 +MLINKS+=ieee.3 copysign.3 ieee.3 copysignf.3 ieee.3 copysignl.3 \ + ieee.3 finite.3 ieee.3 finitef.3 \ + ieee.3 ilogb.3 ieee.3 ilogbf.3 \ + ieee.3 nextafter.3 ieee.3 nextafterf.3 ieee.3 nextafterl.3 \ + ieee.3 nexttoward.3 \ + ieee.3 remainder.3 ieee.3 remainderf.3 \ + ieee.3 scalbn.3 ieee.3 scalbnf.3 +MLINKS+=ieee_test.3 logb.3 ieee_test.3 logbf.3 +MLINKS+=ieee_test.3 scalb.3 ieee_test.3 scalbf.3 +MLINKS+=ieee_test.3 significand.3 ieee_test.3 significandf.3 +MLINKS+=isinff.3 isnanf.3 +MLINKS+=j0.3 j0f.3 j0.3 j1.3 j0.3 j1f.3 j0.3 jn.3 j0.3 jnf.3 \ + j0.3 y0.3 j0.3 y0f.3 j0.3 y1.3 j0.3 y1f.3 j0.3 yn.3 j0.3 ynf.3 +MLINKS+=lgamma.3 lgammaf.3 lgamma.3 lgamma_r.3 lgamma.3 lgammaf_r.3 \ + lgamma.3 gamma.3 lgamma.3 gammaf.3 lgamma.3 gamma_r.3 \ + lgamma.3 gammaf_r.3 +MLINKS+=lrint.3 lrintf.3 lrint.3 llrint.3 lrint.3 llrintf.3 +MLINKS+=rint.3 rintf.3 +MLINKS+=sin.3 sinf.3 +MLINKS+=sinf.3 sinhf.3 +MLINKS+=sqrt.3 sqrtf.3 sqrt.3 cbrt.3 sqrt.3 cbrtf.3 +MLINKS+=tan.3 tanf.3 +MLINKS+=tanh.3 tanhf.3 +MLINKS+=round.3 roundf.3 +MLINKS+=trunc.3 truncf.3 +MLINKS+=fmax.3 fmaxl.3 +MLINKS+=fmax.3 fmaxf.3 +MLINKS+=fmax.3 fmin.3 +MLINKS+=fmax.3 fminl.3 +MLINKS+=fmax.3 fminf.3 +MLINKS+=fdim.3 fdiml.3 +MLINKS+=fdim.3 fdimf.3 + +.if (${MKCOMPLEX} != "no") +.include "${.CURDIR}/complex/Makefile.inc" +.endif + +.include "${.CURDIR}/gen/Makefile.inc" +.include +.include diff --git a/lib/nbsd_libm/arch/i387/.depend b/lib/nbsd_libm/arch/i387/.depend new file mode 100644 index 000000000..0c3366a10 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/.depend @@ -0,0 +1,2 @@ + +empty.o: empty.S diff --git a/lib/nbsd_libm/arch/i387/Makefile b/lib/nbsd_libm/arch/i387/Makefile new file mode 100644 index 000000000..f69310126 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/Makefile @@ -0,0 +1,10 @@ +# $NetBSD: Makefile,v 1.11 2008/06/06 13:35:06 ad Exp $ +# + +USE_SHLIBDIR= yes + +LIB= m387 + +SRCS=empty.S + +.include diff --git a/lib/nbsd_libm/arch/i387/abi.h b/lib/nbsd_libm/arch/i387/abi.h new file mode 100644 index 000000000..968279ecc --- /dev/null +++ b/lib/nbsd_libm/arch/i387/abi.h @@ -0,0 +1,77 @@ +/* $NetBSD: abi.h,v 1.5 2008/06/23 10:24:13 drochner Exp $ */ + +/* + * Written by Frank van der Linden (fvdl@wasabisystems.com) + */ + +/* + * The x86-64 ABI specifies that float, double and long double + * arguments are passed in SSE2 (xmm) registers. Unfortunately, + * there is no way to push those on to the FP stack, which is + * where the fancier instructions get their arguments from. + * + * Define some prologues and epilogues to store and retrieve + * xmm regs to local variables. + */ + +#ifdef __x86_64__ + +#define ARG_DOUBLE_ONE -8(%rsp) +#define ARG_DOUBLE_ONE_LSW -8(%rsp) +#define ARG_DOUBLE_ONE_MSW -4(%rsp) +#define ARG_DOUBLE_TWO -16(%rsp) +#define ARG_FLOAT_ONE -4(%rsp) +#define ARG_FLOAT_TWO -8(%rsp) + +#define XMM_ONE_ARG_DOUBLE_PROLOGUE \ + movsd %xmm0, ARG_DOUBLE_ONE + +#define XMM_TWO_ARG_DOUBLE_PROLOGUE \ + movsd %xmm0, ARG_DOUBLE_ONE ; \ + movsd %xmm1, ARG_DOUBLE_TWO + +#define XMM_ONE_ARG_FLOAT_PROLOGUE \ + movss %xmm0, ARG_FLOAT_ONE + +#define XMM_TWO_ARG_FLOAT_PROLOGUE \ + movss %xmm0, ARG_FLOAT_ONE ; \ + movss %xmm1, ARG_FLOAT_TWO + +#define XMM_DOUBLE_EPILOGUE \ + fstpl ARG_DOUBLE_ONE ; \ + movsd ARG_DOUBLE_ONE, %xmm0 + +#define XMM_FLOAT_EPILOGUE \ + fstps ARG_FLOAT_ONE ; \ + movss ARG_FLOAT_ONE, %xmm0 + +#define FLDL_VAR(x) fldl x(%rip) + +#else + +#define ARG_DOUBLE_ONE 4(%esp) +#define ARG_DOUBLE_ONE_LSW 4(%esp) +#define ARG_DOUBLE_ONE_MSW 8(%esp) +#define ARG_DOUBLE_TWO 12(%esp) +#define ARG_FLOAT_ONE 4(%esp) +#define ARG_FLOAT_TWO 8(%esp) + +#define XMM_ONE_ARG_DOUBLE_PROLOGUE +#define XMM_TWO_ARG_DOUBLE_PROLOGUE +#define XMM_ONE_ARG_FLOAT_PROLOGUE +#define XMM_TWO_ARG_FLOAT_PROLOGUE + +#define XMM_DOUBLE_EPILOGUE +#define XMM_FLOAT_EPILOGUE + +#ifdef PIC +#define FLDL_VAR(x) \ + PIC_PROLOGUE ; \ + fldl PIC_GOTOFF(x) ; \ + PIC_EPILOGUE +#else +#define FLDL_VAR(x) \ + fldl x + +#endif +#endif diff --git a/lib/nbsd_libm/arch/i387/e_acos.S b/lib/nbsd_libm/arch/i387/e_acos.S new file mode 100644 index 000000000..1c19b2090 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_acos.S @@ -0,0 +1,24 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_acos.S,v 1.8 2003/07/26 19:24:57 salo Exp $") + +/* acos = atan (sqrt(1 - x^2) / x) */ +ENTRY(__ieee754_acos) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE /* x */ + fld %st(0) + fmul %st(0) /* x^2 */ + fld1 + fsubp /* 1 - x^2 */ + fsqrt /* sqrt (1 - x^2) */ + fxch %st(1) + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_asin.S b/lib/nbsd_libm/arch/i387/e_asin.S new file mode 100644 index 000000000..43bea55a2 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_asin.S @@ -0,0 +1,23 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_asin.S,v 1.7 2003/07/26 19:24:58 salo Exp $") + +/* asin = atan (x / sqrt(1 - x^2)) */ +ENTRY(__ieee754_asin) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE /* x */ + fld %st(0) + fmul %st(0) /* x^2 */ + fld1 + fsubp /* 1 - x^2 */ + fsqrt /* sqrt (1 - x^2) */ + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_atan2.S b/lib/nbsd_libm/arch/i387/e_atan2.S new file mode 100644 index 000000000..d6d9fa242 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_atan2.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_atan2.S,v 1.6 2003/07/26 19:24:58 salo Exp $") + +ENTRY(__ieee754_atan2) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fldl ARG_DOUBLE_TWO + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_atan2f.S b/lib/nbsd_libm/arch/i387/e_atan2f.S new file mode 100644 index 000000000..3aed18835 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_atan2f.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_atan2f.S,v 1.3 2003/07/26 19:24:58 salo Exp $") + +ENTRY(__ieee754_atan2f) + XMM_TWO_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + flds ARG_FLOAT_TWO + fpatan + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_exp.S b/lib/nbsd_libm/arch/i387/e_exp.S new file mode 100644 index 000000000..e5692fda1 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_exp.S @@ -0,0 +1,108 @@ +/* $NetBSD: e_exp.S,v 1.14 2008/06/23 10:24:13 drochner Exp $ */ + +/* + * Copyright (c) 1993,94 Winning Strategies, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. All advertising materials mentioning features or use of this software + * must display the following acknowledgement: + * This product includes software developed by Winning Strategies, Inc. + * 4. The name of the author may not be used to endorse or promote products + * derived from this software without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +/* + * Written by: + * J.T. Conklin (jtc@wimsey.com), Winning Strategies, Inc. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_exp.S,v 1.14 2008/06/23 10:24:13 drochner Exp $") +#if 0 +RCSID("$FreeBSD: src/lib/msun/i387/e_exp.S,v 1.8.2.1 2000/07/10 09:16:28 obrien Exp $") +#endif + +/* e^x = 2^(x * log2(e)) */ +ENTRY(__ieee754_exp) + XMM_ONE_ARG_DOUBLE_PROLOGUE + /* + * If x is +-Inf, then the subtraction would give Inf-Inf = NaN. + * Avoid this. Also avoid it if x is NaN for convenience. + */ + movl ARG_DOUBLE_ONE_MSW, %eax + andl $0x7fffffff, %eax + cmpl $0x7ff00000, %eax + jae x_Inf_or_NaN + + fldl ARG_DOUBLE_ONE + + /* + * Ensure that the rounding mode is to nearest (to give the smallest + * possible fraction) and that the precision is as high as possible. + * We may as well mask interrupts if we switch the mode. + */ +#define CWSTORE_SAV ARG_DOUBLE_ONE_LSW /* XXX overwrites the argument */ +#define CWSTORE_TMP ARG_DOUBLE_ONE_MSW + fstcw CWSTORE_SAV + movl CWSTORE_SAV, %eax + andl $0x0f00, %eax + cmpl $0x0300, %eax /* RC == 0 && PC == 3? */ + je 1f /* jump if mode is good */ + movl $0x137f, CWSTORE_TMP + fldcw CWSTORE_TMP +1: + fldl2e + fmulp /* x * log2(e) */ + fst %st(1) + frndint /* int(x * log2(e)) */ + fst %st(2) + fsubrp /* fract(x * log2(e)) */ + f2xm1 /* 2^(fract(x * log2(e))) - 1 */ + fld1 + faddp /* 2^(fract(x * log2(e))) */ + fscale /* e^x */ + fstp %st(1) + je 1f + fldcw CWSTORE_SAV +1: + XMM_DOUBLE_EPILOGUE + ret +x_Inf_or_NaN: + /* + * Return 0 if x is -Inf. Otherwise just return x, although the + * C version would return (x + x) (Real Indefinite) if x is a NaN. + */ + cmpl $0xfff00000, ARG_DOUBLE_ONE_MSW + jne x_not_minus_Inf + cmpl $0, ARG_DOUBLE_ONE_LSW + jne x_not_minus_Inf + fldz + XMM_DOUBLE_EPILOGUE + ret + +x_not_minus_Inf: + fldl ARG_DOUBLE_ONE + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_expf.S b/lib/nbsd_libm/arch/i387/e_expf.S new file mode 100644 index 000000000..540b97d89 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_expf.S @@ -0,0 +1,55 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + + +RCSID("$NetBSD: e_expf.S,v 1.6 2008/06/24 17:27:56 drochner Exp $") + +/* e^x = 2^(x * log2(e)) */ +ENTRY(__ieee754_expf) + XMM_ONE_ARG_FLOAT_PROLOGUE + + /* + * catch +/-Inf and NaN arguments + */ + movl ARG_FLOAT_ONE,%eax + andl $0x7fffffff,%eax + cmpl $0x7f800000,%eax + jae x_Inf_or_NaN + + flds ARG_FLOAT_ONE + fldl2e + fmulp /* x * log2(e) */ + fld %st(0) + frndint /* int(x * log2(e)) */ + fsubr %st(0),%st(1) /* fract(x * log2(e)) */ + fxch + f2xm1 /* 2^(fract(x * log2(e))) - 1 */ + fld1 + faddp /* 2^(fract(x * log2(e))) */ + fscale /* e^x */ + fstp %st(1) + XMM_FLOAT_EPILOGUE + ret + +x_Inf_or_NaN: + /* + * Return 0 if x is -Inf. Otherwise just return x, although the + * C version would return (x + x) (Real Indefinite) if x is a NaN. + */ + movl ARG_FLOAT_ONE,%eax + cmpl $0xff800000,%eax + jne x_not_minus_Inf + fldz + XMM_FLOAT_EPILOGUE + ret + +x_not_minus_Inf: + flds ARG_FLOAT_ONE + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_fmod.S b/lib/nbsd_libm/arch/i387/e_fmod.S new file mode 100644 index 000000000..4987f9e35 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_fmod.S @@ -0,0 +1,23 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + + +RCSID("$NetBSD: e_fmod.S,v 1.7 2003/07/26 19:24:58 salo Exp $") + +ENTRY(__ieee754_fmod) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_TWO + fldl ARG_DOUBLE_ONE +1: fprem + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_log.S b/lib/nbsd_libm/arch/i387/e_log.S new file mode 100644 index 000000000..2d7732555 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_log.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_log.S,v 1.6 2003/07/26 19:24:58 salo Exp $") + +ENTRY(__ieee754_log) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldln2 + fldl ARG_DOUBLE_ONE + fyl2x + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_log10.S b/lib/nbsd_libm/arch/i387/e_log10.S new file mode 100644 index 000000000..ce8e3b93a --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_log10.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_log10.S,v 1.6 2003/07/26 19:24:59 salo Exp $") + +ENTRY(__ieee754_log10) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldlg2 + fldl ARG_DOUBLE_ONE + fyl2x + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_log10f.S b/lib/nbsd_libm/arch/i387/e_log10f.S new file mode 100644 index 000000000..76b95579e --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_log10f.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_log10f.S,v 1.3 2003/07/26 19:24:59 salo Exp $") + +ENTRY(__ieee754_log10f) + XMM_ONE_ARG_FLOAT_PROLOGUE + fldlg2 + flds ARG_FLOAT_ONE + fyl2x + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_log2.S b/lib/nbsd_libm/arch/i387/e_log2.S new file mode 100644 index 000000000..13e66f705 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_log2.S @@ -0,0 +1,18 @@ +/* + * Written by Rui Paulo , based on e_log.S. + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_log2.S,v 1.1 2005/07/21 20:58:21 rpaulo Exp $") + +ENTRY(__ieee754_log2) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fld1 + fldl ARG_DOUBLE_ONE + fyl2x + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_log2f.S b/lib/nbsd_libm/arch/i387/e_log2f.S new file mode 100644 index 000000000..d362aae26 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_log2f.S @@ -0,0 +1,18 @@ +/* + * Written by Rui Paulo , based on e_logf.S. + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_log2f.S,v 1.1 2005/07/21 20:58:21 rpaulo Exp $") + +ENTRY(__ieee754_log2f) + XMM_ONE_ARG_FLOAT_PROLOGUE + fld1 + flds ARG_FLOAT_ONE + fyl2x + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_logf.S b/lib/nbsd_libm/arch/i387/e_logf.S new file mode 100644 index 000000000..e3d2e8dfb --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_logf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_logf.S,v 1.4 2003/07/26 19:24:59 salo Exp $") + +ENTRY(__ieee754_logf) + XMM_ONE_ARG_FLOAT_PROLOGUE + fldln2 + flds ARG_FLOAT_ONE + fyl2x + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_remainder.S b/lib/nbsd_libm/arch/i387/e_remainder.S new file mode 100644 index 000000000..70223b2ad --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_remainder.S @@ -0,0 +1,22 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_remainder.S,v 1.7 2003/07/26 19:24:59 salo Exp $") + +ENTRY(__ieee754_remainder) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_TWO + fldl ARG_DOUBLE_ONE +1: fprem1 + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_remainderf.S b/lib/nbsd_libm/arch/i387/e_remainderf.S new file mode 100644 index 000000000..aaee4aab0 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_remainderf.S @@ -0,0 +1,22 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_remainderf.S,v 1.5 2003/07/26 19:24:59 salo Exp $") + +ENTRY(__ieee754_remainderf) + XMM_TWO_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_TWO + flds ARG_FLOAT_ONE +1: fprem1 + fstsw %ax + btw $10,%ax + jc 1b + fstp %st(1) + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_scalb.S b/lib/nbsd_libm/arch/i387/e_scalb.S new file mode 100644 index 000000000..8717aa7cb --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_scalb.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_scalb.S,v 1.7 2003/07/26 19:25:00 salo Exp $") + +ENTRY(__ieee754_scalb) + XMM_TWO_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_TWO + fldl ARG_DOUBLE_ONE + fscale + fstp %st(1) /* bug fix for fp stack overflow */ + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_scalbf.S b/lib/nbsd_libm/arch/i387/e_scalbf.S new file mode 100644 index 000000000..be3b569cb --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_scalbf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: e_scalbf.S,v 1.3 2003/07/26 19:25:00 salo Exp $") + +ENTRY(__ieee754_scalbf) + XMM_TWO_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_TWO + flds ARG_FLOAT_ONE + fscale + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/e_sqrt.S b/lib/nbsd_libm/arch/i387/e_sqrt.S new file mode 100644 index 000000000..afae87ffc --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_sqrt.S @@ -0,0 +1,17 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: e_sqrt.S,v 1.6 2003/07/26 19:25:00 salo Exp $") + +ENTRY(__ieee754_sqrt) +#ifdef __i386__ + fldl 4(%esp) + fsqrt +#else + sqrtsd %xmm0,%xmm0 +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/e_sqrtf.S b/lib/nbsd_libm/arch/i387/e_sqrtf.S new file mode 100644 index 000000000..f9163bab5 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/e_sqrtf.S @@ -0,0 +1,17 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: e_sqrtf.S,v 1.4 2003/07/26 19:25:00 salo Exp $") + +ENTRY(__ieee754_sqrtf) +#ifdef __i386__ + flds 4(%esp) + fsqrt +#else + sqrtss %xmm0,%xmm0 +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/empty.S b/lib/nbsd_libm/arch/i387/empty.S new file mode 100644 index 000000000..8b1378917 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/empty.S @@ -0,0 +1 @@ + diff --git a/lib/nbsd_libm/arch/i387/fenv.c b/lib/nbsd_libm/arch/i387/fenv.c new file mode 100644 index 000000000..035afd3bf --- /dev/null +++ b/lib/nbsd_libm/arch/i387/fenv.c @@ -0,0 +1,514 @@ +/* $NetBSD: fenv.c,v 1.3 2010/08/01 06:34:38 taca Exp $ */ + +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: fenv.c,v 1.3 2010/08/01 06:34:38 taca Exp $"); + +#include +#include +#include +#include +#include +#include + +/* Load x87 Control Word */ +#define __fldcw(__cw) __asm__ __volatile__ \ + ("fldcw %0" : : "m" (__cw)) + +/* No-Wait Store Control Word */ +#define __fnstcw(__cw) __asm__ __volatile__ \ + ("fnstcw %0" : "=m" (*(__cw))) + +/* No-Wait Store Status Word */ +#define __fnstsw(__sw) __asm__ __volatile__ \ + ("fnstsw %0" : "=am" (*(__sw))) + +/* No-Wait Clear Exception Flags */ +#define __fnclex() __asm__ __volatile__ \ + ("fnclex") + +/* Load x87 Environment */ +#define __fldenv(__env) __asm__ __volatile__ \ + ("fldenv %0" : : "m" (__env)) + +/* No-Wait Store x87 environment */ +#define __fnstenv(__env) __asm__ __volatile__ \ + ("fnstenv %0" : "=m" (*(__env))) + +/* Check for and handle pending unmasked x87 pending FPU exceptions */ +#define __fwait(__env) __asm__ __volatile__ \ + ("fwait") + +/* Load the MXCSR register */ +#define __ldmxcsr(__mxcsr) __asm__ __volatile__ \ + ("ldmxcsr %0" : : "m" (__mxcsr)) + +/* Store the MXCSR register state */ +#define __stmxcsr(__mxcsr) __asm__ __volatile__ \ + ("stmxcsr %0" : "=m" (*(__mxcsr))) + +/* + * The following constant represents the default floating-point environment + * (that is, the one installed at program startup) and has type pointer to + * const-qualified fenv_t. + * + * It can be used as an argument to the functions within the header + * that manage the floating-point environment, namely fesetenv() and + * feupdateenv(). + * + * x87 fpu registers are 16bit wide. The upper bits, 31-16, are marked as + * RESERVED. We provide a partial floating-point environment, where we + * define only the lower bits. The reserved bits are extracted and set by the + * consumers of FE_DFL_ENV, during runtime. + */ +fenv_t __fe_dfl_env = { + { + __NetBSD_NPXCW__, /* Control word register */ + 0x0, /* Unused */ + 0x0000, /* Status word register */ + 0x0, /* Unused */ + 0x0000ffff, /* Tag word register */ + 0x0, /* Unused */ + { + 0x0000, 0x0000, + 0x0000, 0xffff + } + }, + __INITIAL_MXCSR__ /* MXCSR register */ +}; + +/* + * Test for SSE support on this processor. + * + * We need to use ldmxcsr/stmxcsr to get correct results if any part + * of the program was compiled to use SSE floating-point, but we can't + * use SSE on older processors. + * + * In order to do so, we need to query the processor capabilities via the CPUID + * instruction. We can make it even simpler though, by querying the machdep.sse + * sysctl. + */ +static int __HAS_SSE = 0; + +static void __test_sse(void) __attribute__ ((constructor)); + +static void __test_sse(void) +{ + size_t oldlen = sizeof(__HAS_SSE); + int rv; + + rv = sysctlbyname("machdep.sse", &__HAS_SSE, &oldlen, NULL, 0); + if (rv == -1) + __HAS_SSE = 0; +} + +/* + * The feclearexcept() function clears the supported floating-point exceptions + * represented by `excepts'. + */ +int +feclearexcept(int excepts) +{ + fenv_t env; + uint32_t mxcsr; + int ex; + + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + /* It's ~3x faster to call fnclex, than store/load fp env */ + if (ex == FE_ALL_EXCEPT) { + __fnclex(); + } else { + __fnstenv(&env); + env.x87.status &= ~ex; + __fldenv(env); + } + + if (__HAS_SSE) { + __stmxcsr(&mxcsr); + mxcsr &= ~ex; + __ldmxcsr(mxcsr); + } + + /* Success */ + return (0); +} + +/* + * The fegetexceptflag() function stores an implementation-defined + * representation of the states of the floating-point status flags indicated by + * the argument excepts in the object pointed to by the argument flagp. + */ +int +fegetexceptflag(fexcept_t *flagp, int excepts) +{ + uint32_t mxcsr; + uint16_t status; + int ex; + + _DIAGASSERT(flagp != NULL); + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + __fnstsw(&status); + if (__HAS_SSE) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + + *flagp = (mxcsr | status) & ex; + + /* Success */ + return (0); +} + +/* + * The feraiseexcept() function raises the supported floating-point exceptions + * represented by the argument `excepts'. + * + * The standard explicitly allows us to execute an instruction that has the + * exception as a side effect, but we choose to manipulate the status register + * directly. + * + * The validation of input is being deferred to fesetexceptflag(). + */ +int +feraiseexcept(int excepts) +{ + fexcept_t ex; + + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + fesetexceptflag(&ex, excepts); + __fwait(); + + /* Success */ + return (0); +} + +/* + * This function sets the floating-point status flags indicated by the argument + * `excepts' to the states stored in the object pointed to by `flagp'. It does + * NOT raise any floating-point exceptions, but only sets the state of the flags. + */ +int +fesetexceptflag(const fexcept_t *flagp, int excepts) +{ + fenv_t env; + uint32_t mxcsr; + int ex; + + _DIAGASSERT(flagp != NULL); + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + __fnstenv(&env); + env.x87.status &= ~ex; + env.x87.status |= *flagp & ex; + __fldenv(env); + + if (__HAS_SSE) { + __stmxcsr(&mxcsr); + mxcsr &= ~ex; + mxcsr |= *flagp & ex; + __ldmxcsr(mxcsr); + } + + /* Success */ + return (0); +} + +/* + * The fetestexcept() function determines which of a specified subset of the + * floating-point exception flags are currently set. The `excepts' argument + * specifies the floating-point status flags to be queried. + */ +int +fetestexcept(int excepts) +{ + uint32_t mxcsr; + uint16_t status; + int ex; + + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + __fnstsw(&status); + if (__HAS_SSE) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + + return ((status | mxcsr) & ex); +} + +int +fegetround(void) +{ + uint16_t control; + + /* + * We assume that the x87 and the SSE unit agree on the + * rounding mode. Reading the control word on the x87 turns + * out to be about 5 times faster than reading it on the SSE + * unit on an Opteron 244. + */ + __fnstcw(&control); + + return (control & __X87_ROUND_MASK); +} + +/* + * The fesetround() function shall establish the rounding direction represented + * by its argument round. If the argument is not equal to the value of a + * rounding direction macro, the rounding direction is not changed. + */ +int +fesetround(int round) +{ + uint32_t mxcsr; + uint16_t control; + + if (round & ~__X87_ROUND_MASK) { + /* Failure */ + return (-1); + } + + __fnstcw(&control); + control &= ~__X87_ROUND_MASK; + control |= round; + __fldcw(control); + + if (__HAS_SSE) { + __stmxcsr(&mxcsr); + mxcsr &= ~(__X87_ROUND_MASK << __SSE_ROUND_SHIFT); + mxcsr |= round << __SSE_ROUND_SHIFT; + __ldmxcsr(mxcsr); + } + + /* Success */ + return (0); +} + +/* + * The fegetenv() function attempts to store the current floating-point + * environment in the object pointed to by envp. + */ +int +fegetenv(fenv_t *envp) +{ + uint32_t mxcsr; + + _DIAGASSERT(flagp != NULL); + + /* + * fnstenv masks all exceptions, so we need to restore the old control + * word to avoid this side effect. + */ + __fnstenv(envp); + __fldcw(envp->x87.control); + if (__HAS_SSE) { + __stmxcsr(&mxcsr); + envp->mxcsr = mxcsr; + } + + /* Success */ + return (0); +} + +/* + * The feholdexcept() function saves the current floating-point environment in + * the object pointed to by envp, clears the floating-point status flags, and + * then installs a non-stop (continue on floating-point exceptions) mode, if + * available, for all floating-point exceptions. + */ +int +feholdexcept(fenv_t *envp) +{ + uint32_t mxcsr; + + _DIAGASSERT(envp != NULL); + + __fnstenv(envp); + __fnclex(); + if (__HAS_SSE) { + __stmxcsr(&mxcsr); + envp->mxcsr = mxcsr; + mxcsr &= ~FE_ALL_EXCEPT; + mxcsr |= FE_ALL_EXCEPT << __SSE_EMASK_SHIFT; + __ldmxcsr(mxcsr); + } + + /* Success */ + return (0); +} + +/* + * The fesetenv() function attempts to establish the floating-point environment + * represented by the object pointed to by envp. The argument `envp' points + * to an object set by a call to fegetenv() or feholdexcept(), or equal a + * floating-point environment macro. The fesetenv() function does not raise + * floating-point exceptions, but only installs the state of the floating-point + * status flags represented through its argument. + */ +int +fesetenv(const fenv_t *envp) +{ + fenv_t env; + + _DIAGASSERT(envp != NULL); + + /* Store the x87 floating-point environment */ + memset(&env, 0, sizeof(env)); + __fnstenv(&env); + + __fe_dfl_env.x87.unused1 = env.x87.unused1; + __fe_dfl_env.x87.unused2 = env.x87.unused2; + __fe_dfl_env.x87.unused3 = env.x87.unused3; + memcpy(__fe_dfl_env.x87.others, + env.x87.others, + sizeof(__fe_dfl_env.x87.others) / sizeof(uint32_t)); + + __fldenv(envp->x87); + if (__HAS_SSE) + __ldmxcsr(envp->mxcsr); + + /* Success */ + return (0); +} + +/* + * The feupdateenv() function saves the currently raised floating-point + * exceptions in its automatic storage, installs the floating-point environment + * represented by the object pointed to by `envp', and then raises the saved + * floating-point exceptions. The argument `envp' shall point to an object set + * by a call to feholdexcept() or fegetenv(), or equal a floating-point + * environment macro. + */ +int +feupdateenv(const fenv_t *envp) +{ + fenv_t env; + uint32_t mxcsr; + uint16_t status; + + _DIAGASSERT(envp != NULL); + + /* Store the x87 floating-point environment */ + memset(&env, 0, sizeof(env)); + __fnstenv(&env); + + __fe_dfl_env.x87.unused1 = env.x87.unused1; + __fe_dfl_env.x87.unused2 = env.x87.unused2; + __fe_dfl_env.x87.unused3 = env.x87.unused3; + memcpy(__fe_dfl_env.x87.others, + env.x87.others, + sizeof(__fe_dfl_env.x87.others) / sizeof(uint32_t)); + + __fnstsw(&status); + if (__HAS_SSE) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + fesetenv(envp); + feraiseexcept((mxcsr | status) & FE_ALL_EXCEPT); + + /* Success */ + return (0); +} + +/* + * The following functions are extentions to the standard + */ +int +feenableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + mask &= FE_ALL_EXCEPT; + __fnstcw(&control); + if (__HAS_SSE) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + + omask = (control | mxcsr >> __SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control &= ~mask; + __fldcw(control); + if (__HAS_SSE) { + mxcsr &= ~(mask << __SSE_EMASK_SHIFT); + __ldmxcsr(mxcsr); + } + + return (~omask); +} + +int +fedisableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + mask &= FE_ALL_EXCEPT; + __fnstcw(&control); + if (__HAS_SSE) + __stmxcsr(&mxcsr); + else + mxcsr = 0; + + omask = (control | mxcsr >> __SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control |= mask; + __fldcw(control); + if (__HAS_SSE) { + mxcsr |= mask << __SSE_EMASK_SHIFT; + __ldmxcsr(mxcsr); + } + + return (~omask); +} + +int +fegetexcept(void) +{ + uint16_t control; + + /* + * We assume that the masks for the x87 and the SSE unit are + * the same. + */ + __fnstcw(&control); + + return (control & FE_ALL_EXCEPT); +} diff --git a/lib/nbsd_libm/arch/i387/lrint.S b/lib/nbsd_libm/arch/i387/lrint.S new file mode 100644 index 000000000..1ae8c8885 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/lrint.S @@ -0,0 +1,23 @@ +/* $NetBSD: lrint.S,v 1.2 2004/10/13 15:18:32 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include + +ENTRY(lrint) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $4,%esp + fldl 8(%ebp) + fistpl (%esp) + movl (%esp),%eax + leave + ret +#else + cvtsd2siq %xmm0,%rax + ret +#endif diff --git a/lib/nbsd_libm/arch/i387/s_atan.S b/lib/nbsd_libm/arch/i387/s_atan.S new file mode 100644 index 000000000..61a093309 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_atan.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_atan.S,v 1.6 2003/07/26 19:25:00 salo Exp $") + +ENTRY(atan) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fld1 + fpatan + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_atanf.S b/lib/nbsd_libm/arch/i387/s_atanf.S new file mode 100644 index 000000000..6eec1944c --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_atanf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_atanf.S,v 1.5 2003/07/26 19:25:00 salo Exp $") + +ENTRY(atanf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fld1 + fpatan + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_ceil.S b/lib/nbsd_libm/arch/i387/s_ceil.S new file mode 100644 index 000000000..05add36fd --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_ceil.S @@ -0,0 +1,45 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_ceil.S,v 1.7 2003/07/26 19:25:00 salo Exp $") + +ENTRY(ceil) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0800,%dx /* round towards +oo */ + andw $0xfbff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + fstcw -12(%rsp) + movw -12(%rsp),%dx + orw $0x0800,%dx + andw $0xfbff,%dx + movw %dx,-16(%rsp) + fldcw -16(%rsp) + movsd %xmm0,-8(%rsp) + fldl -8(%rsp) + frndint + fldcw -12(%rsp) + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_ceilf.S b/lib/nbsd_libm/arch/i387/s_ceilf.S new file mode 100644 index 000000000..9855c5fc0 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_ceilf.S @@ -0,0 +1,43 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_ceilf.S,v 1.8 2004/07/16 18:40:24 drochner Exp $") + +ENTRY(ceilf) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0800,%dx /* round towards +oo */ + andw $0xfbff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + flds 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + fstcw -8(%rsp) + movw -8(%rsp),%dx + orw $0x0800,%dx + andw $0xfbff,%dx + movw %dx,-12(%rsp) + fldcw -12(%rsp) + movss %xmm0,-4(%rsp) + flds -4(%rsp) + frndint + fldcw -8(%rsp) + fstps -4(%rsp) + movss -4(%rsp),%xmm0 +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_copysign.S b/lib/nbsd_libm/arch/i387/s_copysign.S new file mode 100644 index 000000000..54f7b15c7 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_copysign.S @@ -0,0 +1,53 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +/* + * XXXfvdl might as well split this file. + */ + +#include + +RCSID("$NetBSD: s_copysign.S,v 1.6 2003/07/26 19:25:01 salo Exp $") + +#ifdef __x86_64__ +.Lpos: + .quad 0x8000000000000000 +.Lneg: + .quad 0x7fffffffffffffff +#endif + + +ENTRY(copysign) +#ifdef __i386__ + movl 16(%esp),%edx + andl $0x80000000,%edx + movl 8(%esp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,8(%esp) + fldl 4(%esp) +#else +#if 0 + /* + * XXXfvdl gas doesn't grok this yet. + */ + movq .Lpos(%rip),%xmm2 + movq .Lneg(%rip),%xmm3 + pand %xmm2,%xmm1 + pand %xmm3,%xmm0 + por %xmm1,%xmm0 +#else + movsd %xmm0,-8(%rsp) + movsd %xmm1,-16(%rsp) + movl -12(%rsp),%edx + andl $0x80000000,%edx + movl -4(%rsp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,-4(%rsp) + movsd -8(%rsp),%xmm0 +#endif +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_copysignf.S b/lib/nbsd_libm/arch/i387/s_copysignf.S new file mode 100644 index 000000000..bbc5dd97d --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_copysignf.S @@ -0,0 +1,53 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +/* + * XXXfvdl split this file. + */ + +RCSID("$NetBSD: s_copysignf.S,v 1.5 2003/07/26 19:25:01 salo Exp $") + +#ifdef __x86_64__ +.Lneg: + .long 0x7fffffff +.Lpos: + .long 0x80000000 +#endif + +ENTRY(copysignf) +#ifdef __i386__ + movl 8(%esp),%edx + andl $0x80000000,%edx + movl 4(%esp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,4(%esp) + flds 4(%esp) +#else +#if 0 + /* + * XXXfvdl gas doesn't grok this. + * but it's legal according to the p4 manual. + */ + movss .Lpos(%rip),%xmm2 + movss .Lneg(%rip),%xmm3 + pandq %xmm2,%xmm1 + pandq %xmm3,%xmm0 + porq %xmm1,%xmm0 +#else + movss %xmm0,-4(%rsp) + movss %xmm1,-8(%rsp) + movl -8(%rsp),%edx + andl $0x80000000,%edx + movl -4(%rsp),%eax + andl $0x7fffffff,%eax + orl %edx,%eax + movl %eax,-4(%rsp) + movss -4(%rsp),%xmm0 +#endif +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_cos.S b/lib/nbsd_libm/arch/i387/s_cos.S new file mode 100644 index 000000000..2788a7cc8 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_cos.S @@ -0,0 +1,31 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_cos.S,v 1.8 2003/07/26 19:25:01 salo Exp $") + +ENTRY(cos) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fcos + fnstsw %ax + andw $0x400,%ax + jnz 1f + XMM_DOUBLE_EPILOGUE + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fnstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fcos + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_cosf.S b/lib/nbsd_libm/arch/i387/s_cosf.S new file mode 100644 index 000000000..0f9ead601 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_cosf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_cosf.S,v 1.6 2003/07/26 19:25:01 salo Exp $") + +/* A float's domain isn't large enough to require argument reduction. */ +ENTRY(cosf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fcos + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_finite.S b/lib/nbsd_libm/arch/i387/s_finite.S new file mode 100644 index 000000000..73d9cde38 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_finite.S @@ -0,0 +1,26 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_finite.S,v 1.7 2003/07/26 19:25:01 salo Exp $") + +ENTRY(finite) +#ifdef __i386__ + movl 8(%esp),%eax + andl $0x7ff00000, %eax + cmpl $0x7ff00000, %eax + setne %al + andl $0x000000ff, %eax +#else + xorl %eax,%eax + movq $0x7ff0000000000000,%rsi + movq %rsi,%rdi + movsd %xmm0,-8(%rsp) + andq -8(%rsp),%rsi + cmpq %rdi,%rsi + setne %al +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_finitef.S b/lib/nbsd_libm/arch/i387/s_finitef.S new file mode 100644 index 000000000..81bf3bd39 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_finitef.S @@ -0,0 +1,25 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_finitef.S,v 1.6 2003/07/26 19:25:01 salo Exp $") + +ENTRY(finitef) +#ifdef __i386__ + movl 4(%esp),%eax + andl $0x7f800000, %eax + cmpl $0x7f800000, %eax + setne %al + andl $0x000000ff, %eax +#else + xorl %eax,%eax + movl $0x7ff00000,%esi + movss %xmm0,-4(%rsp) + andl -4(%rsp),%esi + cmpl $0x7ff00000,%esi + setne %al +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_floor.S b/lib/nbsd_libm/arch/i387/s_floor.S new file mode 100644 index 000000000..22da00aac --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_floor.S @@ -0,0 +1,43 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_floor.S,v 1.8 2003/07/26 19:25:02 salo Exp $") + +ENTRY(floor) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0400,%dx /* round towards -oo */ + andw $0xf7ff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + fldl 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + movsd %xmm0, -8(%rsp) + fstcw -12(%rsp) + movw -12(%rsp),%dx + orw $0x0400,%dx + andw $0xf7ff,%dx + movw %dx,-16(%rsp) + fldcw -16(%rsp) + fldl -8(%rsp) + frndint + fldcw -12(%rsp) + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_floorf.S b/lib/nbsd_libm/arch/i387/s_floorf.S new file mode 100644 index 000000000..ffa1ae2fc --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_floorf.S @@ -0,0 +1,43 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_floorf.S,v 1.7 2004/07/16 18:40:24 drochner Exp $") + +ENTRY(floorf) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $8,%esp + + fstcw -4(%ebp) /* store fpu control word */ + movw -4(%ebp),%dx + orw $0x0400,%dx /* round towards -oo */ + andw $0xf7ff,%dx + movw %dx,-8(%ebp) + fldcw -8(%ebp) /* load modfied control word */ + + flds 8(%ebp); /* round */ + frndint + + fldcw -4(%ebp) /* restore original control word */ + + leave +#else + movss %xmm0, -4(%rsp) + fstcw -8(%rsp) + movw -8(%rsp),%dx + orw $0x0400,%dx + andw $0xf7ff,%dx + movw %dx,-12(%rsp) + fldcw -12(%rsp) + flds -4(%rsp) + frndint + fldcw -8(%rsp) + fstps -4(%rsp) + movss -4(%rsp),%xmm0 +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_ilogb.S b/lib/nbsd_libm/arch/i387/s_ilogb.S new file mode 100644 index 000000000..4bf7da029 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_ilogb.S @@ -0,0 +1,32 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_ilogb.S,v 1.7 2003/07/26 19:25:02 salo Exp $") + +ENTRY(ilogb) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $4,%esp + + fldl 8(%ebp) + fxtract + fstp %st + + fistpl -4(%ebp) + movl -4(%ebp),%eax + + leave +#else + movsd %xmm0,-8(%rsp) + fldl -8(%rsp) + fxtract + fstp %st + fistpl -8(%rsp) + movl -8(%rsp),%eax +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_ilogbf.S b/lib/nbsd_libm/arch/i387/s_ilogbf.S new file mode 100644 index 000000000..74e8a9233 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_ilogbf.S @@ -0,0 +1,32 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_ilogbf.S,v 1.6 2003/07/26 19:25:02 salo Exp $") + +ENTRY(ilogbf) +#ifdef __i386__ + pushl %ebp + movl %esp,%ebp + subl $4,%esp + + flds 8(%ebp) + fxtract + fstp %st + + fistpl -4(%ebp) + movl -4(%ebp),%eax + + leave +#else + movss %xmm0,-4(%rsp) + flds -4(%rsp) + fxtract + fstp %st + fistpl -4(%rsp) + movl -4(%rsp),%eax +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_log1p.S b/lib/nbsd_libm/arch/i387/s_log1p.S new file mode 100644 index 000000000..93ab11436 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_log1p.S @@ -0,0 +1,76 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +/* + * Modified by Lex Wennmacher + * Still public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_log1p.S,v 1.13 2003/09/16 18:17:11 wennmach Exp $") + +/* + * The log1p() function is provided to compute an accurate value of + * log(1 + x), even for tiny values of x. The i387 FPU provides the + * fyl2xp1 instruction for this purpose. However, the range of this + * instruction is limited to: + * -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1 + * -0.292893 <= x <= 0.414214 + * at least on older processor versions. + * + * log1p() is implemented by testing the range of the argument. + * If it is appropriate for fyl2xp1, this instruction is used. + * Else, we compute log1p(x) = ln(2)*ld(1 + x) the traditional way + * (using fyl2x). + * + * The range testing costs speed, but as the rationale for the very + * existence of this function is accuracy, we accept that. + * + * In order to reduce the cost for testing the range, we check if + * the argument is in the range + * -0.25 <= x <= 0.25 + * which can be done with just one conditional branch. If x is + * inside this range, we use fyl2xp1. Outside of this range, + * the use of fyl2x is accurate enough. + * + */ + +.text + .align 4 +ENTRY(log1p) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fabs + fld1 /* ... x 1 */ + fadd %st(0) /* ... x 2 */ + fadd %st(0) /* ... x 4 */ + fld1 /* ... 4 1 */ + fdivp /* ... x 0.25 */ + fcompp + fnstsw %ax + andb $69,%ah + jne use_fyl2x + jmp use_fyl2xp1 + + .align 4 +use_fyl2x: + fldln2 + fldl ARG_DOUBLE_ONE + fld1 + faddp + fyl2x + XMM_DOUBLE_EPILOGUE + ret + + .align 4 +use_fyl2xp1: + fldln2 + fldl ARG_DOUBLE_ONE + fyl2xp1 + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_log1pf.S b/lib/nbsd_libm/arch/i387/s_log1pf.S new file mode 100644 index 000000000..3ec415983 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_log1pf.S @@ -0,0 +1,76 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +/* + * Modified by Lex Wennmacher + * Still public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_log1pf.S,v 1.10 2003/09/16 18:17:11 wennmach Exp $") + +/* + * The log1pf() function is provided to compute an accurate value of + * log(1 + x), even for tiny values of x. The i387 FPU provides the + * fyl2xp1 instruction for this purpose. However, the range of this + * instruction is limited to: + * -(1 - (sqrt(2) / 2)) <= x <= sqrt(2) - 1 + * -0.292893 <= x <= 0.414214 + * at least on older processor versions. + * + * log1pf() is implemented by testing the range of the argument. + * If it is appropriate for fyl2xp1, this instruction is used. + * Else, we compute log1pf(x) = ln(2)*ld(1 + x) the traditional way + * (using fyl2x). + * + * The range testing costs speed, but as the rationale for the very + * existence of this function is accuracy, we accept that. + * + * In order to reduce the cost for testing the range, we check if + * the argument is in the range + * -0.25 <= x <= 0.25 + * which can be done with just one conditional branch. If x is + * inside this range, we use fyl2xp1. Outside of this range, + * the use of fyl2x is accurate enough. + * + */ + +.text + .align 4 +ENTRY(log1pf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fabs + fld1 /* ... x 1 */ + fadd %st(0) /* ... x 2 */ + fadd %st(0) /* ... x 4 */ + fld1 /* ... 4 1 */ + fdivp /* ... x 0.25 */ + fcompp + fnstsw %ax + andb $69,%ah + jne use_fyl2x + jmp use_fyl2xp1 + + .align 4 +use_fyl2x: + fldln2 + flds ARG_FLOAT_ONE + fld1 + faddp + fyl2x + XMM_FLOAT_EPILOGUE + ret + + .align 4 +use_fyl2xp1: + fldln2 + flds ARG_FLOAT_ONE + fyl2xp1 + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_logb.S b/lib/nbsd_libm/arch/i387/s_logb.S new file mode 100644 index 000000000..f520248c6 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_logb.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_logb.S,v 1.6 2003/07/26 19:25:02 salo Exp $") + +ENTRY(logb) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fxtract + fstp %st + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_logbf.S b/lib/nbsd_libm/arch/i387/s_logbf.S new file mode 100644 index 000000000..d66abc21f --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_logbf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_logbf.S,v 1.5 2003/07/26 19:25:02 salo Exp $") + +ENTRY(logbf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fxtract + fstp %st + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_modf.S b/lib/nbsd_libm/arch/i387/s_modf.S new file mode 100644 index 000000000..36d4c7998 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_modf.S @@ -0,0 +1,106 @@ +/* $NetBSD: s_modf.S,v 1.1 2006/03/22 20:45:58 drochner Exp $ */ + +/*- + * Copyright (c) 1990 The Regents of the University of California. + * All rights reserved. + * + * This code is derived from software contributed to Berkeley by + * Sean Eric Fagan. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * from: @(#)modf.s 5.5 (Berkeley) 3/18/91 + */ + +#include +#if defined(LIBC_SCCS) + RCSID("$NetBSD: s_modf.S,v 1.1 2006/03/22 20:45:58 drochner Exp $") +#endif + +/* + * modf(value, iptr): return fractional part of value, and stores the + * integral part into iptr (a pointer to double). + * + * Written by Sean Eric Fagan (sef@kithrup.COM) + * Sun Mar 11 20:27:30 PST 1990 + */ + +/* With CHOP mode on, frndint behaves as TRUNC does. Useful. */ +ENTRY(modf) +#ifdef __x86_64__ + pushq %rbp + movq %rsp,%rbp + subq $24,%rsp + + /* Set chop mode. */ + fnstcw -12(%rbp) + movw -12(%rbp),%dx + orw $3072,%dx + movw %dx,-16(%rbp) + fldcw -16(%rbp) + + /* Get integral part. */ + movsd %xmm0,-24(%rbp) + fldl -24(%rbp) + frndint + fstpl -8(%rbp) + + /* Restore control word. */ + fldcw -12(%rbp) + + /* Store integral part. */ + movsd -8(%rbp),%xmm0 + movsd %xmm0,(%rdi) + + /* Get fractional part and return it. */ + fldl -24(%rbp) + fsubl -8(%rbp) + fstpl -24(%rbp) + movsd -24(%rbp),%xmm0 +#else + pushl %ebp + movl %esp,%ebp + subl $16,%esp + fnstcw -12(%ebp) + movw -12(%ebp),%dx + orw $3072,%dx + movw %dx,-16(%ebp) + fldcw -16(%ebp) + fldl 8(%ebp) + frndint + fstpl -8(%ebp) + fldcw -12(%ebp) + movl 16(%ebp),%eax + movl -8(%ebp),%edx + movl -4(%ebp),%ecx + movl %edx,(%eax) + movl %ecx,4(%eax) + fldl 8(%ebp) + fsubl -8(%ebp) + jmp L1 +L1: +#endif + leave + ret diff --git a/lib/nbsd_libm/arch/i387/s_rint.S b/lib/nbsd_libm/arch/i387/s_rint.S new file mode 100644 index 000000000..c5300d04d --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_rint.S @@ -0,0 +1,17 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_rint.S,v 1.6 2003/07/26 19:25:03 salo Exp $") + +ENTRY(rint) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + frndint + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_rintf.S b/lib/nbsd_libm/arch/i387/s_rintf.S new file mode 100644 index 000000000..4ac746fba --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_rintf.S @@ -0,0 +1,17 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_rintf.S,v 1.5 2003/07/26 19:25:03 salo Exp $") + +ENTRY(rintf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + frndint + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_scalbn.S b/lib/nbsd_libm/arch/i387/s_scalbn.S new file mode 100644 index 000000000..4d9b31b7b --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_scalbn.S @@ -0,0 +1,30 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_scalbn.S,v 1.9 2010/04/23 19:17:07 drochner Exp $") + +#ifdef WEAK_ALIAS +WEAK_ALIAS(scalbn,_scalbn) +#endif + +ENTRY(_scalbn) +#ifdef __x86_64__ + movl %edi,-12(%rsp) + fildl -12(%rsp) + movsd %xmm0,-8(%rsp) + fldl -8(%rsp) + fscale + fstpl -8(%rsp) + movsd -8(%rsp),%xmm0 + fstp %st(0) +#else + fildl 12(%esp) + fldl 4(%esp) + fscale + fstp %st(1) /* clean up stack */ +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_scalbnf.S b/lib/nbsd_libm/arch/i387/s_scalbnf.S new file mode 100644 index 000000000..f7a95b658 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_scalbnf.S @@ -0,0 +1,30 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +RCSID("$NetBSD: s_scalbnf.S,v 1.8 2010/04/23 19:17:07 drochner Exp $") + +#ifdef WEAK_ALIAS +WEAK_ALIAS(scalbnf,_scalbnf) +#endif + +ENTRY(_scalbnf) +#ifdef __x86_64__ + movl %edi,-8(%rsp) + fildl -8(%rsp) + movss %xmm0,-4(%rsp) + flds -4(%rsp) + fscale + fstps -4(%rsp) + movss -4(%rsp),%xmm0 + fstp %st(0) +#else + fildl 8(%esp) + flds 4(%esp) + fscale + fstp %st(1) /* clean up stack */ +#endif + ret diff --git a/lib/nbsd_libm/arch/i387/s_significand.S b/lib/nbsd_libm/arch/i387/s_significand.S new file mode 100644 index 000000000..e85763a95 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_significand.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_significand.S,v 1.6 2003/07/26 19:25:03 salo Exp $") + +ENTRY(significand) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fxtract + fstp %st(1) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_significandf.S b/lib/nbsd_libm/arch/i387/s_significandf.S new file mode 100644 index 000000000..126fda10a --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_significandf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_significandf.S,v 1.5 2003/07/26 19:25:03 salo Exp $") + +ENTRY(significandf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fxtract + fstp %st(1) + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_sin.S b/lib/nbsd_libm/arch/i387/s_sin.S new file mode 100644 index 000000000..fa6c155da --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_sin.S @@ -0,0 +1,31 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_sin.S,v 1.7 2003/07/26 19:25:03 salo Exp $") + +ENTRY(sin) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fsin + fnstsw %ax + andw $0x400,%ax + jnz 1f + XMM_DOUBLE_EPILOGUE + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fnstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fsin + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_sinf.S b/lib/nbsd_libm/arch/i387/s_sinf.S new file mode 100644 index 000000000..f2cb587ae --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_sinf.S @@ -0,0 +1,18 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_sinf.S,v 1.5 2003/07/26 19:25:04 salo Exp $") + +/* A float's domain isn't large enough to require argument reduction. */ +ENTRY(sinf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fsin + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_tan.S b/lib/nbsd_libm/arch/i387/s_tan.S new file mode 100644 index 000000000..a5bed7b0b --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_tan.S @@ -0,0 +1,33 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_tan.S,v 1.7 2003/07/26 19:25:04 salo Exp $") + +ENTRY(tan) + XMM_ONE_ARG_DOUBLE_PROLOGUE + fldl ARG_DOUBLE_ONE + fptan + fnstsw %ax + andw $0x400,%ax + jnz 1f + fstp %st(0) + XMM_DOUBLE_EPILOGUE + ret +1: fldpi + fadd %st(0) + fxch %st(1) +2: fprem1 + fstsw %ax + andw $0x400,%ax + jnz 2b + fstp %st(1) + fptan + fstp %st(0) + XMM_DOUBLE_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/s_tanf.S b/lib/nbsd_libm/arch/i387/s_tanf.S new file mode 100644 index 000000000..a6d6c5b35 --- /dev/null +++ b/lib/nbsd_libm/arch/i387/s_tanf.S @@ -0,0 +1,19 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#include "abi.h" + +RCSID("$NetBSD: s_tanf.S,v 1.5 2003/07/26 19:25:04 salo Exp $") + +/* A float's domain isn't large enough to require argument reduction. */ +ENTRY(tanf) + XMM_ONE_ARG_FLOAT_PROLOGUE + flds ARG_FLOAT_ONE + fptan + fstp %st(0) + XMM_FLOAT_EPILOGUE + ret diff --git a/lib/nbsd_libm/arch/i387/shlib_version b/lib/nbsd_libm/arch/i387/shlib_version new file mode 100644 index 000000000..f077acaaf --- /dev/null +++ b/lib/nbsd_libm/arch/i387/shlib_version @@ -0,0 +1,5 @@ +# $NetBSD: shlib_version,v 1.2 2005/07/21 22:49:16 rpaulo Exp $ +# Remember to update distrib/sets/lists/base/md.i386 when changing +# +major=0 +minor=1 diff --git a/lib/nbsd_libm/arch/x86_64/fenv.c b/lib/nbsd_libm/arch/x86_64/fenv.c new file mode 100644 index 000000000..9f27fcedc --- /dev/null +++ b/lib/nbsd_libm/arch/x86_64/fenv.c @@ -0,0 +1,524 @@ +/* $NetBSD: fenv.c,v 1.1 2010/07/31 21:47:53 joerg Exp $ */ + +/*- + * Copyright (c) 2004-2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: fenv.c,v 1.1 2010/07/31 21:47:53 joerg Exp $"); + +#include +#include +#include +#include + +/* Load x87 Control Word */ +#define __fldcw(__cw) __asm__ __volatile__ \ + ("fldcw %0" : : "m" (__cw)) + +/* No-Wait Store Control Word */ +#define __fnstcw(__cw) __asm__ __volatile__ \ + ("fnstcw %0" : "=m" (*(__cw))) + +/* No-Wait Store Status Word */ +#define __fnstsw(__sw) __asm__ __volatile__ \ + ("fnstsw %0" : "=am" (*(__sw))) + +/* No-Wait Clear Exception Flags */ +#define __fnclex() __asm__ __volatile__ \ + ("fnclex") + +/* Load x87 Environment */ +#define __fldenv(__env) __asm__ __volatile__ \ + ("fldenv %0" : : "m" (__env)) + +/* No-Wait Store x87 environment */ +#define __fnstenv(__env) __asm__ __volatile__ \ + ("fnstenv %0" : "=m" (*(__env))) + +/* Load the MXCSR register */ +#define __ldmxcsr(__mxcsr) __asm__ __volatile__ \ + ("ldmxcsr %0" : : "m" (__mxcsr)) + +/* Store the MXCSR register state */ +#define __stmxcsr(__mxcsr) __asm__ __volatile__ \ + ("stmxcsr %0" : "=m" (*(__mxcsr))) + +/* + * The following constant represents the default floating-point environment + * (that is, the one installed at program startup) and has type pointer to + * const-qualified fenv_t. + * + * It can be used as an argument to the functions within the header + * that manage the floating-point environment, namely fesetenv() and + * feupdateenv(). + * + * x87 fpu registers are 16bit wide. The upper bits, 31-16, are marked as + * RESERVED. We provide a partial floating-point environment, where we + * define only the lower bits. The reserved bits are extracted and set by + * the consumers of FE_DFL_ENV, during runtime. + */ +fenv_t __fe_dfl_env = { + { + __NetBSD_NPXCW__, /* Control word register */ + 0x00000000, /* Status word register */ + 0x0000ffff, /* Tag word register */ + { + 0x00000000, + 0x00000000, + 0x00000000, + 0x00000000, + }, + }, + __INITIAL_MXCSR__ /* MXCSR register */ +}; +#define FE_DFL_ENV ((const fenv_t *) &__fe_dfl_env) + + +/* + * The feclearexcept() function clears the supported floating-point exceptions + * represented by `excepts'. + */ +int +feclearexcept(int excepts) +{ + fenv_t fenv; + int ex; + + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + /* Store the current x87 floating-point environment */ + __fnstenv(&fenv); + + /* Clear the requested floating-point exceptions */ + fenv.x87.status &= ~ex; + + /* Load the x87 floating-point environent */ + __fldenv(fenv); + + /* Same for SSE environment */ + __stmxcsr(&fenv.mxcsr); + fenv.mxcsr &= ~ex; + __ldmxcsr(fenv.mxcsr); + + /* Success */ + return (0); +} + +/* + * The fegetexceptflag() function stores an implementation-defined + * representation of the states of the floating-point status flags indicated by + * the argument excepts in the object pointed to by the argument flagp. + */ +int +fegetexceptflag(fexcept_t *flagp, int excepts) +{ + uint32_t mxcsr; + uint16_t x87_status; + int ex; + + _DIAGASSERT(flagp != NULL); + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + /* Store the current x87 status register */ + __fnstsw(&x87_status); + + /* Store the MXCSR register */ + __stmxcsr(&mxcsr); + + /* Store the results in flagp */ + *flagp = (x87_status | mxcsr) & ex; + + /* Success */ + return (0); +} + +/* + * The feraiseexcept() function raises the supported floating-point exceptions + * represented by the argument `excepts'. + * + * The standard explicitly allows us to execute an instruction that has the + * exception as a side effect, but we choose to manipulate the status register + * directly. + * + * The validation of input is being deferred to fesetexceptflag(). + */ +int +feraiseexcept(int excepts) +{ + int ex; + + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + fesetexceptflag((unsigned int *)&excepts, excepts); + + /* Success */ + return (0); +} + +/* + * This function sets the floating-point status flags indicated by the argument + * `excepts' to the states stored in the object pointed to by `flagp'. It does + * NOT raise any floating-point exceptions, but only sets the state of the flags. + */ +int +fesetexceptflag(const fexcept_t *flagp, int excepts) +{ + fenv_t fenv; + int ex; + + _DIAGASSERT(flagp != NULL); + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + /* Store the current x87 floating-point environment */ + __fnstenv(&fenv); + + /* Set the requested status flags */ + fenv.x87.status |= *flagp & ex; + + /* Load the x87 floating-point environent */ + __fldenv(fenv); + + /* Same for SSE environment */ + __stmxcsr(&fenv.mxcsr); + fenv.mxcsr |= *flagp & ex; + __ldmxcsr(fenv.mxcsr); + + /* Success */ + return (0); +} + +/* + * The fetestexcept() function determines which of a specified subset of the + * floating-point exception flags are currently set. The `excepts' argument + * specifies the floating-point status flags to be queried. + */ +int +fetestexcept(int excepts) +{ + fenv_t fenv; + uint32_t mxcsr; + uint16_t status; + int ex; + + _DIAGASSERT((excepts & ~FE_ALL_EXCEPT) == 0); + + ex = excepts & FE_ALL_EXCEPT; + + /* Store the current x87 floating-point environment */ + memset(&fenv, 0, sizeof(fenv)); + + __fnstenv(&fenv); + __fnstsw(&status); + + /* Store the MXCSR register state */ + __stmxcsr(&fenv.mxcsr); + __stmxcsr(&mxcsr); + + return ((fenv.x87.status | fenv.mxcsr) & ex); +} + +/* + * The fegetround() function gets the current rounding direction. + */ +int +fegetround(void) +{ + uint32_t mxcsr; + uint16_t control; + + /* + * We check both the x87 floating-point unit _and_ the SSE unit. + * Normally, those two must agree with respect to each other. If they + * don't, it's not our fault and the result is non-determinable, in + * which case POSIX says that a negative value should be returned. + */ + __fnstcw(&control); + __stmxcsr(&mxcsr); + + if ((control & _X87_ROUNDING_MASK) + != ((mxcsr & _SSE_ROUNDING_MASK) >> 3)) { + return (-1); + } + + return (control & _X87_ROUNDING_MASK); +} + +/* + * The fesetround() function establishes the rounding direction represented by + * its argument `round'. If the argument is not equal to the value of a rounding + * direction macro, the rounding direction is not changed. + */ +int +fesetround(int round) +{ + uint32_t mxcsr; + uint16_t control; + + /* Check whether requested rounding direction is supported */ + if (round & (~_X87_ROUNDING_MASK)) + return (-1); + + /* Store the current x87 control word register */ + __fnstcw(&control); + + /* + * Set the rounding direction + * Rounding Control is bits 10-11, so shift appropriately + */ + control &= ~_X87_ROUNDING_MASK; + control |= round; + + /* Load the x87 control word register */ + __fldcw(control); + + /* + * Same for the SSE environment + * Rounding Control is bits 13-14, so shift appropriately + */ + __stmxcsr(&mxcsr); + mxcsr &= ~_SSE_ROUNDING_MASK; + mxcsr |= (round << _SSE_ROUND_SHIFT); + __ldmxcsr(mxcsr); + + /* Success */ + return (0); +} + +/* + * The fegetenv() function attempts to store the current floating-point + * environment in the object pointed to by envp. + */ +int +fegetenv(fenv_t *envp) +{ + _DIAGASSERT(envp != NULL); + + /* Store the current x87 floating-point environment */ + __fnstenv(envp); + + /* Store the MXCSR register state */ + __stmxcsr(&envp->mxcsr); + + /* + * When an FNSTENV instruction is executed, all pending exceptions are + * essentially lost (either the x87 FPU status register is cleared or all + * exceptions are masked). + * + * 8.6 X87 FPU EXCEPTION SYNCHRONIZATION - + * Intel(R) 64 and IA-32 Architectures Softare Developer's Manual - Vol 1 + * + */ + __fldcw(envp->x87.control); + + /* Success */ + return (0); +} + +/* + * The feholdexcept() function saves the current floating-point environment + * in the object pointed to by envp, clears the floating-point status flags, and + * then installs a non-stop (continue on floating-point exceptions) mode, if + * available, for all floating-point exceptions. + */ +int +feholdexcept(fenv_t *envp) +{ + uint32_t mxcsr; + + _DIAGASSERT(envp != NULL); + + /* Store the current x87 floating-point environment */ + __fnstenv(envp); + + /* Clear all exception flags in FPU */ + __fnclex(); + + /* Store the MXCSR register state */ + __stmxcsr(&envp->mxcsr); + + /* Clear exception flags in MXCSR XXX */ + mxcsr = envp->mxcsr; + mxcsr &= ~FE_ALL_EXCEPT; + + /* Mask all exceptions */ + mxcsr |= FE_ALL_EXCEPT << _SSE_EMASK_SHIFT; + + __ldmxcsr(mxcsr); + + /* Success */ + return (0); +} + +/* + * The fesetenv() function attempts to establish the floating-point environment + * represented by the object pointed to by envp. The argument `envp' points + * to an object set by a call to fegetenv() or feholdexcept(), or equal a + * floating-point environment macro. The fesetenv() function does not raise + * floating-point exceptions, but only installs the state of the floating-point + * status flags represented through its argument. + */ +int +fesetenv(const fenv_t *envp) +{ + fenv_t fenv; + + _DIAGASSERT(envp != NULL); + + /* Store the x87 floating-point environment */ + memset(&fenv, 0, sizeof fenv); + __fnstenv(&fenv); + + __fe_dfl_env.x87.control = (fenv.x87.control & 0xffff0000) + | (__fe_dfl_env.x87.control & 0x0000ffff); + __fe_dfl_env.x87.status = (fenv.x87.status & 0xffff0000) + | (__fe_dfl_env.x87.status & 0x0000ffff); + __fe_dfl_env.x87.tag = (fenv.x87.tag & 0xffff0000) + | (__fe_dfl_env.x87.tag & 0x0000ffff); + __fe_dfl_env.x87.others[3] = (fenv.x87.others[3] & 0xffff0000) + | (__fe_dfl_env.x87.others[3] & 0x0000ffff); + __fldenv(*envp); + + /* Store the MXCSR register */ + __ldmxcsr(envp->mxcsr); + + /* Success */ + return (0); +} + +/* + * The feupdateenv() function saves the currently raised floating-point + * exceptions in its automatic storage, installs the floating-point environment + * represented by the object pointed to by `envp', and then raises the saved + * floating-point exceptions. The argument `envp' shall point to an object set + * by a call to feholdexcept() or fegetenv(), or equal a floating-point + * environment macro. + */ +int +feupdateenv(const fenv_t *envp) +{ + fenv_t fenv; + uint32_t mxcsr; + uint16_t sw; + + _DIAGASSERT(envp != NULL); + + /* Store the x87 floating-point environment */ + memset(&fenv, 0, sizeof(fenv)); + __fnstenv(&fenv); + + __fe_dfl_env.x87.control = (fenv.x87.control & 0xffff0000) + | (__fe_dfl_env.x87.control & 0x0000ffff); + __fe_dfl_env.x87.status = (fenv.x87.status & 0xffff0000) + | (__fe_dfl_env.x87.status & 0x0000ffff); + __fe_dfl_env.x87.tag = (fenv.x87.tag & 0xffff0000) + | (__fe_dfl_env.x87.tag & 0x0000ffff); + __fe_dfl_env.x87.others[3] = (fenv.x87.others[3] & 0xffff0000) + | (__fe_dfl_env.x87.others[3] & 0x0000ffff); + + /* Store the x87 status register */ + __fnstsw(&sw); + + /* Store the MXCSR register */ + __stmxcsr(&mxcsr); + + /* Install new floating-point environment */ + fesetenv(envp); + + /* Raise any previously accumulated exceptions */ + feraiseexcept((sw | mxcsr) & FE_ALL_EXCEPT); + + /* Success */ + return (0); +} + +/* + * The following functions are extentions to the standard + */ +int +feenableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + _DIAGASSERT((mask & ~FE_ALL_EXCEPT) == 0); + mask &= FE_ALL_EXCEPT; + + __fnstcw(&control); + __stmxcsr(&mxcsr); + + omask = (control | mxcsr >> _SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control &= ~mask; + __fldcw(control); + + mxcsr &= ~(mask << _SSE_EMASK_SHIFT); + __ldmxcsr(mxcsr); + + return (~omask); + +} + +int +fedisableexcept(int mask) +{ + uint32_t mxcsr, omask; + uint16_t control; + + _DIAGASSERT((mask & ~FE_ALL_EXCEPT) == 0); + + __fnstcw(&control); + __stmxcsr(&mxcsr); + + omask = (control | mxcsr >> _SSE_EMASK_SHIFT) & FE_ALL_EXCEPT; + control |= mask; + __fldcw(control); + + mxcsr |= mask << _SSE_EMASK_SHIFT; + __ldmxcsr(mxcsr); + + return (~omask); +} + +int +fegetexcept(void) +{ + uint16_t control; + + /* + * We assume that the masks for the x87 and the SSE unit are + * the same. + */ + __fnstcw(&control); + + return (control & FE_ALL_EXCEPT); +} + diff --git a/lib/nbsd_libm/compat/compat_cabs.c b/lib/nbsd_libm/compat/compat_cabs.c new file mode 100644 index 000000000..af6c45729 --- /dev/null +++ b/lib/nbsd_libm/compat/compat_cabs.c @@ -0,0 +1,29 @@ +/* + * cabs() wrapper for hypot(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: compat_cabs.c,v 1.2 2007/08/10 21:20:35 drochner Exp $"); +#endif + +#include "../src/namespace.h" +#include + +struct complex { + double x; + double y; +}; + +double cabs(struct complex); +__warn_references(cabs, "warning: reference to compatibility cabs()"); + +double +cabs(struct complex z) +{ + + return hypot(z.x, z.y); +} diff --git a/lib/nbsd_libm/compat/compat_cabsf.c b/lib/nbsd_libm/compat/compat_cabsf.c new file mode 100644 index 000000000..fad6283e9 --- /dev/null +++ b/lib/nbsd_libm/compat/compat_cabsf.c @@ -0,0 +1,29 @@ +/* + * cabsf() wrapper for hypotf(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: compat_cabsf.c,v 1.2 2007/08/10 21:20:35 drochner Exp $"); +#endif + +#include "../src/namespace.h" +#include + +struct complex { + float x; + float y; +}; + +float cabsf __P((struct complex)); +__warn_references(cabsf, "warning: reference to compatibility cabsf()"); + +float +cabsf(struct complex z) +{ + + return hypotf(z.x, z.y); +} diff --git a/lib/nbsd_libm/complex/Makefile.inc b/lib/nbsd_libm/complex/Makefile.inc new file mode 100644 index 000000000..5b305ffac --- /dev/null +++ b/lib/nbsd_libm/complex/Makefile.inc @@ -0,0 +1,28 @@ +# $NetBSD: Makefile.inc,v 1.3 2010/09/15 16:11:29 christos Exp $ + +.PATH: ${.CURDIR}/complex + +SRCS+= cabs.c cabsf.c carg.c cargf.c +SRCS+= creal.c crealf.c creall.c cimag.c cimagf.c cimagl.c +SRCS+= conj.c conjf.c conjl.c +SRCS+= csqrt.c cexp.c clog.c cpow.c +SRCS+= cephes_subr.c csin.c ccos.c ctan.c csinh.c ccosh.c ctanh.c +SRCS+= casin.c cacos.c catan.c casinh.c cacosh.c catanh.c +SRCS+= csqrtf.c cexpf.c clogf.c cpowf.c +SRCS+= cephes_subrf.c csinf.c ccosf.c ctanf.c csinhf.c ccoshf.c ctanhf.c +SRCS+= casinf.c cacosf.c catanf.c casinhf.c cacoshf.c catanhf.c +SRCS+= cproj.c cprojf.c cprojl.c + +MAN+= cabs.3 cacos.3 cacosh.3 carg.3 casin.3 casinh.3 catan.3 catanh.3 +MAN+= ccos.3 ccosh.3 cexp.3 cimag.3 clog.3 conj.3 cpow.3 cproj.3 creal.3 +MAN+= csin.3 csinh.3 csqrt.3 ctan.3 ctanh.3 + +MLINKS+= cabs.3 cabsf.3 cacos.3 cacosf.3 cacosh.3 cacoshf.3 +MLINKS+= carg.3 cargf.3 casin.3 casinf.3 casinh.3 casinhf.3 +MLINKS+= catan.3 catanf.3 catanh.3 catanhf.3 ccos.3 ccosf.3 +MLINKS+= ccosh.3 ccoshf.3 cexp.3 cexpf.3 +MLINKS+= cimag.3 cimagf.3 cimag.3 cimagl.3 +MLINKS+= clog.3 clogf.3 conj.3 conjf.3 cpow.3 cpowf.3 +MLINKS+= creal.3 crealf.3 creal.3 creall.3 +MLINKS+= csin.3 csinf.3 csinh.3 csinhf.3 +MLINKS+= csqrt.3 csqrtf.3 ctan.3 ctanf.3 ctanh.3 ctanhf.3 diff --git a/lib/nbsd_libm/complex/cabs.3 b/lib/nbsd_libm/complex/cabs.3 new file mode 100644 index 000000000..9ee409093 --- /dev/null +++ b/lib/nbsd_libm/complex/cabs.3 @@ -0,0 +1,53 @@ +.\" $NetBSD: cabs.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CABS" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" cabs +.SH NAME +cabs, cabsf \- return a complex absolute value +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double cabs(double complex\fP \fIz\fP\fB); +.br +float cabsf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex absolute value (also called +norm, modulus, or magnitude) of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the complex absolute value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +The Base Definitions volume of IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/cabs.c b/lib/nbsd_libm/complex/cabs.c new file mode 100644 index 000000000..5718bdd8f --- /dev/null +++ b/lib/nbsd_libm/complex/cabs.c @@ -0,0 +1,17 @@ +/* $NetBSD: cabs.c,v 1.1 2007/08/20 16:01:30 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include "../src/namespace.h" +#include +#include + +double +cabs(double complex z) +{ + + return hypot(__real__ z, __imag__ z); +} diff --git a/lib/nbsd_libm/complex/cabsf.c b/lib/nbsd_libm/complex/cabsf.c new file mode 100644 index 000000000..fda7bc7c4 --- /dev/null +++ b/lib/nbsd_libm/complex/cabsf.c @@ -0,0 +1,17 @@ +/* $NetBSD: cabsf.c,v 1.1 2007/08/20 16:01:30 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include "../src/namespace.h" +#include +#include + +float +cabsf(float complex z) +{ + + return hypotf(__real__ z, __imag__ z); +} diff --git a/lib/nbsd_libm/complex/cacos.3 b/lib/nbsd_libm/complex/cacos.3 new file mode 100644 index 000000000..d3459cfdf --- /dev/null +++ b/lib/nbsd_libm/complex/cacos.3 @@ -0,0 +1,57 @@ +.\" $NetBSD: cacos.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CACOS" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" cacos +.SH NAME +cacos, cacosf \- complex arc cosine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex cacos(double complex\fP \fIz\fP\fB); +.br +float complex cacosf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex arc cosine of \fIz\fP, with +branch cuts outside the interval [-1,\ +1] along the +real axis. +.SH RETURN VALUE +.LP +These functions return the complex arc cosine value, in the +range of a strip mathematically unbounded along the imaginary +axis and in the interval [0,\ pi] along the real axis. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIccos\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/cacos.c b/lib/nbsd_libm/complex/cacos.c new file mode 100644 index 000000000..5fe13e9d4 --- /dev/null +++ b/lib/nbsd_libm/complex/cacos.c @@ -0,0 +1,44 @@ +/* $NetBSD: cacos.c,v 1.1 2007/08/20 16:01:30 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +double complex +cacos(double complex z) +{ + double complex w; + + w = casin(z); + w = (M_PI_2 - creal(w)) - cimag(w) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/cacosf.c b/lib/nbsd_libm/complex/cacosf.c new file mode 100644 index 000000000..e3c88557b --- /dev/null +++ b/lib/nbsd_libm/complex/cacosf.c @@ -0,0 +1,44 @@ +/* $NetBSD: cacosf.c,v 1.1 2007/08/20 16:01:30 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +float complex +cacosf(float complex z) +{ + float complex w; + + w = casinf(z); + w = ((float)M_PI_2 - crealf(w)) - cimagf(w) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/cacosh.3 b/lib/nbsd_libm/complex/cacosh.3 new file mode 100644 index 000000000..506e108fd --- /dev/null +++ b/lib/nbsd_libm/complex/cacosh.3 @@ -0,0 +1,58 @@ +.\" $NetBSD: cacosh.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CACOSH" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" cacosh +.SH NAME +cacosh, cacoshf \- complex arc hyperbolic cosine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex cacosh(double complex\fP \fIz\fP\fB); +.br +float complex cacoshf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex arc hyperbolic cosine of +\fIz\fP, with a branch cut at values less than 1 along the +real axis. +.SH RETURN VALUE +.LP +These functions return the complex arc hyperbolic cosine value, +in the range of a half-strip of non-negative values along +the real axis and in the interval [-\fIi\fPpi,\ +\fIi\fPpi] along +the imaginary axis. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIccosh\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/cacosh.c b/lib/nbsd_libm/complex/cacosh.c new file mode 100644 index 000000000..fcfb365be --- /dev/null +++ b/lib/nbsd_libm/complex/cacosh.c @@ -0,0 +1,45 @@ +/* $NetBSD: cacosh.c,v 1.2 2009/08/03 19:41:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include + +double complex +cacosh(double complex z) +{ + double complex w; + +#if 0 /* does not give the principal value */ + w = I * cacos(z); +#else + w = clog(z + csqrt(z + 1) * csqrt(z - 1)); +#endif + return w; +} diff --git a/lib/nbsd_libm/complex/cacoshf.c b/lib/nbsd_libm/complex/cacoshf.c new file mode 100644 index 000000000..76295d597 --- /dev/null +++ b/lib/nbsd_libm/complex/cacoshf.c @@ -0,0 +1,45 @@ +/* $NetBSD: cacoshf.c,v 1.2 2009/08/03 19:41:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include + +float complex +cacoshf(float complex z) +{ + float complex w; + +#if 0 /* does not give the principal value */ + w = I * cacosf(z); +#else + w = clogf(z + csqrtf(z + 1) * csqrtf(z - 1)); +#endif + return w; +} diff --git a/lib/nbsd_libm/complex/carg.3 b/lib/nbsd_libm/complex/carg.3 new file mode 100644 index 000000000..c18923935 --- /dev/null +++ b/lib/nbsd_libm/complex/carg.3 @@ -0,0 +1,56 @@ +.\" $NetBSD: carg.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CARG" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" carg +.SH NAME +carg, cargf \- complex argument functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double carg(double complex\fP \fIz\fP\fB); +.br +float cargf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the argument (also called phase angle) +of \fIz\fP, with a branch cut along the negative real +axis. +.SH RETURN VALUE +.LP +These functions return the value of the argument in the interval +[-pi,\ +pi]. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcimag\fP(), \fIconj\fP(), \fIcproj\fP(), the +Base Definitions volume of IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/carg.c b/lib/nbsd_libm/complex/carg.c new file mode 100644 index 000000000..ace234ef4 --- /dev/null +++ b/lib/nbsd_libm/complex/carg.c @@ -0,0 +1,17 @@ +/* $NetBSD: carg.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include "../src/namespace.h" +#include +#include + +double +carg(double complex z) +{ + + return atan2(__imag__ z, __real__ z); +} diff --git a/lib/nbsd_libm/complex/cargf.c b/lib/nbsd_libm/complex/cargf.c new file mode 100644 index 000000000..2dcb053e0 --- /dev/null +++ b/lib/nbsd_libm/complex/cargf.c @@ -0,0 +1,17 @@ +/* $NetBSD: cargf.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include "../src/namespace.h" +#include +#include + +float +cargf(float complex z) +{ + + return atan2f(__imag__ z, __real__ z); +} diff --git a/lib/nbsd_libm/complex/casin.3 b/lib/nbsd_libm/complex/casin.3 new file mode 100644 index 000000000..cca3792b4 --- /dev/null +++ b/lib/nbsd_libm/complex/casin.3 @@ -0,0 +1,58 @@ +.\" $NetBSD: casin.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CASIN" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" casin +.SH NAME +casin, casinf \- complex arc sine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex casin(double complex\fP \fIz\fP\fB); +.br +float complex casinf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex arc sine of \fIz\fP, with +branch cuts outside the interval [-1,\ +1] along the +real axis. +.SH RETURN VALUE +.LP +These functions return the complex arc sine value, in the range +of a strip mathematically unbounded along the imaginary +axis and in the interval [-pi/2,\ +pi/2] along the +real axis. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcsin\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/casin.c b/lib/nbsd_libm/complex/casin.c new file mode 100644 index 000000000..d58002227 --- /dev/null +++ b/lib/nbsd_libm/complex/casin.c @@ -0,0 +1,120 @@ +/* $NetBSD: casin.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +#ifdef __weak_alias +__weak_alias(casin, _casin) +#endif + +double complex +casin(double complex z) +{ + double complex w; + double complex ca, ct, zz, z2; + double x, y; + + x = creal(z); + y = cimag(z); + +#if 0 /* MD: test is incorrect, casin(>1) is defined */ + if (y == 0.0) { + if (fabs(x) > 1.0) { + w = M_PI_2 + 0.0 * I; +#if 0 + mtherr ("casin", DOMAIN); +#endif + } else { + w = asin(x) + 0.0 * I; + } + return w; + } +#endif + +/* Power series expansion */ +/* +b = cabs(z); +if( b < 0.125 ) +{ +z2.r = (x - y) * (x + y); +z2.i = 2.0 * x * y; + +cn = 1.0; +n = 1.0; +ca.r = x; +ca.i = y; +sum.r = x; +sum.i = y; +do + { + ct.r = z2.r * ca.r - z2.i * ca.i; + ct.i = z2.r * ca.i + z2.i * ca.r; + ca.r = ct.r; + ca.i = ct.i; + + cn *= n; + n += 1.0; + cn /= n; + n += 1.0; + b = cn/n; + + ct.r *= b; + ct.i *= b; + sum.r += ct.r; + sum.i += ct.i; + b = fabs(ct.r) + fabs(ct.i); + } +while( b > MACHEP ); +w->r = sum.r; +w->i = sum.i; +return; +} +*/ + + + ca = x + y * I; + ct = ca * I; + /* sqrt( 1 - z*z) */ + /* cmul( &ca, &ca, &zz ) */ + /*x * x - y * y */ + zz = (x - y) * (x + y) + (2.0 * x * y) * I; + + zz = 1.0 - creal(zz) - cimag(zz) * I; + z2 = csqrt(zz); + + zz = ct + z2; + zz = clog(zz); + /* multiply by 1/i = -i */ + w = zz * (-1.0 * I); + return w; +} diff --git a/lib/nbsd_libm/complex/casinf.c b/lib/nbsd_libm/complex/casinf.c new file mode 100644 index 000000000..3bd0b06c9 --- /dev/null +++ b/lib/nbsd_libm/complex/casinf.c @@ -0,0 +1,120 @@ +/* $NetBSD: casinf.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +#ifdef __weak_alias +__weak_alias(casinf, _casinf) +#endif + +float complex +casinf(float complex z) +{ + float complex w; + float complex ca, ct, zz, z2; + float x, y; + + x = crealf(z); + y = cimagf(z); + +#if 0 /* MD: test is incorrect, casin(>1) is defined */ + if (y == 0.0f) { + if (fabsf(x) > 1.0) { + w = M_PI_2 + 0.0f * I; +#if 0 + mtherr ("casin", DOMAIN); +#endif + } else { + w = asinf(x) + 0.0f * I; + } + return w; + } +#endif + +/* Power series expansion */ +/* +b = cabsf(z); +if( b < 0.125 ) +{ +z2.r = (x - y) * (x + y); +z2.i = 2.0 * x * y; + +cn = 1.0; +n = 1.0; +ca.r = x; +ca.i = y; +sum.r = x; +sum.i = y; +do + { + ct.r = z2.r * ca.r - z2.i * ca.i; + ct.i = z2.r * ca.i + z2.i * ca.r; + ca.r = ct.r; + ca.i = ct.i; + + cn *= n; + n += 1.0; + cn /= n; + n += 1.0; + b = cn/n; + + ct.r *= b; + ct.i *= b; + sum.r += ct.r; + sum.i += ct.i; + b = fabsf(ct.r) + fabsf(ct.i); + } +while( b > MACHEP ); +w->r = sum.r; +w->i = sum.i; +return; +} +*/ + + + ca = x + y * I; + ct = ca * I; + /* sqrt( 1 - z*z) */ + /* cmul( &ca, &ca, &zz ) */ + /*x * x - y * y */ + zz = (x - y) * (x + y) + (2.0f * x * y) * I; + + zz = 1.0f - crealf(zz) - cimagf(zz) * I; + z2 = csqrtf(zz); + + zz = ct + z2; + zz = clogf(zz); + /* multiply by 1/i = -i */ + w = zz * (-1.0f * I); + return w; +} diff --git a/lib/nbsd_libm/complex/casinh.3 b/lib/nbsd_libm/complex/casinh.3 new file mode 100644 index 000000000..56e264122 --- /dev/null +++ b/lib/nbsd_libm/complex/casinh.3 @@ -0,0 +1,58 @@ +.\" $NetBSD: casinh.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CASINH" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" casinh +.SH NAME +casinh, casinhf \- complex arc hyperbolic sine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex casinh(double complex\fP \fIz\fP\fB); +.br +float complex casinhf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex arc hyperbolic sine of \fIz\fP, +with branch cuts outside the interval +[-\fIi\fP,\ +\fIi\fP] along the imaginary axis. +.SH RETURN VALUE +.LP +These functions return the complex arc hyperbolic sine value, +in the range of a strip mathematically unbounded along the +real axis and in the interval [-\fIi\fPpi/2,\ +\fIi\fPpi/2] along +the imaginary axis. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcsinh\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/casinh.c b/lib/nbsd_libm/complex/casinh.c new file mode 100644 index 000000000..73a3c32aa --- /dev/null +++ b/lib/nbsd_libm/complex/casinh.c @@ -0,0 +1,42 @@ +/* $NetBSD: casinh.c,v 1.1 2007/08/20 16:01:31 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include + +double complex +casinh(double complex z) +{ + double complex w; + + w = -1.0 * I * casin(z * I); + return w; +} diff --git a/lib/nbsd_libm/complex/casinhf.c b/lib/nbsd_libm/complex/casinhf.c new file mode 100644 index 000000000..1a9a051dc --- /dev/null +++ b/lib/nbsd_libm/complex/casinhf.c @@ -0,0 +1,42 @@ +/* $NetBSD: casinhf.c,v 1.1 2007/08/20 16:01:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include + +float complex +casinhf(float complex z) +{ + float complex w; + + w = -1.0f * I * casinf(z * I); + return w; +} diff --git a/lib/nbsd_libm/complex/catan.3 b/lib/nbsd_libm/complex/catan.3 new file mode 100644 index 000000000..bb28b4345 --- /dev/null +++ b/lib/nbsd_libm/complex/catan.3 @@ -0,0 +1,58 @@ +.\" $NetBSD: catan.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CATAN" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" catan +.SH NAME +catan, catanf \- complex arc tangent functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex catan(double complex\fP \fIz\fP\fB); +.br +float complex catanf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex arc tangent of \fIz\fP, +with branch cuts outside the interval +[-\fIi\fP,\ +\fIi\fP] along the imaginary axis. +.SH RETURN VALUE +.LP +These functions return the complex arc tangent value, in the +range of a strip mathematically unbounded along the imaginary +axis and in the interval [-pi/2,\ +pi/2] along the +real axis. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIctan\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/catan.c b/lib/nbsd_libm/complex/catan.c new file mode 100644 index 000000000..3b9422024 --- /dev/null +++ b/lib/nbsd_libm/complex/catan.c @@ -0,0 +1,79 @@ +/* $NetBSD: catan.c,v 1.1 2007/08/20 16:01:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subr.h" + +#ifdef __weak_alias +__weak_alias(catan, _catan) +#endif + +#define MAXNUM 1.0e308 + +double complex +catan(double complex z) +{ + double complex w; + double a, t, x, x2, y; + + x = creal(z); + y = cimag(z); + + if ((x == 0.0) && (y > 1.0)) + goto ovrf; + + x2 = x * x; + a = 1.0 - x2 - (y * y); + if (a == 0.0) + goto ovrf; + + t = 0.5 * atan2(2.0 * x, a); + w = _redupi(t); + + t = y - 1.0; + a = x2 + (t * t); + if (a == 0.0) + goto ovrf; + + t = y + 1.0; + a = (x2 + (t * t))/a; + w = w + (0.25 * log(a)) * I; + return w; + +ovrf: +#if 0 + mtherr ("catan", OVERFLOW); +#endif + w = MAXNUM + MAXNUM * I; + return w; +} diff --git a/lib/nbsd_libm/complex/catanf.c b/lib/nbsd_libm/complex/catanf.c new file mode 100644 index 000000000..4c9987183 --- /dev/null +++ b/lib/nbsd_libm/complex/catanf.c @@ -0,0 +1,79 @@ +/* $NetBSD: catanf.c,v 1.1 2007/08/20 16:01:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subrf.h" + +#ifdef __weak_alias +__weak_alias(catanf, _catanf) +#endif + +#define MAXNUMF 1.0e38F + +float complex +catanf(float complex z) +{ + float complex w; + float a, t, x, x2, y; + + x = crealf(z); + y = cimagf(z); + + if ((x == 0.0f) && (y > 1.0f)) + goto ovrf; + + x2 = x * x; + a = 1.0f - x2 - (y * y); + if (a == 0.0f) + goto ovrf; + + t = 0.5f * atan2f(2.0f * x, a); + w = _redupif(t); + + t = y - 1.0f; + a = x2 + (t * t); + if (a == 0.0f) + goto ovrf; + + t = y + 1.0f; + a = (x2 + (t * t))/a; + w = w + (0.25f * logf(a)) * I; + return w; + +ovrf: +#if 0 + mtherr ("catan", OVERFLOW); +#endif + w = MAXNUMF + MAXNUMF * I; + return w; +} diff --git a/lib/nbsd_libm/complex/catanh.3 b/lib/nbsd_libm/complex/catanh.3 new file mode 100644 index 000000000..bad2411a0 --- /dev/null +++ b/lib/nbsd_libm/complex/catanh.3 @@ -0,0 +1,58 @@ +.\" $NetBSD: catanh.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CATANH" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" catanh +.SH NAME +catanh, catanhf \- complex arc hyperbolic tangent functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex catanh(double complex\fP \fIz\fP\fB); +.br +float complex catanhf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex arc hyperbolic tangent of +\fIz\fP, with branch cuts outside the interval +[-1,\ +1] along the real axis. +.SH RETURN VALUE +.LP +These functions return the complex arc hyperbolic tangent value, +in the range of a strip mathematically unbounded along +the real axis and in the interval [-\fIi\fPpi/2,\ +\fIi\fPpi/2] along +the imaginary axis. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIctanh\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/catanh.c b/lib/nbsd_libm/complex/catanh.c new file mode 100644 index 000000000..16ed59b1d --- /dev/null +++ b/lib/nbsd_libm/complex/catanh.c @@ -0,0 +1,42 @@ +/* $NetBSD: catanh.c,v 1.1 2007/08/20 16:01:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include + +double complex +catanh(double complex z) +{ + double complex w; + + w = -1.0 * I * catan(z * I); + return w; +} diff --git a/lib/nbsd_libm/complex/catanhf.c b/lib/nbsd_libm/complex/catanhf.c new file mode 100644 index 000000000..2a6db0a17 --- /dev/null +++ b/lib/nbsd_libm/complex/catanhf.c @@ -0,0 +1,42 @@ +/* $NetBSD: catanhf.c,v 1.1 2007/08/20 16:01:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include + +float complex +catanhf(float complex z) +{ + float complex w; + + w = -1.0f * I * catanf(z * I); + return w; +} diff --git a/lib/nbsd_libm/complex/ccos.3 b/lib/nbsd_libm/complex/ccos.3 new file mode 100644 index 000000000..5812b43f0 --- /dev/null +++ b/lib/nbsd_libm/complex/ccos.3 @@ -0,0 +1,53 @@ +.\" $NetBSD: ccos.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CCOS" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" ccos +.SH NAME +ccos, ccosf \- complex cosine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex ccos(double complex\fP \fIz\fP\fB); +.br +float complex ccosf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex cosine of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the complex cosine value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcacos\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/ccos.c b/lib/nbsd_libm/complex/ccos.c new file mode 100644 index 000000000..755d712ac --- /dev/null +++ b/lib/nbsd_libm/complex/ccos.c @@ -0,0 +1,46 @@ +/* $NetBSD: ccos.c,v 1.1 2007/08/20 16:01:32 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subr.h" + +double complex +ccos(double complex z) +{ + double complex w; + double ch, sh; + + _cchsh(cimag(z), &ch, &sh); + w = cos(creal(z)) * ch - (sin(creal(z)) * sh) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/ccosf.c b/lib/nbsd_libm/complex/ccosf.c new file mode 100644 index 000000000..4b6feb0e7 --- /dev/null +++ b/lib/nbsd_libm/complex/ccosf.c @@ -0,0 +1,46 @@ +/* $NetBSD: ccosf.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subrf.h" + +float complex +ccosf(float complex z) +{ + float complex w; + float ch, sh; + + _cchshf(cimagf(z), &ch, &sh); + w = cosf(crealf(z)) * ch - (sinf(crealf(z)) * sh) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/ccosh.3 b/lib/nbsd_libm/complex/ccosh.3 new file mode 100644 index 000000000..248a2dcf8 --- /dev/null +++ b/lib/nbsd_libm/complex/ccosh.3 @@ -0,0 +1,53 @@ +.\" $NetBSD: ccosh.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CCOSH" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" ccosh +.SH NAME +ccosh, ccoshf \- complex hyperbolic cosine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex ccosh(double complex\fP \fIz\fP\fB); +.br +float complex ccoshf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex hyperbolic cosine of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the complex hyperbolic cosine value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcacosh\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/ccosh.c b/lib/nbsd_libm/complex/ccosh.c new file mode 100644 index 000000000..e05516543 --- /dev/null +++ b/lib/nbsd_libm/complex/ccosh.c @@ -0,0 +1,46 @@ +/* $NetBSD: ccosh.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +double complex +ccosh(double complex z) +{ + double complex w; + double x, y; + + x = creal(z); + y = cimag(z); + w = cosh(x) * cos(y) + (sinh(x) * sin(y)) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/ccoshf.c b/lib/nbsd_libm/complex/ccoshf.c new file mode 100644 index 000000000..66b3eaff7 --- /dev/null +++ b/lib/nbsd_libm/complex/ccoshf.c @@ -0,0 +1,46 @@ +/* $NetBSD: ccoshf.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +float complex +ccoshf(float complex z) +{ + float complex w; + float x, y; + + x = crealf(z); + y = cimagf(z); + w = coshf(x) * cosf(y) + (sinhf(x) * sinf(y)) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/cephes_subr.c b/lib/nbsd_libm/complex/cephes_subr.c new file mode 100644 index 000000000..afbc0075c --- /dev/null +++ b/lib/nbsd_libm/complex/cephes_subr.c @@ -0,0 +1,124 @@ +/* $NetBSD: cephes_subr.c,v 1.1 2007/08/20 16:01:33 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subr.h" + +/* calculate cosh and sinh */ + +void +_cchsh(double x, double *c, double *s) +{ + double e, ei; + + if (fabs(x) <= 0.5) { + *c = cosh(x); + *s = sinh(x); + } else { + e = exp(x); + ei = 0.5 / e; + e = 0.5 * e; + *s = e - ei; + *c = e + ei; + } +} + +/* Program to subtract nearest integer multiple of PI */ + +/* extended precision value of PI: */ +static const double DP1 = 3.14159265160560607910E0; +static const double DP2 = 1.98418714791870343106E-9; +static const double DP3 = 1.14423774522196636802E-17; +#define MACHEP 1.1e-16 + +double +_redupi(double x) +{ + double t; + long i; + + t = x / M_PI; + if (t >= 0.0) + t += 0.5; + else + t -= 0.5; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return t; +} + +/* Taylor series expansion for cosh(2y) - cos(2x) */ + +double +_ctans(double complex z) +{ + double f, x, x2, y, y2, rn, t; + double d; + + x = fabs(2.0 * creal(z)); + y = fabs(2.0 * cimag(z)); + + x = _redupi(x); + + x = x * x; + y = y * y; + x2 = 1.0; + y2 = 1.0; + f = 1.0; + rn = 0.0; + d = 0.0; + do { + rn += 1.0; + f *= rn; + rn += 1.0; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 + x2; + t /= f; + d += t; + + rn += 1.0; + f *= rn; + rn += 1.0; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 - x2; + t /= f; + d += t; + } while (fabs(t/d) > MACHEP); + return d; +} diff --git a/lib/nbsd_libm/complex/cephes_subr.h b/lib/nbsd_libm/complex/cephes_subr.h new file mode 100644 index 000000000..7d230525f --- /dev/null +++ b/lib/nbsd_libm/complex/cephes_subr.h @@ -0,0 +1,5 @@ +/* $NetBSD: cephes_subr.h,v 1.1 2007/08/20 16:01:33 drochner Exp $ */ + +void _cchsh(double, double *, double *); +double _redupi(double); +double _ctans(double complex); diff --git a/lib/nbsd_libm/complex/cephes_subrf.c b/lib/nbsd_libm/complex/cephes_subrf.c new file mode 100644 index 000000000..da61f106f --- /dev/null +++ b/lib/nbsd_libm/complex/cephes_subrf.c @@ -0,0 +1,123 @@ +/* $NetBSD: cephes_subrf.c,v 1.1 2007/08/20 16:01:34 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subrf.h" + +/* calculate cosh and sinh */ + +void +_cchshf(float x, float *c, float *s) +{ + float e, ei; + + if (fabsf(x) <= 0.5f) { + *c = coshf(x); + *s = sinhf(x); + } else { + e = expf(x); + ei = 0.5f / e; + e = 0.5f * e; + *s = e - ei; + *c = e + ei; + } +} + +/* Program to subtract nearest integer multiple of PI */ + +/* extended precision value of PI: */ +static const double DP1 = 3.140625; +static const double DP2 = 9.67502593994140625E-4; +static const double DP3 = 1.509957990978376432E-7; +#define MACHEPF 3.0e-8 + +float +_redupif(float x) +{ + float t; + long i; + + t = x / (float)M_PI; + if (t >= 0.0f) + t += 0.5f; + else + t -= 0.5f; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return t; +} + +/* Taylor series expansion for cosh(2y) - cos(2x) */ + +float +_ctansf(float complex z) +{ + float f, x, x2, y, y2, rn, t, d; + + x = fabsf(2.0f * crealf(z)); + y = fabsf(2.0f * cimagf(z)); + + x = _redupif(x); + + x = x * x; + y = y * y; + x2 = 1.0f; + y2 = 1.0f; + f = 1.0f; + rn = 0.0f; + d = 0.0f; + do { + rn += 1.0f; + f *= rn; + rn += 1.0f; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 + x2; + t /= f; + d += t; + + rn += 1.0f; + f *= rn; + rn += 1.0f; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 - x2; + t /= f; + d += t; + } while (fabsf(t/d) > MACHEPF); + return d; +} diff --git a/lib/nbsd_libm/complex/cephes_subrf.h b/lib/nbsd_libm/complex/cephes_subrf.h new file mode 100644 index 000000000..81aec4630 --- /dev/null +++ b/lib/nbsd_libm/complex/cephes_subrf.h @@ -0,0 +1,5 @@ +/* $NetBSD: cephes_subrf.h,v 1.1 2007/08/20 16:01:34 drochner Exp $ */ + +void _cchshf(float, float *, float *); +float _redupif(float); +float _ctansf(float complex); diff --git a/lib/nbsd_libm/complex/cexp.3 b/lib/nbsd_libm/complex/cexp.3 new file mode 100644 index 000000000..703ebbc42 --- /dev/null +++ b/lib/nbsd_libm/complex/cexp.3 @@ -0,0 +1,54 @@ +.\" $NetBSD: cexp.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CEXP" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" cexp +.SH NAME +cexp, cexpf \- complex exponential functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex cexp(double complex\fP \fIz\fP\fB); +.br +float complex cexpf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex exponent of \fIz\fP, defined +as \fIe**z\fP. +.SH RETURN VALUE +.LP +These functions return the complex exponential value of \fIz\fP. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIclog\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/cexp.c b/lib/nbsd_libm/complex/cexp.c new file mode 100644 index 000000000..3ea768ab0 --- /dev/null +++ b/lib/nbsd_libm/complex/cexp.c @@ -0,0 +1,47 @@ +/* $NetBSD: cexp.c,v 1.1 2007/08/20 16:01:34 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +double complex +cexp(double complex z) +{ + double complex w; + double r, x, y; + + x = creal(z); + y = cimag(z); + r = exp(x); + w = r * cos(y) + r * sin(y) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/cexpf.c b/lib/nbsd_libm/complex/cexpf.c new file mode 100644 index 000000000..e4dec4a4b --- /dev/null +++ b/lib/nbsd_libm/complex/cexpf.c @@ -0,0 +1,47 @@ +/* $NetBSD: cexpf.c,v 1.1 2007/08/20 16:01:34 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +float complex +cexpf(float complex z) +{ + float complex w; + float r, x, y; + + x = crealf(z); + y = cimagf(z); + r = expf(x); + w = r * cosf(y) + r * sinf(y) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/cimag.3 b/lib/nbsd_libm/complex/cimag.3 new file mode 100644 index 000000000..e6fc1e8bc --- /dev/null +++ b/lib/nbsd_libm/complex/cimag.3 @@ -0,0 +1,63 @@ +.\" $NetBSD: cimag.3,v 1.3 2010/09/15 18:40:27 wiz Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CIMAG" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" cimag +.SH NAME +cimag, cimagf \- complex imaginary functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double cimag(double complex\fP \fIz\fP\fB); +.br +float cimagf(float complex\fP \fIz\fP\fB); +.br +long double cimagl(long double complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the imaginary part of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the imaginary part value (as a real). +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +For a variable \fIz\fP of complex type: +.sp +.RS +.nf + +\fBz == creal(z) + cimag(z)*I +\fP +.fi +.RE +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcarg\fP(), \fIconj\fP(), \fIcproj\fP(), \fIcreal\fP(), the +Base Definitions volume of IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/cimag.c b/lib/nbsd_libm/complex/cimag.c new file mode 100644 index 000000000..5e98447c4 --- /dev/null +++ b/lib/nbsd_libm/complex/cimag.c @@ -0,0 +1,17 @@ +/* $NetBSD: cimag.c,v 1.2 2010/09/15 16:11:29 christos Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include +#include "../src/math_private.h" + +double +cimag(double complex z) +{ + double_complex w = { .z = z }; + + return (IMAG_PART(w)); +} diff --git a/lib/nbsd_libm/complex/cimagf.c b/lib/nbsd_libm/complex/cimagf.c new file mode 100644 index 000000000..a82d696fb --- /dev/null +++ b/lib/nbsd_libm/complex/cimagf.c @@ -0,0 +1,17 @@ +/* $NetBSD: cimagf.c,v 1.2 2010/09/15 16:11:29 christos Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include +#include "../src/math_private.h" + +float +cimagf(float complex z) +{ + float_complex w = { .z = z }; + + return (IMAG_PART(w)); +} diff --git a/lib/nbsd_libm/complex/cimagl.c b/lib/nbsd_libm/complex/cimagl.c new file mode 100644 index 000000000..75897907b --- /dev/null +++ b/lib/nbsd_libm/complex/cimagl.c @@ -0,0 +1,44 @@ +/* $NetBSD: cimagl.c,v 1.3 2010/09/20 16:55:20 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: cimagl.c,v 1.3 2010/09/20 16:55:20 christos Exp $"); + +#include +#include "../src/math_private.h" + +/* + * cimagl(long double complex z) + * This function returns the imaginary part value (as a real) of z. + */ +long double +cimagl(long double complex z) +{ + long_double_complex w = { .z = z }; + + return (IMAG_PART(w)); +} diff --git a/lib/nbsd_libm/complex/clog.3 b/lib/nbsd_libm/complex/clog.3 new file mode 100644 index 000000000..6c937cace --- /dev/null +++ b/lib/nbsd_libm/complex/clog.3 @@ -0,0 +1,58 @@ +.\" $NetBSD: clog.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CLOG" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" clog +.SH NAME +clog, clogf \- complex natural logarithm functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex clog(double complex\fP \fIz\fP\fB); +.br +float complex clogf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex natural (base \fIe\fP) logarithm +of \fIz\fP, with a branch cut along the negative +real axis. +.SH RETURN VALUE +.LP +These functions return the complex natural logarithm value, +in the range of a strip mathematically unbounded along the +real axis and in the interval [-\fIi\fPpi,\ +\fIi\fPpi] along the +imaginary axis. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcexp\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/clog.c b/lib/nbsd_libm/complex/clog.c new file mode 100644 index 000000000..6362c4456 --- /dev/null +++ b/lib/nbsd_libm/complex/clog.c @@ -0,0 +1,47 @@ +/* $NetBSD: clog.c,v 1.1 2007/08/20 16:01:35 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +double complex +clog(double complex z) +{ + double complex w; + double p, rr; + + rr = cabs(z); + p = log(rr); + rr = atan2(cimag(z), creal(z)); + w = p + rr * I; + return w; +} diff --git a/lib/nbsd_libm/complex/clogf.c b/lib/nbsd_libm/complex/clogf.c new file mode 100644 index 000000000..c3cdad07f --- /dev/null +++ b/lib/nbsd_libm/complex/clogf.c @@ -0,0 +1,47 @@ +/* $NetBSD: clogf.c,v 1.1 2007/08/20 16:01:35 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +float complex +clogf(float complex z) +{ + float complex w; + float p, rr; + + rr = cabsf(z); + p = logf(rr); + rr = atan2f(cimagf(z), crealf(z)); + w = p + rr * I; + return w; +} diff --git a/lib/nbsd_libm/complex/conj.3 b/lib/nbsd_libm/complex/conj.3 new file mode 100644 index 000000000..6f0fe7818 --- /dev/null +++ b/lib/nbsd_libm/complex/conj.3 @@ -0,0 +1,56 @@ +.\" $NetBSD: conj.3,v 1.3 2010/09/15 18:40:27 wiz Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CONJ" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" conj +.SH NAME +conj, conjf \- complex conjugate functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex conj(double complex\fP \fIz\fP\fB); +.br +float complex conjf(float complex\fP \fIz\fP\fB); +.br +long double complex conjl(long double complex\fP \fIz\fP\fB, long double complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex conjugate of \fIz\fP, by +reversing the sign of its imaginary part. +.SH RETURN VALUE +.LP +These functions return the complex conjugate value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcarg\fP(), \fIcimag\fP(), \fIcproj\fP(), \fIcreal\fP(), the +Base Definitions volume of IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/conj.c b/lib/nbsd_libm/complex/conj.c new file mode 100644 index 000000000..ba8713dda --- /dev/null +++ b/lib/nbsd_libm/complex/conj.c @@ -0,0 +1,19 @@ +/* $NetBSD: conj.c,v 1.2 2010/09/15 16:11:29 christos Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include +#include "../src/math_private.h" + +double complex +conj(double complex z) +{ + double_complex w = { .z = z }; + + IMAG_PART(w) = -IMAG_PART(w); + + return (w.z); +} diff --git a/lib/nbsd_libm/complex/conjf.c b/lib/nbsd_libm/complex/conjf.c new file mode 100644 index 000000000..4b7dacb4f --- /dev/null +++ b/lib/nbsd_libm/complex/conjf.c @@ -0,0 +1,19 @@ +/* $NetBSD: conjf.c,v 1.2 2010/09/15 16:11:29 christos Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include +#include "../src/math_private.h" + +float complex +conjf(float complex z) +{ + float_complex w = { .z = z }; + + IMAG_PART(w) = -IMAG_PART(w); + + return (w.z); +} diff --git a/lib/nbsd_libm/complex/conjl.c b/lib/nbsd_libm/complex/conjl.c new file mode 100644 index 000000000..5c894a380 --- /dev/null +++ b/lib/nbsd_libm/complex/conjl.c @@ -0,0 +1,48 @@ +/* $NetBSD: conjl.c,v 1.4 2010/09/20 16:55:20 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: conjl.c,v 1.4 2010/09/20 16:55:20 christos Exp $"); + +#include +#include + +#include "../src/math_private.h" + +/* + * conjl(long double complex z) + * This function returns the complex conjugate value of its argument, z. + */ +long double complex +conjl(long double complex z) +{ + long_double_complex w = { .z = z }; + + IMAG_PART(w) = -IMAG_PART(w); + + return (w.z); +} diff --git a/lib/nbsd_libm/complex/cpow.3 b/lib/nbsd_libm/complex/cpow.3 new file mode 100644 index 000000000..8c4cca8f5 --- /dev/null +++ b/lib/nbsd_libm/complex/cpow.3 @@ -0,0 +1,57 @@ +.\" $NetBSD: cpow.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CPOW" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" cpow +.SH NAME +cpow, cpowf \- complex power functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex cpow(double complex\fP \fIx\fP\fB, double complex\fP +\fIy\fP\fB); +.br +float complex cpowf(float complex\fP \fIx\fP\fB, float complex\fP +\fIy\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex power function \fIx**y\fP, +with a branch cut for the first +parameter along the negative real axis. +.SH RETURN VALUE +.LP +These functions return the complex power function value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcabs\fP(), \fIcsqrt\fP(), the Base Definitions volume of +IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/cpow.c b/lib/nbsd_libm/complex/cpow.c new file mode 100644 index 000000000..5bc8d3f60 --- /dev/null +++ b/lib/nbsd_libm/complex/cpow.c @@ -0,0 +1,57 @@ +/* $NetBSD: cpow.c,v 1.1 2007/08/20 16:01:35 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +double complex +cpow(double complex a, double complex z) +{ + double complex w; + double x, y, r, theta, absa, arga; + + x = creal(z); + y = cimag(z); + absa = cabs(a); + if (absa == 0.0) { + return (0.0 + 0.0 * I); + } + arga = carg(a); + r = pow(absa, x); + theta = x * arga; + if (y != 0.0) { + r = r * exp(-y * arga); + theta = theta + y * log(absa); + } + w = r * cos(theta) + (r * sin(theta)) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/cpowf.c b/lib/nbsd_libm/complex/cpowf.c new file mode 100644 index 000000000..f7af10ae7 --- /dev/null +++ b/lib/nbsd_libm/complex/cpowf.c @@ -0,0 +1,57 @@ +/* $NetBSD: cpowf.c,v 1.1 2007/08/20 16:01:36 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +float complex +cpowf(float complex a, float complex z) +{ + float complex w; + float x, y, r, theta, absa, arga; + + x = crealf(z); + y = cimagf(z); + absa = cabsf(a); + if (absa == 0.0f) { + return (0.0f + 0.0f * I); + } + arga = cargf(a); + r = powf(absa, x); + theta = x * arga; + if (y != 0.0f) { + r = r * expf(-y * arga); + theta = theta + y * logf(absa); + } + w = r * cosf(theta) + (r * sinf(theta)) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/cproj.3 b/lib/nbsd_libm/complex/cproj.3 new file mode 100644 index 000000000..228dfa69e --- /dev/null +++ b/lib/nbsd_libm/complex/cproj.3 @@ -0,0 +1,59 @@ +.\" $NetBSD: cproj.3,v 1.2 2010/09/15 18:40:27 wiz Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CPROJ" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" cproj +.SH NAME +cproj, cprojf, cprojl \- complex projection functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double cproj(double complex\fP \fIz\fP\fB); +.br +float cprojf(float complex\fP \fIz\fP\fB); +.br +long double cprojl(long double complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute a projection of \fIz\fP ono the Riemann sphere: +\fIz\fP projects to \fIz\fP , except that all complex infinities (even those +with one infinite part and one NaN part) project to positive infinity on the +real axis. If \fIz\fP has an infinite part, then cproj(z) shall be equivalent to: +INFINITY + I * copysign(0.0, cimag(z)) +.SH RETURN VALUE +.LP +These functions return the value of the projection onto the Riemann sphere. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcarg\fP(), \fIcimag\fP(), \fIconj\fP(), \fIcreal\fP() the +Base Definitions volume of IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/cproj.c b/lib/nbsd_libm/complex/cproj.c new file mode 100644 index 000000000..7c0322a9e --- /dev/null +++ b/lib/nbsd_libm/complex/cproj.c @@ -0,0 +1,63 @@ +/* $NetBSD: cproj.c,v 1.3 2010/09/20 17:51:38 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: cproj.c,v 1.3 2010/09/20 17:51:38 christos Exp $"); + +#include +#include + +#include "../src/math_private.h" + +/* + * cproj(double complex z) + * + * These functions return the value of the projection (not stereographic!) + * onto the Riemann sphere. + * + * z projects to z, except that all complex infinities (even those with one + * infinite part and one NaN part) project to positive infinity on the real axis. + * If z has an infinite part, then cproj(z) shall be equivalent to: + * + * INFINITY + I * copysign(0.0, cimag(z)) + */ +double complex +cproj(double complex z) +{ + double_complex w = { .z = z }; + + if (isinf(creal(z) || isinf(cimag(z)))) { +#ifdef __INFINITY + REAL_PART(w) = __INFINITY; +#else + REAL_PART(w) = INFINITY; +#endif + IMAG_PART(w) = copysign(0.0, cimag(z)); + } + + return (w.z); +} diff --git a/lib/nbsd_libm/complex/cprojf.c b/lib/nbsd_libm/complex/cprojf.c new file mode 100644 index 000000000..0c0e61827 --- /dev/null +++ b/lib/nbsd_libm/complex/cprojf.c @@ -0,0 +1,64 @@ +/* $NetBSD: cprojf.c,v 1.3 2010/09/20 17:51:38 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: cprojf.c,v 1.3 2010/09/20 17:51:38 christos Exp $"); + +#include +#include + +#include "../src/math_private.h" + +/* + * cprojf(float complex z) + * + * These functions return the value of the projection (not stereographic!) + * onto the Riemann sphere. + * + * z projects to z, except that all complex infinities (even those with one + * infinite part and one NaN part) project to positive infinity on the real axis. + * If z has an infinite part, then cproj(z) shall be equivalent to: + * + * INFINITY + I * copysign(0.0, cimag(z)) + */ + +float complex +cprojf(float complex z) +{ + float_complex w = { .z = z }; + + if (isinf(crealf(z) || isinf(cimagf(z)))) { +#ifdef __INFINITY + REAL_PART(w) = __INFINITY; +#else + REAL_PART(w) = INFINITY; +#endif + IMAG_PART(w) = copysignf(0.0, cimagf(z)); + } + + return (w.z); +} diff --git a/lib/nbsd_libm/complex/cprojl.c b/lib/nbsd_libm/complex/cprojl.c new file mode 100644 index 000000000..5ce07ac08 --- /dev/null +++ b/lib/nbsd_libm/complex/cprojl.c @@ -0,0 +1,63 @@ +/* $NetBSD: cprojl.c,v 1.4 2010/09/20 17:51:38 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: cprojl.c,v 1.4 2010/09/20 17:51:38 christos Exp $"); + +#include +#include + +#include "../src/math_private.h" + +/* + * cprojl(long double complex z) + * + * These functions return the value of the projection (not stereographic!) + * onto the Riemann sphere. + * + * z projects to z, except that all complex infinities (even those with one + * infinite part and one NaN part) project to positive infinity on the real axis. + * If z has an infinite part, then cproj(z) shall be equivalent to: + * + * INFINITY + I * copysign(0.0, cimag(z)) + */ +long double complex +cprojl(long double complex z) +{ + long_double_complex w = { .z = z }; + + if (isinf(creall(z) || isinf(cimagl(z)))) { +#ifdef __INFINITY + REAL_PART(w) = __INFINITY; +#else + REAL_PART(w) = INFINITY; +#endif + IMAG_PART(w) = copysignl(0.0, cimagl(z)); + } + + return (w.z); +} diff --git a/lib/nbsd_libm/complex/creal.3 b/lib/nbsd_libm/complex/creal.3 new file mode 100644 index 000000000..ff6ecc0fb --- /dev/null +++ b/lib/nbsd_libm/complex/creal.3 @@ -0,0 +1,63 @@ +.\" $NetBSD: creal.3,v 1.3 2010/09/15 18:40:27 wiz Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CREAL" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" creal +.SH NAME +creal, crealf \- complex real functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double creal(double complex\fP \fIz\fP\fB); +.br +float crealf(float complex\fP \fIz\fP\fB); +.br +long double creall(long double complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the real part of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the real part value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +For a variable \fIz\fP of type \fBcomplex\fP: +.sp +.RS +.nf + +\fBz == creal(z) + cimag(z)*I +\fP +.fi +.RE +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcarg\fP(), \fIcimag\fP(), \fIconj\fP(), \fIcproj\fP(), the +Base Definitions volume of IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/creal.c b/lib/nbsd_libm/complex/creal.c new file mode 100644 index 000000000..98c5cb5a1 --- /dev/null +++ b/lib/nbsd_libm/complex/creal.c @@ -0,0 +1,17 @@ +/* $NetBSD: creal.c,v 1.2 2010/09/15 16:11:29 christos Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include +#include "../src/math_private.h" + +double +creal(double complex z) +{ + double_complex w = { .z = z }; + + return (REAL_PART(w)); +} diff --git a/lib/nbsd_libm/complex/crealf.c b/lib/nbsd_libm/complex/crealf.c new file mode 100644 index 000000000..5499c8de9 --- /dev/null +++ b/lib/nbsd_libm/complex/crealf.c @@ -0,0 +1,17 @@ +/* $NetBSD: crealf.c,v 1.2 2010/09/15 16:11:29 christos Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#include +#include "../src/math_private.h" + +float +crealf(float complex z) +{ + float_complex w = { .z = z }; + + return (REAL_PART(w)); +} diff --git a/lib/nbsd_libm/complex/creall.c b/lib/nbsd_libm/complex/creall.c new file mode 100644 index 000000000..1eafd6aec --- /dev/null +++ b/lib/nbsd_libm/complex/creall.c @@ -0,0 +1,44 @@ +/* $NetBSD: creall.c,v 1.3 2010/09/20 16:55:20 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: creall.c,v 1.3 2010/09/20 16:55:20 christos Exp $"); + +#include +#include "../src/math_private.h" + +/* + * creall(long double complex z) + * This function returns the real part value of z. + */ +long double +creall(long double complex z) +{ + long_double_complex w = { .z = z }; + + return (REAL_PART(w)); +} diff --git a/lib/nbsd_libm/complex/csin.3 b/lib/nbsd_libm/complex/csin.3 new file mode 100644 index 000000000..e478bea30 --- /dev/null +++ b/lib/nbsd_libm/complex/csin.3 @@ -0,0 +1,53 @@ +.\" $NetBSD: csin.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CSIN" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" csin +.SH NAME +csin, csinf \- complex sine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex csin(double complex\fP \fIz\fP\fB); +.br +float complex csinf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex sine of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the complex sine value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcasin\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/csin.c b/lib/nbsd_libm/complex/csin.c new file mode 100644 index 000000000..d5b01fd32 --- /dev/null +++ b/lib/nbsd_libm/complex/csin.c @@ -0,0 +1,46 @@ +/* $NetBSD: csin.c,v 1.1 2007/08/20 16:01:36 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subr.h" + +double complex +csin(double complex z) +{ + double complex w; + double ch, sh; + + _cchsh(cimag(z), &ch, &sh); + w = sin(creal(z)) * ch + (cos(creal(z)) * sh) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/csinf.c b/lib/nbsd_libm/complex/csinf.c new file mode 100644 index 000000000..76882a02a --- /dev/null +++ b/lib/nbsd_libm/complex/csinf.c @@ -0,0 +1,46 @@ +/* $NetBSD: csinf.c,v 1.1 2007/08/20 16:01:36 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subrf.h" + +float complex +csinf(float complex z) +{ + float complex w; + float ch, sh; + + _cchshf(cimagf(z), &ch, &sh); + w = sinf(crealf(z)) * ch + (cosf(crealf(z)) * sh) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/csinh.3 b/lib/nbsd_libm/complex/csinh.3 new file mode 100644 index 000000000..86d44259e --- /dev/null +++ b/lib/nbsd_libm/complex/csinh.3 @@ -0,0 +1,53 @@ +.\" $NetBSD: csinh.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CSINH" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" csinh +.SH NAME +csinh, csinhf \- complex hyperbolic sine functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex csinh(double complex\fP \fIz\fP\fB); +.br +float complex csinhf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex hyperbolic sine of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the complex hyperbolic sine value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcasinh\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/csinh.c b/lib/nbsd_libm/complex/csinh.c new file mode 100644 index 000000000..593664f3b --- /dev/null +++ b/lib/nbsd_libm/complex/csinh.c @@ -0,0 +1,46 @@ +/* $NetBSD: csinh.c,v 1.1 2007/08/20 16:01:36 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +double complex +csinh(double complex z) +{ + double complex w; + double x, y; + + x = creal(z); + y = cimag(z); + w = sinh(x) * cos(y) + (cosh(x) * sin(y)) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/csinhf.c b/lib/nbsd_libm/complex/csinhf.c new file mode 100644 index 000000000..161b00b70 --- /dev/null +++ b/lib/nbsd_libm/complex/csinhf.c @@ -0,0 +1,46 @@ +/* $NetBSD: csinhf.c,v 1.1 2007/08/20 16:01:37 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +float complex +csinhf(float complex z) +{ + float complex w; + float x, y; + + x = crealf(z); + y = cimagf(z); + w = sinhf(x) * cosf(y) + (coshf(x) * sinf(y)) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/csqrt.3 b/lib/nbsd_libm/complex/csqrt.3 new file mode 100644 index 000000000..8f82b1156 --- /dev/null +++ b/lib/nbsd_libm/complex/csqrt.3 @@ -0,0 +1,56 @@ +.\" $NetBSD: csqrt.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CSQRT" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" csqrt +.SH NAME +csqrt, csqrtf \- complex square root functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex csqrt(double complex\fP \fIz\fP\fB); +.br +float complex csqrtf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex square root of \fIz\fP, +with a branch cut along the negative real axis. +.SH RETURN VALUE +.LP +These functions return the complex square root value, in the +range of the right half-plane (including the imaginary +axis). +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcabs\fP(), \fIcpow\fP(), the Base Definitions volume of +IEEE\ Std\ 1003.1-2001, \fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/csqrt.c b/lib/nbsd_libm/complex/csqrt.c new file mode 100644 index 000000000..f9267ec13 --- /dev/null +++ b/lib/nbsd_libm/complex/csqrt.c @@ -0,0 +1,99 @@ +/* $NetBSD: csqrt.c,v 1.1 2007/08/20 16:01:37 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include + +double complex +csqrt(double complex z) +{ + double complex w; + double x, y, r, t, scale; + + x = creal (z); + y = cimag (z); + + if (y == 0.0) { + if (x == 0.0) { + w = 0.0 + y * I; + } else { + r = fabs(x); + r = sqrt(r); + if (x < 0.0) { + w = 0.0 + r * I; + } else { + w = r + y * I; + } + } + return w; + } + if (x == 0.0) { + r = fabs(y); + r = sqrt(0.5 * r); + if (y > 0) + w = r + r * I; + else + w = r - r * I; + return w; + } + /* Rescale to avoid internal overflow or underflow. */ + if ((fabs(x) > 4.0) || (fabs(y) > 4.0)) { + x *= 0.25; + y *= 0.25; + scale = 2.0; + } else { +#if 1 + x *= 1.8014398509481984e16; /* 2^54 */ + y *= 1.8014398509481984e16; + scale = 7.450580596923828125e-9; /* 2^-27 */ +#else + x *= 4.0; + y *= 4.0; + scale = 0.5; +#endif + } + w = x + y * I; + r = cabs(w); + if (x > 0) { + t = sqrt(0.5 * r + 0.5 * x); + r = scale * fabs((0.5 * y) / t ); + t *= scale; + } else { + r = sqrt(0.5 * r - 0.5 * x); + t = scale * fabs((0.5 * y) / r); + r *= scale; + } + if (y < 0) + w = t - r * I; + else + w = t + r * I; + return w; +} diff --git a/lib/nbsd_libm/complex/csqrtf.c b/lib/nbsd_libm/complex/csqrtf.c new file mode 100644 index 000000000..a230430a8 --- /dev/null +++ b/lib/nbsd_libm/complex/csqrtf.c @@ -0,0 +1,99 @@ +/* $NetBSD: csqrtf.c,v 1.1 2007/08/20 16:01:37 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#include + +float complex +csqrtf(float complex z) +{ + float complex w; + float x, y, r, t, scale; + + x = crealf (z); + y = cimagf (z); + + if (y == 0.0f) { + if (x < 0.0f) { + w = 0.0f + sqrtf(-x) * I; + return w; + } else if (x == 0.0f) { + return (0.0f + y * I); + } else { + w = sqrtf(x) + y * I; + return w; + } + } + + if (x == 0.0f) { + r = fabsf(y); + r = sqrtf(0.5f * r); + if (y > 0) + w = r + r * I; + else + w = r - r * I; + return w; + } + + /* Rescale to avoid internal overflow or underflow. */ + if ((fabsf(x) > 4.0f) || (fabsf(y) > 4.0f)) { + x *= 0.25f; + y *= 0.25f; + scale = 2.0f; + } else { +#if 1 + x *= 6.7108864e7f; /* 2^26 */ + y *= 6.7108864e7f; + scale = 1.220703125e-4f; /* 2^-13 */ +#else + x *= 4.0f; + y *= 4.0f; + scale = 0.5f; +#endif + } + w = x + y * I; + r = cabsf(w); + if( x > 0 ) { + t = sqrtf(0.5f * r + 0.5f * x); + r = scale * fabsf((0.5f * y) / t); + t *= scale; + } else { + r = sqrtf(0.5f * r - 0.5f * x); + t = scale * fabsf((0.5f * y) / r); + r *= scale; + } + + if (y < 0) + w = t - r * I; + else + w = t + r * I; + return w; +} diff --git a/lib/nbsd_libm/complex/ctan.3 b/lib/nbsd_libm/complex/ctan.3 new file mode 100644 index 000000000..5553758e2 --- /dev/null +++ b/lib/nbsd_libm/complex/ctan.3 @@ -0,0 +1,53 @@ +.\" $NetBSD: ctan.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CTAN" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" ctan +.SH NAME +ctan, ctanf \- complex tangent functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex ctan(double complex\fP \fIz\fP\fB); +.br +float complex ctanf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex tangent of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the complex tangent value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcatan\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/ctan.c b/lib/nbsd_libm/complex/ctan.c new file mode 100644 index 000000000..3397eec4b --- /dev/null +++ b/lib/nbsd_libm/complex/ctan.c @@ -0,0 +1,58 @@ +/* $NetBSD: ctan.c,v 1.1 2007/08/20 16:01:37 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subr.h" + +#define MAXNUM 1.0e308 + +double complex +ctan(double complex z) +{ + double complex w; + double d; + + d = cos(2.0 * creal(z)) + cosh(2.0 * cimag(z)); + + if (fabs(d) < 0.25) + d = _ctans(z); + + if (d == 0.0) { + /* mtherr ("ctan", OVERFLOW); */ + w = MAXNUM + MAXNUM * I; + return w; + } + + w = sin(2.0 * creal(z)) / d + (sinh(2.0 * cimag(z)) / d) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/ctanf.c b/lib/nbsd_libm/complex/ctanf.c new file mode 100644 index 000000000..e9881d235 --- /dev/null +++ b/lib/nbsd_libm/complex/ctanf.c @@ -0,0 +1,58 @@ +/* $NetBSD: ctanf.c,v 1.1 2007/08/20 16:01:38 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include +#include "cephes_subrf.h" + +#define MAXNUMF 1.0e38f + +float complex +ctanf(float complex z) +{ + float complex w; + float d; + + d = cosf(2.0f * crealf(z)) + coshf(2.0f * cimagf(z)); + + if (fabsf(d) < 0.25f) + d = _ctansf(z); + + if (d == 0.0f) { + /* mtherr ("ctan", OVERFLOW); */ + w = MAXNUMF + MAXNUMF * I; + return w; + } + + w = sinf(2.0f * crealf(z)) / d + (sinhf(2.0f * cimagf(z)) / d) * I; + return w; +} diff --git a/lib/nbsd_libm/complex/ctanh.3 b/lib/nbsd_libm/complex/ctanh.3 new file mode 100644 index 000000000..cf945ab88 --- /dev/null +++ b/lib/nbsd_libm/complex/ctanh.3 @@ -0,0 +1,53 @@ +.\" $NetBSD: ctanh.3,v 1.1 2008/02/20 09:55:38 drochner Exp $ +.\" Copyright (c) 2001-2003 The Open Group, All Rights Reserved +.TH "CTANH" 3P 2003 "IEEE/The Open Group" "POSIX Programmer's Manual" +.\" ctanh +.SH NAME +ctanh, ctanhf \- complex hyperbolic tangent functions +.SH SYNOPSIS +.LP +\fB#include +.br +.sp +double complex ctanh(double complex\fP \fIz\fP\fB); +.br +float complex ctanhf(float complex\fP \fIz\fP\fB); +.br +\fP +.SH DESCRIPTION +.LP +These functions compute the complex hyperbolic tangent of \fIz\fP. +.SH RETURN VALUE +.LP +These functions return the complex hyperbolic tangent value. +.SH ERRORS +.LP +No errors are defined. +.LP +\fIThe following sections are informative.\fP +.SH EXAMPLES +.LP +None. +.SH APPLICATION USAGE +.LP +None. +.SH RATIONALE +.LP +None. +.SH FUTURE DIRECTIONS +.LP +None. +.SH SEE ALSO +.LP +\fIcatanh\fP(), the Base Definitions volume of IEEE\ Std\ 1003.1-2001, +\fI\fP +.SH COPYRIGHT +Portions of this text are reprinted and reproduced in electronic form +from IEEE Std 1003.1, 2003 Edition, Standard for Information Technology +-- Portable Operating System Interface (POSIX), The Open Group Base +Specifications Issue 6, Copyright (C) 2001-2003 by the Institute of +Electrical and Electronics Engineers, Inc and The Open Group. In the +event of any discrepancy between this version and the original IEEE and +The Open Group Standard, the original IEEE and The Open Group Standard +is the referee document. The original Standard can be obtained online at +http://www.opengroup.org/unix/online.html . diff --git a/lib/nbsd_libm/complex/ctanh.c b/lib/nbsd_libm/complex/ctanh.c new file mode 100644 index 000000000..c1aaeec10 --- /dev/null +++ b/lib/nbsd_libm/complex/ctanh.c @@ -0,0 +1,48 @@ +/* $NetBSD: ctanh.c,v 1.1 2007/08/20 16:01:38 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +double complex +ctanh(double complex z) +{ + double complex w; + double x, y, d; + + x = creal(z); + y = cimag(z); + d = cosh(2.0 * x) + cos(2.0 * y); + w = sinh(2.0 * x) / d + (sin(2.0 * y) / d) * I; + + return w; +} diff --git a/lib/nbsd_libm/complex/ctanhf.c b/lib/nbsd_libm/complex/ctanhf.c new file mode 100644 index 000000000..26bcd59c5 --- /dev/null +++ b/lib/nbsd_libm/complex/ctanhf.c @@ -0,0 +1,48 @@ +/* $NetBSD: ctanhf.c,v 1.1 2007/08/20 16:01:38 drochner Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include "../src/namespace.h" +#include +#include + +float complex +ctanhf(float complex z) +{ + float complex w; + float x, y, d; + + x = crealf(z); + y = cimagf(z); + d = coshf(2.0f * x) + cosf(2.0f * y); + w = sinhf(2.0f * x) / d + (sinf(2.0f * y) / d) * I; + + return w; +} diff --git a/lib/nbsd_libm/gen/Makefile.inc b/lib/nbsd_libm/gen/Makefile.inc new file mode 100644 index 000000000..b16498f91 --- /dev/null +++ b/lib/nbsd_libm/gen/Makefile.inc @@ -0,0 +1,12 @@ +# $NetBSD: Makefile.inc,v 1.1 2006/03/15 22:07:09 kleink Exp $ + +# gen sources +.PATH: ${.CURDIR}/gen +CPPFLAGS+=-I${.CURDIR}/gen + +SRCS+= nan.c nanf.c nanl.c + +MAN+= nan.3 + +MLINKS+=nan.3 nanf.3 \ + nan.3 nanl.3 diff --git a/lib/nbsd_libm/gen/nan.3 b/lib/nbsd_libm/gen/nan.3 new file mode 100644 index 000000000..8dfc0620e --- /dev/null +++ b/lib/nbsd_libm/gen/nan.3 @@ -0,0 +1,95 @@ +.\" $NetBSD: nan.3,v 1.3 2010/12/17 23:57:07 njoly Exp $ +.\" +.\" Copyright (c) 2006 The NetBSD Foundation, Inc. +.\" All rights reserved. +.\" +.\" This code is derived from software contributed to The NetBSD Foundation +.\" by Klaus Klein. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS +.\" ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED +.\" TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +.\" PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS +.\" BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR +.\" CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF +.\" SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS +.\" INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN +.\" CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) +.\" ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE +.\" POSSIBILITY OF SUCH DAMAGE. +.\" +.Dd March 15, 2006 +.Dt NAN 3 +.Os +.Sh NAME +.Nm nan , +.Nm nanf , +.Nm nanl +.Nd return quiet NaN +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn nan "const char *tagp" +.Ft float +.Fn nanf "const char *tagp" +.Ft long double +.Fn nanl "const char *tagp" +.Sh DESCRIPTION +The call +.Fn nan "\*qn-char-sequence\*q" +is equivalent to the call +.Fn strod "\*qNAN(n-char-sequence)\*q" "NULL" . +The call +.Fn nan "\*q\*q" +is equivalent to the call +.Fn strod "\*qNAN()\*q" "NULL" . +.Pp +The +.Fn nanf +and +.Fn nanl +functions are equivalent to +.Fn nan +but substituting +.Fn strtof +and +.Fn strtod , +respectively. +.Sh RETURN VALUES +.Ss IEEE 754 +The +.Fn nan , +.Fn nanf , +and +.Fn nanl +functions return a quiet NaN as specified by +.Fa tagp . +.Ss VAX +The +.Fn nan , +.Fn nanf , +and +.Fn nanl +functions return zero. +.Sh SEE ALSO +.Xr math 3 , +.Xr strtod 3 +.Sh STANDARDS +The +.Fn nan , +.Fn nanf , +and +.Fn nanl +functions conform to +.St -isoC-99 . diff --git a/lib/nbsd_libm/gen/nan.c b/lib/nbsd_libm/gen/nan.c new file mode 100644 index 000000000..5028a13ef --- /dev/null +++ b/lib/nbsd_libm/gen/nan.c @@ -0,0 +1,85 @@ +/* $NetBSD: nan.c,v 1.2 2008/04/28 20:23:01 martin Exp $ */ + +/*- + * Copyright (c) 2006 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) && !defined(NAN_FUNCTION) +__RCSID("$NetBSD: nan.c,v 1.2 2008/04/28 20:23:01 martin Exp $"); +#endif /* LIBM_SCCS and not lint */ + +#include +#include +#include +#include +#include + + +#ifndef NAN_FUNCTION +#define NAN_FUNCTION nan +#define NAN_TYPE double +#define NAN_STRTOD strtod +#endif + +NAN_TYPE +NAN_FUNCTION(const char *tagp) +{ + const char *nstr; + char *buf; + NAN_TYPE res; + + _DIAGASSERT(tagp != NULL); + + nstr = "NAN()"; + buf = NULL; + + if (tagp[0] != '\0') { + size_t l; + + l = strlen(tagp); + buf = malloc(5 + l + 1); + + if (buf != NULL) { + /* Avoiding stdio in libm. */ + memcpy(buf, "NAN(", 4); + memcpy(buf + 4, tagp, l); + memcpy(buf + 4 + l, ")", 2); + nstr = buf; + } else { + /* Best effort: Fall back to "NAN()". */ + } + } + + res = NAN_STRTOD(nstr, NULL); + + if (buf != NULL) + free(buf); + + return res; +} diff --git a/lib/nbsd_libm/gen/nanf.c b/lib/nbsd_libm/gen/nanf.c new file mode 100644 index 000000000..5ff2cd9c6 --- /dev/null +++ b/lib/nbsd_libm/gen/nanf.c @@ -0,0 +1,41 @@ +/* $NetBSD: nanf.c,v 1.2 2008/04/28 20:23:01 martin Exp $ */ + +/*- + * Copyright (c) 2006 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: nanf.c,v 1.2 2008/04/28 20:23:01 martin Exp $"); +#endif /* LIBM_SCCS and not lint */ + +#define NAN_FUNCTION nanf +#define NAN_TYPE float +#define NAN_STRTOD strtof + +#include "nan.c" diff --git a/lib/nbsd_libm/gen/nanl.c b/lib/nbsd_libm/gen/nanl.c new file mode 100644 index 000000000..ca96b82cd --- /dev/null +++ b/lib/nbsd_libm/gen/nanl.c @@ -0,0 +1,41 @@ +/* $NetBSD: nanl.c,v 1.2 2008/04/28 20:23:01 martin Exp $ */ + +/*- + * Copyright (c) 2006 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software contributed to The NetBSD Foundation + * by Klaus Klein. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: nanl.c,v 1.2 2008/04/28 20:23:01 martin Exp $"); +#endif /* LIBM_SCCS and not lint */ + +#define NAN_FUNCTION nanl +#define NAN_TYPE long double +#define NAN_STRTOD strtold + +#include "nan.c" diff --git a/lib/nbsd_libm/man/acos.3 b/lib/nbsd_libm/man/acos.3 new file mode 100644 index 000000000..2a6adbc1c --- /dev/null +++ b/lib/nbsd_libm/man/acos.3 @@ -0,0 +1,83 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)acos.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: acos.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt ACOS 3 +.Os +.Sh NAME +.Nm acos , +.Nm acosf +.Nd arc cosine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn acos "double x" +.Ft float +.Fn acosf "float x" +.Sh DESCRIPTION +The +.Fn acos +and +.Fn acosf +functions compute the principal value of the arc cosine of +.Fa x +in the range +.Bq 0 , \*(Pi . +.Sh RETURN VALUES +If |x|\*[Gt]1, +.Fn acos "x" +and +.Fn acosf "x" +.\" POSIX_MODE +set the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn acos +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/acosh.3 b/lib/nbsd_libm/man/acosh.3 new file mode 100644 index 000000000..eecdbfbfe --- /dev/null +++ b/lib/nbsd_libm/man/acosh.3 @@ -0,0 +1,77 @@ +.\" Copyright (c) 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)acosh.3 5.2 (Berkeley) 5/6/91 +.\" $NetBSD: acosh.3,v 1.15 2003/08/07 16:44:46 agc Exp $ +.\" +.Dd May 6, 1991 +.Dt ACOSH 3 +.Os +.Sh NAME +.Nm acosh , +.Nm acoshf +.Nd inverse hyperbolic cosine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn acosh "double x" +.Ft float +.Fn acoshf "float x" +.Sh DESCRIPTION +The +.Fn acosh +and +.Fn acoshf +functions compute the inverse hyperbolic cosine +of the real +argument +.Ar x . +.Sh RETURN VALUES +.\" POSIX_MODE +If x is less than one, +.Fn acosh "x" +and +.Fn acoshf "x" +return NaN and set the global variable +.Va errno +to EDOM. +.\" SVR4_MODE +.\" call +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr asinh 3 , +.Xr atanh 3 , +.Xr exp 3 , +.Xr math 3 +.\" .Xr matherr 3 +.Sh HISTORY +The +.Fn acosh +function appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/asin.3 b/lib/nbsd_libm/man/asin.3 new file mode 100644 index 000000000..a12e265d9 --- /dev/null +++ b/lib/nbsd_libm/man/asin.3 @@ -0,0 +1,85 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)asin.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: asin.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt ASIN 3 +.Os +.Sh NAME +.Nm asin , +.Nm asinf +.Nd arc sine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn asin "double x" +.Ft float +.Fn asinf "float x" +.Sh DESCRIPTION +The +.Fn asin +and +.Fn asinf +functions compute the principal value of the arc sine of +.Fa x +in the range +.Bk -words +.Bq -\*(Pi/2, +\*(Pi/2 . +.Ek +.Sh RETURN VALUES +.\" POSIX_MODE +If |x|\*[Gt]1, +.Fn asin "x" +and +.Fn asinf "x" +return NaN and set the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr acos 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn asin +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/asinh.3 b/lib/nbsd_libm/man/asinh.3 new file mode 100644 index 000000000..813238bdc --- /dev/null +++ b/lib/nbsd_libm/man/asinh.3 @@ -0,0 +1,75 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)asinh.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: asinh.3,v 1.15 2003/08/07 16:44:46 agc Exp $ +.\" +.Dd May 6, 1991 +.Dt ASINH 3 +.Os +.Sh NAME +.Nm asinh , +.Nm asinhf +.Nd inverse hyperbolic sine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn asinh "double x" +.Ft float +.Fn asinhf "float x" +.Sh DESCRIPTION +The +.Fn asinh +and +.Fn asinhf +functions compute the inverse hyperbolic sine +of the real +argument +.Sh RETURN VALUES +The +.Fn asinh +and +.Fn asinhf +functions return the inverse hyperbolic sine of +.Ar x . +.\" SYSV_MODE +.\" .Sh RETURN VALUES +.\" Exceptional cases are handled by +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr acosh 3 , +.Xr atanh 3 , +.Xr exp 3 , +.Xr math 3 +.\" .Xr matherr 3 +.Sh HISTORY +The +.Fn asinh +function appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/atan.3 b/lib/nbsd_libm/man/atan.3 new file mode 100644 index 000000000..01bb39741 --- /dev/null +++ b/lib/nbsd_libm/man/atan.3 @@ -0,0 +1,77 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)atan.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: atan.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt ATAN 3 +.Os +.Sh NAME +.Nm atan , +.Nm atanf +.Nd arc tangent function of one variable +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn atan "double x" +.Ft float +.Fn atanf "float x" +.Sh DESCRIPTION +The +.Fn atan +and +.Fn atanf +functions compute the principal value of the arc tangent of +.Fa x +in the range +.Bk -words +.Bq -\*(Pi/2 , +\*(Pi/2 . +.Ek +.\" SYSV_MODE +.\" .Sh RETURN VALUES +.\" Exceptional cases are handled by +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn atan +functions conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/atan2.3 b/lib/nbsd_libm/man/atan2.3 new file mode 100644 index 000000000..c9094e1e5 --- /dev/null +++ b/lib/nbsd_libm/man/atan2.3 @@ -0,0 +1,192 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)atan2.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: atan2.3,v 1.16 2003/08/07 16:44:46 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt ATAN2 3 +.Os +.Sh NAME +.Nm atan2 , +.Nm atan2f +.Nd arc tangent function of two variables +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn atan2 "double y" "double x" +.Ft float +.Fn atan2f "float y" "float x" +.Sh DESCRIPTION +The +.Fn atan2 +and +.Fn atan2f +functions compute the principal value of the arc tangent of +.Ar y/ Ns Ar x , +using the signs of both arguments to determine the quadrant of +the return value. +.Sh RETURN VALUES +The +.Fn atan2 +function, if successful, +returns the arc tangent of +.Ar y/ Ns Ar x +in the range +.Bk -words +.Bq \&- Ns \*(Pi , \&+ Ns \*(Pi +.Ek +radians. +If both +.Ar x +and +.Ar y +are zero, the global variable +.Va errno +is set to +.Er EDOM . +On the +.Tn VAX : +.Bl -column atan_(y,x)_:=____ sign(y)_(Pi_atan2(Xy_xX))___ +.It Fn atan2 y x No := Ta +.Fn atan y/x Ta +if +.Ar x +\*[Gt] 0, +.It Ta sign( Ns Ar y Ns )*(\*(Pi - +.Fn atan "\\*(Bay/x\\*(Ba" ) Ta +if +.Ar x +\*[Lt] 0, +.It Ta +.No 0 Ta +if x = y = 0, or +.It Ta +.Pf sign( Ar y Ns )*\\*(Pi/2 Ta +if +.Ar x += 0 \*(!= +.Ar y . +.El +.Sh NOTES +The function +.Fn atan2 +defines "if x \*[Gt] 0," +.Fn atan2 0 0 += 0 on a +.Tn VAX +despite that previously +.Fn atan2 0 0 +may have generated an error message. +The reasons for assigning a value to +.Fn atan2 0 0 +are these: +.Bl -enum -offset indent +.It +Programs that test arguments to avoid computing +.Fn atan2 0 0 +must be indifferent to its value. +Programs that require it to be invalid are vulnerable +to diverse reactions to that invalidity on diverse computer systems. +.It +The +.Fn atan2 +function is used mostly to convert from rectangular (x,y) +to polar +.if n\ +(r,theta) +.if t\ +(r,\(*h) +coordinates that must satisfy x = +.if n\ +r\(**cos theta +.if t\ +r\(**cos\(*h +and y = +.if n\ +r\(**sin theta. +.if t\ +r\(**sin\(*h. +These equations are satisfied when (x=0,y=0) +is mapped to +.if n \ +(r=0,theta=0) +.if t \ +(r=0,\(*h=0) +on a VAX. +In general, conversions to polar coordinates should be computed thus: +.Bd -unfilled -offset indent +.if n \{\ +r := hypot(x,y); ... := sqrt(x\(**x+y\(**y) +theta := atan2(y,x). +.\} +.if t \{\ +r := hypot(x,y); ... := \(sr(x\u\s82\s10\d+y\u\s82\s10\d) +\(*h := atan2(y,x). +.\} +.Ed +.It +The foregoing formulas need not be altered to cope in a +reasonable way with signed zeros and infinities +on a machine that conforms to +.Tn IEEE 754 ; +the versions of +.Xr hypot 3 +and +.Fn atan2 +provided for +such a machine are designed to handle all cases. +That is why +.Fn atan2 \(+-0 \-0 += \(+-\*(Pi +for instance. +In general the formulas above are equivalent to these: +.Bd -unfilled -offset indent +.if n \ +r := sqrt(x\(**x+y\(**y); if r = 0 then x := copysign(1,x); +.if t \ +r := \(sr(x\(**x+y\(**y);\0\0if r = 0 then x := copysign(1,x); +.Ed +.El +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn atan2 +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/atanh.3 b/lib/nbsd_libm/man/atanh.3 new file mode 100644 index 000000000..e3c76fad9 --- /dev/null +++ b/lib/nbsd_libm/man/atanh.3 @@ -0,0 +1,77 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)atanh.3 5.2 (Berkeley) 5/6/91 +.\" $NetBSD: atanh.3,v 1.15 2003/08/07 16:44:46 agc Exp $ +.\" +.Dd May 6, 1991 +.Dt ATANH 3 +.Os +.Sh NAME +.Nm atanh , +.Nm atanhf +.Nd inverse hyperbolic tangent function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn atanh "double x" +.Ft float +.Fn atanhf "float x" +.Sh DESCRIPTION +The +.Fn atanh +and +.Fn atanhf +functions compute the inverse hyperbolic tangent +of the real +argument +.Ar x . +.Sh RETURN VALUES +If |x|\*[Ge]1, +.Fn atanh "x" +and +.Fn atanhf "x" +.\" POSIX_MODE +return +inf, -inf or NaN, and sets the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr acosh 3 , +.Xr asinh 3 , +.Xr exp 3 , +.Xr math 3 +.\" .Xr matherr 3 +.Sh HISTORY +The +.Fn atanh +function appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/ceil.3 b/lib/nbsd_libm/man/ceil.3 new file mode 100644 index 000000000..49d0f745d --- /dev/null +++ b/lib/nbsd_libm/man/ceil.3 @@ -0,0 +1,65 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)ceil.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: ceil.3,v 1.17 2003/08/07 16:44:47 agc Exp $ +.\" +.Dd March 10, 1994 +.Dt CEIL 3 +.Os +.Sh NAME +.Nm ceil , +.Nm ceilf +.Nd "round to smallest integral value greater than or equal to x" +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn ceil "double x" +.Ft float +.Fn ceilf "float x" +.Sh DESCRIPTION +The +.Fn ceil +and +.Fn ceilf +functions return the smallest integral value +greater than or equal to +.Fa x . +.Sh SEE ALSO +.Xr abs 3 , +.Xr fabs 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 +.Sh STANDARDS +The +.Fn ceil +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/cos.3 b/lib/nbsd_libm/man/cos.3 new file mode 100644 index 000000000..e88719056 --- /dev/null +++ b/lib/nbsd_libm/man/cos.3 @@ -0,0 +1,77 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)cos.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: cos.3,v 1.15 2003/08/07 16:44:47 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt COS 3 +.Os +.Sh NAME +.Nm cos , +.Nm cosf +.Nd cosine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn cos "double x" +.Ft float +.Fn cosf "float x" +.Sh DESCRIPTION +The +.Fn cos +and +.Fn cosf +functions compute the cosine of +.Fa x +(measured in radians). +A large magnitude argument may yield a result with little or no +significance. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn cos +function returns the cosine value. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn cos +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/cosh.3 b/lib/nbsd_libm/man/cosh.3 new file mode 100644 index 000000000..3e9832d16 --- /dev/null +++ b/lib/nbsd_libm/man/cosh.3 @@ -0,0 +1,81 @@ +.\" Copyright (c) 1989, 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)cosh.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: cosh.3,v 1.15 2003/08/07 16:44:47 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt COSH 3 +.Os +.Sh NAME +.Nm cosh , +.Nm coshf +.Nd hyperbolic cosine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn cosh "double x" +.Ft float +.Fn coshf "float x" +.Sh DESCRIPTION +The +.Fn cosh +and +.Fn coshf +functions compute the hyperbolic cosine of +.Fa x . +.Sh RETURN VALUES +If the magnitude of x is too large, +.Fn cosh "x" +and +.Fn coshf "x" +.\" POSIX_MODE +return Inf and sets the global variable +.Va errno +to ERANGE. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn cosh +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/erf.3 b/lib/nbsd_libm/man/erf.3 new file mode 100644 index 000000000..260729e3a --- /dev/null +++ b/lib/nbsd_libm/man/erf.3 @@ -0,0 +1,87 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)erf.3 6.4 (Berkeley) 4/20/91 +.\" $NetBSD: erf.3,v 1.12 2003/08/07 16:44:47 agc Exp $ +.\" +.Dd April 20, 1991 +.Dt ERF 3 +.Os +.Sh NAME +.Nm erf , +.Nm erff , +.Nm erfc , +.Nm erfcf +.Nd error function operators +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn erf "double x" +.Ft float +.Fn erff "float x" +.Ft double +.Fn erfc "double x" +.Ft float +.Fn erfcf "float x" +.Sh DESCRIPTION +These functions calculate the error function of +.Fa x . +.Pp +The +.Fn erf +calculates the error function of x; where +.Bd -filled -offset indent +.if n \{\ +erf(x) = 2/sqrt(pi)\(**\|integral from 0 to x of exp(\-t\(**t) dt. \} +.if t \{\ +erf\|(x) := +(2/\(sr\(*p)\|\(is\d\s8\z0\s10\u\u\s8x\s10\d\|exp(\-t\u\s82\s10\d)\|dt. \} +.Ed +.Pp +The +.Fn erfc +function calculates the complementary error function of +.Fa x ; +that is +.Fn erfc +subtracts the result of the error function +.Fn erf x +from 1.0. +This is useful, since for large +.Fa x +places disappear. +.Sh SEE ALSO +.Xr math 3 +.Sh HISTORY +The +.Fn erf +and +.Fn erfc +functions appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/exp.3 b/lib/nbsd_libm/man/exp.3 new file mode 100644 index 000000000..579d6160c --- /dev/null +++ b/lib/nbsd_libm/man/exp.3 @@ -0,0 +1,385 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)exp.3 6.12 (Berkeley) 7/31/91 +.\" $FreeBSD: src/lib/msun/man/exp.3,v 1.24 2008/01/18 21:43:00 das Exp $ +.\" $NetBSD: exp.3,v 1.26 2010/05/03 05:35:58 jruoho Exp $ +.\" +.Dd May 3, 2010 +.Dt EXP 3 +.Os +.Sh NAME +.Nm exp , +.Nm expf , +.\" The sorting error is intentional. exp and expf should be adjacent. +.Nm exp2 , +.Nm exp2f , +.\" .Nm exp2l , +.Nm expm1 , +.Nm expm1f , +.Nm log , +.Nm logf , +.Nm log2 , +.Nm log2f , +.Nm log10 , +.Nm log10f , +.Nm log1p , +.Nm log1pf , +.Nm pow , +.Nm powf +.Nd exponential, logarithm, power functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn exp "double x" +.Ft float +.Fn expf "float x" +.Ft double +.Fn exp2 "double x" +.Ft float +.Fn exp2f "float x" +.\" .Ft long double +.\" .Fn exp2l "long double x" +.Ft double +.Fn expm1 "double x" +.Ft float +.Fn expm1f "float x" +.Ft double +.Fn log "double x" +.Ft float +.Fn logf "float x" +.Ft double +.Fn log2 "double x" +.Ft float +.Fn log2f "float x" +.Ft double +.Fn log10 "double x" +.Ft float +.Fn log10f "float x" +.Ft double +.Fn log1p "double x" +.Ft float +.Fn log1pf "float x" +.Ft double +.Fn pow "double x" "double y" +.Ft float +.Fn powf "float x" "float y" +.Sh DESCRIPTION +The +.Fn exp +and the +.Fn expf +functions compute the base +.Ms e +exponential value of the given argument +.Fa x . +.Pp +The +.Fn exp2 , +and +.Fn exp2f +.\" .Fn exp2f , +.\" and +.\" .Fn exp2l +functions compute the base 2 exponential of the given argument +.Fa x . +.Pp +The +.Fn expm1 +and the +.Fn expm1f +functions computes the value exp(x)\-1 accurately even for tiny argument +.Fa x . +.Pp +The +.Fn log +function computes the value of the natural logarithm of argument +.Fa x . +.Pp +The +.Fn log10 +function computes the value of the logarithm of argument +.Fa x +to base 10. +.Pp +The +.Fn log1p +function computes +the value of log(1+x) accurately even for tiny argument +.Fa x . +.Pp +The +.Fn log2 +and the +.Fn log2f +functions compute the value of the logarithm of argument +.Fa x +to base 2. +.Pp +The +.Fn pow +and +.Fn powf +functions compute the value +of +.Ar x +to the exponent +.Ar y . +.Sh RETURN VALUES +These functions will return the appropriate computation unless an error +occurs or an argument is out of range. +The functions +.Fn exp , +.Fn expm1 +and +.Fn pow +detect if the computed value will overflow, +set the global variable +.Va errno +to +.Er ERANGE +and cause a reserved operand fault on a +.Tn VAX . +The function +.Fn pow x y +checks to see if +.Fa x +\*[Lt] 0 and +.Fa y +is not an integer, in the event this is true, +the global variable +.Va errno +is set to +.Er EDOM +and on the +.Tn VAX +generate a reserved operand fault. +On a +.Tn VAX , +.Va errno +is set to +.Er EDOM +and the reserved operand is returned +by log unless +.Fa x +\*[Gt] 0, by +.Fn log1p +unless +.Fa x +\*[Gt] \-1. +.Sh ERRORS +The values of +.Fn exp x , +.Fn expm1 x , +.Fn exp2 x , +.Fn log x , +and +.Fn log1p x , +are exact provided that they are representable. +Otherwise the error in these functions is generally below one +.Em ulp . +The values of +.Fn log10 x +are within about 2 +.Em ulps ; +an +.Em ulp +is one +.Em Unit +in the +.Em Last +.Em Place . +The error in +.Fn pow x y +is below about 2 +.Em ulps +when its +magnitude is moderate, but increases as +.Fn pow x y +approaches +the over/underflow thresholds until almost as many bits could be +lost as are occupied by the floating\-point format's exponent +field; that is 8 bits for +.Tn "VAX D" +and 11 bits for IEEE 754 Double. +No such drastic loss has been exposed by testing; the worst +errors observed have been below 20 +.Em ulps +for +.Tn "VAX D" , +300 +.Em ulps +for +.Tn IEEE +754 Double. +Moderate values of +.Fn pow x y +are accurate enough that +.Fn pow integer integer +is exact until it is bigger than 2**56 on a +.Tn VAX , +2**53 for +.Tn IEEE +754. +.Sh NOTES +The functions +.Fn exp x\ \-\ 1 +and +.Fn log 1\ \+\ x +are called +.Fn expm1 x +and +.Fn logp1 x +in +.Tn BASIC +on the Hewlett\-Packard +.Tn HP Ns \-71B +and +.Tn APPLE +Macintosh, +.Tn EXP1 +and +.Tn LN1 +in Pascal, +.Fn exp1 x +and +.Fn log1 x +in C +on +.Tn APPLE +Macintoshes, where they have been provided to make +sure financial calculations of ((1+x)**n\-1)/x, namely +expm1(n*log1p(x))/x, will be accurate when x is tiny. +They also provide accurate inverse hyperbolic functions. +.Pp +The function +.Fn pow x 0 +returns x**0 = 1 for all x including x = 0, +.if n \ +Infinity +.if t \ +\(if +(not found on a +.Tn VAX ) , +and +.Em NaN +(the reserved +operand on a +.Tn VAX ) . +Previous implementations of pow may +have defined x**0 to be undefined in some or all of these +cases. +Here are reasons for returning x**0 = 1 always: +.Bl -enum -width indent +.It +Any program that already tests whether x is zero (or +infinite or \*(Na) before computing x**0 cannot care +whether 0**0 = 1 or not. +Any program that depends +upon 0**0 to be invalid is dubious anyway since that +expression's meaning and, if invalid, its consequences +vary from one computer system to another. +.It +Some Algebra texts (e.g. Sigler's) define x**0 = 1 for +all x, including x = 0. +This is compatible with the convention that accepts a[0] +as the value of polynomial +.Bd -literal -offset indent +p(x) = a[0]\(**x**0 + a[1]\(**x**1 + a[2]\(**x**2 +...+ a[n]\(**x**n +.Ed +.Pp +at x = 0 rather than reject a[0]\(**0**0 as invalid. +.It +Analysts will accept 0**0 = 1 despite that x**y can +approach anything or nothing as x and y approach 0 +independently. +The reason for setting 0**0 = 1 anyway is this: +.Bd -filled -offset indent +If x(z) and y(z) are +.Em any +functions analytic (expandable +in power series) in z around z = 0, and if there +x(0) = y(0) = 0, then x(z)**y(z) \(-\*[Gt] 1 as z \(-\*[Gt] 0. +.Ed +.It +If 0**0 = 1, then +.if n \ +infinity**0 = 1/0**0 = 1 too; and +.if t \ +\(if**0 = 1/0**0 = 1 too; and +then \*(Na**0 = 1 too because x**0 = 1 for all finite +and infinite x, i.e., independently of x. +.El +.Sh SEE ALSO +.Xr math 3 +.Sh STANDARDS +The +.Fn exp , +.Fn log , +.Fn log10 +and +.Fn pow +functions conform to +.St -ansiC . +The +.Fn exp2 , +.Fn exp2f , +.Fn expf , +.Fn expm1 , +.Fn expm1f , +.Fn log1p , +.Fn log1pf , +.Fn log2 , +.Fn log2f , +.Fn log10f , +.Fn logf , +and +.Fn powf +functions conform to +.St -isoC-99 . +.Sh HISTORY +A +.Fn exp , +.Fn log +and +.Fn pow +functions +appeared in +.At v6 . +A +.Fn log10 +function +appeared in +.At v7 . +The +.Fn log1p +and +.Fn expm1 +functions appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/fabs.3 b/lib/nbsd_libm/man/fabs.3 new file mode 100644 index 000000000..11cd89ddc --- /dev/null +++ b/lib/nbsd_libm/man/fabs.3 @@ -0,0 +1,69 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)fabs.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: fabs.3,v 1.14 2003/08/07 16:44:47 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt FABS 3 +.Os +.Sh NAME +.Nm fabs , +.Nm fabsf +.Nd floating-point absolute value function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn fabs "double x" +.Ft float +.Fn fabsf "float x" +.Sh DESCRIPTION +The +.Fn fabs +and +.Fn fabsf +functions compute the absolute value of a floating-point number +.Fa x . +.Sh RETURN VALUES +The +.Fn fabs +function returns the absolute value of +.Fa x . +.Sh SEE ALSO +.Xr abs 3 , +.Xr ceil 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 +.Sh STANDARDS +The +.Fn fabs +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/fdim.3 b/lib/nbsd_libm/man/fdim.3 new file mode 100644 index 000000000..f80318163 --- /dev/null +++ b/lib/nbsd_libm/man/fdim.3 @@ -0,0 +1,89 @@ +.\" Copyright (c) 2004 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" $FreeBSD: src/lib/msun/man/fdim.3,v 1.1 2004/06/30 07:04:01 das Exp $ +.\" $NetBSD$ +.\" +.Dd June 29, 2004 +.Dt FDIM 3 +.Os +.Sh NAME +.Nm fdim , +.Nm fdimf , +.Nm fdiml +.Nd positive difference functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn fdim "double x" "double y" +.Ft float +.Fn fdimf "float x" "float y" +.Ft long double +.Fn fdiml "long double x" "long double y" +.Sh DESCRIPTION +The +.Fn fdim , +.Fn fdimf , +and +.Fn fdiml +functions return the positive difference between +.Fa x +and +.Fa y . +That is, if +.Fa x\- Ns Fa y +is positive, then +.Fa x\- Ns Fa y +is returned. +If either +.Fa x +or +.Fa y +is an \*(Na, then an \*(Na is returned. +Otherwise, the result is +.Li +0.0 . +.Pp +Overflow or underflow may occur iff the exact result is not +representable in the return type. +No other exceptions are raised. +.Sh SEE ALSO +.Xr fabs 3 , +.Xr fmax 3 , +.Xr fmin 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn fdim , +.Fn fdimf , +and +.Fn fdiml +functions conform to +.St -isoC-99 . +.Sh HISTORY +These routines first appeared in +.Fx 5.3 +and +.Nx 5.1 . diff --git a/lib/nbsd_libm/man/feclearexcept.3 b/lib/nbsd_libm/man/feclearexcept.3 new file mode 100644 index 000000000..5e2a60416 --- /dev/null +++ b/lib/nbsd_libm/man/feclearexcept.3 @@ -0,0 +1,139 @@ +.\" $NetBSD: feclearexcept.3,v 1.2 2010/08/07 18:13:12 wiz Exp $ +.\" Copyright (c) 2004 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.Dd May 8, 2004 +.Dt FECLEAREXCEPT 3 +.Os +.Sh NAME +.Nm feclearexcept , +.Nm fegetexceptflag , +.Nm feraiseexcept , +.Nm fesetexceptflag , +.Nm fetestexcept +.Nd floating-point exception flag manipulation +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In fenv.h +.Fd "#pragma STDC FENV_ACCESS ON" +.Ft int +.Fn feclearexcept "int excepts" +.Ft int +.Fn fegetexceptflag "fexcept_t *flagp" "int excepts" +.Ft int +.Fn feraiseexcept "int excepts" +.Ft int +.Fn fesetexceptflag "const fexcept_t *flagp" "int excepts" +.Ft int +.Fn fetestexcept "int excepts" +.Sh DESCRIPTION +The +.Fn feclearexcept +routine clears the floating-point exception flags specified by +.Fa excepts , +whereas +.Fn feraiseexcept +raises the specified exceptions. +Raising an exception causes the corresponding flag to be set, +and a +.Dv SIGFPE +is delivered to the process if the exception is unmasked. +.Pp +The +.Fn fetestexcept +function determines which flags are currently set, of those specified by +.Fa excepts . +.Pp +The +.Fn fegetexceptflag +function stores the state of the exception flags specified in +.Fa excepts +in the opaque object pointed to by +.Fa flagp . +Similarly, +.Fn fesetexceptflag +changes the specified exception flags to reflect the state stored in +the object pointed to by +.Fa flagp . +Note that the flags restored with +.Fn fesetexceptflag +must be a (not necessarily proper) subset of the flags recorded by +a prior call to +.Fn fegetexceptflag . +.Pp +For all of these functions, the possible types of exceptions +include those described in +.Xr fenv 3 . +Some architectures may define other types of floating-point exceptions. +.Sh IMPLEMENTATION NOTES +On some architectures, raising an overflow or underflow exception +also causes an inexact exception to be raised. +In these cases, the overflow or underflow will be raised first. +.Pp +The +.Fn fegetexceptflag +and +.Fn fesetexceptflag +routines are preferred to +.Fn fetestexcept +and +.Fn feraiseexcept , +respectively, for saving and restoring exception flags. +The latter do not re-raise exceptions and may preserve +architecture-specific information such as addresses where +exceptions occurred. +.Sh RETURN VALUES +The +.Fn feclearexcept , +.Fn fegetexceptflag , +.Fn feraiseexcept , +and +.Fn fesetexceptflag +functions return 0 upon success, and non-zero otherwise. +The +.Fn fetestexcept +function returns the bitwise OR of the values of the current exception +flags that were requested. +.Sh SEE ALSO +.Xr sigaction 2 , +.Xr feholdexcept 3 , +.Xr fenv 3 , +.Xr feupdateenv 3 , +.Xr fpgetsticky 3 +.Sh STANDARDS +The +.Fn feclearexcept , +.Fn fegetexceptflag , +.Fn feraiseexcept , +.Fn fesetexceptflag , +and +.Fn fetestexcept +routines conform to +.St -isoC-99 . +.Sh HISTORY +These functions first appeared in +.Fx 5.3 +and +.Nx 6.0 . diff --git a/lib/nbsd_libm/man/feenableexcept.3 b/lib/nbsd_libm/man/feenableexcept.3 new file mode 100644 index 000000000..06bb28b29 --- /dev/null +++ b/lib/nbsd_libm/man/feenableexcept.3 @@ -0,0 +1,97 @@ +.\" $NetBSD: feenableexcept.3,v 1.1 2010/07/31 21:47:53 joerg Exp $ +.\" Copyright (c) 2004 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.Dd March 16, 2005 +.Dt FEENABLEEXCEPT 3 +.Os +.Sh NAME +.Nm feenableexcept , +.Nm fedisableexcept , +.Nm fegetexcept +.Nd floating-point exception masking +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In fenv.h +.Fd "#pragma STDC FENV_ACCESS ON" +.Ft int +.Fn feenableexcept "int excepts" +.Ft int +.Fn fedisableexcept "int excepts" +.Ft int +.Fn fegetexcept "void" +.Sh DESCRIPTION +The +.Fn feenableexcept +and +.Fn fedisableexcept +functions +unmask and mask (respectively) exceptions specified in +.Fa excepts . +The +.Fn fegetexcept +function +returns the current exception mask. +All exceptions are masked by default. +.Pp +Floating-point operations that produce unmasked exceptions will trap, and a +.Dv SIGFPE +will be delivered to the process. +By installing a signal handler for +.Dv SIGFPE , +applications can take appropriate action immediately without +testing the exception flags after every operation. +Note that the trap may not be immediate, but it should occur +before the next floating-point instruction is executed. +.Pp +For all of these functions, the possible types of exceptions +include those described in +.Xr fenv 3 . +Some architectures may define other types of floating-point exceptions. +.Sh RETURN VALUES +The +.Fn feenableexcept , +.Fn fedisableexcept , +and +.Fn fegetexcept +functions return a bitmap of the exceptions that were unmasked +prior to the call. +.Sh SEE ALSO +.Xr sigaction 2 , +.Xr feclearexcept 3 , +.Xr feholdexcept 3 , +.Xr fenv 3 , +.Xr feupdateenv 3 +.Sh BUGS +Functions in the standard library may trigger exceptions multiple +times as a result of intermediate computations; +however, they generally do not trigger spurious exceptions. +.Pp +No interface is provided to permit exceptions to be handled in +nontrivial ways. +There is no uniform way for an exception handler to access +information about the exception-causing instruction, or +to determine whether that instruction should be reexecuted +after returning from the handler. diff --git a/lib/nbsd_libm/man/fegetenv.3 b/lib/nbsd_libm/man/fegetenv.3 new file mode 100644 index 000000000..c163b72cd --- /dev/null +++ b/lib/nbsd_libm/man/fegetenv.3 @@ -0,0 +1,114 @@ +.\" $NetBSD: fegetenv.3,v 1.2 2010/08/04 18:58:18 wiz Exp $ +.\" Copyright (c) 2004 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.Dd May 8, 2004 +.Dt FEGETENV 3 +.Os +.Sh NAME +.Nm fegetenv , +.Nm feholdexcept , +.Nm fesetenv , +.Nm feupdateenv +.Nd floating-point environment save and restore +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In fenv.h +.Fd "#pragma STDC FENV_ACCESS ON" +.Ft int +.Fn fegetenv "fenv_t *envp" +.Ft int +.Fn feholdexcept "fenv_t *envp" +.Ft int +.Fn fesetenv "const fenv_t *envp" +.Ft int +.Fn feupdateenv "const fenv_t *envp" +.Sh DESCRIPTION +The floating-point environment includes exception flags and masks, the +current rounding mode, and other architecture-specific settings. +However, it does not include the floating-point register file. +.Pp +The +.Fn fegetenv +function stores the current floating-point environment in the object +pointed to by +.Fa envp , +whereas +.Fn feholdexcept +saves the current environment, then clears all exception flags +and masks all floating-point exceptions. +.Pp +The +.Fn fesetenv +function restores a previously saved environment. +The +.Fn feupdateenv +function restores a saved environment as well, but it also +raises any exceptions that were set in the environment it +replaces. +.Pp +The +.Fn feholdexcept +function is often used with +.Fn feupdateenv +or +.Fn fesetenv +to suppress spurious exceptions that occur as a result of +intermediate computations. +An example in +.Xr fenv 3 +demonstrates how to do this. +.Sh RETURN VALUES +The +.Fn fegetenv , +.Fn feholdexcept , +.Fn fesetenv , +and +.Fn feupdateenv +functions return 0 if they succeed, and non-zero otherwise. +.Sh SEE ALSO +.Xr feclearexcept 3 , +.Xr fenv 3 , +.Xr feraiseexcept 3 , +.Xr fesetenv 3 , +.Xr fetestexcept 3 , +.Xr fpgetmask 3 , +.\"Xr fpgetprec 3 , +.Xr fpsetmask 3 +.\"Xr fpsetprec 3 +.Sh STANDARDS +The +.Fn fegetenv , +.Fn feholdexcept , +.Fn fesetenv , +and +.Fn feupdateenv +functions conform to +.St -isoC-99 . +.Sh HISTORY +These routines first appeared in +.Fx 5.3 +and +.Nx 6.0 . diff --git a/lib/nbsd_libm/man/fegetround.3 b/lib/nbsd_libm/man/fegetround.3 new file mode 100644 index 000000000..6fd9d779f --- /dev/null +++ b/lib/nbsd_libm/man/fegetround.3 @@ -0,0 +1,84 @@ +.\" $NetBSD: fegetround.3,v 1.1 2010/07/31 21:47:53 joerg Exp $ +.\" Copyright (c) 2004 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.Dd May 8, 2004 +.Dt FEGETROUND 3 +.Os +.Sh NAME +.Nm fegetround , +.Nm fesetround +.Nd floating-point rounding control +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In fenv.h +.Fd "#pragma STDC FENV_ACCESS ON" +.Ft int +.Fn fegetround void +.Ft int +.Fn fesetround "int round" +.Sh DESCRIPTION +The +.Fn fegetround +function determines the current floating-point rounding mode, +and the +.Fn fesetround +function sets the current rounding mode to +.Fa round . +The rounding mode is one of +.Dv FE_TONEAREST , FE_DOWNWARD , FE_UPWARD , +or +.Dv FE_TOWARDZERO , +as described in +.Xr fenv 3 . +.Sh RETURN VALUES +The +.Fn fegetround +routine returns the current rounding mode. +The +.Fn fesetround +function returns 0 on success and non-zero otherwise; +however, the present implementation always succeeds. +.Sh SEE ALSO +.Xr fenv 3 , +.Xr fpgetround 3 , +.Xr fpsetround 3 +.Sh STANDARDS +The +.Fn fegetround +and +.Fn fesetround +functions conform to +.St -isoC-99 . +.Sh HISTORY +These routines first appeared in +.Fx 5.3 +and +.Nx 6.0 . +They supersede the non-standard +.Xr fpgetround 3 +and +.Xr fpsetround 3 +functions. diff --git a/lib/nbsd_libm/man/fenv.3 b/lib/nbsd_libm/man/fenv.3 new file mode 100644 index 000000000..c77a9f9c4 --- /dev/null +++ b/lib/nbsd_libm/man/fenv.3 @@ -0,0 +1,283 @@ +.\" $NetBSD: fenv.3,v 1.2 2010/08/04 18:58:28 wiz Exp $ +.\" Copyright (c) 2004 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.Dd March 16, 2005 +.Dt FENV 3 +.Os +.Sh NAME +.Nm feclearexcept , +.Nm fegetexceptflag , +.Nm feraiseexcept , +.Nm fesetexceptflag , +.Nm fetestexcept , +.Nm fegetround , +.Nm fesetround , +.Nm fegetenv , +.Nm feholdexcept , +.Nm fesetenv , +.Nm feupdateenv , +.Nm feenableexcept , +.Nm fedisableexcept , +.Nm fegetexcept +.Nd floating-point environment control +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In fenv.h +.Fd "#pragma STDC FENV_ACCESS ON" +.Ft int +.Fn feclearexcept "int excepts" +.Ft int +.Fn fegetexceptflag "fexcept_t *flagp" "int excepts" +.Ft int +.Fn feraiseexcept "int excepts" +.Ft int +.Fn fesetexceptflag "const fexcept_t *flagp" "int excepts" +.Ft int +.Fn fetestexcept "int excepts" +.Ft int +.Fn fegetround void +.Ft int +.Fn fesetround "int round" +.Ft int +.Fn fegetenv "fenv_t *envp" +.Ft int +.Fn feholdexcept "fenv_t *envp" +.Ft int +.Fn fesetenv "const fenv_t *envp" +.Ft int +.Fn feupdateenv "const fenv_t *envp" +.Ft int +.Fn feenableexcept "int excepts" +.Ft int +.Fn fedisableexcept "int excepts" +.Ft int +.Fn fegetexcept void +.Sh DESCRIPTION +The +.In fenv.h +routines manipulate the floating-point environment, +which includes the exception flags and rounding modes defined in +.St -ieee754 . +.Ss Exceptions +Exception flags are set as side-effects of floating-point arithmetic +operations and math library routines, and they remain set until +explicitly cleared. +The following macros expand to bit flags of type +.Vt int +representing the five standard floating-point exceptions. +.Bl -tag -width ".Dv FE_DIVBYZERO" +.It Dv FE_DIVBYZERO +A divide-by-zero exception occurs when the program attempts to +divide a finite non-zero number by zero. +.It Dv FE_INEXACT +An inexact exception is raised whenever there is a loss of precision +due to rounding. +.It Dv FE_INVALID +Invalid operation exceptions occur when a program attempts to +perform calculations for which there is no reasonable representable +answer. +For instance, subtraction of infinities, division of zero by zero, +ordered comparison involving \*(Nas, and taking the square root of a +negative number are all invalid operations. +.It Dv FE_OVERFLOW +An overflow exception occurs when the magnitude of the result of a +computation is too large to fit in the destination type. +.It Dv FE_UNDERFLOW +Underflow occurs when the result of a computation is too close to zero +to be represented as a non-zero value in the destination type. +.El +.Pp +Additionally, the +.Dv FE_ALL_EXCEPT +macro expands to the bitwise OR of the above flags and any +architecture-specific flags. +Combinations of these flags are passed to the +.Fn feclearexcept , +.Fn fegetexceptflag , +.Fn feraiseexcept , +.Fn fesetexceptflag , +and +.Fn fetestexcept +functions to clear, save, raise, restore, and examine the +processor's floating-point exception flags, respectively. +.Pp +Exceptions may be +.Em unmasked +with +.Fn feenableexcept +and masked with +.Fn fedisableexcept . +Unmasked exceptions cause a trap when they are produced, and +all exceptions are masked by default. +The current mask can be tested with +.Fn fegetexcept . +.Ss Rounding Modes +.St -ieee754 +specifies four rounding modes. +These modes control the direction in which results are rounded +from their exact values in order to fit them into binary +floating-point variables. +The four modes correspond with the following symbolic constants. +.Bl -tag -width ".Dv FE_TOWARDZERO" +.It Dv FE_TONEAREST +Results are rounded to the closest representable value. +If the exact result is exactly half way between two representable +values, the value whose last binary digit is even (zero) is chosen. +This is the default mode. +.It Dv FE_DOWNWARD +Results are rounded towards negative \*[If]. +.It Dv FE_UPWARD +Results are rounded towards positive \*[If]. +.It Dv FE_TOWARDZERO +Results are rounded towards zero. +.El +.Pp +The +.Fn fegetround +and +.Fn fesetround +functions query and set the rounding mode. +.Ss Environment Control +The +.Fn fegetenv +and +.Fn fesetenv +functions save and restore the floating-point environment, +which includes exception flags, the current exception mask, +the rounding mode, and possibly other implementation-specific +state. +The +.Fn feholdexcept +function behaves like +.Fn fegetenv , +but with the additional effect of clearing the exception flags and +installing a +.Em non-stop +mode. +In non-stop mode, floating-point operations will set exception flags +as usual, but no +.Dv SIGFPE +signals will be generated as a result. +Non-stop mode is the default, but it may be altered by +non-standard mechanisms. +.\" XXX Mention fe[gs]etmask() here after the interface is finalized +.\" XXX and ready to be officially documented. +The +.Fn feupdateenv +function restores a saved environment similarly to +.Fn fesetenv , +but it also re-raises any floating-point exceptions from the old +environment. +.Pp +The macro +.Dv FE_DFL_ENV +expands to a pointer to the default environment. +.Sh EXAMPLES +The following routine computes the square root function. +It explicitly raises an invalid exception on appropriate inputs using +.Fn feraiseexcept . +It also defers inexact exceptions while it computes intermediate +values, and then it allows an inexact exception to be raised only if +the final answer is inexact. +.Bd -literal -offset indent +#pragma STDC FENV_ACCESS ON +double sqrt(double n) { + double x = 1.0; + fenv_t env; + + if (isnan(n) || n \*[Lt] 0.0) { + feraiseexcept(FE_INVALID); + return (NAN); + } + if (isinf(n) || n == 0.0) + return (n); + feholdexcept(\*[Am]env); + while (fabs((x * x) - n) \*[Gt] DBL_EPSILON * 2 * x) + x = (x / 2) + (n / (2 * x)); + if (x * x == n) + feclearexcept(FE_INEXACT); + feupdateenv(\*[Am]env); + return (x); +} +.Ed +.Sh SEE ALSO +.Xr c99 1 , +.Xr feclearexcept 3 , +.Xr fedisableexcept 3 , +.Xr feenableexcept 3 , +.Xr fegetenv 3 , +.Xr fegetexcept 3 , +.Xr fegetexceptflag 3 , +.Xr fegetround 3 , +.Xr feholdexcept 3 , +.Xr feraiseexcept 3 , +.Xr fesetenv 3 , +.Xr fesetexceptflag 3 , +.Xr fesetround 3 , +.Xr fetestexcept 3 , +.Xr feupdateenv 3 +.\"Xr fpgetprec 3 , +.\"Xr fpsetprec 3 +.Sh STANDARDS +Except as noted below, +.In fenv.h +conforms to +.St -isoC-99 . +The +.Fn feenableexcept , +.Fn fedisableexcept , +and +.Fn fegetexcept +routines are extensions. +.Sh HISTORY +The +.In fenv.h +header first appeared in +.Fx 5.3 +and +.Nx 6.0 . +It supersedes the non-standard routines defined in +.In ieeefp.h +and documented in +.Xr fpgetround 3 . +.Sh CAVEATS +The FENV_ACCESS pragma can be enabled with +.Dl "#pragma STDC FENV_ACCESS ON" +and disabled with the +.Dl "#pragma STDC FENV_ACCESS OFF" +directive. +This lexically-scoped annotation tells the compiler that the program +may access the floating-point environment, so optimizations that would +violate strict IEEE-754 semantics are disabled. +If execution reaches a block of code for which +.Dv FENV_ACCESS +is off, the floating-point environment will become undefined. +.Sh BUGS +The +.Dv FENV_ACCESS +pragma is unimplemented in the system compiler. +However, non-constant expressions generally produce the correct +side-effects at low optimization levels. diff --git a/lib/nbsd_libm/man/floor.3 b/lib/nbsd_libm/man/floor.3 new file mode 100644 index 000000000..29ed2db85 --- /dev/null +++ b/lib/nbsd_libm/man/floor.3 @@ -0,0 +1,65 @@ +.\" Copyright (c) 1985, 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)floor.3 6.5 (Berkeley) 4/19/91 +.\" $NetBSD: floor.3,v 1.14 2003/08/07 16:44:47 agc Exp $ +.\" +.Dd March 10, 1994 +.Dt FLOOR 3 +.Os +.Sh NAME +.Nm floor , +.Nm floorf +.Nd round to largest integral value not greater than x +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn floor "double x" +.Ft float +.Fn floorf "float x" +.Sh DESCRIPTION +The +.Fn floor +and +.Fn floorf +functions return the largest integral value +less than or equal to +.Fa x . +.Sh SEE ALSO +.Xr abs 3 , +.Xr ceil 3 , +.Xr fabs 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 +.Sh STANDARDS +The +.Fn floor +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/fmax.3 b/lib/nbsd_libm/man/fmax.3 new file mode 100644 index 000000000..1124d624e --- /dev/null +++ b/lib/nbsd_libm/man/fmax.3 @@ -0,0 +1,100 @@ +.\" Copyright (c) 2004 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" $FreeBSD: src/lib/msun/man/fmax.3,v 1.2 2005/01/14 09:12:05 ru Exp $ +.\" $NetBSD$ +.\" +.Dd June 29, 2004 +.Dt FMAX 3 +.Os +.Sh NAME +.Nm fmax , +.Nm fmaxf , +.Nm fmaxl , +.Nm fmin , +.Nm fminf , +.Nm fminl +.Nd floating-point maximum and minimum functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn fmax "double x" "double y" +.Ft float +.Fn fmaxf "float x" "float y" +.Ft "long double" +.Fn fmaxl "long double x" "long double y" +.Ft double +.Fn fmin "double x" "double y" +.Ft float +.Fn fminf "float x" "float y" +.Ft "long double" +.Fn fminl "long double x" "long double y" +.Sh DESCRIPTION +The +.Fn fmax , +.Fn fmaxf , +and +.Fn fmaxl +functions return the larger of +.Fa x +and +.Fa y , +and likewise, the +.Fn fmin , +.Fn fminf , +and +.Fn fminl +functions return the smaller of +.Fa x +and +.Fa y . +They treat +.Li +0.0 +as being larger than +.Li -0.0 . +If one argument is an \*(Na, then the other argument is returned. +If both arguments are \*(Nas, then the result is an \*(Na. +These routines do not raise any floating-point exceptions. +.Sh SEE ALSO +.Xr fabs 3 , +.Xr fdim 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn fmax , +.Fn fmaxf , +.Fn fmaxl , +.Fn fmin , +.Fn fminf , +and +.Fn fminl +functions conform to +.St -isoC-99 . +.Sh HISTORY +These routines first appeared in +.Fx 5.3 +and +.Nx 5.1 . diff --git a/lib/nbsd_libm/man/fmod.3 b/lib/nbsd_libm/man/fmod.3 new file mode 100644 index 000000000..e33463aaa --- /dev/null +++ b/lib/nbsd_libm/man/fmod.3 @@ -0,0 +1,79 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)fmod.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: fmod.3,v 1.11 2003/08/07 16:44:47 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt FMOD 3 +.Os +.Sh NAME +.Nm fmod , +.Nm fmodf +.Nd floating-point remainder function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn fmod "double x" "double y" +.Ft float +.Fn fmodf "float x" "float y" +.Sh DESCRIPTION +The +.Fn fmod +function computes the floating-point remainder of +.Fa x Ns / Fa y . +.Sh RETURN VALUES +The +.Fn fmod +and +.Fn fmodf +functions return the value +.Sm off +.Fa x - Em i * Fa y , +.Sm on +for some integer +.Em i +such that, if +.Fa y +is non-zero, the result has the same sign as +.Fa x +and magnitude less than the magnitude of +.Fa y . +If +.Fa y +is zero, whether a domain error occurs or the +.Fn fmod +function returns zero is implementation-defined. +.Sh SEE ALSO +.Xr math 3 +.Sh STANDARDS +The +.Fn fmod +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/frexp.3 b/lib/nbsd_libm/man/frexp.3 new file mode 100644 index 000000000..4b1124d7c --- /dev/null +++ b/lib/nbsd_libm/man/frexp.3 @@ -0,0 +1,85 @@ +.\" $NetBSD: frexp.3,v 1.2 2010/04/29 08:35:03 joerg Exp $ +.\" +.\" Copyright (c) 1991, 1993 +.\" The Regents of the University of California. All rights reserved. +.\" +.\" This code is derived from software contributed to Berkeley by +.\" the American National Standards Committee X3, on Information +.\" Processing Systems. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" @(#)frexp.3 8.1 (Berkeley) 6/4/93 +.\" +.Dd March 21, 2006 +.Dt FREXP 3 +.Os +.Sh NAME +.Nm frexp +.Nd convert floating-point number to fractional and integral components +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn frexp "double value" "int *exp" +.Ft float +.Fn frexpf "float value" "int *exp" +.Sh DESCRIPTION +The +.Fn frexp +function breaks a floating-point number into a normalized +fraction and an integral power of 2. +It stores the integer in the +.Em int +object pointed to by +.Fa exp . +.Sh RETURN VALUES +The +.Fn frexp +function returns the value +.Em x , +such that +.Em x +is a +.Em double +with magnitude in the interval [1/2, 1) or zero, and +.Fa value +equals +.Em x +times 2 raised to the power +.Fa *exp . +If +.Fa value +is zero, both parts of the result are zero. +.Sh SEE ALSO +.Xr ldexp 3 , +.Xr math 3 , +.Xr modf 3 +.Sh STANDARDS +The +.Fn frexp +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/hypot.3 b/lib/nbsd_libm/man/hypot.3 new file mode 100644 index 000000000..67d650ae1 --- /dev/null +++ b/lib/nbsd_libm/man/hypot.3 @@ -0,0 +1,124 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)hypot.3 6.7 (Berkeley) 5/6/91 +.\" $NetBSD: hypot.3,v 1.17 2007/02/22 22:08:20 drochner Exp $ +.\" +.Dd February 12, 2007 +.Dt HYPOT 3 +.Os +.Sh NAME +.Nm hypot , +.Nm hypotf +.Nd Euclidean distance and complex absolute value functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn hypot "double x" "double y" +.Ft float +.Fn hypotf "float x" "float y" +.Sh DESCRIPTION +The +.Fn hypot +functions +compute the +sqrt(x*x+y*y) +in such a way that underflow will not happen, and overflow +occurs only if the final result deserves it. +.Pp +.Fn hypot "\*(If" "v" += +.Fn hypot "v" "\*(If" += +\*(If for all +.Ar v , +including \*(Na. +.Sh ERRORS +Below 0.97 +.Em ulps . +Consequently +.Fn hypot "5.0" "12.0" += 13.0 +exactly; +in general, hypot returns an integer whenever an +integer might be expected. +.Pp +The same cannot be said for the shorter and faster version of hypot +that is provided in the comments in cabs.c; its error can +exceed 1.2 +.Em ulps . +.Sh NOTES +As might be expected, +.Fn hypot "v" "\*(Na" +and +.Fn hypot "\*(Na" "v" +are \*(Na for all +.Em finite +.Ar v ; +with "reserved operand" in place of "\*(Na", the +same is true on a +.Tn VAX . +But programmers on machines other than a +.Tn VAX +(it has no \*(If) +might be surprised at first to discover that +.Fn hypot "\(+-\*(If" "\*(Na" += +\*(If. +This is intentional; it happens because +.Fn hypot "\*(If" "v" += +\*(If +for +.Em all +.Ar v , +finite or infinite. +Hence +.Fn hypot "\*(If" "v" +is independent of +.Ar v . +Unlike the reserved operand fault on a +.Tn VAX , +the +.Tn IEEE +\*(Na is designed to +disappear when it turns out to be irrelevant, as it does in +.Fn hypot "\*(If" "\*(Na" . +.Sh SEE ALSO +.Xr math 3 , +.Xr sqrt 3 +.Sh HISTORY +Both a +.Fn hypot +function and a +.Fn cabs +function +appeared in +.At v7 . +.Fn cabs +was removed from public namespace in +.Nx 5.0 +to avoid conflicts with the complex function in C99. diff --git a/lib/nbsd_libm/man/ieee.3 b/lib/nbsd_libm/man/ieee.3 new file mode 100644 index 000000000..e042b3fbb --- /dev/null +++ b/lib/nbsd_libm/man/ieee.3 @@ -0,0 +1,189 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: ieee.3,v 1.21 2010/09/15 16:11:30 christos Exp $ +.\" +.Dd February 25, 1994 +.Dt IEEE 3 +.Os +.Sh NAME +.Nm copysign , +.Nm copysignf , +.Nm copysignl , +.Nm finite , +.Nm finitef , +.Nm ilogb , +.Nm ilogbf , +.Nm nextafter , +.Nm nextafterf , +.Nm nextafterl , +.Nm nexttoward , +.Nm remainder , +.Nm remainderf , +.Nm scalbn , +.Nm scalbnf +.Nd functions for IEEE arithmetic +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn copysign "double x" "double y" +.Ft float +.Fn copysignf "float x" "float y" +.Ft long double +.Fn copysignl "long double x" "long double y" +.Ft int +.Fn finite "double x" +.Ft int +.Fn finitef "float x" +.Ft int +.Fn ilogb "double x" +.Ft int +.Fn ilogbf "float x" +.Ft double +.Fn nextafter "double x" "double y" +.Ft float +.Fn nextafterf "float x" "float y" +.Ft long double +.Fn nextafterl "long double x" "long double y" +.Ft double +.Fn nexttoward "double x" "long double y" +.Ft double +.Fn remainder "double x" "double y" +.Ft float +.Fn remainderf "float x" "float y" +.Ft double +.Fn scalbn "double x" "int n" +.Ft float +.Fn scalbnf "float x" "int n" +.Sh DESCRIPTION +These functions are required or recommended by +.St -ieee754 . +.Pp +.Fn copysign +returns +.Fa x +with its sign changed to +.Fa y Ns 's . +.Pp +.Fn finite +returns the value 1 just when +\-\*(If \*(Lt +.Fa x +\*(Lt +\*(If; +otherwise a +zero is returned +(when +.Pf \*(Ba Ns Fa x Ns \*(Ba += \*(If or +.Fa x +is \*(Na). +.Pp +.Fn ilogb +returns +.Fa x Ns 's exponent +.Fa n , +in integer format. +.Fn ilogb \*(Pm\*(If +returns +.Dv INT_MAX +and +.Fn ilogb 0 +returns +.Dv INT_MIN . +.Pp +.Fn nextafter +returns the next machine representable number from +.Fa x +in direction +.Fa y . +.Pp +.Fn nexttoward +is equivalent to +.Fn nextafter , +except that the second parameter has type +.Ft long double +and the function returns +.Dv y +converted to the type of the function if +.Dv x +equals +.Dv y . +.Pp +.Fn remainder +returns the remainder +.Fa r +:= +.Fa x +\- +.Fa n\(**y +where +.Fa n +is the integer nearest the exact value of +.Bk -words +.Fa x Ns / Ns Fa y ; +.Ek +moreover if +.Pf \*(Ba Fa n +\- +.Sm off +.Fa x No / Fa y No \*(Ba +.Sm on += +1/2 +then +.Fa n +is even. +Consequently the remainder is computed exactly and +.Sm off +.Pf \*(Ba Fa r No \*(Ba +.Sm on +\*(Le +.Sm off +.Pf \*(Ba Fa y No \*(Ba/2 . +.Sm on +But +.Fn remainder x 0 +and +.Fn remainder \*(If 0 +are invalid operations that produce a \*(Na. +.Pp +.Fn scalbn +returns +.Fa x Ns \(**(2** Ns Fa n ) +computed by exponent manipulation. +.Sh SEE ALSO +.Xr math 3 +.Sh STANDARDS +.St -ieee754 +.Sh HISTORY +The +.Nm ieee +functions appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/ieee_test.3 b/lib/nbsd_libm/man/ieee_test.3 new file mode 100644 index 000000000..c82e4cf6a --- /dev/null +++ b/lib/nbsd_libm/man/ieee_test.3 @@ -0,0 +1,96 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)ieee.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: ieee_test.3,v 1.10 2003/08/07 16:44:48 agc Exp $ +.\" +.Dd March 10, 1994 +.Dt IEEE_TEST 3 +.Os +.Sh NAME +.Nm logb , +.Nm logbf , +.Nm scalb , +.Nm scalbf , +.Nm significand , +.Nm significandf +.Nd IEEE test functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn logb "double x" +.Ft float +.Fn logbf "float x" +.Ft double +.Fn scalb "double x" "double n" +.Ft float +.Fn scalbf "float x" "float n" +.Ft double +.Fn significand "double x" +.Ft float +.Fn significandf "float x" +.Sh DESCRIPTION +These functions allow users to test conformance to +.St -ieee754 . +Their use is not otherwise recommended. +.Pp +.Fn logb x +returns +.Fa x Ns 's exponent +.Fa n , +a signed integer converted to double\-precision floating\-point. +.Fn logb \*(Pm\*(If += +\*(If; +.Fn logb 0 += -\*(If with a division by zero exception. +.Pp +.Fn scalbn x n +returns +.Fa x Ns \(**(2** Ns Fa n ) +computed by exponent manipulation. +.Pp +.Fn significand x +returns +.Fa sig , +where +.Fa x +:= +.Fa sig No \(** 2** Ns Fa n +with 1 \*[Le] +.Fa sig +\*[Lt] 2. +.Fn significand x +is not defined when +.Fa x +is 0, \*(Pm\*(If, or \*(Na. +.Sh SEE ALSO +.Xr ieee 3 , +.Xr math 3 +.Sh STANDARDS +.St -ieee754 diff --git a/lib/nbsd_libm/man/isinff.3 b/lib/nbsd_libm/man/isinff.3 new file mode 100644 index 000000000..189bda2e8 --- /dev/null +++ b/lib/nbsd_libm/man/isinff.3 @@ -0,0 +1,76 @@ +.\" $NetBSD: isinff.3,v 1.6 2010/05/14 03:10:24 joerg Exp $ +.\" +.\" Copyright (c) 1991, 1993 +.\" The Regents of the University of California. All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)isinf.3 8.2 (Berkeley) 1/29/94 +.\" from: NetBSD: isinf.3,v 1.5 1998/08/02 04:52:54 mycroft Exp +.\" +.Dd August 16, 1999 +.Dt ISINFF 3 +.Os +.Sh NAME +.Nm isinff , +.Nm isnanf +.Nd test for infinity or not-a-number +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft int +.Fn isinff float +.Ft int +.Fn isnanf float +.Sh DESCRIPTION +The +.Fn isinff +function +returns 1 if the number is +.Dq \*(If , +otherwise 0. +.Pp +The +.Fn isnanf +function +returns 1 if the number is +.Dq not-a-number , +otherwise 0. +.Sh SEE ALSO +.Xr isinf 3 , +.Xr isnan 3 , +.Xr math 3 +.Rs +.%T "IEEE Standard for Binary Floating-Point Arithmetic" +.%Q ANSI +.%R Std 754-1985 +.Re +.Sh BUGS +Neither the +.Tn VAX +nor the Tahoe floating point have distinguished values +for either infinity or not-a-number. +These routines always return 0 on those architectures. diff --git a/lib/nbsd_libm/man/j0.3 b/lib/nbsd_libm/man/j0.3 new file mode 100644 index 000000000..85604ed77 --- /dev/null +++ b/lib/nbsd_libm/man/j0.3 @@ -0,0 +1,153 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)j0.3 6.7 (Berkeley) 4/19/91 +.\" $NetBSD: j0.3,v 1.16 2003/08/07 16:44:48 agc Exp $ +.\" +.Dd April 19, 1991 +.Dt J0 3 +.Os +.Sh NAME +.Nm j0 , +.Nm j0f , +.Nm j1 , +.Nm j1f , +.Nm jn , +.Nm jnf , +.Nm y0 , +.Nm y0f , +.Nm y1 , +.Nm y1f , +.Nm yn , +.Nm ynf +.Nd Bessel functions of first and second kind +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn j0 "double x" +.Ft float +.Fn j0f "float x" +.Ft double +.Fn j1 "double x" +.Ft float +.Fn j1f "float x" +.Ft double +.Fn jn "int n" "double x" +.Ft float +.Fn jnf "int n" "float x" +.Ft double +.Fn y0 "double x" +.Ft float +.Fn y0f "float x" +.Ft double +.Fn y1 "double x" +.Ft float +.Fn y1f "float x" +.Ft double +.Fn yn "int n" "double x" +.Ft float +.Fn ynf "int n" "float x" +.Sh DESCRIPTION +The functions +.Fn j0 , +.Fn j0f , +.Fn j1 +and +.Fn j1f +compute the +.Em Bessel function of the first kind of the order +0 and the +.Em order +1, respectively, +for the +real value +.Fa x ; +the functions +.Fn jn +and +.Fn jnf +compute the +.Em Bessel function of the first kind of the integer order +.Fa n +for the real value +.Fa x . +.Pp +The functions +.Fn y0 , +.Fn y0f , +.Fn y1 +and +.Fn y1f +compute the linearly independent +.Em Bessel function of the second kind of the order +0 and the +.Em order +1, respectively, +for the +positive +.Em integer +value +.Fa x +(expressed as a double); +the functions +.Fn yn +and +.Fn ynf +compute the +.Em Bessel function of the second kind for the integer order +.Fa n +for the positive +.Em integer +value +.Fa x +(expressed as a double). +.Sh RETURN VALUES +If these functions are successful, +the computed value is returned, otherwise +the global +variable +.Va errno +is set to +.Er EDOM +and a reserve operand fault is generated. +.\" On the +.\" .Tn VAX +.\" and +.\" .Tn Tahoe +.\" architectures, a negative +.\" .Fa x +.\" value +.\" results in an error. +.Sh SEE ALSO +.Xr math 3 +.\" .Xr matherr 3 +.Sh HISTORY +This set of functions +appeared in +.At v7 . diff --git a/lib/nbsd_libm/man/ldexp.3 b/lib/nbsd_libm/man/ldexp.3 new file mode 100644 index 000000000..e1eaaec80 --- /dev/null +++ b/lib/nbsd_libm/man/ldexp.3 @@ -0,0 +1,89 @@ +.\" $NetBSD: ldexp.3,v 1.1 2006/07/03 16:03:56 drochner Exp $ +.\" +.\" Copyright (c) 1991, 1993 +.\" The Regents of the University of California. All rights reserved. +.\" +.\" This code is derived from software contributed to Berkeley by +.\" the American National Standards Committee X3, on Information +.\" Processing Systems. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" @(#)ldexp.3 8.2 (Berkeley) 4/19/94 +.\" +.Dd March 21, 2006 +.Dt LDEXP 3 +.Os +.Sh NAME +.Nm ldexp +.Nd multiply floating-point number by integral power of 2 +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn ldexp "double x" "int exp" +.Ft float +.Fn ldexpf "float x" "int exp" +.Sh DESCRIPTION +The +.Fn ldexp +function multiplies a floating-point number by an integral +power of 2. +.Sh RETURN VALUES +The +.Fn ldexp +function returns the value of +.Fa x +times 2 raised to the power +.Fa exp . +.Pp +If the input +.Va x +is a NaN, infinity, or 0.0, it is returned unchanged. +.Pp +If the result would cause an overflow, +the global variable +.Va errno +is set to +.Er ERANGE +and infinity is returned, with the same sign as +.Fa x . +.Pp +If the result would cause underflow to 0.0, +the global variable +.Va errno +is set to +.Er ERANGE +and the value 0.0 is returned. +.Sh SEE ALSO +.Xr frexp 3 , +.Xr math 3 , +.Xr modf 3 +.Sh STANDARDS +The +.Fn ldexp +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/lgamma.3 b/lib/nbsd_libm/man/lgamma.3 new file mode 100644 index 000000000..90fbba6cc --- /dev/null +++ b/lib/nbsd_libm/man/lgamma.3 @@ -0,0 +1,123 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)lgamma.3 6.6 (Berkeley) 12/3/92 +.\" $NetBSD: lgamma.3,v 1.21 2003/08/07 16:44:48 agc Exp $ +.\" +.Dd December 3, 1992 +.Dt LGAMMA 3 +.Os +.Sh NAME +.Nm lgamma , +.Nm lgammaf , +.Nm lgamma_r , +.Nm lgammaf_r , +.Nm gamma , +.Nm gammaf , +.Nm gamma_r , +.Nm gammaf_r +.Nd log gamma function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft extern int +.Fa signgam ; +.sp +.Ft double +.Fn lgamma "double x" +.Ft float +.Fn lgammaf "float x" +.Ft double +.Fn lgamma_r "double x" "int *sign" +.Ft float +.Fn lgammaf_r "float x" "int *sign" +.Ft double +.Fn gamma "double x" +.Ft float +.Fn gammaf "float x" +.Ft double +.Fn gamma_r "double x" "int *sign" +.Ft float +.Fn gammaf_r "float x" "int *sign" +.Sh DESCRIPTION +.Fn lgamma x +.if t \{\ +returns ln\||\(*G(x)| where +.Bd -unfilled -offset indent +\(*G(x) = \(is\d\s8\z0\s10\u\u\s8\(if\s10\d t\u\s8x\-1\s10\d e\u\s8\-t\s10\d dt for x \*[Gt] 0 and +.br +\(*G(x) = \(*p/(\(*G(1\-x)\|sin(\(*px)) for x \*[Lt] 1. +.Ed +.\} +.if n \ +returns ln\||\(*G(x)|. +.Pp +The external integer +.Fa signgam +returns the sign of \(*G(x). +.Pp +.Fn lgamma_r +is a reentrant interface that performs identically to +.Fn lgamma , +differing in that the sign of \(*G(x) is stored in the location +pointed to by the +.Fa sign +argument and +.Fa signgam +is not modified. +.Sh IDIOSYNCRASIES +Do not use the expression +.Dq Li signgam\(**exp(lgamma(x)) +to compute g := \(*G(x). +Instead use a program like this (in C): +.Bd -literal -offset indent +lg = lgamma(x); g = signgam\(**exp(lg); +.Ed +.Pp +Only after +.Fn lgamma +has returned can signgam be correct. +.Sh RETURN VALUES +.Fn lgamma +returns appropriate values unless an argument is out of range. +Overflow will occur for sufficiently large positive values, and +non-positive integers. +On the +.Tn VAX , +the reserved operator is returned, +and +.Va errno +is set to +.Er ERANGE . +.Sh SEE ALSO +.Xr math 3 +.Sh HISTORY +The +.Nm lgamma +function appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/lrint.3 b/lib/nbsd_libm/man/lrint.3 new file mode 100644 index 000000000..b29dfffcd --- /dev/null +++ b/lib/nbsd_libm/man/lrint.3 @@ -0,0 +1,103 @@ +.\" $NetBSD: lrint.3,v 1.1 2005/09/16 15:26:47 wiz Exp $ +.\" +.\" Copyright (c) 2005 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" $FreeBSD: /repoman/r/ncvs/src/lib/msun/man/lrint.3,v 1.2.2.2 2005/03/01 16:18:39 brueffer Exp $ +.\" +.Dd January 11, 2005 +.Dt LRINT 3 +.Os +.Sh NAME +.Nm llrint , +.Nm llrintf , +.Nm lrint , +.Nm lrintf +.Nd convert to integer +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft long long +.Fn llrint "double x" +.Ft long long +.Fn llrintf "float x" +.Ft long +.Fn lrint "double x" +.Ft long +.Fn lrintf "float x" +.Sh DESCRIPTION +The +.Fn lrint +function returns the integer nearest to its argument +.Fa x +according to the current rounding mode. +.Pp +The +.Fn llrint , +.Fn llrintf , +and +.Fn lrintf +functions differ from +.Fn lrint +only in their input and output types. +.Sh RETURN VALUES +The +.Nm llrint , +.Nm llrintf , +.Nm lrint , +and +.Nm lrintf +functions return the integer nearest to their argument +.Fa x +according to the current rounding mode. +If the rounded result is too large to be represented as a +.Vt long long +or +.Vt long +value, respectively, +.\" an invalid exception is raised and +the return value is undefined. +.\" Otherwise, if +.\" .Fa x +.\" is not an integer, +.\" .Fn lrint +.\" raises an inexact exception. +.\" If +.\" .Fa x +.\" is too large, a range error may occur. +.Sh SEE ALSO +.\" .Xr lround 3 , +.Xr math 3 , +.Xr rint 3 , +.Xr round 3 +.Sh STANDARDS +The +.Fn llrint , +.Fn llrintf , +.Fn lrint , +and +.Fn lrintf +functions conform to +.St -isoC-99 . diff --git a/lib/nbsd_libm/man/math.3 b/lib/nbsd_libm/man/math.3 new file mode 100644 index 000000000..90f431367 --- /dev/null +++ b/lib/nbsd_libm/man/math.3 @@ -0,0 +1,682 @@ +.\" $NetBSD: math.3,v 1.22 2007/02/26 12:10:56 drochner Exp $ +.\" +.\" Copyright (c) 1985 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)math.3 6.10 (Berkeley) 5/6/91 +.\" +.TH MATH 3 "February 23, 2007" +.UC 4 +.ds up \fIulp\fR +.ds nn \fINaN\fR +.de If +.if n \\ +\\$1Infinity\\$2 +.if t \\ +\\$1\\(if\\$2 +.. +.SH NAME +math \- introduction to mathematical library functions +.SH DESCRIPTION +These functions constitute the C math library, +.I libm. +The link editor searches this library under the \*(lq\-lm\*(rq option. +Declarations for these functions may be obtained from the include file +.RI \*[Lt] math.h \*[Gt]. +.\" The Fortran math library is described in ``man 3f intro''. +.SH "LIST OF FUNCTIONS" +.sp 2 +.nf +.ta \w'copysign'u+2n +\w'lgamma.3'u+10n +\w'inverse trigonometric func'u +\fIName\fP \fIAppears on Page\fP \fIDescription\fP \fIError Bound (ULPs)\fP +.ta \w'copysign'u+4n +\w'lgamma.3'u+4n +\w'inverse trigonometric function'u+6nC +.sp 5p +acos acos.3 inverse trigonometric function 3 +acosh acosh.3 inverse hyperbolic function 3 +asin asin.3 inverse trigonometric function 3 +asinh asinh.3 inverse hyperbolic function 3 +atan atan.3 inverse trigonometric function 1 +atanh atanh.3 inverse hyperbolic function 3 +atan2 atan2.3 inverse trigonometric function 2 +cbrt sqrt.3 cube root 1 +ceil ceil.3 integer no less than 0 +copysign ieee.3 copy sign bit 0 +cos cos.3 trigonometric function 1 +cosh cosh.3 hyperbolic function 3 +erf erf.3 error function ??? +erfc erf.3 complementary error function ??? +exp exp.3 exponential 1 +expm1 exp.3 exp(x)\-1 1 +fabs fabs.3 absolute value 0 +finite ieee.3 test for finity 0 +floor floor.3 integer no greater than 0 +fmod fmod.3 remainder ??? +hypot hypot.3 Euclidean distance 1 +ilogb ieee.3 exponent extraction 0 +isinf isinf.3 test for infinity 0 +isnan isnan.3 test for not-a-number 0 +j0 j0.3 Bessel function ??? +j1 j0.3 Bessel function ??? +jn j0.3 Bessel function ??? +lgamma lgamma.3 log gamma function ??? +log exp.3 natural logarithm 1 +log10 exp.3 logarithm to base 10 3 +log1p exp.3 log(1+x) 1 +nan nan.3 return quiet \*(nn 0 +nextafter ieee.3 next representable number 0 +pow exp.3 exponential x**y 60\-500 +remainder ieee.3 remainder 0 +rint rint.3 round to nearest integer 0 +scalbn ieee.3 exponent adjustment 0 +sin sin.3 trigonometric function 1 +sinh sinh.3 hyperbolic function 3 +sqrt sqrt.3 square root 1 +tan tan.3 trigonometric function 3 +tanh tanh.3 hyperbolic function 3 +trunc trunc.3 nearest integral value 3 +y0 j0.3 Bessel function ??? +y1 j0.3 Bessel function ??? +yn j0.3 Bessel function ??? +.ta +.fi +.SH "LIST OF DEFINED VALUES" +.sp 2 +.nf +.ta \w'M_2_SQRTPI'u+2n +\w'1.12837916709551257390'u+4n +\w'2/sqrt(pi)'u+6nC +\fIName\fP \fIValue\fP \fIDescription\fP +.ta \w'M_2_SQRTPI'u+2n +\w'1.12837916709551257390'u+4n +\w'2/sqrt(pi)'u+6nC +.sp 3p +M_E 2.7182818284590452354 e +M_LOG2E 1.4426950408889634074 log 2e +M_LOG10E 0.43429448190325182765 log 10e +M_LN2 0.69314718055994530942 log e2 +M_LN10 2.30258509299404568402 log e10 +M_PI 3.14159265358979323846 pi +M_PI_2 1.57079632679489661923 pi/2 +M_PI_4 0.78539816339744830962 pi/4 +M_1_PI 0.31830988618379067154 1/pi +M_2_PI 0.63661977236758134308 2/pi +M_2_SQRTPI 1.12837916709551257390 2/sqrt(pi) +M_SQRT2 1.41421356237309504880 sqrt(2) +M_SQRT1_2 0.70710678118654752440 1/sqrt(2) +.ta +.fi +.SH NOTES +In 4.3 BSD, distributed from the University of California +in late 1985, most of the foregoing functions come in two +versions, one for the double\-precision "D" format in the +DEC VAX\-11 family of computers, another for double\-precision +arithmetic conforming to the IEEE Standard 754 for Binary +Floating\-Point Arithmetic. +The two versions behave very +similarly, as should be expected from programs more accurate +and robust than was the norm when UNIX was born. +For instance, the programs are accurate to within the numbers +of \*(ups tabulated above; an \*(up is one \fIU\fRnit in the \fIL\fRast +\fIP\fRlace. +And the programs have been cured of anomalies that +afflicted the older math library \fIlibm\fR in which incidents like +the following had been reported: +.RS +sqrt(\-1.0) = 0.0 and log(\-1.0) = \-1.7e38. +.br +cos(1.0e\-11) \*[Gt] cos(0.0) \*[Gt] 1.0. +.br +pow(x,1.0) +.if n \ +!= +.if t \ +\(!= +x when x = 2.0, 3.0, 4.0, ..., 9.0. +.br +pow(\-1.0,1.0e10) trapped on Integer Overflow. +.br +sqrt(1.0e30) and sqrt(1.0e\-30) were very slow. +.RE +However the two versions do differ in ways that have to be +explained, to which end the following notes are provided. +.PP +\fBDEC VAX\-11 D_floating\-point:\fR +.PP +This is the format for which the original math library \fIlibm\fR +was developed, and to which this manual is still principally dedicated. +It is \fIthe\fR double\-precision format for the PDP\-11 +and the earlier VAX\-11 machines; VAX\-11s after 1983 were +provided with an optional "G" format closer to the IEEE +double\-precision format. +The earlier DEC MicroVAXs have no D format, only G double\-precision. +(Why? +Why not?) +.PP +Properties of D_floating\-point: +.RS +Wordsize: 64 bits, 8 bytes. +Radix: Binary. +.br +Precision: 56 +.if n \ +sig. +.if t \ +significant +bits, roughly like 17 +.if n \ +sig. +.if t \ +significant +decimals. +.RS +If x and x' are consecutive positive D_floating\-point +numbers (they differ by 1 \*(up), then +.br +1.3e\-17 \*[Lt] 0.5**56 \*[Lt] (x'\-x)/x \*[Le] 0.5**55 \*[Lt] 2.8e\-17. +.RE +.nf +.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**127'u+1n +Range: Overflow threshold = 2.0**127 = 1.7e38. + Underflow threshold = 0.5**128 = 2.9e\-39. + NOTE: THIS RANGE IS COMPARATIVELY NARROW. +.ta +.fi +.RS +Overflow customarily stops computation. +.br +Underflow is customarily flushed quietly to zero. +.br +CAUTION: +.RS +It is possible to have x +.if n \ +!= +.if t \ +\(!= +y and yet +x\-y = 0 because of underflow. +Similarly x \*[Gt] y \*[Gt] 0 cannot prevent either x\(**y = 0 +or y/x = 0 from happening without warning. +.RE +.RE +Zero is represented ambiguously. +.RS +Although 2**55 different representations of zero are accepted by +the hardware, only the obvious representation is ever produced. +There is no \-0 on a VAX. +.RE +.If +is not part of the VAX architecture. +.br +Reserved operands: +.RS +of the 2**55 that the hardware +recognizes, only one of them is ever produced. +Any floating\-point operation upon a reserved +operand, even a MOVF or MOVD, customarily stops +computation, so they are not much used. +.RE +Exceptions: +.RS +Divisions by zero and operations that +overflow are invalid operations that customarily +stop computation or, in earlier machines, produce +reserved operands that will stop computation. +.RE +Rounding: +.RS +Every rational operation (+, \-, \(**, /) on a +VAX (but not necessarily on a PDP\-11), if not an +over/underflow nor division by zero, is rounded to +within half an \*(up, and when the rounding error is +exactly half an \*(up then rounding is away from 0. +.RE +.RE +.PP +Except for its narrow range, D_floating\-point is one of the +better computer arithmetics designed in the 1960's. +Its properties are reflected fairly faithfully in the elementary +functions for a VAX distributed in 4.3 BSD. +They over/underflow only if their results have to lie out of range +or very nearly so, and then they behave much as any rational +arithmetic operation that over/underflowed would behave. +Similarly, expressions like log(0) and atanh(1) behave +like 1/0; and sqrt(\-3) and acos(3) behave like 0/0; +they all produce reserved operands and/or stop computation! +The situation is described in more detail in manual pages. +.RS +.ll -0.5i +\fIThis response seems excessively punitive, so it is destined +to be replaced at some time in the foreseeable future by a +more flexible but still uniform scheme being developed to +handle all floating\-point arithmetic exceptions neatly.\fR +.ll +0.5i +.RE +.PP +How do the functions in 4.3 BSD's new \fIlibm\fR for UNIX +compare with their counterparts in DEC's VAX/VMS library? +Some of the VMS functions are a little faster, some are +a little more accurate, some are more puritanical about +exceptions (like pow(0.0,0.0) and atan2(0.0,0.0)), +and most occupy much more memory than their counterparts in +\fIlibm\fR. +The VMS codes interpolate in large table to achieve +speed and accuracy; the \fIlibm\fR codes use tricky formulas +compact enough that all of them may some day fit into a ROM. +.PP +More important, DEC regards the VMS codes as proprietary +and guards them zealously against unauthorized use. +But the \fIlibm\fR codes in 4.3 BSD are intended for the public domain; +they may be copied freely provided their provenance is always +acknowledged, and provided users assist the authors in their +researches by reporting experience with the codes. +Therefore no user of UNIX on a machine whose arithmetic resembles +VAX D_floating\-point need use anything worse than the new \fIlibm\fR. +.PP +\fBIEEE STANDARD 754 Floating\-Point Arithmetic:\fR +.PP +This standard is on its way to becoming more widely adopted +than any other design for computer arithmetic. +VLSI chips that conform to some version of that standard have been +produced by a host of manufacturers, among them ... +.nf +.ta 0.5i +\w'Intel i8070, i80287'u+6n + Intel i8087, i80287 National Semiconductor 32081 + Motorola 68881 Weitek WTL-1032, ... , -1165 + Zilog Z8070 Western Electric (AT\*[Am]T) WE32106. +.ta +.fi +Other implementations range from software, done thoroughly +in the Apple Macintosh, through VLSI in the Hewlett\-Packard +9000 series, to the ELXSI 6400 running ECL at 3 Megaflops. +Several other companies have adopted the formats +of IEEE 754 without, alas, adhering to the standard's way +of handling rounding and exceptions like over/underflow. +The DEC VAX G_floating\-point format is very similar to the IEEE +754 Double format, so similar that the C programs for the +IEEE versions of most of the elementary functions listed +above could easily be converted to run on a MicroVAX, though +nobody has volunteered to do that yet. +.PP +The codes in 4.3 BSD's \fIlibm\fR for machines that conform to +IEEE 754 are intended primarily for the National Semi. 32081 +and WTL 1164/65. +To use these codes with the Intel or Zilog +chips, or with the Apple Macintosh or ELXSI 6400, is to +forego the use of better codes provided (perhaps freely) by +those companies and designed by some of the authors of the +codes above. +Except for \fIatan\fR, \fIcbrt\fR, \fIerf\fR, +\fIerfc\fR, \fIhypot\fR, \fIj0\-jn\fR, \fIlgamma\fR, \fIpow\fR +and \fIy0\-yn\fR, +the Motorola 68881 has all the functions in \fIlibm\fR on chip, +and faster and more accurate; +it, Apple, the i8087, Z8070 and WE32106 all use 64 +.if n \ +sig. +.if t \ +significant +bits. +The main virtue of 4.3 BSD's +\fIlibm\fR codes is that they are intended for the public domain; +they may be copied freely provided their provenance is always +acknowledged, and provided users assist the authors in their +researches by reporting experience with the codes. +Therefore no user of UNIX on a machine that conforms to +IEEE 754 need use anything worse than the new \fIlibm\fR. +.PP +Properties of IEEE 754 Double\-Precision: +.RS +Wordsize: 64 bits, 8 bytes. +Radix: Binary. +.br +Precision: 53 +.if n \ +sig. +.if t \ +significant +bits, roughly like 16 +.if n \ +sig. +.if t \ +significant +decimals. +.RS +If x and x' are consecutive positive Double\-Precision +numbers (they differ by 1 \*(up), then +.br +1.1e\-16 \*[Lt] 0.5**53 \*[Lt] (x'\-x)/x \*[Le] 0.5**52 \*[Lt] 2.3e\-16. +.RE +.nf +.ta \w'Range:'u+1n +\w'Underflow threshold'u+1n +\w'= 2.0**1024'u+1n +Range: Overflow threshold = 2.0**1024 = 1.8e308 + Underflow threshold = 0.5**1022 = 2.2e\-308 +.ta +.fi +.RS +Overflow goes by default to a signed +.If "" . +.br +Underflow is \fIGradual,\fR rounding to the nearest +integer multiple of 0.5**1074 = 4.9e\-324. +.RE +Zero is represented ambiguously as +0 or \-0. +.RS +Its sign transforms correctly through multiplication or +division, and is preserved by addition of zeros +with like signs; but x\-x yields +0 for every +finite x. +The only operations that reveal zero's +sign are division by zero and copysign(x,\(+-0). +In particular, comparison (x \*[Gt] y, x \*[Ge] y, etc.) +cannot be affected by the sign of zero; but if +finite x = y then +.If +\&= 1/(x\-y) +.if n \ +!= +.if t \ +\(!= +\-1/(y\-x) = +.If \- . +.RE +.If +is signed. +.RS +it persists when added to itself +or to any finite number. +Its sign transforms +correctly through multiplication and division, and +.If (finite)/\(+- \0=\0\(+-0 +(nonzero)/0 = +.If \(+- . +But +.if n \ +Infinity\-Infinity, Infinity\(**0 and Infinity/Infinity +.if t \ +\(if\-\(if, \(if\(**0 and \(if/\(if +are, like 0/0 and sqrt(\-3), +invalid operations that produce \*(nn. ... +.RE +Reserved operands: +.RS +there are 2**53\-2 of them, all +called \*(nn (\fIN\fRot \fIa N\fRumber). +Some, called Signaling \*(nns, trap any floating\-point operation +performed upon them; they are used to mark missing +or uninitialized values, or nonexistent elements of arrays. +The rest are Quiet \*(nns; they are +the default results of Invalid Operations, and +propagate through subsequent arithmetic operations. +If x +.if n \ +!= +.if t \ +\(!= +x then x is \*(nn; every other predicate +(x \*[Gt] y, x = y, x \*[Lt] y, ...) is FALSE if \*(nn is involved. +.br +NOTE: Trichotomy is violated by \*(nn. +.RS +Besides being FALSE, predicates that entail ordered +comparison, rather than mere (in)equality, +signal Invalid Operation when \*(nn is involved. +.RE +.RE +Rounding: +.RS +Every algebraic operation (+, \-, \(**, /, +.if n \ +sqrt) +.if t \ +\(sr) +is rounded by default to within half an \*(up, and +when the rounding error is exactly half an \*(up then +the rounded value's least significant bit is zero. +This kind of rounding is usually the best kind, +sometimes provably so; for instance, for every +x = 1.0, 2.0, 3.0, 4.0, ..., 2.0**52, we find +(x/3.0)\(**3.0 == x and (x/10.0)\(**10.0 == x and ... +despite that both the quotients and the products +have been rounded. +Only rounding like IEEE 754 can do that. +But no single kind of rounding can be +proved best for every circumstance, so IEEE 754 +provides rounding towards zero or towards +.If + +or towards +.If \- +at the programmer's option. +And the same kinds of rounding are specified for +Binary\-Decimal Conversions, at least for magnitudes +between roughly 1.0e\-10 and 1.0e37. +.RE +Exceptions: +.RS +IEEE 754 recognizes five kinds of floating\-point exceptions, +listed below in declining order of probable importance. +.RS +.nf +.ta \w'Invalid Operation'u+6n +\w'Gradual Underflow'u+2n +Exception Default Result +.tc \(ru + +.tc +Invalid Operation \*(nn, or FALSE +.if n \{\ +Overflow \(+-Infinity +Divide by Zero \(+-Infinity \} +.if t \{\ +Overflow \(+-\(if +Divide by Zero \(+-\(if \} +Underflow Gradual Underflow +Inexact Rounded value +.ta +.fi +.RE +NOTE: An Exception is not an Error unless handled badly. +What makes a class of exceptions exceptional +is that no single default response can be satisfactory +in every instance. +On the other hand, if a default +response will serve most instances satisfactorily, +the unsatisfactory instances cannot justify aborting +computation every time the exception occurs. +.RE +.PP +For each kind of floating\-point exception, IEEE 754 +provides a Flag that is raised each time its exception +is signaled, and stays raised until the program resets it. +Programs may also test, save and restore a flag. +Thus, IEEE 754 provides three ways by which programs +may cope with exceptions for which the default result +might be unsatisfactory: +.IP 1) \w'\0\0\0\0'u +Test for a condition that might cause an exception +later, and branch to avoid the exception. +.IP 2) \w'\0\0\0\0'u +Test a flag to see whether an exception has occurred +since the program last reset its flag. +.IP 3) \w'\0\0\0\0'u +Test a result to see whether it is a value that only +an exception could have produced. +.RS +CAUTION: The only reliable ways to discover +whether Underflow has occurred are to test whether +products or quotients lie closer to zero than the +underflow threshold, or to test the Underflow flag. +(Sums and differences cannot underflow in +IEEE 754; if x +.if n \ +!= +.if t \ +\(!= +y then x\-y is correct to +full precision and certainly nonzero regardless of +how tiny it may be.) +Products and quotients that +underflow gradually can lose accuracy gradually +without vanishing, so comparing them with zero +(as one might on a VAX) will not reveal the loss. +Fortunately, if a gradually underflowed value is +destined to be added to something bigger than the +underflow threshold, as is almost always the case, +digits lost to gradual underflow will not be missed +because they would have been rounded off anyway. +So gradual underflows are usually \fIprovably\fR ignorable. +The same cannot be said of underflows flushed to 0. +.RE +.PP +At the option of an implementor conforming to IEEE 754, +other ways to cope with exceptions may be provided: +.IP 4) \w'\0\0\0\0'u +ABORT. +This mechanism classifies an exception in +advance as an incident to be handled by means +traditionally associated with error\-handling +statements like "ON ERROR GO TO ...". +Different languages offer different forms of this statement, +but most share the following characteristics: +.IP \(em \w'\0\0\0\0'u +No means is provided to substitute a value for +the offending operation's result and resume +computation from what may be the middle of an expression. +An exceptional result is abandoned. +.IP \(em \w'\0\0\0\0'u +In a subprogram that lacks an error\-handling +statement, an exception causes the subprogram to +abort within whatever program called it, and so +on back up the chain of calling subprograms until +an error\-handling statement is encountered or the +whole task is aborted and memory is dumped. +.IP 5) \w'\0\0\0\0'u +STOP. +This mechanism, requiring an interactive +debugging environment, is more for the programmer +than the program. +It classifies an exception in +advance as a symptom of a programmer's error; the +exception suspends execution as near as it can to +the offending operation so that the programmer can +look around to see how it happened. +Quite often +the first several exceptions turn out to be quite +unexceptionable, so the programmer ought ideally +to be able to resume execution after each one as if +execution had not been stopped. +.IP 6) \w'\0\0\0\0'u +\&... Other ways lie beyond the scope of this document. +.RE +.PP +The crucial problem for exception handling is the problem of +Scope, and the problem's solution is understood, but not +enough manpower was available to implement it fully in time +to be distributed in 4.3 BSD's \fIlibm\fR. +Ideally, each elementary function should act +as if it were indivisible, or atomic, in the sense that ... +.IP i) \w'iii)'u+2n +No exception should be signaled that is not deserved by +the data supplied to that function. +.IP ii) \w'iii)'u+2n +Any exception signaled should be identified with that +function rather than with one of its subroutines. +.IP iii) \w'iii)'u+2n +The internal behavior of an atomic function should not +be disrupted when a calling program changes from +one to another of the five or so ways of handling +exceptions listed above, although the definition +of the function may be correlated intentionally +with exception handling. +.PP +Ideally, every programmer should be able \fIconveniently\fR to +turn a debugged subprogram into one that appears atomic to +its users. +But simulating all three characteristics of an +atomic function is still a tedious affair, entailing hosts +of tests and saves\-restores; work is under way to ameliorate +the inconvenience. +.PP +Meanwhile, the functions in \fIlibm\fR are only approximately atomic. +They signal no inappropriate exception except possibly ... +.RS +Over/Underflow +.RS +when a result, if properly computed, might have lain barely within range, and +.RE +Inexact in \fIcbrt\fR, \fIhypot\fR, \fIlog10\fR and \fIpow\fR +.RS +when it happens to be exact, thanks to fortuitous cancellation of errors. +.RE +.RE +Otherwise, ... +.RS +Invalid Operation is signaled only when +.RS +any result but \*(nn would probably be misleading. +.RE +Overflow is signaled only when +.RS +the exact result would be finite but beyond the overflow threshold. +.RE +Divide\-by\-Zero is signaled only when +.RS +a function takes exactly infinite values at finite operands. +.RE +Underflow is signaled only when +.RS +the exact result would be nonzero but tinier than the underflow threshold. +.RE +Inexact is signaled only when +.RS +greater range or precision would be needed to represent the exact result. +.RE +.RE +.\" .Sh FILES +.\" .Bl -tag -width /usr/lib/libm_p.a -compact +.\" .It Pa /usr/lib/libm.a +.\" the static math library +.\" .It Pa /usr/lib/libm.so +.\" the dynamic math library +.\" .It Pa /usr/lib/libm_p.a +.\" the static math library compiled for profiling +.\" .El +.SH SEE ALSO +An explanation of IEEE 754 and its proposed extension p854 +was published in the IEEE magazine MICRO in August 1984 under +the title "A Proposed Radix\- and Word\-length\-independent +Standard for Floating\-point Arithmetic" by W. J. Cody et al. +The manuals for Pascal, C and BASIC on the Apple Macintosh +document the features of IEEE 754 pretty well. +Articles in the IEEE magazine COMPUTER vol. 14 no. 3 (Mar. 1981), +and in the ACM SIGNUM Newsletter Special Issue of +Oct. 1979, may be helpful although they pertain to +superseded drafts of the standard. +.SH BUGS +When signals are appropriate, they are emitted by certain +operations within the codes, so a subroutine\-trace may be +needed to identify the function with its signal in case +method 5) above is in use. +And the codes all take the +IEEE 754 defaults for granted; this means that a decision to +trap all divisions by zero could disrupt a code that would +otherwise get correct results despite division by zero. diff --git a/lib/nbsd_libm/man/modf.3 b/lib/nbsd_libm/man/modf.3 new file mode 100644 index 000000000..6e362964d --- /dev/null +++ b/lib/nbsd_libm/man/modf.3 @@ -0,0 +1,74 @@ +.\" $NetBSD: modf.3,v 1.1 2006/07/03 16:03:56 drochner Exp $ +.\" +.\" Copyright (c) 1991, 1993 +.\" The Regents of the University of California. All rights reserved. +.\" +.\" This code is derived from software contributed to Berkeley by +.\" the American National Standards Committee X3, on Information +.\" Processing Systems. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" @(#)modf.3 8.1 (Berkeley) 6/4/93 +.\" +.Dd March 21, 2006 +.Dt MODF 3 +.Os +.Sh NAME +.Nm modf +.Nd extract signed integral and fractional values from floating-point number +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn modf "double value" "double *iptr" +.Ft float +.Fn modff "float value" "float *iptr" +.Sh DESCRIPTION +The +.Fn modf +function breaks the argument +.Fa value +into integral and fractional parts, each of which has the +same sign as the argument. +It stores the integral part as a +.Em double +in the object pointed to by +.Fa iptr . +.Sh RETURN VALUES +The +.Fn modf +function returns the signed fractional part of +.Fa value . +.Sh SEE ALSO +.Xr frexp 3 , +.Xr ldexp 3 , +.Xr math 3 +.Sh STANDARDS +The +.Fn modf +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/rint.3 b/lib/nbsd_libm/man/rint.3 new file mode 100644 index 000000000..5bd693b92 --- /dev/null +++ b/lib/nbsd_libm/man/rint.3 @@ -0,0 +1,64 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)rint.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: rint.3,v 1.12 2003/08/07 16:44:48 agc Exp $ +.\" +.Dd March 10, 1994 +.Dt RINT 3 +.Os +.Sh NAME +.Nm rint , +.Nm rintf +.Nd round to integral value in floating-point format +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn rint "double x" +.Ft float +.Fn rintf "float x" +.Sh DESCRIPTION +The +.Fn rint +function returns the integral value (represented as a double precision number) +nearest to +.Fa x +according to the prevailing rounding mode. +.Sh SEE ALSO +.Xr abs 3 , +.Xr ceil 3 , +.Xr fabs 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 +.Sh HISTORY +A +.Fn rint +function appeared in +.At v6 . diff --git a/lib/nbsd_libm/man/round.3 b/lib/nbsd_libm/man/round.3 new file mode 100644 index 000000000..9400d82af --- /dev/null +++ b/lib/nbsd_libm/man/round.3 @@ -0,0 +1,76 @@ +.\" $NetBSD: round.3,v 1.5 2006/03/25 20:01:36 uwe Exp $ +.\" +.\" Copyright (c) 2003, Steven G. Kargl +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" $FreeBSD: src/lib/msun/man/round.3,v 1.2 2004/06/20 09:27:17 das Exp $ +.\" +.Dd July 15, 2004 +.Dt ROUND 3 +.Os +.Sh NAME +.Nm round , +.Nm roundf +.Nd round to nearest integral value +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn round "double x" +.Ft float +.Fn roundf "float x" +.Sh DESCRIPTION +The +.Fn round +and +.Fn roundf +functions return the nearest integral value to +.Fa x ; +if +.Fa x +lies halfway between two integral values, then these +functions return the integral value with the larger +absolute value (i.e., they round away from zero). +.Sh SEE ALSO +.Xr ceil 3 , +.Xr floor 3 , +.Xr ieee 3 , +.Xr math 3 , +.Xr rint 3 , +.Xr trunc 3 +.Sh STANDARDS +The +.Fn round +and +.Fn roundf +functions conform to +.St -isoC-99 . +.Sh HISTORY +The +.Fn round +and +.Fn roundf +functions appeared in +.Nx 2.0 . diff --git a/lib/nbsd_libm/man/sin.3 b/lib/nbsd_libm/man/sin.3 new file mode 100644 index 000000000..dd37a33b6 --- /dev/null +++ b/lib/nbsd_libm/man/sin.3 @@ -0,0 +1,73 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)sin.3 6.7 (Berkeley) 4/19/91 +.\" $NetBSD: sin.3,v 1.14 2003/08/07 16:44:49 agc Exp $ +.\" +.Dd April 19, 1991 +.Dt SIN 3 +.Os +.Sh NAME +.Nm sin , +.Nm sinf +.Nd sine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn sin "double x" +.Ft float +.Fn sinf "float x" +.Sh DESCRIPTION +The +.Fn sin +function computes the sine of +.Fa x +(measured in radians). +A large magnitude argument may yield a result with little +or no significance. +.Sh RETURN VALUES +The +.Fn sin +function returns the sine value. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sinh 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn sin +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/sinh.3 b/lib/nbsd_libm/man/sinh.3 new file mode 100644 index 000000000..1059668ba --- /dev/null +++ b/lib/nbsd_libm/man/sinh.3 @@ -0,0 +1,75 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)sinh.3 6.6 (Berkeley) 4/19/91 +.\" $NetBSD: sinh.3,v 1.14 2003/08/07 16:44:49 agc Exp $ +.Dd April 19, 1991 +.Dt SINH 3 +.Os +.Sh NAME +.Nm sinh , +.Nm sinhf +.Nd hyperbolic sine function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn sinh "double x" +.Ft float +.Fn sinhf "float x" +.Sh DESCRIPTION +The +.Fn sinh +function computes the hyperbolic sine of +.Fa x . +.Sh RETURN VALUES +The +.Fn sinh +function returns the hyperbolic sine value unless +the magnitude of +.Fa x +is too large; in this event, the global variable +.Va errno +is set to +.Er ERANGE . +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr tan 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn sinh +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/sqrt.3 b/lib/nbsd_libm/man/sqrt.3 new file mode 100644 index 000000000..8f35a193e --- /dev/null +++ b/lib/nbsd_libm/man/sqrt.3 @@ -0,0 +1,91 @@ +.\" Copyright (c) 1985, 1991 Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)sqrt.3 6.4 (Berkeley) 5/6/91 +.\" $NetBSD: sqrt.3,v 1.13 2003/08/07 16:44:49 agc Exp $ +.\" +.Dd May 6, 1991 +.Dt SQRT 3 +.Os +.Sh NAME +.Nm cbrt , +.Nm cbrtf , +.Nm sqrt , +.Nm sqrtf +.Nd cube root and square root functions +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn cbrt "double x" +.Ft float +.Fn cbrtf "float x" +.Ft double +.Fn sqrt "double x" +.Ft float +.Fn sqrtf "float x" +.Sh DESCRIPTION +The +.Fn cbrt +and +.Fn cbrtf +functions compute +the cube root of +.Ar x . +.Pp +The +.Fn sqrt +and +.Fn sqrtf +functions compute +the non-negative square root of x. +.Sh RETURN VALUES +If x is negative, +.Fn sqrt "x" +and +.Fn sqrtf "x" +.\" POSIX_MODE +set the global variable +.Va errno +to EDOM. +.\" SYSV_MODE +.\" call +.\" .Xr matherr 3 . +.Sh SEE ALSO +.Xr math 3 +.\" .Xr matherr 3 +.Sh STANDARDS +The +.Fn sqrt +function conforms to +.St -ansiC . +.Sh HISTORY +The +.Fn cbrt +function appeared in +.Bx 4.3 . diff --git a/lib/nbsd_libm/man/tan.3 b/lib/nbsd_libm/man/tan.3 new file mode 100644 index 000000000..05afbf007 --- /dev/null +++ b/lib/nbsd_libm/man/tan.3 @@ -0,0 +1,77 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)tan.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: tan.3,v 1.13 2003/08/07 16:44:49 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt TAN 3 +.Os +.Sh NAME +.Nm tan , +.Nm tanf +.Nd tangent function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn tan "double x" +.Ft float +.Fn tanf "float x" +.Sh DESCRIPTION +The +.Fn tan +and +.Fn tanf +functions compute the tangent of +.Fa x +(measured in radians). +A large magnitude argument may yield a result +with little or no significance. +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn tan +function returns the tangent value. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tanh 3 +.Sh STANDARDS +The +.Fn tan +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/tanh.3 b/lib/nbsd_libm/man/tanh.3 new file mode 100644 index 000000000..b8a2d1df1 --- /dev/null +++ b/lib/nbsd_libm/man/tanh.3 @@ -0,0 +1,74 @@ +.\" Copyright (c) 1991 The Regents of the University of California. +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" 3. Neither the name of the University nor the names of its contributors +.\" may be used to endorse or promote products derived from this software +.\" without specific prior written permission. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" from: @(#)tanh.3 5.1 (Berkeley) 5/2/91 +.\" $NetBSD: tanh.3,v 1.12 2003/08/07 16:44:49 agc Exp $ +.\" +.Dd May 2, 1991 +.Dt TANH 3 +.Os +.Sh NAME +.Nm tanh , +.Nm tanhf +.Nd hyperbolic tangent function +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn tanh "double x" +.Ft float +.Fn tanhf "float x" +.Sh DESCRIPTION +The +.Fn tanh +and +.Fn tanhf +functions compute the hyperbolic tangent of +.Fa x . +For a discussion of error due to roundoff, see +.Xr math 3 . +.Sh RETURN VALUES +The +.Fn tanh +function returns the hyperbolic tangent value. +.Sh SEE ALSO +.Xr acos 3 , +.Xr asin 3 , +.Xr atan 3 , +.Xr atan2 3 , +.Xr cos 3 , +.Xr cosh 3 , +.Xr math 3 , +.Xr sin 3 , +.Xr sinh 3 , +.Xr tan 3 +.Sh STANDARDS +The +.Fn tanh +function conforms to +.St -ansiC . diff --git a/lib/nbsd_libm/man/trunc.3 b/lib/nbsd_libm/man/trunc.3 new file mode 100644 index 000000000..19f6c2ce7 --- /dev/null +++ b/lib/nbsd_libm/man/trunc.3 @@ -0,0 +1,79 @@ +.\" $NetBSD: trunc.3,v 1.5 2006/04/04 20:26:33 wiz Exp $ +.\" +.\" Copyright (c) 2004, 2005 David Schultz +.\" All rights reserved. +.\" +.\" Redistribution and use in source and binary forms, with or without +.\" modification, are permitted provided that the following conditions +.\" are met: +.\" 1. Redistributions of source code must retain the above copyright +.\" notice, this list of conditions and the following disclaimer. +.\" 2. Redistributions in binary form must reproduce the above copyright +.\" notice, this list of conditions and the following disclaimer in the +.\" documentation and/or other materials provided with the distribution. +.\" +.\" THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND +.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE +.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE +.\" ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE +.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL +.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS +.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) +.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT +.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY +.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF +.\" SUCH DAMAGE. +.\" +.\" $FreeBSD: src/lib/msun/man/trunc.3,v 1.3 2005/06/15 19:04:04 ru Exp $ +.\" +.Dd March 31, 2006 +.Dt TRUNC 3 +.Os +.Sh NAME +.Nm trunc , +.Nm truncf +.\" .Nm truncl +.Nd "nearest integral value with magnitude less than or equal to |x|" +.Sh LIBRARY +.Lb libm +.Sh SYNOPSIS +.In math.h +.Ft double +.Fn trunc "double x" +.Ft float +.Fn truncf "float x" +.\" .Ft "long double" +.\" .Fn truncl "long double x" +.Sh DESCRIPTION +The +.Fn trunc +and +.Fn truncf +.\" .Fn truncl +functions return the nearest integral value with magnitude less than +or equal to +.Pf | Fa x Ns | . +They are equivalent to +.Fn rint +and +.Fn rintf +.\" .Fn rintl +respectively, in the +.Dv FP_RZ +rounding mode. +.Sh SEE ALSO +.Xr ceil 3 , +.Xr floor 3 , +.Xr fpsetround 3 , +.Xr math 3 , +.Xr nextafter 3 , +.Xr rint 3 , +.Xr round 3 +.Sh STANDARDS +The +.Fn trunc +and +.Fn truncf +.\" .Fn truncl +functions conform to +.St -isoC-99 . diff --git a/lib/nbsd_libm/noieee_src/mathimpl.h b/lib/nbsd_libm/noieee_src/mathimpl.h new file mode 100644 index 000000000..92e578fab --- /dev/null +++ b/lib/nbsd_libm/noieee_src/mathimpl.h @@ -0,0 +1,114 @@ +/* $NetBSD: mathimpl.h,v 1.9 2008/05/01 15:33:15 christos Exp $ */ +/* + * Copyright (c) 1988, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * @(#)mathimpl.h 8.1 (Berkeley) 6/4/93 + */ +#ifndef _NOIEEE_SRC_MATHIMPL_H_ +#define _NOIEEE_SRC_MATHIMPL_H_ + +#include +#include +#include + +#if defined(__vax__) || defined(tahoe) + +/* Deal with different ways to concatenate in cpp */ +#define cat3(a,b,c) a ## b ## c + +/* Deal with vax/tahoe byte order issues */ +# ifdef __vax__ +# define cat3t(a,b,c) cat3(a,b,c) +# else +# define cat3t(a,b,c) cat3(a,c,b) +# endif + +# define vccast(name) (cat3(__,name,x).d) + + /* + * Define a constant to high precision on a Vax or Tahoe. + * + * Args are the name to define, the decimal floating point value, + * four 16-bit chunks of the float value in hex + * (because the vax and tahoe differ in float format!), the power + * of 2 of the hex-float exponent, and the hex-float mantissa. + * Most of these arguments are not used at compile time; they are + * used in a post-check to make sure the constants were compiled + * correctly. + * + * People who want to use the constant will have to do their own + * #define foo vccast(foo) + * since CPP cannot do this for them from inside another macro (sigh). + * We define "vccast" if this needs doing. + */ +#ifdef _LIBM_DECLARE +# define vc(name, value, x1,x2,x3,x4, bexp, xval) \ + const union { uint32_t l[2]; double d; } cat3(__,name,x) = { \ + .l = { [0] = cat3t(0x,x1,x2), [1] = cat3t(0x,x3,x4) } }; +#elif defined(_LIBM_STATIC) +# define vc(name, value, x1,x2,x3,x4, bexp, xval) \ + static const union { uint32_t l[2]; double d; } cat3(__,name,x) = { \ + .l = { [0] = cat3t(0x,x1,x2), [1] = cat3t(0x,x3,x4) } }; +#else +# define vc(name, value, x1,x2,x3,x4, bexp, xval) \ + extern const union { uint32_t l[2]; double d; } cat3(__,name,x); +#endif +# define ic(name, value, bexp, xval) + +#else /* __vax__ or tahoe */ + + /* Hooray, we have an IEEE machine */ +# undef vccast +# define vc(name, value, x1,x2,x3,x4, bexp, xval) + +#ifdef _LIBM_DECLARE +# define ic(name, value, bexp, xval) \ + const double __CONCAT(__,name) = value; +#elif _LIBM_STATIC +# define ic(name, value, bexp, xval) \ + static const double __CONCAT(__,name) = value; +#else +# define ic(name, value, bexp, xval) \ + extern const double __CONCAT(__,name); +#endif + +#endif /* defined(__vax__)||defined(tahoe) */ + + +/* + * Functions internal to the math package, yet not static. + */ +extern double __exp__E(double, double); +extern double __log__L(double); +extern int infnan(int); + +struct Double {double a, b;}; +double __exp__D(double, double); +struct Double __log__D(double); + +#endif /* _NOIEEE_SRC_MATHIMPL_H_ */ diff --git a/lib/nbsd_libm/noieee_src/n_acosh.c b/lib/nbsd_libm/noieee_src/n_acosh.c new file mode 100644 index 000000000..7b553480d --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_acosh.c @@ -0,0 +1,102 @@ +/* $NetBSD: n_acosh.c,v 1.6 2003/08/07 16:44:50 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)acosh.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* ACOSH(X) + * RETURN THE INVERSE HYPERBOLIC COSINE OF X + * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 2/16/85; + * REVISED BY K.C. NG on 3/6/85, 3/24/85, 4/16/85, 8/17/85. + * + * Required system supported functions : + * sqrt(x) + * + * Required kernel function: + * log1p(x) ...return log(1+x) + * + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log1p(x)+ln2, if (x > 1.0E20); else + * acosh(x) := log1p( sqrt(x-1) * (sqrt(x-1) + sqrt(x+1)) ) . + * These formulae avoid the over/underflow complication. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + * + * Accuracy: + * acosh(x) returns the exact inverse hyperbolic cosine of x nearly + * rounded. In a test run with 512,000 random arguments on a VAX, the + * maximum observed error was 3.30 ulps (units of the last place) at + * x=1.0070493753568216 . + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) + +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#endif + +double +acosh(double x) +{ + double t,big=1.E20; /* big+1==big */ + +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + + /* return log1p(x) + log(2) if x is large */ + if(x>big) {t=log1p(x)+ln2lo; return(t+ln2hi);} + + t=sqrt(x-1.0); + return(log1p(t*(t+sqrt(x+1.0)))); +} diff --git a/lib/nbsd_libm/noieee_src/n_asincos.c b/lib/nbsd_libm/noieee_src/n_asincos.c new file mode 100644 index 000000000..09da31e15 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_asincos.c @@ -0,0 +1,170 @@ +/* $NetBSD: n_asincos.c,v 1.7 2003/08/07 16:44:50 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)asincos.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* ASIN(X) + * RETURNS ARC SINE OF X + * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) + * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. + * + * Required system supported functions: + * copysign(x,y) + * sqrt(x) + * + * Required kernel function: + * atan2(y,x) + * + * Method : + * asin(x) = atan2(x,sqrt(1-x*x)); for better accuracy, 1-x*x is + * computed as follows + * 1-x*x if x < 0.5, + * 2*(1-|x|)-(1-|x|)*(1-|x|) if x >= 0.5. + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN. + * + * Accuracy: + * 1) If atan2() uses machine PI, then + * + * asin(x) returns (PI/pi) * (the exact arc sine of x) nearly rounded; + * and PI is the exact pi rounded to machine precision (see atan2 for + * details): + * + * in decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * in hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps + * + * In a test run with more than 200,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 2.06 ulps. (comparing against (PI/pi)*(exact asin(x))); + * + * 2) If atan2() uses true pi, then + * + * asin(x) returns the exact asin(x) with error below about 2 ulps. + * + * In a test run with more than 1,024,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 1.99 ulps. + */ + +#include "mathimpl.h" + +double +asin(double x) +{ + double s,t,one=1.0; +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + s=copysign(x,one); + if(s <= 0.5) + return(atan2(x,sqrt(one-x*x))); + else + { t=one-s; s=t+t; return(atan2(x,sqrt(s-t*t))); } + +} + +/* ACOS(X) + * RETURNS ARC COS OF X + * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) + * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. + * + * Required system supported functions: + * copysign(x,y) + * sqrt(x) + * + * Required kernel function: + * atan2(y,x) + * + * Method : + * ________ + * / 1 - x + * acos(x) = 2*atan2( / -------- , 1 ) . + * \/ 1 + x + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN. + * + * Accuracy: + * 1) If atan2() uses machine PI, then + * + * acos(x) returns (PI/pi) * (the exact arc cosine of x) nearly rounded; + * and PI is the exact pi rounded to machine precision (see atan2 for + * details): + * + * in decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * in hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps + * + * In a test run with more than 200,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 2.07 ulps. (comparing against (PI/pi)*(exact acos(x))); + * + * 2) If atan2() uses true pi, then + * + * acos(x) returns the exact acos(x) with error below about 2 ulps. + * + * In a test run with more than 1,024,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 2.15 ulps. + */ + +double +acos(double x) +{ + double t,one=1.0; +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if( x != -1.0) + t=atan2(sqrt((one-x)/(one+x)),one); + else + t=atan2(one,0.0); /* t = PI/2 */ + return(t+t); +} diff --git a/lib/nbsd_libm/noieee_src/n_asinh.c b/lib/nbsd_libm/noieee_src/n_asinh.c new file mode 100644 index 000000000..bbf48e02d --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_asinh.c @@ -0,0 +1,101 @@ +/* $NetBSD: n_asinh.c,v 1.7 2008/04/29 15:10:02 uwe Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)asinh.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* ASINH(X) + * RETURN THE INVERSE HYPERBOLIC SINE OF X + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 2/16/85; + * REVISED BY K.C. NG on 3/7/85, 3/24/85, 4/16/85. + * + * Required system supported functions : + * copysign(x,y) + * sqrt(x) + * + * Required kernel function: + * log1p(x) ...return log(1+x) + * + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log1p(x)+ln2)) if sqrt(1+x*x)=x, else + * := sign(x)*log1p(|x| + |x|/(1/|x| + sqrt(1+(1/|x|)^2)) ) + * + * Accuracy: + * asinh(x) returns the exact inverse hyperbolic sine of x nearly rounded. + * In a test run with 52,000 random arguments on a VAX, the maximum + * observed error was 1.58 ulps (units in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) + +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#endif + +double +asinh(double x) +{ + double t,s; + static const double small=1.0E-10, /* fl(1+small*small) == 1 */ + big =1.0E20, /* fl(1+big) == big */ + one =1.0 ; + +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if((t=copysign(x,one))>small) + if(t big */ + {s=log1p(t)+ln2lo; return(copysign(s+ln2hi,x));} + else /* if |x| < small */ + return(x); +} diff --git a/lib/nbsd_libm/noieee_src/n_atan.c b/lib/nbsd_libm/noieee_src/n_atan.c new file mode 100644 index 000000000..fd15ebf9b --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_atan.c @@ -0,0 +1,87 @@ +/* $NetBSD: n_atan.c,v 1.5 2003/08/07 16:44:50 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)atan.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* ATAN(X) + * RETURNS ARC TANGENT OF X + * DOUBLE PRECISION (IEEE DOUBLE 53 bits, VAX D FORMAT 56 bits) + * CODED IN C BY K.C. NG, 4/16/85, REVISED ON 6/10/85. + * + * Required kernel function: + * atan2(y,x) + * + * Method: + * atan(x) = atan2(x,1.0). + * + * Special case: + * if x is NaN, return x itself. + * + * Accuracy: + * 1) If atan2() uses machine PI, then + * + * atan(x) returns (PI/pi) * (the exact arc tangent of x) nearly rounded; + * and PI is the exact pi rounded to machine precision (see atan2 for + * details): + * + * in decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * in hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps + * + * In a test run with more than 200,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 0.86 ulps. (comparing against (PI/pi)*(exact atan(x))). + * + * 2) If atan2() uses true pi, then + * + * atan(x) returns the exact atan(x) with error below about 2 ulps. + * + * In a test run with more than 1,024,000 random arguments on a VAX, the + * maximum observed error in ulps (units in the last place) was + * 0.85 ulps. + */ +#include "mathimpl.h" + +double +atan(double x) +{ + double one=1.0; + return(atan2(x,one)); +} diff --git a/lib/nbsd_libm/noieee_src/n_atan2.c b/lib/nbsd_libm/noieee_src/n_atan2.c new file mode 100644 index 000000000..a1fcdc5a4 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_atan2.c @@ -0,0 +1,279 @@ +/* $NetBSD: n_atan2.c,v 1.6 2003/08/07 16:44:50 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)atan2.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* ATAN2(Y,X) + * RETURN ARG (X+iY) + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/8/85; + * REVISED BY K.C. NG on 2/7/85, 2/13/85, 3/7/85, 3/30/85, 6/29/85. + * + * Required system supported functions : + * copysign(x,y) + * scalb(x,y) + * logb(x) + * + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * 3. According to the integer k=4t+0.25 truncated , t=y/x, the argument + * is further reduced to one of the following intervals and the + * arctangent of y/x is evaluated by the corresponding formula: + * + * [0,7/16] atan(y/x) = t - t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(y/x) = atan(1/2) + atan( (y-x/2)/(x+y/2) ) + * [11/16.19/16] atan(y/x) = atan( 1 ) + atan( (y-x)/(x+y) ) + * [19/16,39/16] atan(y/x) = atan(3/2) + atan( (y-1.5x)/(x+1.5y) ) + * [39/16,INF] atan(y/x) = atan(INF) + atan( -x/y ) + * + * Special cases: + * Notations: atan2(y,x) == ARG (x+iy) == ARG(x,y). + * + * ARG( NAN , (anything) ) is NaN; + * ARG( (anything), NaN ) is NaN; + * ARG(+(anything but NaN), +-0) is +-0 ; + * ARG(-(anything but NaN), +-0) is +-PI ; + * ARG( 0, +-(anything but 0 and NaN) ) is +-PI/2; + * ARG( +INF,+-(anything but INF and NaN) ) is +-0 ; + * ARG( -INF,+-(anything but INF and NaN) ) is +-PI; + * ARG( +INF,+-INF ) is +-PI/4 ; + * ARG( -INF,+-INF ) is +-3PI/4; + * ARG( (anything but,0,NaN, and INF),+-INF ) is +-PI/2; + * + * Accuracy: + * atan2(y,x) returns (PI/pi) * the exact ARG (x+iy) nearly rounded, + * where + * + * in decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * in hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 error=.276ulps + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 error=.206ulps + * + * In a test run with 356,000 random argument on [-1,1] * [-1,1] on a + * VAX, the maximum observed error was 1.41 ulps (units of the last place) + * compared with (PI/pi)*(the exact ARG(x+iy)). + * + * Note: + * We use machine PI (the true pi rounded) in place of the actual + * value of pi for all the trig and inverse trig functions. In general, + * if trig is one of sin, cos, tan, then computed trig(y) returns the + * exact trig(y*pi/PI) nearly rounded; correspondingly, computed arctrig + * returns the exact arctrig(y)*PI/pi nearly rounded. These guarantee the + * trig functions have period PI, and trig(arctrig(x)) returns x for + * all critical values x. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(athfhi, 4.6364760900080611433E-1 ,6338,3fed,da7b,2b0d, -1, .ED63382B0DDA7B) +vc(athflo, 1.9338828231967579916E-19 ,5005,2164,92c0,9cfe, -62, .E450059CFE92C0) +vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2) +vc(at1fhi, 9.8279372324732906796E-1 ,985e,407b,b4d9,940f, 0, .FB985E940FB4D9) +vc(at1flo,-3.5540295636764633916E-18 ,1edc,a383,eaea,34d6, -57,-.831EDC34D6EAEA) +vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2) +vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2) +vc(a1, 3.3333333333333473730E-1 ,aaaa,3faa,ab75,aaaa, -1, .AAAAAAAAAAAB75) +vc(a2, -2.0000000000017730678E-1 ,cccc,bf4c,946e,cccd, -2,-.CCCCCCCCCD946E) +vc(a3, 1.4285714286694640301E-1 ,4924,3f12,4262,9274, -2, .92492492744262) +vc(a4, -1.1111111135032672795E-1 ,8e38,bee3,6292,ebc6, -3,-.E38E38EBC66292) +vc(a5, 9.0909091380563043783E-2 ,2e8b,3eba,d70c,b31b, -3, .BA2E8BB31BD70C) +vc(a6, -7.6922954286089459397E-2 ,89c8,be9d,7f18,27c3, -3,-.9D89C827C37F18) +vc(a7, 6.6663180891693915586E-2 ,86b4,3e88,9e58,ae37, -3, .8886B4AE379E58) +vc(a8, -5.8772703698290408927E-2 ,bba5,be70,a942,8481, -4,-.F0BBA58481A942) +vc(a9, 5.2170707402812969804E-2 ,b0f3,3e55,13ab,a1ab, -4, .D5B0F3A1AB13AB) +vc(a10, -4.4895863157820361210E-2 ,e4b9,be37,048f,7fd1, -4,-.B7E4B97FD1048F) +vc(a11, 3.3006147437343875094E-2 ,3174,3e07,2d87,3cf7, -4, .8731743CF72D87) +vc(a12, -1.4614844866464185439E-2 ,731a,bd6f,76d9,2f34, -6,-.EF731A2F3476D9) + +ic(athfhi, 4.6364760900080609352E-1 , -2, 1.DAC670561BB4F) +ic(athflo, 4.6249969567426939759E-18 , -58, 1.5543B8F253271) +ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18) +ic(at1fhi, 9.8279372324732905408E-1 , -1, 1.F730BD281F69B) +ic(at1flo,-2.4407677060164810007E-17 , -56, -1.C23DFEFEAE6B5) +ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18) +ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18) +ic(a1, 3.3333333333333942106E-1 , -2, 1.55555555555C3) +ic(a2, -1.9999999999979536924E-1 , -3, -1.9999999997CCD) +ic(a3, 1.4285714278004377209E-1 , -3, 1.24924921EC1D7) +ic(a4, -1.1111110579344973814E-1 , -4, -1.C71C7059AF280) +ic(a5, 9.0908906105474668324E-2 , -4, 1.745CE5AA35DB2) +ic(a6, -7.6919217767468239799E-2 , -4, -1.3B0FA54BEC400) +ic(a7, 6.6614695906082474486E-2 , -4, 1.10DA924597FFF) +ic(a8, -5.8358371008508623523E-2 , -5, -1.DE125FDDBD793) +ic(a9, 4.9850617156082015213E-2 , -5, 1.9860524BDD807) +ic(a10, -3.6700606902093604877E-2 , -5, -1.2CA6C04C6937A) +ic(a11, 1.6438029044759730479E-2 , -6, 1.0D52174A1BB54) + +#ifdef vccast +#define athfhi vccast(athfhi) +#define athflo vccast(athflo) +#define PIo4 vccast(PIo4) +#define at1fhi vccast(at1fhi) +#define at1flo vccast(at1flo) +#define PIo2 vccast(PIo2) +#define PI vccast(PI) +#define a1 vccast(a1) +#define a2 vccast(a2) +#define a3 vccast(a3) +#define a4 vccast(a4) +#define a5 vccast(a5) +#define a6 vccast(a6) +#define a7 vccast(a7) +#define a8 vccast(a8) +#define a9 vccast(a9) +#define a10 vccast(a10) +#define a11 vccast(a11) +#define a12 vccast(a12) +#endif + +double +atan2(double y, double x) +{ + static const double zero=0, one=1, small=1.0E-9, big=1.0E18; + double t,z,signy,signx,hi,lo; + int k,m; + +#if !defined(__vax__)&&!defined(tahoe) + /* if x or y is NAN */ + if(x!=x) return(x); if(y!=y) return(y); +#endif /* !defined(__vax__)&&!defined(tahoe) */ + + /* copy down the sign of y and x */ + signy = copysign(one,y) ; + signx = copysign(one,x) ; + + /* if x is 1.0, goto begin */ + if(x==1) { y=copysign(y,one); t=y; if(finite(t)) goto begin;} + + /* when y = 0 */ + if(y==zero) return((signx==one)?y:copysign(PI,signy)); + + /* when x = 0 */ + if(x==zero) return(copysign(PIo2,signy)); + + /* when x is INF */ + if(!finite(x)) + if(!finite(y)) + return(copysign((signx==one)?PIo4:3*PIo4,signy)); + else + return(copysign((signx==one)?zero:PI,signy)); + + /* when y is INF */ + if(!finite(y)) return(copysign(PIo2,signy)); + + /* compute y/x */ + x=copysign(x,one); + y=copysign(y,one); + if((m=(k=logb(y))-logb(x)) > 60) t=big+big; + else if(m < -80 ) t=y/x; + else { t = y/x ; y = scalb(y,-k); x=scalb(x,-k); } + + /* begin argument reduction */ +begin: + if (t < 2.4375) { + + /* truncate 4(t+1/16) to integer for branching */ + k = 4 * (t+0.0625); + switch (k) { + + /* t is in [0,7/16] */ + case 0: + case 1: + if (t < small) + { big + small ; /* raise inexact flag */ + return (copysign((signx>zero)?t:PI-t,signy)); } + + hi = zero; lo = zero; break; + + /* t is in [7/16,11/16] */ + case 2: + hi = athfhi; lo = athflo; + z = x+x; + t = ( (y+y) - x ) / ( z + y ); break; + + /* t is in [11/16,19/16] */ + case 3: + case 4: + hi = PIo4; lo = zero; + t = ( y - x ) / ( x + y ); break; + + /* t is in [19/16,39/16] */ + default: + hi = at1fhi; lo = at1flo; + z = y-x; y=y+y+y; t = x+x; + t = ( (z+z)-x ) / ( t + y ); break; + } + } + /* end of if (t < 2.4375) */ + + else + { + hi = PIo2; lo = zero; + + /* t is in [2.4375, big] */ + if (t <= big) t = - x / y; + + /* t is in [big, INF] */ + else + { big+small; /* raise inexact flag */ + t = zero; } + } + /* end of argument reduction */ + + /* compute atan(t) for t in [-.4375, .4375] */ + z = t*t; +#if defined(__vax__)||defined(tahoe) + z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+ + z*(a9+z*(a10+z*(a11+z*a12)))))))))))); +#else /* defined(__vax__)||defined(tahoe) */ + z = t*(z*(a1+z*(a2+z*(a3+z*(a4+z*(a5+z*(a6+z*(a7+z*(a8+ + z*(a9+z*(a10+z*a11))))))))))); +#endif /* defined(__vax__)||defined(tahoe) */ + z = lo - z; z += t; z += hi; + + return(copysign((signx>zero)?z:PI-z,signy)); +} diff --git a/lib/nbsd_libm/noieee_src/n_atanh.c b/lib/nbsd_libm/noieee_src/n_atanh.c new file mode 100644 index 000000000..6498ee844 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_atanh.c @@ -0,0 +1,82 @@ +/* $NetBSD: n_atanh.c,v 1.7 2003/08/07 16:44:50 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)atanh.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* ATANH(X) + * RETURN THE HYPERBOLIC ARC TANGENT OF X + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/8/85; + * REVISED BY K.C. NG on 2/7/85, 3/7/85, 8/18/85. + * + * Required kernel function: + * log1p(x) ...return log(1+x) + * + * Method : + * Return + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + * Accuracy: + * atanh(x) returns the exact hyperbolic arc tangent of x nearly rounded. + * In a test run with 512,000 random arguments on a VAX, the maximum + * observed error was 1.87 ulps (units in the last place) at + * x= -3.8962076028810414000e-03. + */ +#include "mathimpl.h" + +#if defined(__vax__)||defined(tahoe) +#include +#endif /* defined(__vax__)||defined(tahoe) */ + +double +atanh(double x) +{ + double z; + z = copysign(0.5,x); + x = copysign(x,1.0); +#if defined(__vax__)||defined(tahoe) + if (x == 1.0) { + return(copysign(1.0,z)*infnan(ERANGE)); /* sign(x)*INF */ + } +#endif /* defined(__vax__)||defined(tahoe) */ + x = x/(1.0-x); + return( z*log1p(x+x) ); +} diff --git a/lib/nbsd_libm/noieee_src/n_cabs.c b/lib/nbsd_libm/noieee_src/n_cabs.c new file mode 100644 index 000000000..d21b543e4 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_cabs.c @@ -0,0 +1,227 @@ +/* $NetBSD: n_cabs.c,v 1.5 2003/08/07 16:44:50 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)cabs.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +/* HYPOT(X,Y) + * RETURN THE SQUARE ROOT OF X^2 + Y^2 WHERE Z=X+iY + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 11/28/84; + * REVISED BY K.C. NG, 7/12/85. + * + * Required system supported functions : + * copysign(x,y) + * finite(x) + * scalb(x,N) + * sqrt(x) + * + * Method : + * 1. replace x by |x| and y by |y|, and swap x and + * y if y > x (hence x is never smaller than y). + * 2. Hypot(x,y) is computed by: + * Case I, x/y > 2 + * + * y + * hypot = x + ----------------------------- + * 2 + * sqrt ( 1 + [x/y] ) + x/y + * + * Case II, x/y <= 2 + * y + * hypot = x + -------------------------------------------------- + * 2 + * [x/y] - 2 + * (sqrt(2)+1) + (x-y)/y + ----------------------------- + * 2 + * sqrt ( 1 + [x/y] ) + sqrt(2) + * + * + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns the sqrt(x^2+y^2) with error less than 1 ulps (units + * in the last place). See Kahan's "Interval Arithmetic Options in the + * Proposed IEEE Floating Point Arithmetic Standard", Interval Mathematics + * 1980, Edited by Karl L.E. Nickel, pp 99-128. (A faster but less accurate + * code follows in comments.) In a test run with 500,000 random arguments + * on a VAX, the maximum observed error was .959 ulps. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(r2p1hi, 2.4142135623730950345E0 ,8279,411a,ef32,99fc, 2, .9A827999FCEF32) +vc(r2p1lo, 1.4349369327986523769E-17 ,597d,2484,754b,89b3, -55, .84597D89B3754B) +vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65) + +ic(r2p1hi, 2.4142135623730949234E0 , 1, 1.3504F333F9DE6) +ic(r2p1lo, 1.2537167179050217666E-16 , -53, 1.21165F626CDD5) +ic(sqrt2, 1.4142135623730951455E0 , 0, 1.6A09E667F3BCD) + +#ifdef vccast +#define r2p1hi vccast(r2p1hi) +#define r2p1lo vccast(r2p1lo) +#define sqrt2 vccast(sqrt2) +#endif + +double +hypot(double x, double y) +{ + static const double zero=0, one=1, + small=1.0E-18; /* fl(1+small)==1 */ + static const ibig=30; /* fl(1+2**(2*ibig))==1 */ + double t,r; + int exp; + + if(finite(x)) + if(finite(y)) + { + x=copysign(x,one); + y=copysign(y,one); + if(y > x) + { t=x; x=y; y=t; } + if(x == zero) return(zero); + if(y == zero) return(x); + exp= logb(x); + if(exp-(int)logb(y) > ibig ) + /* raise inexact flag and return |x| */ + { one+small; return(x); } + + /* start computing sqrt(x^2 + y^2) */ + r=x-y; + if(r>y) { /* x/y > 2 */ + r=x/y; + r=r+sqrt(one+r*r); } + else { /* 1 <= x/y <= 2 */ + r/=y; t=r*(r+2.0); + r+=t/(sqrt2+sqrt(2.0+t)); + r+=r2p1lo; r+=r2p1hi; } + + r=y/r; + return(x+r); + + } + + else if(y==y) /* y is +-INF */ + return(copysign(y,one)); + else + return(y); /* y is NaN and x is finite */ + + else if(x==x) /* x is +-INF */ + return (copysign(x,one)); + else if(finite(y)) + return(x); /* x is NaN, y is finite */ +#if !defined(__vax__)&&!defined(tahoe) + else if(y!=y) return(y); /* x and y is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + else return(copysign(y,one)); /* y is INF */ +} + +/* CABS(Z) + * RETURN THE ABSOLUTE VALUE OF THE COMPLEX NUMBER Z = X + iY + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 11/28/84. + * REVISED BY K.C. NG, 7/12/85. + * + * Required kernel function : + * hypot(x,y) + * + * Method : + * cabs(z) = hypot(x,y) . + */ + +struct complex { double x, y; }; + +double +cabs(z) +struct complex z; +{ + return hypot(z.x,z.y); +} + +double +z_abs(z) +struct complex *z; +{ + return hypot(z->x,z->y); +} + +/* A faster but less accurate version of cabs(x,y) */ +#if 0 +double hypot(x,y) +double x, y; +{ + static const double zero=0, one=1; + small=1.0E-18; /* fl(1+small)==1 */ + static const ibig=30; /* fl(1+2**(2*ibig))==1 */ + double temp; + int exp; + + if(finite(x)) + if(finite(y)) + { + x=copysign(x,one); + y=copysign(y,one); + if(y > x) + { temp=x; x=y; y=temp; } + if(x == zero) return(zero); + if(y == zero) return(x); + exp= logb(x); + x=scalb(x,-exp); + if(exp-(int)logb(y) > ibig ) + /* raise inexact flag and return |x| */ + { one+small; return(scalb(x,exp)); } + else y=scalb(y,-exp); + return(scalb(sqrt(x*x+y*y),exp)); + } + + else if(y==y) /* y is +-INF */ + return(copysign(y,one)); + else + return(y); /* y is NaN and x is finite */ + + else if(x==x) /* x is +-INF */ + return (copysign(x,one)); + else if(finite(y)) + return(x); /* x is NaN, y is finite */ + else if(y!=y) return(y); /* x and y is NaN */ + else return(copysign(y,one)); /* y is INF */ +} +#endif diff --git a/lib/nbsd_libm/noieee_src/n_cbrt.c b/lib/nbsd_libm/noieee_src/n_cbrt.c new file mode 100644 index 000000000..806f9e5f9 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_cbrt.c @@ -0,0 +1,117 @@ +/* $NetBSD: n_cbrt.c,v 1.5 2003/08/07 16:44:50 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +static char sccsid[] = "@(#)cbrt.c 8.1 (Berkeley) 6/4/93"; +#endif /* not lint */ + +#include + +/* kahan's cube root (53 bits IEEE double precision) + * for IEEE machines only + * coded in C by K.C. Ng, 4/30/85 + * + * Accuracy: + * better than 0.667 ulps according to an error analysis. Maximum + * error observed was 0.666 ulps in an 1,000,000 random arguments test. + * + * Warning: this code is semi machine dependent; the ordering of words in + * a floating point number must be known in advance. I assume that the + * long interger at the address of a floating point number will be the + * leading 32 bits of that floating point number (i.e., sign, exponent, + * and the 20 most significant bits). + * On a National machine, it has different ordering; therefore, this code + * must be compiled with flag -DNATIONAL. + */ +#if !defined(__vax__)&&!defined(tahoe) + +static const unsigned long + B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ +static const double + C= 19./35., + D= -864./1225., + E= 99./70., + F= 45./28., + G= 5./14.; + +double +cbrt(double x) +{ + double r,s,t=0.0,w; + unsigned long *px = (unsigned long *) &x, + *pt = (unsigned long *) &t, + mexp,sign; + +#ifdef national /* ordering of words in a floating points number */ + const int n0=1,n1=0; +#else /* national */ + const int n0=0,n1=1; +#endif /* national */ + + mexp=px[n0]&0x7ff00000; + if(mexp==0x7ff00000) return(x); /* cbrt(NaN,INF) is itself */ + if(x==0.0) return(x); /* cbrt(0) is itself */ + + sign=px[n0]&0x80000000; /* sign= sign(x) */ + px[n0] ^= sign; /* x=|x| */ + + + /* rough cbrt to 5 bits */ + if(mexp==0) /* subnormal number */ + {pt[n0]=0x43500000; /* set t= 2**54 */ + t*=x; pt[n0]=pt[n0]/3+B2; + } + else + pt[n0]=px[n0]/3+B1; + + + /* new cbrt to 23 bits, may be implemented in single precision */ + r=t*t/x; + s=C+r*t; + t*=G+F/(s+E+D/s); + + /* chopped to 20 bits and make it larger than cbrt(x) */ + pt[n1]=0; pt[n0]+=0x00000001; + + + /* one step newton iteration to 53 bits with error less than 0.667 ulps */ + s=t*t; /* t*t is exact */ + r=x/s; + w=t+t; + r=(r-t)/(w+r); /* r-t is exact */ + t=t+t*r; + + + /* retore the sign bit */ + pt[n0] |= sign; + return(t); +} +#endif diff --git a/lib/nbsd_libm/noieee_src/n_cosh.c b/lib/nbsd_libm/noieee_src/n_cosh.c new file mode 100644 index 000000000..5e86353f4 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_cosh.c @@ -0,0 +1,146 @@ +/* $NetBSD: n_cosh.c,v 1.8 2008/03/20 16:41:26 mhitch Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)cosh.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* COSH(X) + * RETURN THE HYPERBOLIC COSINE OF X + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/8/85; + * REVISED BY K.C. NG on 2/8/85, 2/23/85, 3/7/85, 3/29/85, 4/16/85. + * + * Required system supported functions : + * copysign(x,y) + * scalb(x,N) + * + * Required kernel function: + * exp(x) + * exp__E(x,c) ...return exp(x+c)-1-x for |x|<0.3465 + * + * Method : + * 1. Replace x by |x|. + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= 0.3465 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * 0.3465 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovfl : cosh(x) := exp(x)/2 + * lnovfl <= x <= lnovfl+log(2) + * : cosh(x) := exp(x)/2 (avoid overflow) + * log(2)+lnovfl < x < INF: overflow to INF + * + * Note: .3465 is a number near one half of ln2. + * + * Special cases: + * cosh(x) is x if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + * + * Accuracy: + * cosh(x) returns the exact hyperbolic cosine of x nearly rounded. + * In a test run with 768,000 random arguments on a VAX, the maximum + * observed error was 1.23 ulps (units in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "../src/namespace.h" +#include "mathimpl.h" + +#ifdef __weak_alias +__weak_alias(cosh, _cosh); +__weak_alias(coshf, _coshf); +#endif + +vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) +vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) +vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) + +ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) +ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) +ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) + +#ifdef vccast +#define mln2hi vccast(mln2hi) +#define mln2lo vccast(mln2lo) +#define lnovfl vccast(lnovfl) +#endif + +#if defined(__vax__)||defined(tahoe) +#define EXPMAX 126 +#else +#define EXPMAX 1023 +#endif /* defined(__vax__)||defined(tahoe) */ + +double +cosh(double x) +{ + static const double half=1.0/2.0, + one=1.0, small=1.0E-18; /* fl(1+small)==1 */ + double t; + +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if((x=copysign(x,one)) <= 22) { + if(x<0.3465) { + if(x= 1.25 (error 1.7ulp vs ~6ulp) + * Replaced even+odd with direct calculation for x < .84375, + * to avoid destructive cancellation. + * + * Performance of erfc(x): + * In 300000 trials in the range [.83, .84375] the + * maximum observed error was 3.6ulp. + * + * In [.84735,1.25] the maximum observed error was <2.5ulp in + * 100000 runs in the range [1.2, 1.25]. + * + * In [1.25,26] (Not including subnormal results) + * the error is < 1.7ulp. + */ + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * + * Method: + * 1. Reduce x to |x| by erf(-x) = -erf(x) + * 2. For x in [0, 0.84375] + * erf(x) = x + x*P(x^2) + * erfc(x) = 1 - erf(x) if x<=0.25 + * = 0.5 + ((0.5-x)-x*P) if x in [0.25,0.84375] + * where + * 2 2 4 20 + * P = P(x ) = (p0 + p1 * x + p2 * x + ... + p10 * x ) + * is an approximation to (erf(x)-x)/x with precision + * + * -56.45 + * | P - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fixed + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 3. For x in [0.84375,1.25], let s = x - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = c + P1(s)/Q1(s) + * erfc(x) = (1-c) - P1(s)/Q1(s) + * |P1/Q1 - (erf(x)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 4. For x in [1.25, 2]; [2, 4] + * erf(x) = 1.0 - tiny + * erfc(x) = (1/x)exp(-x*x-(.5*log(pi) -.5z + R(z)/S(z)) + * + * Where z = 1/(x*x), R is degree 9, and S is degree 3; + * + * 5. For x in [4,28] + * erf(x) = 1.0 - tiny + * erfc(x) = (1/x)exp(-x*x-(.5*log(pi)+eps + zP(z)) + * + * Where P is degree 14 polynomial in 1/(x*x). + * + * Notes: + * Here 4 and 5 make use of the asymptotic series + * exp(-x*x) + * erfc(x) ~ ---------- * ( 1 + Poly(1/x^2) ); + * x*sqrt(pi) + * + * where for z = 1/(x*x) + * P(z) ~ z/2*(-1 + z*3/2*(1 + z*5/2*(-1 + z*7/2*(1 +...)))) + * + * Thus we use rational approximation to approximate + * erfc*x*exp(x*x) ~ 1/sqrt(pi); + * + * The error bound for the target function, G(z) for + * the interval + * [4, 28]: + * |eps + 1/(z)P(z) - G(z)| < 2**(-56.61) + * for [2, 4]: + * |R(z)/S(z) - G(z)| < 2**(-58.24) + * for [1.25, 2]: + * |R(z)/S(z) - G(z)| < 2**(-58.12) + * + * 6. For inf > x >= 28 + * erf(x) = 1 - tiny (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) + * + * 7. Special cases: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + +#if defined(__vax__) || defined(tahoe) +#define _IEEE 0 +#define TRUNC(x) (x) = (float)(x) +#else +#define _IEEE 1 +#define TRUNC(x) *(((int *) &x) + 1) &= 0xf8000000 +#define infnan(x) 0.0 +#endif + +#ifdef _IEEE_LIBM +/* + * redefining "___function" to "function" in _IEEE_LIBM mode + */ +#include "ieee_libm.h" +#endif + +static const double +tiny = 1e-300, +half = 0.5, +one = 1.0, +two = 2.0, +c = 8.45062911510467529297e-01, /* (float)0.84506291151 */ +/* + * Coefficients for approximation to erf in [0,0.84375] + */ +p0t8 = 1.02703333676410051049867154944018394163280, +p0 = 1.283791670955125638123339436800229927041e-0001, +p1 = -3.761263890318340796574473028946097022260e-0001, +p2 = 1.128379167093567004871858633779992337238e-0001, +p3 = -2.686617064084433642889526516177508374437e-0002, +p4 = 5.223977576966219409445780927846432273191e-0003, +p5 = -8.548323822001639515038738961618255438422e-0004, +p6 = 1.205520092530505090384383082516403772317e-0004, +p7 = -1.492214100762529635365672665955239554276e-0005, +p8 = 1.640186161764254363152286358441771740838e-0006, +p9 = -1.571599331700515057841960987689515895479e-0007, +p10= 1.073087585213621540635426191486561494058e-0008; +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +static const double +pa0 = -2.362118560752659485957248365514511540287e-0003, +pa1 = 4.148561186837483359654781492060070469522e-0001, +pa2 = -3.722078760357013107593507594535478633044e-0001, +pa3 = 3.183466199011617316853636418691420262160e-0001, +pa4 = -1.108946942823966771253985510891237782544e-0001, +pa5 = 3.547830432561823343969797140537411825179e-0002, +pa6 = -2.166375594868790886906539848893221184820e-0003, +qa1 = 1.064208804008442270765369280952419863524e-0001, +qa2 = 5.403979177021710663441167681878575087235e-0001, +qa3 = 7.182865441419627066207655332170665812023e-0002, +qa4 = 1.261712198087616469108438860983447773726e-0001, +qa5 = 1.363708391202905087876983523620537833157e-0002, +qa6 = 1.198449984679910764099772682882189711364e-0002; +/* + * log(sqrt(pi)) for large x expansions. + * The tail (lsqrtPI_lo) is included in the rational + * approximations. +*/ +static const double + lsqrtPI_hi = .5723649429247000819387380943226; +/* + * lsqrtPI_lo = .000000000000000005132975581353913; + * + * Coefficients for approximation to erfc in [2, 4] +*/ +static const double +rb0 = -1.5306508387410807582e-010, /* includes lsqrtPI_lo */ +rb1 = 2.15592846101742183841910806188e-008, +rb2 = 6.24998557732436510470108714799e-001, +rb3 = 8.24849222231141787631258921465e+000, +rb4 = 2.63974967372233173534823436057e+001, +rb5 = 9.86383092541570505318304640241e+000, +rb6 = -7.28024154841991322228977878694e+000, +rb7 = 5.96303287280680116566600190708e+000, +rb8 = -4.40070358507372993983608466806e+000, +rb9 = 2.39923700182518073731330332521e+000, +rb10 = -6.89257464785841156285073338950e-001, +sb1 = 1.56641558965626774835300238919e+001, +sb2 = 7.20522741000949622502957936376e+001, +sb3 = 9.60121069770492994166488642804e+001; +/* + * Coefficients for approximation to erfc in [1.25, 2] +*/ +static const double +rc0 = -2.47925334685189288817e-007, /* includes lsqrtPI_lo */ +rc1 = 1.28735722546372485255126993930e-005, +rc2 = 6.24664954087883916855616917019e-001, +rc3 = 4.69798884785807402408863708843e+000, +rc4 = 7.61618295853929705430118701770e+000, +rc5 = 9.15640208659364240872946538730e-001, +rc6 = -3.59753040425048631334448145935e-001, +rc7 = 1.42862267989304403403849619281e-001, +rc8 = -4.74392758811439801958087514322e-002, +rc9 = 1.09964787987580810135757047874e-002, +rc10 = -1.28856240494889325194638463046e-003, +sc1 = 9.97395106984001955652274773456e+000, +sc2 = 2.80952153365721279953959310660e+001, +sc3 = 2.19826478142545234106819407316e+001; +/* + * Coefficients for approximation to erfc in [4,28] + */ +static const double +rd0 = -2.1491361969012978677e-016, /* includes lsqrtPI_lo */ +rd1 = -4.99999999999640086151350330820e-001, +rd2 = 6.24999999772906433825880867516e-001, +rd3 = -1.54166659428052432723177389562e+000, +rd4 = 5.51561147405411844601985649206e+000, +rd5 = -2.55046307982949826964613748714e+001, +rd6 = 1.43631424382843846387913799845e+002, +rd7 = -9.45789244999420134263345971704e+002, +rd8 = 6.94834146607051206956384703517e+003, +rd9 = -5.27176414235983393155038356781e+004, +rd10 = 3.68530281128672766499221324921e+005, +rd11 = -2.06466642800404317677021026611e+006, +rd12 = 7.78293889471135381609201431274e+006, +rd13 = -1.42821001129434127360582351685e+007; + +double +erf(double x) +{ + double R,S,P,Q,ax,s,y,z,r; + if(!finite(x)) { /* erf(nan)=nan */ + if (isnan(x)) + return(x); + return (x > 0 ? one : -one); /* erf(+/-inf)= +/-1 */ + } + if ((ax = x) < 0) + ax = - ax; + if (ax < .84375) { + if (ax < 3.7e-09) { + if (ax < 1.0e-308) + return 0.125*(8.0*x+p0t8*x); /*avoid underflow */ + return x + p0*x; + } + y = x*x; + r = y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+ + y*(p6+y*(p7+y*(p8+y*(p9+y*p10))))))))); + return x + x*(p0+r); + } + if (ax < 1.25) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if (x>=0) + return (c + P/Q); + else + return (-c - P/Q); + } + if (ax >= 6.0) { /* inf>|x|>=6 */ + if (x >= 0.0) + return (one-tiny); + else + return (tiny-one); + } + /* 1.25 <= |x| < 6 */ + z = -ax*ax; + s = -one/z; + if (ax < 2.0) { + R = rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+ + s*(rc6+s*(rc7+s*(rc8+s*(rc9+s*rc10))))))))); + S = one+s*(sc1+s*(sc2+s*sc3)); + } else { + R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+ + s*(rb6+s*(rb7+s*(rb8+s*(rb9+s*rb10))))))))); + S = one+s*(sb1+s*(sb2+s*sb3)); + } + y = (R/S -.5*s) - lsqrtPI_hi; + z += y; + z = exp(z)/ax; + if (x >= 0) + return (one-z); + else + return (z-one); +} + +double +erfc(double x) +{ + double R,S,P,Q,s,ax,y,z,r; + if (!finite(x)) { + if (isnan(x)) /* erfc(NaN) = NaN */ + return(x); + else if (x > 0) /* erfc(+-inf)=0,2 */ + return 0.0; + else + return 2.0; + } + if ((ax = x) < 0) + ax = -ax; + if (ax < .84375) { /* |x|<0.84375 */ + if (ax < 1.38777878078144568e-17) /* |x|<2**-56 */ + return one-x; + y = x*x; + r = y*(p1+y*(p2+y*(p3+y*(p4+y*(p5+ + y*(p6+y*(p7+y*(p8+y*(p9+y*p10))))))))); + if (ax < .0625) { /* |x|<2**-4 */ + return (one-(x+x*(p0+r))); + } else { + r = x*(p0+r); + r += (x-half); + return (half - r); + } + } + if (ax < 1.25) { /* 0.84375 <= |x| < 1.25 */ + s = ax-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if (x>=0) { + z = one-c; return z - P/Q; + } else { + z = c+P/Q; return one+z; + } + } + if (ax >= 28) { /* Out of range */ + if (x>0) + return (tiny*tiny); + else + return (two-tiny); + } + z = ax; + TRUNC(z); + y = z - ax; y *= (ax+z); + z *= -z; /* Here z + y = -x^2 */ + s = one/(-z-y); /* 1/(x*x) */ + if (ax >= 4) { /* 6 <= ax */ + R = s*(rd1+s*(rd2+s*(rd3+s*(rd4+s*(rd5+ + s*(rd6+s*(rd7+s*(rd8+s*(rd9+s*(rd10 + +s*(rd11+s*(rd12+s*rd13)))))))))))); + y += rd0; + } else if (ax >= 2) { + R = rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*(rb5+ + s*(rb6+s*(rb7+s*(rb8+s*(rb9+s*rb10))))))))); + S = one+s*(sb1+s*(sb2+s*sb3)); + y += R/S; + R = -.5*s; + } else { + R = rc0+s*(rc1+s*(rc2+s*(rc3+s*(rc4+s*(rc5+ + s*(rc6+s*(rc7+s*(rc8+s*(rc9+s*rc10))))))))); + S = one+s*(sc1+s*(sc2+s*sc3)); + y += R/S; + R = -.5*s; + } + /* return exp(-x^2 - lsqrtPI_hi + R + y)/x; */ + s = ((R + y) - lsqrtPI_hi) + z; + y = (((z-s) - lsqrtPI_hi) + R) + y; + r = __exp__D(s, y)/x; + if (x>0) + return r; + else + return two-r; +} diff --git a/lib/nbsd_libm/noieee_src/n_exp.c b/lib/nbsd_libm/noieee_src/n_exp.c new file mode 100644 index 000000000..68cf6e8bc --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_exp.c @@ -0,0 +1,215 @@ +/* $NetBSD: n_exp.c,v 1.8 2008/03/20 16:41:26 mhitch Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)exp.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* EXP(X) + * RETURN THE EXPONENTIAL OF X + * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. NG on 2/6/85, 2/15/85, 3/7/85, 3/24/85, 4/16/85, 6/14/86. + * + * Required system supported functions: + * scalb(x,n) + * copysign(x,y) + * finite(x) + * + * Method: + * 1. Argument Reduction: given the input x, find r and integer k such + * that + * x = k*ln2 + r, |r| <= 0.5*ln2 . + * r will be represented as r := z+c for better accuracy. + * + * 2. Compute exp(r) by + * + * exp(r) = 1 + r + r*R1/(2-R1), + * where + * R1 = x - x^2*(p1+x^2*(p2+x^2*(p3+x^2*(p4+p5*x^2)))). + * + * 3. exp(x) = 2^k * exp(r) . + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF)= 0; + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * exp(x) returns the exponential of x nearly rounded. In a test run + * with 1,156,000 random arguments on a VAX, the maximum observed + * error was 0.869 ulps (units in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "../src/namespace.h" +#include "mathimpl.h" + +#ifdef __weak_alias +__weak_alias(exp, _exp); +__weak_alias(expf, _expf); +#endif + +vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) +vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010) +vc(lntiny,-9.5654310917272452386E1 ,4f01,c3bf,33af,d72e, 7,-.BF4F01D72E33AF) +vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1) +vc(p1, 1.6666666666666602251E-1 ,aaaa,3f2a,a9f1,aaaa, -2, .AAAAAAAAAAA9F1) +vc(p2, -2.7777777777015591216E-3 ,0b60,bc36,ec94,b5f5, -8,-.B60B60B5F5EC94) +vc(p3, 6.6137563214379341918E-5 ,b355,398a,f15f,792e, -13, .8AB355792EF15F) +vc(p4, -1.6533902205465250480E-6 ,ea0e,b6dd,5f84,2e93, -19,-.DDEA0E2E935F84) +vc(p5, 4.1381367970572387085E-8 ,bb4b,3431,2683,95f5, -24, .B1BB4B95F52683) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#define lnhuge vccast(lnhuge) +#define lntiny vccast(lntiny) +#define invln2 vccast(invln2) +#define p1 vccast(p1) +#define p2 vccast(p2) +#define p3 vccast(p3) +#define p4 vccast(p4) +#define p5 vccast(p5) +#endif + +ic(p1, 1.6666666666666601904E-1, -3, 1.555555555553E) +ic(p2, -2.7777777777015593384E-3, -9, -1.6C16C16BEBD93) +ic(p3, 6.6137563214379343612E-5, -14, 1.1566AAF25DE2C) +ic(p4, -1.6533902205465251539E-6, -20, -1.BBD41C5D26BF1) +ic(p5, 4.1381367970572384604E-8, -25, 1.6376972BEA4D0) +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10,-33, 1.A39EF35793C76) +ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2) +ic(lntiny,-7.5137154372698068983E2, 9, -1.77AF8EBEAE354) +ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE) + +double +exp(double x) +{ + double z,hi,lo,c; + int k; + +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if( x <= lnhuge ) { + if( x >= lntiny ) { + + /* argument reduction : x --> x - k*ln2 */ + + k=invln2*x+copysign(0.5,x); /* k=NINT(x/ln2) */ + + /* express x-k*ln2 as hi-lo and let x=hi-lo rounded */ + + hi=x-k*ln2hi; + x=hi-(lo=k*ln2lo); + + /* return 2^k*[1+x+x*c/(2+c)] */ + z=x*x; + c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); + return scalb(1.0+(hi-(lo-(x*c)/(2.0-c))),k); + + } + /* end of x > lntiny */ + + else + /* exp(-big#) underflows to zero */ + if(finite(x)) return(scalb(1.0,-5000)); + + /* exp(-INF) is zero */ + else return(0.0); + } + /* end of x < lnhuge */ + + else + /* exp(INF) is INF, exp(+big#) overflows to INF */ + return( finite(x) ? scalb(1.0,5000) : x); +} + +float +expf(float x) +{ + return(exp((double)x)); +} + +/* returns exp(r = x + c) for |c| < |x| with no overlap. */ + +double +__exp__D(double x, double c) +{ + double z,hi,lo; + int k; + +#if !defined(__vax__)&&!defined(tahoe) + if (x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if ( x <= lnhuge ) { + if ( x >= lntiny ) { + + /* argument reduction : x --> x - k*ln2 */ + z = invln2*x; + k = z + copysign(.5, x); + + /* express (x+c)-k*ln2 as hi-lo and let x=hi-lo rounded */ + + hi=(x-k*ln2hi); /* Exact. */ + x= hi - (lo = k*ln2lo-c); + /* return 2^k*[1+x+x*c/(2+c)] */ + z=x*x; + c= x - z*(p1+z*(p2+z*(p3+z*(p4+z*p5)))); + c = (x*c)/(2.0-c); + + return scalb(1.+(hi-(lo - c)), k); + } + /* end of x > lntiny */ + + else + /* exp(-big#) underflows to zero */ + if(finite(x)) return(scalb(1.0,-5000)); + + /* exp(-INF) is zero */ + else return(0.0); + } + /* end of x < lnhuge */ + + else + /* exp(INF) is INF, exp(+big#) overflows to INF */ + return( finite(x) ? scalb(1.0,5000) : x); +} diff --git a/lib/nbsd_libm/noieee_src/n_exp__E.c b/lib/nbsd_libm/noieee_src/n_exp__E.c new file mode 100644 index 000000000..ed99a0e29 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_exp__E.c @@ -0,0 +1,136 @@ +/* $NetBSD: n_exp__E.c,v 1.7 2008/04/29 15:10:02 uwe Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)exp__E.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* exp__E(x,c) + * ASSUMPTION: c << x SO THAT fl(x+c)=x. + * (c is the correction term for x) + * exp__E RETURNS + * + * / exp(x+c) - 1 - x , 1E-19 < |x| < .3465736 + * exp__E(x,c) = | + * \ 0 , |x| < 1E-19. + * + * DOUBLE PRECISION (IEEE 53 bits, VAX D FORMAT 56 BITS) + * KERNEL FUNCTION OF EXP, EXPM1, POW FUNCTIONS + * CODED IN C BY K.C. NG, 1/31/85; + * REVISED BY K.C. NG on 3/16/85, 4/16/85. + * + * Required system supported function: + * copysign(x,y) + * + * Method: + * 1. Rational approximation. Let r=x+c. + * Based on + * 2 * sinh(r/2) + * exp(r) - 1 = ---------------------- , + * cosh(r/2) - sinh(r/2) + * exp__E(r) is computed using + * x*x (x/2)*W - ( Q - ( 2*P + x*P ) ) + * --- + (c + x*[---------------------------------- + c ]) + * 2 1 - W + * where P := p1*x^2 + p2*x^4, + * Q := q1*x^2 + q2*x^4 (for 56 bits precision, add q3*x^6) + * W := x/2-(Q-x*P), + * + * (See the listing below for the values of p1,p2,q1,q2,q3. The poly- + * nomials P and Q may be regarded as the approximations to sinh + * and cosh : + * sinh(r/2) = r/2 + r * P , cosh(r/2) = 1 + Q . ) + * + * The coefficients were obtained by a special Remez algorithm. + * + * Approximation error: + * + * | exp(x) - 1 | 2**(-57), (IEEE double) + * | ------------ - (exp__E(x,0)+x)/x | <= + * | x | 2**(-69). (VAX D) + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(p1, 1.5150724356786683059E-2 ,3abe,3d78,066a,67e1, -6, .F83ABE67E1066A) +vc(p2, 6.3112487873718332688E-5 ,5b42,3984,0173,48cd, -13, .845B4248CD0173) +vc(q1, 1.1363478204690669916E-1 ,b95a,3ee8,ec45,44a2, -3, .E8B95A44A2EC45) +vc(q2, 1.2624568129896839182E-3 ,7905,3ba5,f5e7,72e4, -9, .A5790572E4F5E7) +vc(q3, 1.5021856115869022674E-6 ,9eb4,36c9,c395,604a, -19, .C99EB4604AC395) + +ic(p1, 1.3887401997267371720E-2, -7, 1.C70FF8B3CC2CF) +ic(p2, 3.3044019718331897649E-5, -15, 1.15317DF4526C4) +ic(q1, 1.1110813732786649355E-1, -4, 1.C719538248597) +ic(q2, 9.9176615021572857300E-4, -10, 1.03FC4CB8C98E8) + +#ifdef vccast +#define p1 vccast(p1) +#define p2 vccast(p2) +#define q1 vccast(q1) +#define q2 vccast(q2) +#define q3 vccast(q3) +#endif + +double +__exp__E(double x, double c) +{ + static const double zero=0.0, one=1.0, half=1.0/2.0, small=1.0E-19; + double z,p,q,xp,xh,w; + if(copysign(x,one)>small) { + z = x*x ; + p = z*( p1 +z* p2 ); +#if defined(__vax__)||defined(tahoe) + q = z*( q1 +z*( q2 +z* q3 )); +#else /* defined(__vax__)||defined(tahoe) */ + q = z*( q1 +z* q2 ); +#endif /* defined(__vax__)||defined(tahoe) */ + xp= x*p ; + xh= x*half ; + w = xh-(q-xp) ; + p = p+p; + c += x*((xh*w-(q-(p+xp)))/(one-w)+c); + return(z*half+c); + } + /* end of |x| > small */ + + else { + if(x!=zero) w=one+small; /* raise the inexact flag ??? -ragge */ + return(copysign(zero,x)); + } +} diff --git a/lib/nbsd_libm/noieee_src/n_expm1.c b/lib/nbsd_libm/noieee_src/n_expm1.c new file mode 100644 index 000000000..28b94bc1e --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_expm1.c @@ -0,0 +1,168 @@ +/* $NetBSD: n_expm1.c,v 1.7 2008/04/29 15:10:02 uwe Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)expm1.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* EXPM1(X) + * RETURN THE EXPONENTIAL OF X MINUS ONE + * DOUBLE PRECISION (IEEE 53 BITS, VAX D FORMAT 56 BITS) + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/21/85, 4/16/85. + * + * Required system supported functions: + * scalb(x,n) + * copysign(x,y) + * finite(x) + * + * Kernel function: + * exp__E(x,c) + * + * Method: + * 1. Argument Reduction: given the input x, find r and integer k such + * that + * x = k*ln2 + r, |r| <= 0.5*ln2 . + * r will be represented as r := z+c for better accuracy. + * + * 2. Compute EXPM1(r)=exp(r)-1 by + * + * EXPM1(r=z+c) := z + exp__E(z,c) + * + * 3. EXPM1(x) = 2^k * ( EXPM1(r) + 1-2^-k ). + * + * Remarks: + * 1. When k=1 and z < -0.25, we use the following formula for + * better accuracy: + * EXPM1(x) = 2 * ( (z+0.5) + exp__E(z,c) ) + * 2. To avoid rounding error in 1-2^-k where k is large, we use + * EXPM1(x) = 2^k * { [z+(exp__E(z,c)-2^-k )] + 1 } + * when k>56. + * + * Special cases: + * EXPM1(INF) is INF, EXPM1(NaN) is NaN; + * EXPM1(-INF)= -1; + * for finite argument, only EXPM1(0)=0 is exact. + * + * Accuracy: + * EXPM1(x) returns the exact (exp(x)-1) nearly rounded. In a test run with + * 1,166,000 random arguments on a VAX, the maximum observed error was + * .872 ulps (units of the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) +vc(lnhuge, 9.4961163736712506989E1 ,ec1d,43bd,9010,a73e, 7, .BDEC1DA73E9010) +vc(invln2, 1.4426950408889634148E0 ,aa3b,40b8,17f1,295c, 1, .B8AA3B295C17F1) + +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) +ic(lnhuge, 7.1602103751842355450E2, 9, 1.6602B15B7ECF2) +ic(invln2, 1.4426950408889633870E0, 0, 1.71547652B82FE) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#define lnhuge vccast(lnhuge) +#define invln2 vccast(invln2) +#endif + +#if defined(__vax__)||defined(tahoe) +#define PREC 56 +#else /* defined(__vax__)||defined(tahoe) */ +#define PREC 53 +#endif /* defined(__vax__)||defined(tahoe) */ + +double +expm1(double x) +{ + static const double one=1.0, half=1.0/2.0; + double z,hi,lo,c; + int k; + +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + + if( x <= lnhuge ) { + if( x >= -40.0 ) { + + /* argument reduction : x - k*ln2 */ + k= invln2 *x+copysign(0.5,x); /* k=NINT(x/ln2) */ + hi=x-k*ln2hi ; + z=hi-(lo=k*ln2lo); + c=(hi-z)-lo; + + if(k==0) return(z+__exp__E(z,c)); + if(k==1) + if(z< -0.25) + {x=z+half;x +=__exp__E(z,c); return(x+x);} + else + {z+=__exp__E(z,c); x=half+z; return(x+x);} + /* end of k=1 */ + + else { + if(k<=PREC) + { x=one-scalb(one,-k); z += __exp__E(z,c);} + else if(k<100) + { x = __exp__E(z,c)-scalb(one,-k); x+=z; z=one;} + else + { x = __exp__E(z,c)+z; z=one;} + + return (scalb(x+z,k)); + } + } + /* end of x > lnunfl */ + + else + /* expm1(-big#) rounded to -1 (inexact) */ + if(finite(x)) + { c=ln2hi+ln2lo; return(-one);} /* ??? -ragge */ + + /* expm1(-INF) is -1 */ + else return(-one); + } + /* end of x < lnhuge */ + + else + /* expm1(INF) is INF, expm1(+big#) overflows to INF */ + return( finite(x) ? scalb(one,5000) : x); +} diff --git a/lib/nbsd_libm/noieee_src/n_floor.c b/lib/nbsd_libm/noieee_src/n_floor.c new file mode 100644 index 000000000..2299aeb98 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_floor.c @@ -0,0 +1,218 @@ +/* $NetBSD: n_floor.c,v 1.7 2010/12/09 22:52:59 abs Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)floor.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(L, 4503599627370496.0E0 ,0000,5c00,0000,0000, 55, 1.0) /* 2**55 */ + +ic(L, 4503599627370496.0E0, 52, 1.0) /* 2**52 */ + +#ifdef vccast +#define L vccast(L) +#endif + +/* + * floor(x) := the largest integer no larger than x; + * ceil(x) := -floor(-x), for all real x. + * + * Note: Inexact will be signaled if x is not an integer, as is + * customary for IEEE 754. No other signal can be emitted. + */ +double +floor(double x) +{ + volatile double y; + + if ( +#if !defined(__vax__)&&!defined(tahoe) + x != x || /* NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + x >= L) /* already an even integer */ + return x; + else if (x < (double)0) + return -ceil(-x); + else { /* now 0 <= x < L */ + y = L+x; /* destructive store must be forced */ + y -= L; /* an integer, and |x-y| < 1 */ + return x < y ? y-(double)1 : y; + } +} + +float +floorf(float x) +{ + return floor((double)x); +} + +double +ceil(double x) +{ + volatile double y; + + if ( +#if !defined(__vax__)&&!defined(tahoe) + x != x || /* NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + x >= L) /* already an even integer */ + return x; + else if (x < (double)0) + return -floor(-x); + else { /* now 0 <= x < L */ + y = L+x; /* destructive store must be forced */ + y -= L; /* an integer, and |x-y| < 1 */ + return x > y ? y+(double)1 : y; + } +} + +float +ceilf(float x) +{ + return ceil((double)x); +} + +#ifndef ns32000 /* rint() is in ./NATIONAL/support.s */ +/* + * algorithm for rint(x) in pseudo-pascal form ... + * + * real rint(x): real x; + * ... delivers integer nearest x in direction of prevailing rounding + * ... mode + * const L = (last consecutive integer)/2 + * = 2**55; for VAX D + * = 2**52; for IEEE 754 Double + * real s,t; + * begin + * if x != x then return x; ... NaN + * if |x| >= L then return x; ... already an integer + * s := copysign(L,x); + * t := x + s; ... = (x+s) rounded to integer + * return t - s + * end; + * + * Note: Inexact will be signaled if x is not an integer, as is + * customary for IEEE 754. No other signal can be emitted. + */ +double +rint(double x) +{ + double s; + volatile double t; + const double one = 1.0; + +#if !defined(__vax__)&&!defined(tahoe) + if (x != x) /* NaN */ + return (x); +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if (copysign(x,one) >= L) /* already an integer */ + return (x); + s = copysign(L,x); + t = x + s; /* x+s rounded to integer */ + return (t - s); +} +#endif /* not national */ + +long +lrint(double x) +{ + double s; + volatile double t; + const double one = 1.0; + +#if !defined(__vax__)&&!defined(tahoe) + if (x != x) /* NaN */ + return (x); +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if (copysign(x,one) >= L) /* already an integer */ + return (x); + s = copysign(L,x); + t = x + s; /* x+s rounded to integer */ + return (t - s); +} + +long long +llrint(double x) +{ + double s; + volatile double t; + const double one = 1.0; + +#if !defined(__vax__)&&!defined(tahoe) + if (x != x) /* NaN */ + return (x); +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if (copysign(x,one) >= L) /* already an integer */ + return (x); + s = copysign(L,x); + t = x + s; /* x+s rounded to integer */ + return (t - s); +} + +long +lrintf(float x) +{ + float s; + volatile float t; + const float one = 1.0; + +#if !defined(__vax__)&&!defined(tahoe) + if (x != x) /* NaN */ + return (x); +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if (copysign(x,one) >= L) /* already an integer */ + return (x); + s = copysign(L,x); + t = x + s; /* x+s rounded to integer */ + return (t - s); +} + +long long +llrintf(float x) +{ + float s; + volatile float t; + const float one = 1.0; + +#if !defined(__vax__)&&!defined(tahoe) + if (x != x) /* NaN */ + return (x); +#endif /* !defined(__vax__)&&!defined(tahoe) */ + if (copysign(x,one) >= L) /* already an integer */ + return (x); + s = copysign(L,x); + t = x + s; /* x+s rounded to integer */ + return (t - s); +} diff --git a/lib/nbsd_libm/noieee_src/n_fmax.c b/lib/nbsd_libm/noieee_src/n_fmax.c new file mode 100644 index 000000000..5abe177b4 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_fmax.c @@ -0,0 +1,38 @@ +/* + * Copyright (c) 2011 Jonathan A. Kollasch + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR + * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; + * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, + * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR + * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF + * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_fmax.c,v 1.1 2011/01/09 02:32:13 jakllsch Exp $"); +#endif + +#include + +double +fmax(double x, double y) +{ + return x > y ? x : y; +} diff --git a/lib/nbsd_libm/noieee_src/n_fmaxf.c b/lib/nbsd_libm/noieee_src/n_fmaxf.c new file mode 100644 index 000000000..de27d4e9e --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_fmaxf.c @@ -0,0 +1,38 @@ +/* + * Copyright (c) 2011 Jonathan A. Kollasch + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR + * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; + * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, + * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR + * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF + * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_fmaxf.c,v 1.1 2011/01/09 02:32:13 jakllsch Exp $"); +#endif + +#include + +float +fmaxf(float x, float y) +{ + return x > y ? x : y; +} diff --git a/lib/nbsd_libm/noieee_src/n_fmin.c b/lib/nbsd_libm/noieee_src/n_fmin.c new file mode 100644 index 000000000..823b239d4 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_fmin.c @@ -0,0 +1,38 @@ +/* + * Copyright (c) 2011 Jonathan A. Kollasch + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR + * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; + * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, + * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR + * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF + * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_fmin.c,v 1.1 2011/01/09 02:32:13 jakllsch Exp $"); +#endif + +#include + +double +fmin(double x, double y) +{ + return x < y ? x : y; +} diff --git a/lib/nbsd_libm/noieee_src/n_fminf.c b/lib/nbsd_libm/noieee_src/n_fminf.c new file mode 100644 index 000000000..510e8f378 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_fminf.c @@ -0,0 +1,38 @@ +/* + * Copyright (c) 2011 Jonathan A. Kollasch + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS + * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR + * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, + * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, + * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; + * OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, + * WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR + * OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF + * ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_fminf.c,v 1.1 2011/01/09 02:32:13 jakllsch Exp $"); +#endif + +#include + +float +fminf(float x, float y) +{ + return x < y ? x : y; +} diff --git a/lib/nbsd_libm/noieee_src/n_fmod.c b/lib/nbsd_libm/noieee_src/n_fmod.c new file mode 100644 index 000000000..2c07aaca6 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_fmod.c @@ -0,0 +1,154 @@ +/* $NetBSD: n_fmod.c,v 1.5 2003/08/07 16:44:51 agc Exp $ */ +/* + * Copyright (c) 1989, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)fmod.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +#include "mathimpl.h" + +/* fmod.c + * + * SYNOPSIS + * + * #include + * double fmod(double x, double y) + * + * DESCRIPTION + * + * The fmod function computes the floating-point remainder of x/y. + * + * RETURNS + * + * The fmod function returns the value x-i*y, for some integer i + * such that, if y is nonzero, the result has the same sign as x and + * magnitude less than the magnitude of y. + * + * On a VAX or CCI, + * + * fmod(x,0) traps/faults on floating-point divided-by-zero. + * + * On IEEE-754 conforming machines with "isnan()" primitive, + * + * fmod(x,0), fmod(INF,y) are invalid operations and NaN is returned. + * + */ +#if !defined(__vax__) && !defined(tahoe) +extern int isnan(),finite(); +#endif /* !defined(__vax__) && !defined(tahoe) */ + +#ifdef TEST_FMOD +static double +_fmod(double x, double y) +#else /* TEST_FMOD */ +double +fmod(double x, double y) +#endif /* TEST_FMOD */ +{ + int ir,iy; + double r,w; + + if (y == (double)0 +#if !defined(__vax__) && !defined(tahoe) /* per "fmod" manual entry, SunOS 4.0 */ + || isnan(y) || !finite(x) +#endif /* !defined(__vax__) && !defined(tahoe) */ + ) + return (x*y)/(x*y); + + r = fabs(x); + y = fabs(y); + (void)frexp(y,&iy); + while (r >= y) { + (void)frexp(r,&ir); + w = ldexp(y,ir-iy); + r -= w <= r ? w : w*(double)0.5; + } + return x >= (double)0 ? r : -r; +} + +#ifdef TEST_FMOD +extern long random(); +extern double fmod(); + +#define NTEST 10000 +#define NCASES 3 + +static int nfail = 0; + +static void +doit(double x, double y) +{ + double ro = fmod(x,y),rn = _fmod(x,y); + if (ro != rn) { + (void)printf(" x = 0x%08.8x %08.8x (%24.16e)\n",x,x); + (void)printf(" y = 0x%08.8x %08.8x (%24.16e)\n",y,y); + (void)printf(" fmod = 0x%08.8x %08.8x (%24.16e)\n",ro,ro); + (void)printf("_fmod = 0x%08.8x %08.8x (%24.16e)\n",rn,rn); + (void)printf("\n"); + } +} + +int +main(int argc, char **argv) +{ + int i,cases; + double x,y; + + srandom(12345); + for (i = 0; i < NTEST; i++) { + x = (double)random(); + y = (double)random(); + for (cases = 0; cases < NCASES; cases++) { + switch (cases) { + case 0: + break; + case 1: + y = (double)1/y; break; + case 2: + x = (double)1/x; break; + default: + abort(); break; + } + doit(x,y); + doit(x,-y); + doit(-x,y); + doit(-x,-y); + } + } + if (nfail) + (void)printf("Number of failures: %d (out of a total of %d)\n", + nfail,NTEST*NCASES*4); + else + (void)printf("No discrepancies were found\n"); + exit(0); +} +#endif /* TEST_FMOD */ diff --git a/lib/nbsd_libm/noieee_src/n_gamma.c b/lib/nbsd_libm/noieee_src/n_gamma.c new file mode 100644 index 000000000..607b0e213 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_gamma.c @@ -0,0 +1,333 @@ +/* $NetBSD: n_gamma.c,v 1.6 2006/11/24 21:15:54 wiz Exp $ */ +/*- + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)gamma.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* + * This code by P. McIlroy, Oct 1992; + * + * The financial support of UUNET Communications Services is gratefully + * acknowledged. + */ + +#include +#include "mathimpl.h" +#include + +/* METHOD: + * x < 0: Use reflection formula, G(x) = pi/(sin(pi*x)*x*G(x)) + * At negative integers, return +Inf, and set errno. + * + * x < 6.5: + * Use argument reduction G(x+1) = xG(x) to reach the + * range [1.066124,2.066124]. Use a rational + * approximation centered at the minimum (x0+1) to + * ensure monotonicity. + * + * x >= 6.5: Use the asymptotic approximation (Stirling's formula) + * adjusted for equal-ripples: + * + * log(G(x)) ~= (x-.5)*(log(x)-1) + .5(log(2*pi)-1) + 1/x*P(1/(x*x)) + * + * Keep extra precision in multiplying (x-.5)(log(x)-1), to + * avoid premature round-off. + * + * Special values: + * non-positive integer: Set overflow trap; return +Inf; + * x > 171.63: Set overflow trap; return +Inf; + * NaN: Set invalid trap; return NaN + * + * Accuracy: Gamma(x) is accurate to within + * x > 0: error provably < 0.9ulp. + * Maximum observed in 1,000,000 trials was .87ulp. + * x < 0: + * Maximum observed error < 4ulp in 1,000,000 trials. + */ + +static double neg_gam (double); +static double small_gam (double); +static double smaller_gam (double); +static struct Double large_gam (double); +static struct Double ratfun_gam (double, double); + +/* + * Rational approximation, A0 + x*x*P(x)/Q(x), on the interval + * [1.066.., 2.066..] accurate to 4.25e-19. + */ +#define LEFT -.3955078125 /* left boundary for rat. approx */ +#define x0 .461632144968362356785 /* xmin - 1 */ + +#define a0_hi 0.88560319441088874992 +#define a0_lo -.00000000000000004996427036469019695 +#define P0 6.21389571821820863029017800727e-01 +#define P1 2.65757198651533466104979197553e-01 +#define P2 5.53859446429917461063308081748e-03 +#define P3 1.38456698304096573887145282811e-03 +#define P4 2.40659950032711365819348969808e-03 +#define Q0 1.45019531250000000000000000000e+00 +#define Q1 1.06258521948016171343454061571e+00 +#define Q2 -2.07474561943859936441469926649e-01 +#define Q3 -1.46734131782005422506287573015e-01 +#define Q4 3.07878176156175520361557573779e-02 +#define Q5 5.12449347980666221336054633184e-03 +#define Q6 -1.76012741431666995019222898833e-03 +#define Q7 9.35021023573788935372153030556e-05 +#define Q8 6.13275507472443958924745652239e-06 +/* + * Constants for large x approximation (x in [6, Inf]) + * (Accurate to 2.8*10^-19 absolute) + */ +#define lns2pi_hi 0.418945312500000 +#define lns2pi_lo -.000006779295327258219670263595 +#define Pa0 8.33333333333333148296162562474e-02 +#define Pa1 -2.77777777774548123579378966497e-03 +#define Pa2 7.93650778754435631476282786423e-04 +#define Pa3 -5.95235082566672847950717262222e-04 +#define Pa4 8.41428560346653702135821806252e-04 +#define Pa5 -1.89773526463879200348872089421e-03 +#define Pa6 5.69394463439411649408050664078e-03 +#define Pa7 -1.44705562421428915453880392761e-02 + +static const double zero = 0., one = 1.0, tiny = 1e-300; +/* + * TRUNC sets trailing bits in a floating-point number to zero. + * is a temporary variable. + */ +#if defined(__vax__) || defined(tahoe) +#define _IEEE 0 +#define TRUNC(x) x = (double) (float) (x) +#else +static int endian; +#define _IEEE 1 +#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000 +#define infnan(x) 0.0 +#endif + +double +gamma(x) + double x; +{ + double b; + struct Double u; +#if _IEEE + int endian = (*(int *) &one) ? 1 : 0; +#endif + + if (x >= 6) { + if(x > 171.63) + return(one/zero); + u = large_gam(x); + return(__exp__D(u.a, u.b)); + } else if (x >= 1.0 + LEFT + x0) { + return (small_gam(x)); + } else if (x > 1.e-17) { + return (smaller_gam(x)); + } else if (x > -1.e-17) { + if (x == 0.0) { + if (!_IEEE) return (infnan(ERANGE)); + else return (one/x); + } + b =one+1e-20; /* Raise inexact flag. ??? -ragge */ + return (one/x); + } else if (!finite(x)) { + if (_IEEE) /* x = NaN, -Inf */ + return (x*x); + else + return (infnan(EDOM)); + } else + return (neg_gam(x)); +} +/* + * Accurate to max(ulp(1/128) absolute, 2^-66 relative) error. + */ +static struct Double +large_gam(double x) +{ + double z, p; + struct Double t, u, v; + + z = one/(x*x); + p = Pa0+z*(Pa1+z*(Pa2+z*(Pa3+z*(Pa4+z*(Pa5+z*(Pa6+z*Pa7)))))); + p = p/x; + + u = __log__D(x); + u.a -= one; + v.a = (x -= .5); + TRUNC(v.a); + v.b = x - v.a; + t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */ + t.b = v.b*u.a + x*u.b; + /* return t.a + t.b + lns2pi_hi + lns2pi_lo + p */ + t.b += lns2pi_lo; t.b += p; + u.a = lns2pi_hi + t.b; u.a += t.a; + u.b = t.a - u.a; + u.b += lns2pi_hi; u.b += t.b; + return (u); +} +/* + * Good to < 1 ulp. (provably .90 ulp; .87 ulp on 1,000,000 runs.) + * It also has correct monotonicity. + */ +static double +small_gam(double x) +{ + double y, ym1, t; + struct Double yy, r; + y = x - one; + ym1 = y - one; + if (y <= 1.0 + (LEFT + x0)) { + yy = ratfun_gam(y - x0, 0); + return (yy.a + yy.b); + } + r.a = y; + TRUNC(r.a); + yy.a = r.a - one; + y = ym1; + yy.b = r.b = y - yy.a; + /* Argument reduction: G(x+1) = x*G(x) */ + for (ym1 = y-one; ym1 > LEFT + x0; y = ym1--, yy.a--) { + t = r.a*yy.a; + r.b = r.a*yy.b + y*r.b; + r.a = t; + TRUNC(r.a); + r.b += (t - r.a); + } + /* Return r*gamma(y). */ + yy = ratfun_gam(y - x0, 0); + y = r.b*(yy.a + yy.b) + r.a*yy.b; + y += yy.a*r.a; + return (y); +} +/* + * Good on (0, 1+x0+LEFT]. Accurate to 1ulp. + */ +static double +smaller_gam(double x) +{ + double t, d; + struct Double r, xx; + if (x < x0 + LEFT) { + t = x, TRUNC(t); + d = (t+x)*(x-t); + t *= t; + xx.a = (t + x), TRUNC(xx.a); + xx.b = x - xx.a; xx.b += t; xx.b += d; + t = (one-x0); t += x; + d = (one-x0); d -= t; d += x; + x = xx.a + xx.b; + } else { + xx.a = x, TRUNC(xx.a); + xx.b = x - xx.a; + t = x - x0; + d = (-x0 -t); d += x; + } + r = ratfun_gam(t, d); + d = r.a/x, TRUNC(d); + r.a -= d*xx.a; r.a -= d*xx.b; r.a += r.b; + return (d + r.a/x); +} +/* + * returns (z+c)^2 * P(z)/Q(z) + a0 + */ +static struct Double +ratfun_gam(double z, double c) +{ + double p, q; + struct Double r, t; + + q = Q0 +z*(Q1+z*(Q2+z*(Q3+z*(Q4+z*(Q5+z*(Q6+z*(Q7+z*Q8))))))); + p = P0 + z*(P1 + z*(P2 + z*(P3 + z*P4))); + + /* return r.a + r.b = a0 + (z+c)^2*p/q, with r.a truncated to 26 bits. */ + p = p/q; + t.a = z, TRUNC(t.a); /* t ~= z + c */ + t.b = (z - t.a) + c; + t.b *= (t.a + z); + q = (t.a *= t.a); /* t = (z+c)^2 */ + TRUNC(t.a); + t.b += (q - t.a); + r.a = p, TRUNC(r.a); /* r = P/Q */ + r.b = p - r.a; + t.b = t.b*p + t.a*r.b + a0_lo; + t.a *= r.a; /* t = (z+c)^2*(P/Q) */ + r.a = t.a + a0_hi, TRUNC(r.a); + r.b = ((a0_hi-r.a) + t.a) + t.b; + return (r); /* r = a0 + t */ +} + +static double +neg_gam(double x) +{ + int sgn = 1; + struct Double lg, lsine; + double y, z; + + y = floor(x + .5); + if (y == x) { /* Negative integer. */ + if(!_IEEE) + return (infnan(ERANGE)); + else + return (one/zero); + } + z = fabs(x - y); + y = .5*ceil(x); + if (y == ceil(y)) + sgn = -1; + if (z < .25) + z = sin(M_PI*z); + else + z = cos(M_PI*(0.5-z)); + /* Special case: G(1-x) = Inf; G(x) may be nonzero. */ + if (x < -170) { + if (x < -190) + return ((double)sgn*tiny*tiny); + y = one - x; /* exact: 128 < |x| < 255 */ + lg = large_gam(y); + lsine = __log__D(M_PI/z); /* = TRUNC(log(u)) + small */ + lg.a -= lsine.a; /* exact (opposite signs) */ + lg.b -= lsine.b; + y = -(lg.a + lg.b); + z = (y + lg.a) + lg.b; + y = __exp__D(y, z); + if (sgn < 0) y = -y; + return (y); + } + y = one-x; + if (one-y == x) + y = gamma(y); + else /* 1-x is inexact */ + y = -x*gamma(-x); + if (sgn < 0) y = -y; + return (M_PI / (y*z)); +} diff --git a/lib/nbsd_libm/noieee_src/n_j0.c b/lib/nbsd_libm/noieee_src/n_j0.c new file mode 100644 index 000000000..73adcc90d --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_j0.c @@ -0,0 +1,444 @@ +/* $NetBSD: n_j0.c,v 1.6 2003/08/07 16:44:51 agc Exp $ */ +/*- + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)j0.c 8.2 (Berkeley) 11/30/93"; +#endif +#endif /* not lint */ + +/* + * 16 December 1992 + * Minor modifications by Peter McIlroy to adapt non-IEEE architecture. + */ + +/* + * ==================================================== + * Copyright (C) 1992 by Sun Microsystems, Inc. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * ******************* WARNING ******************** + * This is an alpha version of SunPro's FDLIBM (Freely + * Distributable Math Library) for IEEE double precision + * arithmetic. FDLIBM is a basic math library written + * in C that runs on machines that conform to IEEE + * Standard 754/854. This alpha version is distributed + * for testing purpose. Those who use this software + * should report any bugs to + * + * fdlibm-comments@sunpro.eng.sun.com + * + * -- K.C. Ng, Oct 12, 1992 + * ************************************************ + */ + +/* double j0(double x), y0(double x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u0 + u1*z + ... + u6*z^6 + * V(z) = 1 + v1*z + ... + v4*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include "mathimpl.h" +#include +#include + +#if defined(__vax__) || defined(tahoe) +#define _IEEE 0 +#else +#define _IEEE 1 +#define infnan(x) (0.0) +#endif + +static double pzero (double), qzero (double); + +static const double +huge = 1e300, +zero = 0.0, +one = 1.0, +invsqrtpi= 5.641895835477562869480794515607725858441e-0001, +tpi = 0.636619772367581343075535053490057448, + /* R0/S0 on [0, 2.00] */ +r02 = 1.562499999999999408594634421055018003102e-0002, +r03 = -1.899792942388547334476601771991800712355e-0004, +r04 = 1.829540495327006565964161150603950916854e-0006, +r05 = -4.618326885321032060803075217804816988758e-0009, +s01 = 1.561910294648900170180789369288114642057e-0002, +s02 = 1.169267846633374484918570613449245536323e-0004, +s03 = 5.135465502073181376284426245689510134134e-0007, +s04 = 1.166140033337900097836930825478674320464e-0009; + +double +j0(double x) +{ + double z, s,c,ss,cc,r,u,v; + + if (!finite(x)) { + if (_IEEE) return one/(x*x); + else return (0); + } + x = fabs(x); + if (x >= 2.0) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + if (x < .5 * DBL_MAX) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c) 6.80564733841876927e+38) /* 2^129 */ + z = (invsqrtpi*cc)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/sqrt(x); + } + return z; + } + if (x < 1.220703125e-004) { /* |x| < 2**-13 */ + if (huge+x > one) { /* raise inexact if x != 0 */ + if (x < 7.450580596923828125e-009) /* |x|<2**-27 */ + return one; + else return (one - 0.25*x*x); + } + } + z = x*x; + r = z*(r02+z*(r03+z*(r04+z*r05))); + s = one+z*(s01+z*(s02+z*(s03+z*s04))); + if (x < one) { /* |x| < 1.00 */ + return (one + z*(-0.25+(r/s))); + } else { + u = 0.5*x; + return ((one+u)*(one-u)+z*(r/s)); + } +} + +static const double +u00 = -7.380429510868722527422411862872999615628e-0002, +u01 = 1.766664525091811069896442906220827182707e-0001, +u02 = -1.381856719455968955440002438182885835344e-0002, +u03 = 3.474534320936836562092566861515617053954e-0004, +u04 = -3.814070537243641752631729276103284491172e-0006, +u05 = 1.955901370350229170025509706510038090009e-0008, +u06 = -3.982051941321034108350630097330144576337e-0011, +v01 = 1.273048348341237002944554656529224780561e-0002, +v02 = 7.600686273503532807462101309675806839635e-0005, +v03 = 2.591508518404578033173189144579208685163e-0007, +v04 = 4.411103113326754838596529339004302243157e-0010; + +double +y0(double x) +{ + double z, s, c, ss, cc, u, v; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if (!finite(x)) { + if (_IEEE) + return (one/(x+x*x)); + else + return (0); + } + if (x == 0) { + if (_IEEE) return (-one/zero); + else return(infnan(-ERANGE)); + } + if (x<0) { + if (_IEEE) return (zero/zero); + else return (infnan(EDOM)); + } + if (x >= 2.00) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if (x < .5 * DBL_MAX) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c) 6.80564733841876927e+38) /* > 2^129 */ + z = (invsqrtpi*ss)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if (x <= 7.450580596923828125e-009) { /* x < 2**-27 */ + return (u00 + tpi*log(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return (u/v + tpi*(j0(x)*log(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0, + -7.031249999999003994151563066182798210142e-0002, + -8.081670412753498508883963849859423939871e+0000, + -2.570631056797048755890526455854482662510e+0002, + -2.485216410094288379417154382189125598962e+0003, + -5.253043804907295692946647153614119665649e+0003, +}; +static const double ps8[5] = { + 1.165343646196681758075176077627332052048e+0002, + 3.833744753641218451213253490882686307027e+0003, + 4.059785726484725470626341023967186966531e+0004, + 1.167529725643759169416844015694440325519e+0005, + 4.762772841467309430100106254805711722972e+0004, +}; + +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.141254646918944974922813501362824060117e-0011, + -7.031249408735992804117367183001996028304e-0002, + -4.159610644705877925119684455252125760478e+0000, + -6.767476522651671942610538094335912346253e+0001, + -3.312312996491729755731871867397057689078e+0002, + -3.464333883656048910814187305901796723256e+0002, +}; +static const double ps5[5] = { + 6.075393826923003305967637195319271932944e+0001, + 1.051252305957045869801410979087427910437e+0003, + 5.978970943338558182743915287887408780344e+0003, + 9.625445143577745335793221135208591603029e+0003, + 2.406058159229391070820491174867406875471e+0003, +}; + +static const double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.547046017719519317420607587742992297519e-0009, + -7.031196163814817199050629727406231152464e-0002, + -2.409032215495295917537157371488126555072e+0000, + -2.196597747348830936268718293366935843223e+0001, + -5.807917047017375458527187341817239891940e+0001, + -3.144794705948885090518775074177485744176e+0001, +}; +static const double ps3[5] = { + 3.585603380552097167919946472266854507059e+0001, + 3.615139830503038919981567245265266294189e+0002, + 1.193607837921115243628631691509851364715e+0003, + 1.127996798569074250675414186814529958010e+0003, + 1.735809308133357510239737333055228118910e+0002, +}; + +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.875343330325263874525704514800809730145e-0008, + -7.030309954836247756556445443331044338352e-0002, + -1.450738467809529910662233622603401167409e+0000, + -7.635696138235277739186371273434739292491e+0000, + -1.119316688603567398846655082201614524650e+0001, + -3.233645793513353260006821113608134669030e+0000, +}; +static const double ps2[5] = { + 2.222029975320888079364901247548798910952e+0001, + 1.362067942182152109590340823043813120940e+0002, + 2.704702786580835044524562897256790293238e+0002, + 1.538753942083203315263554770476850028583e+0002, + 1.465761769482561965099880599279699314477e+0001, +}; + +static double +pzero(double x) +{ + const double *p,*q; + double z,r,s; + if (x >= 8.00) {p = pr8; q= ps8;} + else if (x >= 4.54545211791992188) {p = pr5; q= ps5;} + else if (x >= 2.85714149475097656) {p = pr3; q= ps3;} + else /* if (x >= 2.00) */ {p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qr0 + qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs0*s^2 + ... + qs5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0, + 7.324218749999350414479738504551775297096e-0002, + 1.176820646822526933903301695932765232456e+0001, + 5.576733802564018422407734683549251364365e+0002, + 8.859197207564685717547076568608235802317e+0003, + 3.701462677768878501173055581933725704809e+0004, +}; +static const double qs8[6] = { + 1.637760268956898345680262381842235272369e+0002, + 8.098344946564498460163123708054674227492e+0003, + 1.425382914191204905277585267143216379136e+0005, + 8.033092571195144136565231198526081387047e+0005, + 8.405015798190605130722042369969184811488e+0005, + -3.438992935378666373204500729736454421006e+0005, +}; + +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.840859635945155400568380711372759921179e-0011, + 7.324217666126847411304688081129741939255e-0002, + 5.835635089620569401157245917610984757296e+0000, + 1.351115772864498375785526599119895942361e+0002, + 1.027243765961641042977177679021711341529e+0003, + 1.989977858646053872589042328678602481924e+0003, +}; +static const double qs5[6] = { + 8.277661022365377058749454444343415524509e+0001, + 2.077814164213929827140178285401017305309e+0003, + 1.884728877857180787101956800212453218179e+0004, + 5.675111228949473657576693406600265778689e+0004, + 3.597675384251145011342454247417399490174e+0004, + -5.354342756019447546671440667961399442388e+0003, +}; + +static const double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.377410140897386263955149197672576223054e-0009, + 7.324111800429115152536250525131924283018e-0002, + 3.344231375161707158666412987337679317358e+0000, + 4.262184407454126175974453269277100206290e+0001, + 1.708080913405656078640701512007621675724e+0002, + 1.667339486966511691019925923456050558293e+0002, +}; +static const double qs3[6] = { + 4.875887297245871932865584382810260676713e+0001, + 7.096892210566060535416958362640184894280e+0002, + 3.704148226201113687434290319905207398682e+0003, + 6.460425167525689088321109036469797462086e+0003, + 2.516333689203689683999196167394889715078e+0003, + -1.492474518361563818275130131510339371048e+0002, +}; + +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.504444448869832780257436041633206366087e-0007, + 7.322342659630792930894554535717104926902e-0002, + 1.998191740938159956838594407540292600331e+0000, + 1.449560293478857407645853071687125850962e+0001, + 3.166623175047815297062638132537957315395e+0001, + 1.625270757109292688799540258329430963726e+0001, +}; +static const double qs2[6] = { + 3.036558483552191922522729838478169383969e+0001, + 2.693481186080498724211751445725708524507e+0002, + 8.447837575953201460013136756723746023736e+0002, + 8.829358451124885811233995083187666981299e+0002, + 2.126663885117988324180482985363624996652e+0002, + -5.310954938826669402431816125780738924463e+0000, +}; + +static double +qzero(double x) +{ + const double *p,*q; + double s,r,z; + if (x >= 8.00) {p = qr8; q= qs8;} + else if (x >= 4.54545211791992188) {p = qr5; q= qs5;} + else if (x >= 2.85714149475097656) {p = qr3; q= qs3;} + else /* if (x >= 2.00) */ {p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-.125 + r/s)/x; +} diff --git a/lib/nbsd_libm/noieee_src/n_j1.c b/lib/nbsd_libm/noieee_src/n_j1.c new file mode 100644 index 000000000..9f824ce33 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_j1.c @@ -0,0 +1,448 @@ +/* $NetBSD: n_j1.c,v 1.6 2003/08/07 16:44:51 agc Exp $ */ +/*- + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)j1.c 8.2 (Berkeley) 11/30/93"; +#endif +#endif /* not lint */ + +/* + * 16 December 1992 + * Minor modifications by Peter McIlroy to adapt non-IEEE architecture. + */ + +/* + * ==================================================== + * Copyright (C) 1992 by Sun Microsystems, Inc. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * ******************* WARNING ******************** + * This is an alpha version of SunPro's FDLIBM (Freely + * Distributable Math Library) for IEEE double precision + * arithmetic. FDLIBM is a basic math library written + * in C that runs on machines that conform to IEEE + * Standard 754/854. This alpha version is distributed + * for testing purpose. Those who use this software + * should report any bugs to + * + * fdlibm-comments@sunpro.eng.sun.com + * + * -- K.C. Ng, Oct 12, 1992 + * ************************************************ + */ + +/* double j1(double x), y1(double x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follows: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = u0 + u1*z + ... + u4*z^4 + * V(z) = 1 + v1*z + ... + v5*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include "mathimpl.h" +#include +#include + +#if defined(__vax__) || defined(tahoe) +#define _IEEE 0 +#else +#define _IEEE 1 +#define infnan(x) (0.0) +#endif + +static double pone (double), qone (double); + +static const double +huge = 1e300, +zero = 0.0, +one = 1.0, +invsqrtpi= 5.641895835477562869480794515607725858441e-0001, +tpi = 0.636619772367581343075535053490057448, + + /* R0/S0 on [0,2] */ +r00 = -6.250000000000000020842322918309200910191e-0002, +r01 = 1.407056669551897148204830386691427791200e-0003, +r02 = -1.599556310840356073980727783817809847071e-0005, +r03 = 4.967279996095844750387702652791615403527e-0008, +s01 = 1.915375995383634614394860200531091839635e-0002, +s02 = 1.859467855886309024045655476348872850396e-0004, +s03 = 1.177184640426236767593432585906758230822e-0006, +s04 = 5.046362570762170559046714468225101016915e-0009, +s05 = 1.235422744261379203512624973117299248281e-0011; + +#define two_129 6.80564733841876926e+038 /* 2^129 */ +#define two_m54 5.55111512312578270e-017 /* 2^-54 */ + +double +j1(double x) +{ + double z, s,c,ss,cc,r,u,v,y; + y = fabs(x); + if (!finite(x)) { /* Inf or NaN */ + if (_IEEE && x != x) + return(x); + else + return (copysign(x, zero)); + } + y = fabs(x); + if (y >= 2) { /* |x| >= 2.0 */ + s = sin(y); + c = cos(y); + ss = -s-c; + cc = s-c; + if (y < .5*DBL_MAX) { /* make sure y+y not overflow */ + z = cos(y+y); + if ((s*c) two_129) /* x > 2^129 */ + z = (invsqrtpi*cc)/sqrt(y); + else +#endif /* defined(__vax__) || defined(tahoe) */ + { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/sqrt(y); + } + if (x < 0) return -z; + else return z; + } + if (y < 7.450580596923828125e-009) { /* |x|<2**-27 */ + if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return (x*0.5+r/s); +} + +static const double u0[5] = { + -1.960570906462389484206891092512047539632e-0001, + 5.044387166398112572026169863174882070274e-0002, + -1.912568958757635383926261729464141209569e-0003, + 2.352526005616105109577368905595045204577e-0005, + -9.190991580398788465315411784276789663849e-0008, +}; +static const double v0[5] = { + 1.991673182366499064031901734535479833387e-0002, + 2.025525810251351806268483867032781294682e-0004, + 1.356088010975162198085369545564475416398e-0006, + 6.227414523646214811803898435084697863445e-0009, + 1.665592462079920695971450872592458916421e-0011, +}; + +double +y1(double x) +{ + double z, s, c, ss, cc, u, v; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if (!finite(x)) { + if (!_IEEE) return (infnan(EDOM)); + else if (x < 0) + return(zero/zero); + else if (x > 0) + return (0); + else + return(x); + } + if (x <= 0) { + if (_IEEE && x == 0) return -one/zero; + else if(x == 0) return(infnan(-ERANGE)); + else if(_IEEE) return (zero/zero); + else return(infnan(EDOM)); + } + if (x >= 2) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = -s-c; + cc = s-c; + if (x < .5 * DBL_MAX) { /* make sure x+x not overflow */ + z = cos(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if (_IEEE && x>two_129) { + z = (invsqrtpi*ss)/sqrt(x); + } else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if (x <= two_m54) { /* x < 2**-54 */ + return (-tpi/x); + } + z = x*x; + u = u0[0]+z*(u0[1]+z*(u0[2]+z*(u0[3]+z*u0[4]))); + v = one+z*(v0[0]+z*(v0[1]+z*(v0[2]+z*(v0[3]+z*v0[4])))); + return (x*(u/v) + tpi*(j1(x)*log(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0, + 1.171874999999886486643746274751925399540e-0001, + 1.323948065930735690925827997575471527252e+0001, + 4.120518543073785433325860184116512799375e+0002, + 3.874745389139605254931106878336700275601e+0003, + 7.914479540318917214253998253147871806507e+0003, +}; +static const double ps8[5] = { + 1.142073703756784104235066368252692471887e+0002, + 3.650930834208534511135396060708677099382e+0003, + 3.695620602690334708579444954937638371808e+0004, + 9.760279359349508334916300080109196824151e+0004, + 3.080427206278887984185421142572315054499e+0004, +}; + +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.319905195562435287967533851581013807103e-0011, + 1.171874931906140985709584817065144884218e-0001, + 6.802751278684328781830052995333841452280e+0000, + 1.083081829901891089952869437126160568246e+0002, + 5.176361395331997166796512844100442096318e+0002, + 5.287152013633375676874794230748055786553e+0002, +}; +static const double ps5[5] = { + 5.928059872211313557747989128353699746120e+0001, + 9.914014187336144114070148769222018425781e+0002, + 5.353266952914879348427003712029704477451e+0003, + 7.844690317495512717451367787640014588422e+0003, + 1.504046888103610723953792002716816255382e+0003, +}; + +static const double pr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 3.025039161373736032825049903408701962756e-0009, + 1.171868655672535980750284752227495879921e-0001, + 3.932977500333156527232725812363183251138e+0000, + 3.511940355916369600741054592597098912682e+0001, + 9.105501107507812029367749771053045219094e+0001, + 4.855906851973649494139275085628195457113e+0001, +}; +static const double ps3[5] = { + 3.479130950012515114598605916318694946754e+0001, + 3.367624587478257581844639171605788622549e+0002, + 1.046871399757751279180649307467612538415e+0003, + 8.908113463982564638443204408234739237639e+0002, + 1.037879324396392739952487012284401031859e+0002, +}; + +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.077108301068737449490056513753865482831e-0007, + 1.171762194626833490512746348050035171545e-0001, + 2.368514966676087902251125130227221462134e+0000, + 1.224261091482612280835153832574115951447e+0001, + 1.769397112716877301904532320376586509782e+0001, + 5.073523125888185399030700509321145995160e+0000, +}; +static const double ps2[5] = { + 2.143648593638214170243114358933327983793e+0001, + 1.252902271684027493309211410842525120355e+0002, + 2.322764690571628159027850677565128301361e+0002, + 1.176793732871470939654351793502076106651e+0002, + 8.364638933716182492500902115164881195742e+0000, +}; + +static double +pone(double x) +{ + const double *p,*q; + double z,r,s; + if (x >= 8.0) {p = pr8; q= ps8;} + else if (x >= 4.54545211791992188) {p = pr5; q= ps5;} + else if (x >= 2.85714149475097656) {p = pr3; q= ps3;} + else /* if (x >= 2.0) */ {p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return (one + r/s); +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0, + -1.025390624999927207385863635575804210817e-0001, + -1.627175345445899724355852152103771510209e+0001, + -7.596017225139501519843072766973047217159e+0002, + -1.184980667024295901645301570813228628541e+0004, + -4.843851242857503225866761992518949647041e+0004, +}; +static const double qs8[6] = { + 1.613953697007229231029079421446916397904e+0002, + 7.825385999233484705298782500926834217525e+0003, + 1.338753362872495800748094112937868089032e+0005, + 7.196577236832409151461363171617204036929e+0005, + 6.666012326177764020898162762642290294625e+0005, + -2.944902643038346618211973470809456636830e+0005, +}; + +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.089799311417640889742251585097264715678e-0011, + -1.025390502413754195402736294609692303708e-0001, + -8.056448281239359746193011295417408828404e+0000, + -1.836696074748883785606784430098756513222e+0002, + -1.373193760655081612991329358017247355921e+0003, + -2.612444404532156676659706427295870995743e+0003, +}; +static const double qs5[6] = { + 8.127655013843357670881559763225310973118e+0001, + 1.991798734604859732508048816860471197220e+0003, + 1.746848519249089131627491835267411777366e+0004, + 4.985142709103522808438758919150738000353e+0004, + 2.794807516389181249227113445299675335543e+0004, + -4.719183547951285076111596613593553911065e+0003, +}; + +static const double qr3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -5.078312264617665927595954813341838734288e-0009, + -1.025378298208370901410560259001035577681e-0001, + -4.610115811394734131557983832055607679242e+0000, + -5.784722165627836421815348508816936196402e+0001, + -2.282445407376317023842545937526967035712e+0002, + -2.192101284789093123936441805496580237676e+0002, +}; +static const double qs3[6] = { + 4.766515503237295155392317984171640809318e+0001, + 6.738651126766996691330687210949984203167e+0002, + 3.380152866795263466426219644231687474174e+0003, + 5.547729097207227642358288160210745890345e+0003, + 1.903119193388108072238947732674639066045e+0003, + -1.352011914443073322978097159157678748982e+0002, +}; + +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.783817275109588656126772316921194887979e-0007, + -1.025170426079855506812435356168903694433e-0001, + -2.752205682781874520495702498875020485552e+0000, + -1.966361626437037351076756351268110418862e+0001, + -4.232531333728305108194363846333841480336e+0001, + -2.137192117037040574661406572497288723430e+0001, +}; +static const double qs2[6] = { + 2.953336290605238495019307530224241335502e+0001, + 2.529815499821905343698811319455305266409e+0002, + 7.575028348686454070022561120722815892346e+0002, + 7.393932053204672479746835719678434981599e+0002, + 1.559490033366661142496448853793707126179e+0002, + -4.959498988226281813825263003231704397158e+0000, +}; + +static double +qone(double x) +{ + const double *p,*q; + double s,r,z; + if (x >= 8.0) {p = qr8; q= qs8;} + else if (x >= 4.54545211791992188) {p = qr5; q= qs5;} + else if (x >= 2.85714149475097656) {p = qr3; q= qs3;} + else /* if (x >= 2.0) */ {p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (.375 + r/s)/x; +} diff --git a/lib/nbsd_libm/noieee_src/n_jn.c b/lib/nbsd_libm/noieee_src/n_jn.c new file mode 100644 index 000000000..ac04f3fda --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_jn.c @@ -0,0 +1,311 @@ +/* $NetBSD: n_jn.c,v 1.6 2003/08/07 16:44:51 agc Exp $ */ +/*- + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)jn.c 8.2 (Berkeley) 11/30/93"; +#endif +#endif /* not lint */ + +/* + * 16 December 1992 + * Minor modifications by Peter McIlroy to adapt non-IEEE architecture. + */ + +/* + * ==================================================== + * Copyright (C) 1992 by Sun Microsystems, Inc. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + * ******************* WARNING ******************** + * This is an alpha version of SunPro's FDLIBM (Freely + * Distributable Math Library) for IEEE double precision + * arithmetic. FDLIBM is a basic math library written + * in C that runs on machines that conform to IEEE + * Standard 754/854. This alpha version is distributed + * for testing purpose. Those who use this software + * should report any bugs to + * + * fdlibm-comments@sunpro.eng.sun.com + * + * -- K.C. Ng, Oct 12, 1992 + * ************************************************ + */ + +/* + * jn(int n, double x), yn(int n, double x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for nx, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "mathimpl.h" +#include +#include + +#if defined(__vax__) || defined(tahoe) +#define _IEEE 0 +#else +#define _IEEE 1 +#define infnan(x) (0.0) +#endif + +static const double +invsqrtpi= 5.641895835477562869480794515607725858441e-0001, +two = 2.0, +zero = 0.0, +one = 1.0; + +double +jn(int n, double x) +{ + int i, sgn; + double a, b, temp; + double z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + /* if J(n,NaN) is NaN */ + if (_IEEE && isnan(x)) return x+x; + if (n<0){ + n = -n; + x = -x; + } + if (n==0) return(j0(x)); + if (n==1) return(j1(x)); + sgn = (n&1)&(x < zero); /* even n -- 0, odd n -- sign(x) */ + x = fabs(x); + if (x == 0 || !finite (x)) /* if x is 0 or inf */ + b = zero; + else if ((double) n <= x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if (_IEEE && x >= 8.148143905337944345e+090) { + /* x >= 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = cos(x)+sin(x); break; + case 1: temp = -cos(x)+sin(x); break; + case 2: temp = -cos(x)-sin(x); break; + case 3: temp = cos(x)-sin(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + a = j0(x); + b = j1(x); + for(i=1;i 33) /* underflow */ + b = zero; + else { + temp = x*0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (double)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t,v; + double q0,q1,h,tmp; int k,m; + w = (n+n)/(double)x; h = 2.0/(double)x; + q0 = w; z = w+h; q1 = w*z - 1.0; k=1; + while (q1<1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result will + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*log(fabs(v*tmp)); + for (i=n-1;i>0;i--){ + temp = b; + b = ((i+i)/x)*b - a; + a = temp; + /* scale b to avoid spurious overflow */ +# if defined(__vax__) || defined(tahoe) +# define BMAX 1e13 +# else +# define BMAX 1e100 +# endif /* defined(__vax__) || defined(tahoe) */ + if (b > BMAX) { + a /= b; + t /= b; + b = one; + } + } + b = (t*j0(x)/b); + } + } + return ((sgn == 1) ? -b : b); +} + +double +yn(int n, double x) +{ + int i, sign; + double a, b, temp; + + /* Y(n,NaN), Y(n, x < 0) is NaN */ + if (x <= 0 || (_IEEE && x != x)) + if (_IEEE && x < 0) return zero/zero; + else if (x < 0) return (infnan(EDOM)); + else if (_IEEE) return -one/zero; + else return(infnan(-ERANGE)); + else if (!finite(x)) return(0); + sign = 1; + if (n<0){ + n = -n; + sign = 1 - ((n&1)<<2); + } + if (n == 0) return(y0(x)); + if (n == 1) return(sign*y1(x)); + if(_IEEE && x >= 8.148143905337944345e+090) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch (n&3) { + case 0: temp = sin(x)-cos(x); break; + case 1: temp = -sin(x)-cos(x); break; + case 2: temp = -sin(x)+cos(x); break; + case 3: temp = sin(x)+cos(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + a = y0(x); + b = y1(x); + /* quit if b is -inf */ + for (i = 1; i < n && !finite(b); i++){ + temp = b; + b = ((double)(i+i)/x)*b - a; + a = temp; + } + } + if (!_IEEE && !finite(b)) + return (infnan(-sign * ERANGE)); + return ((sign > 0) ? b : -b); +} diff --git a/lib/nbsd_libm/noieee_src/n_lgamma.c b/lib/nbsd_libm/noieee_src/n_lgamma.c new file mode 100644 index 000000000..b5740c43a --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_lgamma.c @@ -0,0 +1,308 @@ +/* $NetBSD: n_lgamma.c,v 1.6 2006/11/24 21:15:54 wiz Exp $ */ +/*- + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)lgamma.c 8.2 (Berkeley) 11/30/93"; +#endif +#endif /* not lint */ + +/* + * Coded by Peter McIlroy, Nov 1992; + * + * The financial support of UUNET Communications Services is gratefully + * acknowledged. + */ + +#include +#include + +#include "mathimpl.h" + +/* Log gamma function. + * Error: x > 0 error < 1.3ulp. + * x > 4, error < 1ulp. + * x > 9, error < .6ulp. + * x < 0, all bets are off. (When G(x) ~ 1, log(G(x)) ~ 0) + * Method: + * x > 6: + * Use the asymptotic expansion (Stirling's Formula) + * 0 < x < 6: + * Use gamma(x+1) = x*gamma(x) for argument reduction. + * Use rational approximation in + * the range 1.2, 2.5 + * Two approximations are used, one centered at the + * minimum to ensure monotonicity; one centered at 2 + * to maintain small relative error. + * x < 0: + * Use the reflection formula, + * G(1-x)G(x) = PI/sin(PI*x) + * Special values: + * non-positive integer returns +Inf. + * NaN returns NaN +*/ +#if defined(__vax__) || defined(tahoe) +#define _IEEE 0 +/* double and float have same size exponent field */ +#define TRUNC(x) x = (double) (float) (x) +#else +static int endian; +#define _IEEE 1 +#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000 +#define infnan(x) 0.0 +#endif + +static double small_lgam(double); +static double large_lgam(double); +static double neg_lgam(double); +static const double one = 1.0; +int signgam; + +#define UNDERFL (1e-1020 * 1e-1020) + +#define LEFT (1.0 - (x0 + .25)) +#define RIGHT (x0 - .218) +/* + * Constants for approximation in [1.244,1.712] +*/ +#define x0 0.461632144968362356785 +#define x0_lo -.000000000000000015522348162858676890521 +#define a0_hi -0.12148629128932952880859 +#define a0_lo .0000000007534799204229502 +#define r0 -2.771227512955130520e-002 +#define r1 -2.980729795228150847e-001 +#define r2 -3.257411333183093394e-001 +#define r3 -1.126814387531706041e-001 +#define r4 -1.129130057170225562e-002 +#define r5 -2.259650588213369095e-005 +#define s0 1.714457160001714442e+000 +#define s1 2.786469504618194648e+000 +#define s2 1.564546365519179805e+000 +#define s3 3.485846389981109850e-001 +#define s4 2.467759345363656348e-002 +/* + * Constants for approximation in [1.71, 2.5] +*/ +#define a1_hi 4.227843350984671344505727574870e-01 +#define a1_lo 4.670126436531227189e-18 +#define p0 3.224670334241133695662995251041e-01 +#define p1 3.569659696950364669021382724168e-01 +#define p2 1.342918716072560025853732668111e-01 +#define p3 1.950702176409779831089963408886e-02 +#define p4 8.546740251667538090796227834289e-04 +#define q0 1.000000000000000444089209850062e+00 +#define q1 1.315850076960161985084596381057e+00 +#define q2 6.274644311862156431658377186977e-01 +#define q3 1.304706631926259297049597307705e-01 +#define q4 1.102815279606722369265536798366e-02 +#define q5 2.512690594856678929537585620579e-04 +#define q6 -1.003597548112371003358107325598e-06 +/* + * Stirling's Formula, adjusted for equal-ripple. x in [6,Inf]. +*/ +#define lns2pi .418938533204672741780329736405 +#define pb0 8.33333333333333148296162562474e-02 +#define pb1 -2.77777777774548123579378966497e-03 +#define pb2 7.93650778754435631476282786423e-04 +#define pb3 -5.95235082566672847950717262222e-04 +#define pb4 8.41428560346653702135821806252e-04 +#define pb5 -1.89773526463879200348872089421e-03 +#define pb6 5.69394463439411649408050664078e-03 +#define pb7 -1.44705562421428915453880392761e-02 + +__pure double +lgamma(double x) +{ + double r; + + signgam = 1; +#if _IEEE + endian = ((*(int *) &one)) ? 1 : 0; +#endif + + if (!finite(x)) { + if (_IEEE) + return (x+x); + else return (infnan(EDOM)); + } + + if (x > 6 + RIGHT) { + r = large_lgam(x); + return (r); + } else if (x > 1e-16) + return (small_lgam(x)); + else if (x > -1e-16) { + if (x < 0) + signgam = -1, x = -x; + return (-log(x)); + } else + return (neg_lgam(x)); +} + +static double +large_lgam(double x) +{ + double z, p, x1; + struct Double t, u, v; + u = __log__D(x); + u.a -= 1.0; + if (x > 1e15) { + v.a = x - 0.5; + TRUNC(v.a); + v.b = (x - v.a) - 0.5; + t.a = u.a*v.a; + t.b = x*u.b + v.b*u.a; + if (_IEEE == 0 && !finite(t.a)) + return(infnan(ERANGE)); + return(t.a + t.b); + } + x1 = 1./x; + z = x1*x1; + p = pb0+z*(pb1+z*(pb2+z*(pb3+z*(pb4+z*(pb5+z*(pb6+z*pb7)))))); + /* error in approximation = 2.8e-19 */ + + p = p*x1; /* error < 2.3e-18 absolute */ + /* 0 < p < 1/64 (at x = 5.5) */ + v.a = x = x - 0.5; + TRUNC(v.a); /* truncate v.a to 26 bits. */ + v.b = x - v.a; + t.a = v.a*u.a; /* t = (x-.5)*(log(x)-1) */ + t.b = v.b*u.a + x*u.b; + t.b += p; t.b += lns2pi; /* return t + lns2pi + p */ + return (t.a + t.b); +} + +static double +small_lgam(double x) +{ + int x_int; + double y, z, t, r = 0, p, q, hi, lo; + struct Double rr; + x_int = (x + .5); + y = x - x_int; + if (x_int <= 2 && y > RIGHT) { + t = y - x0; + y--; x_int++; + goto CONTINUE; + } else if (y < -LEFT) { + t = y +(1.0-x0); +CONTINUE: + z = t - x0_lo; + p = r0+z*(r1+z*(r2+z*(r3+z*(r4+z*r5)))); + q = s0+z*(s1+z*(s2+z*(s3+z*s4))); + r = t*(z*(p/q) - x0_lo); + t = .5*t*t; + z = 1.0; + switch (x_int) { + case 6: z = (y + 5); + case 5: z *= (y + 4); + case 4: z *= (y + 3); + case 3: z *= (y + 2); + rr = __log__D(z); + rr.b += a0_lo; rr.a += a0_hi; + return(((r+rr.b)+t+rr.a)); + case 2: return(((r+a0_lo)+t)+a0_hi); + case 0: r -= log1p(x); + default: rr = __log__D(x); + rr.a -= a0_hi; rr.b -= a0_lo; + return(((r - rr.b) + t) - rr.a); + } + } else { + p = p0+y*(p1+y*(p2+y*(p3+y*p4))); + q = q0+y*(q1+y*(q2+y*(q3+y*(q4+y*(q5+y*q6))))); + p = p*(y/q); + t = (double)(float) y; + z = y-t; + hi = (double)(float) (p+a1_hi); + lo = a1_hi - hi; lo += p; lo += a1_lo; + r = lo*y + z*hi; /* q + r = y*(a0+p/q) */ + q = hi*t; + z = 1.0; + switch (x_int) { + case 6: z = (y + 5); + case 5: z *= (y + 4); + case 4: z *= (y + 3); + case 3: z *= (y + 2); + rr = __log__D(z); + r += rr.b; r += q; + return(rr.a + r); + case 2: return (q+ r); + case 0: rr = __log__D(x); + r -= rr.b; r -= log1p(x); + r += q; r-= rr.a; + return(r); + default: rr = __log__D(x); + r -= rr.b; + q -= rr.a; + return (r+q); + } + } +} + +static double +neg_lgam(double x) +{ + int xi; + double y, z, zero = 0.0; + + /* avoid destructive cancellation as much as possible */ + if (x > -170) { + xi = x; + if (xi == x) { + if (_IEEE) + return(one/zero); + else + return(infnan(ERANGE)); + } + y = gamma(x); + if (y < 0) + y = -y, signgam = -1; + return (log(y)); + } + z = floor(x + .5); + if (z == x) { /* convention: G(-(integer)) -> +Inf */ + if (_IEEE) + return (one/zero); + else + return (infnan(ERANGE)); + } + y = .5*ceil(x); + if (y == ceil(y)) + signgam = -1; + x = -x; + z = fabs(x + z); /* 0 < z <= .5 */ + if (z < .25) + z = sin(M_PI*z); + else + z = cos(M_PI*(0.5-z)); + z = log(M_PI/(z*x)); + y = large_lgam(x); + return (z - y); +} diff --git a/lib/nbsd_libm/noieee_src/n_log.c b/lib/nbsd_libm/noieee_src/n_log.c new file mode 100644 index 000000000..917629320 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_log.c @@ -0,0 +1,491 @@ +/* $NetBSD: n_log.c,v 1.7 2008/03/20 16:41:26 mhitch Exp $ */ +/* + * Copyright (c) 1992, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)log.c 8.2 (Berkeley) 11/30/93"; +#endif +#endif /* not lint */ + +#include "../src/namespace.h" + +#include +#include + +#include "mathimpl.h" + +#ifdef __weak_alias +__weak_alias(log, _log); +__weak_alias(logf, _logf); +#endif + +/* Table-driven natural logarithm. + * + * This code was derived, with minor modifications, from: + * Peter Tang, "Table-Driven Implementation of the + * Logarithm in IEEE Floating-Point arithmetic." ACM Trans. + * Math Software, vol 16. no 4, pp 378-400, Dec 1990). + * + * Calculates log(2^m*F*(1+f/F)), |f/j| <= 1/256, + * where F = j/128 for j an integer in [0, 128]. + * + * log(2^m) = log2_hi*m + log2_tail*m + * since m is an integer, the dominant term is exact. + * m has at most 10 digits (for subnormal numbers), + * and log2_hi has 11 trailing zero bits. + * + * log(F) = logF_hi[j] + logF_lo[j] is in tabular form in log_table.h + * logF_hi[] + 512 is exact. + * + * log(1+f/F) = 2*f/(2*F + f) + 1/12 * (2*f/(2*F + f))**3 + ... + * the leading term is calculated to extra precision in two + * parts, the larger of which adds exactly to the dominant + * m and F terms. + * There are two cases: + * 1. when m, j are non-zero (m | j), use absolute + * precision for the leading term. + * 2. when m = j = 0, |1-x| < 1/256, and log(x) ~= (x-1). + * In this case, use a relative precision of 24 bits. + * (This is done differently in the original paper) + * + * Special cases: + * 0 return signalling -Inf + * neg return signalling NaN + * +Inf return +Inf +*/ + +#if defined(__vax__) || defined(tahoe) +#define _IEEE 0 +#define TRUNC(x) x = (double) (float) (x) +#else +#define _IEEE 1 +#define endian (((*(int *) &one)) ? 1 : 0) +#define TRUNC(x) *(((int *) &x) + endian) &= 0xf8000000 +#define infnan(x) 0.0 +#endif + +#define N 128 + +/* Table of log(Fj) = logF_head[j] + logF_tail[j], for Fj = 1+j/128. + * Used for generation of extend precision logarithms. + * The constant 35184372088832 is 2^45, so the divide is exact. + * It ensures correct reading of logF_head, even for inaccurate + * decimal-to-binary conversion routines. (Everybody gets the + * right answer for integers less than 2^53.) + * Values for log(F) were generated using error < 10^-57 absolute + * with the bc -l package. +*/ +static const double A1 = .08333333333333178827; +static const double A2 = .01250000000377174923; +static const double A3 = .002232139987919447809; +static const double A4 = .0004348877777076145742; + +static const double logF_head[N+1] = { + 0., + .007782140442060381246, + .015504186535963526694, + .023167059281547608406, + .030771658666765233647, + .038318864302141264488, + .045809536031242714670, + .053244514518837604555, + .060624621816486978786, + .067950661908525944454, + .075223421237524235039, + .082443669210988446138, + .089612158689760690322, + .096729626458454731618, + .103796793681567578460, + .110814366340264314203, + .117783035656430001836, + .124703478501032805070, + .131576357788617315236, + .138402322859292326029, + .145182009844575077295, + .151916042025732167530, + .158605030176659056451, + .165249572895390883786, + .171850256926518341060, + .178407657472689606947, + .184922338493834104156, + .191394852999565046047, + .197825743329758552135, + .204215541428766300668, + .210564769107350002741, + .216873938300523150246, + .223143551314024080056, + .229374101064877322642, + .235566071312860003672, + .241719936886966024758, + .247836163904594286577, + .253915209980732470285, + .259957524436686071567, + .265963548496984003577, + .271933715484010463114, + .277868451003087102435, + .283768173130738432519, + .289633292582948342896, + .295464212893421063199, + .301261330578199704177, + .307025035294827830512, + .312755710004239517729, + .318453731118097493890, + .324119468654316733591, + .329753286372579168528, + .335355541920762334484, + .340926586970454081892, + .346466767346100823488, + .351976423156884266063, + .357455888922231679316, + .362905493689140712376, + .368325561158599157352, + .373716409793814818840, + .379078352934811846353, + .384411698910298582632, + .389716751140440464951, + .394993808240542421117, + .400243164127459749579, + .405465108107819105498, + .410659924985338875558, + .415827895143593195825, + .420969294644237379543, + .426084395310681429691, + .431173464818130014464, + .436236766774527495726, + .441274560805140936281, + .446287102628048160113, + .451274644139630254358, + .456237433481874177232, + .461175715122408291790, + .466089729924533457960, + .470979715219073113985, + .475845904869856894947, + .480688529345570714212, + .485507815781602403149, + .490303988045525329653, + .495077266798034543171, + .499827869556611403822, + .504556010751912253908, + .509261901790523552335, + .513945751101346104405, + .518607764208354637958, + .523248143765158602036, + .527867089620485785417, + .532464798869114019908, + .537041465897345915436, + .541597282432121573947, + .546132437597407260909, + .550647117952394182793, + .555141507540611200965, + .559615787935399566777, + .564070138285387656651, + .568504735352689749561, + .572919753562018740922, + .577315365035246941260, + .581691739635061821900, + .586049045003164792433, + .590387446602107957005, + .594707107746216934174, + .599008189645246602594, + .603290851438941899687, + .607555250224322662688, + .611801541106615331955, + .616029877215623855590, + .620240409751204424537, + .624433288012369303032, + .628608659422752680256, + .632766669570628437213, + .636907462236194987781, + .641031179420679109171, + .645137961373620782978, + .649227946625615004450, + .653301272011958644725, + .657358072709030238911, + .661398482245203922502, + .665422632544505177065, + .669430653942981734871, + .673422675212350441142, + .677398823590920073911, + .681359224807238206267, + .685304003098281100392, + .689233281238557538017, + .693147180560117703862 +}; + +static const double logF_tail[N+1] = { + 0., + -.00000000000000543229938420049, + .00000000000000172745674997061, + -.00000000000001323017818229233, + -.00000000000001154527628289872, + -.00000000000000466529469958300, + .00000000000005148849572685810, + -.00000000000002532168943117445, + -.00000000000005213620639136504, + -.00000000000001819506003016881, + .00000000000006329065958724544, + .00000000000008614512936087814, + -.00000000000007355770219435028, + .00000000000009638067658552277, + .00000000000007598636597194141, + .00000000000002579999128306990, + -.00000000000004654729747598444, + -.00000000000007556920687451336, + .00000000000010195735223708472, + -.00000000000017319034406422306, + -.00000000000007718001336828098, + .00000000000010980754099855238, + -.00000000000002047235780046195, + -.00000000000008372091099235912, + .00000000000014088127937111135, + .00000000000012869017157588257, + .00000000000017788850778198106, + .00000000000006440856150696891, + .00000000000016132822667240822, + -.00000000000007540916511956188, + -.00000000000000036507188831790, + .00000000000009120937249914984, + .00000000000018567570959796010, + -.00000000000003149265065191483, + -.00000000000009309459495196889, + .00000000000017914338601329117, + -.00000000000001302979717330866, + .00000000000023097385217586939, + .00000000000023999540484211737, + .00000000000015393776174455408, + -.00000000000036870428315837678, + .00000000000036920375082080089, + -.00000000000009383417223663699, + .00000000000009433398189512690, + .00000000000041481318704258568, + -.00000000000003792316480209314, + .00000000000008403156304792424, + -.00000000000034262934348285429, + .00000000000043712191957429145, + -.00000000000010475750058776541, + -.00000000000011118671389559323, + .00000000000037549577257259853, + .00000000000013912841212197565, + .00000000000010775743037572640, + .00000000000029391859187648000, + -.00000000000042790509060060774, + .00000000000022774076114039555, + .00000000000010849569622967912, + -.00000000000023073801945705758, + .00000000000015761203773969435, + .00000000000003345710269544082, + -.00000000000041525158063436123, + .00000000000032655698896907146, + -.00000000000044704265010452446, + .00000000000034527647952039772, + -.00000000000007048962392109746, + .00000000000011776978751369214, + -.00000000000010774341461609578, + .00000000000021863343293215910, + .00000000000024132639491333131, + .00000000000039057462209830700, + -.00000000000026570679203560751, + .00000000000037135141919592021, + -.00000000000017166921336082431, + -.00000000000028658285157914353, + -.00000000000023812542263446809, + .00000000000006576659768580062, + -.00000000000028210143846181267, + .00000000000010701931762114254, + .00000000000018119346366441110, + .00000000000009840465278232627, + -.00000000000033149150282752542, + -.00000000000018302857356041668, + -.00000000000016207400156744949, + .00000000000048303314949553201, + -.00000000000071560553172382115, + .00000000000088821239518571855, + -.00000000000030900580513238244, + -.00000000000061076551972851496, + .00000000000035659969663347830, + .00000000000035782396591276383, + -.00000000000046226087001544578, + .00000000000062279762917225156, + .00000000000072838947272065741, + .00000000000026809646615211673, + -.00000000000010960825046059278, + .00000000000002311949383800537, + -.00000000000058469058005299247, + -.00000000000002103748251144494, + -.00000000000023323182945587408, + -.00000000000042333694288141916, + -.00000000000043933937969737844, + .00000000000041341647073835565, + .00000000000006841763641591466, + .00000000000047585534004430641, + .00000000000083679678674757695, + -.00000000000085763734646658640, + .00000000000021913281229340092, + -.00000000000062242842536431148, + -.00000000000010983594325438430, + .00000000000065310431377633651, + -.00000000000047580199021710769, + -.00000000000037854251265457040, + .00000000000040939233218678664, + .00000000000087424383914858291, + .00000000000025218188456842882, + -.00000000000003608131360422557, + -.00000000000050518555924280902, + .00000000000078699403323355317, + -.00000000000067020876961949060, + .00000000000016108575753932458, + .00000000000058527188436251509, + -.00000000000035246757297904791, + -.00000000000018372084495629058, + .00000000000088606689813494916, + .00000000000066486268071468700, + .00000000000063831615170646519, + .00000000000025144230728376072, + -.00000000000017239444525614834 +}; + +double +log(double x) +{ + int m, j; + double F, f, g, q, u, u2, v, zero = 0.0, one = 1.0; + volatile double u1; + + /* Catch special cases */ + if (x <= 0) { + if (_IEEE && x == zero) /* log(0) = -Inf */ + return (-one/zero); + else if (_IEEE) /* log(neg) = NaN */ + return (zero/zero); + else if (x == zero) /* NOT REACHED IF _IEEE */ + return (infnan(-ERANGE)); + else + return (infnan(EDOM)); + } else if (!finite(x)) { + if (_IEEE) /* x = NaN, Inf */ + return (x+x); + else + return (infnan(ERANGE)); + } + + /* Argument reduction: 1 <= g < 2; x/2^m = g; */ + /* y = F*(1 + f/F) for |f| <= 2^-8 */ + + m = logb(x); + g = ldexp(x, -m); + if (_IEEE && m == -1022) { + j = logb(g), m += j; + g = ldexp(g, -j); + } + j = N*(g-1) + .5; + F = (1.0/N) * j + 1; /* F*128 is an integer in [128, 512] */ + f = g - F; + + /* Approximate expansion for log(1+f/F) ~= u + q */ + g = 1/(2*F+f); + u = 2*f*g; + v = u*u; + q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); + + /* case 1: u1 = u rounded to 2^-43 absolute. Since u < 2^-8, + * u1 has at most 35 bits, and F*u1 is exact, as F has < 8 bits. + * It also adds exactly to |m*log2_hi + log_F_head[j] | < 750 + */ + if (m | j) + u1 = u + 513, u1 -= 513; + + /* case 2: |1-x| < 1/256. The m- and j- dependent terms are zero; + * u1 = u to 24 bits. + */ + else + u1 = u, TRUNC(u1); + u2 = (2.0*(f - F*u1) - u1*f) * g; + /* u1 + u2 = 2f/(2F+f) to extra precision. */ + + /* log(x) = log(2^m*F*(1+f/F)) = */ + /* (m*log2_hi+logF_head[j]+u1) + (m*log2_lo+logF_tail[j]+q); */ + /* (exact) + (tiny) */ + + u1 += m*logF_head[N] + logF_head[j]; /* exact */ + u2 = (u2 + logF_tail[j]) + q; /* tiny */ + u2 += logF_tail[N]*m; + return (u1 + u2); +} + +/* + * Extra precision variant, returning struct {double a, b;}; + * log(x) = a+b to 63 bits, with a is rounded to 26 bits. + */ +struct Double +__log__D(double x) +{ + int m, j; + double F, f, g, q, u, v, u2; + volatile double u1; + struct Double r; + + /* Argument reduction: 1 <= g < 2; x/2^m = g; */ + /* y = F*(1 + f/F) for |f| <= 2^-8 */ + + m = logb(x); + g = ldexp(x, -m); + if (_IEEE && m == -1022) { + j = logb(g), m += j; + g = ldexp(g, -j); + } + j = N*(g-1) + .5; + F = (1.0/N) * j + 1; + f = g - F; + + g = 1/(2*F+f); + u = 2*f*g; + v = u*u; + q = u*v*(A1 + v*(A2 + v*(A3 + v*A4))); + if (m | j) + u1 = u + 513, u1 -= 513; + else + u1 = u, TRUNC(u1); + u2 = (2.0*(f - F*u1) - u1*f) * g; + + u1 += m*logF_head[N] + logF_head[j]; + + u2 += logF_tail[j]; u2 += q; + u2 += logF_tail[N]*m; + r.a = u1 + u2; /* Only difference is here */ + TRUNC(r.a); + r.b = (u1 - r.a) + u2; + return (r); +} + +float +logf(float x) +{ + return(log((double)x)); +} diff --git a/lib/nbsd_libm/noieee_src/n_log10.c b/lib/nbsd_libm/noieee_src/n_log10.c new file mode 100644 index 000000000..02b5b91a4 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_log10.c @@ -0,0 +1,95 @@ +/* $NetBSD: n_log10.c,v 1.6 2003/08/07 16:44:52 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)log10.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* LOG10(X) + * RETURN THE BASE 10 LOGARITHM OF x + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/20/85; + * REVISED BY K.C. NG on 1/23/85, 3/7/85, 4/16/85. + * + * Required kernel function: + * log(x) + * + * Method : + * log(x) + * log10(x) = --------- or [1/log(10)]*log(x) + * log(10) + * + * Note: + * [log(10)] rounded to 56 bits has error .0895 ulps, + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * therefore, for better accuracy, in VAX D format, we divide + * log(x) by log(10), but in IEEE Double format, we multiply + * log(x) by [1/log(10)]. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal. + * + * Accuracy: + * log10(X) returns the exact log10(x) nearly rounded. In a test run + * with 1,536,000 random arguments on a VAX, the maximum observed + * error was 1.74 ulps (units in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(ln10hi, 2.3025850929940456790E0 ,5d8d,4113,a8ac,ddaa, 2, .935D8DDDAAA8AC) + +ic(ivln10, 4.3429448190325181667E-1, -2, 1.BCB7B1526E50E) + +#ifdef vccast +#define ln10hi vccast(ln10hi) +#endif + + +double +log10(double x) +{ +#if defined(__vax__)||defined(tahoe) + return(log(x)/ln10hi); +#else /* defined(__vax__)||defined(tahoe) */ + return(ivln10*log(x)); +#endif /* defined(__vax__)||defined(tahoe) */ +} diff --git a/lib/nbsd_libm/noieee_src/n_log1p.c b/lib/nbsd_libm/noieee_src/n_log1p.c new file mode 100644 index 000000000..03613d8b9 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_log1p.c @@ -0,0 +1,170 @@ +/* $NetBSD: n_log1p.c,v 1.7 2008/04/29 15:10:02 uwe Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)log1p.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* LOG1P(x) + * RETURN THE LOGARITHM OF 1+x + * DOUBLE PRECISION (VAX D FORMAT 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. NG on 2/6/85, 3/7/85, 3/24/85, 4/16/85. + * + * Required system supported functions: + * scalb(x,n) + * copysign(x,y) + * logb(x) + * finite(x) + * + * Required kernel function: + * log__L(z) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * log(1+f) is computed by + * + * log(1+f) = 2s + s*log__L(s*s) + * where + * log__L(z) = z*(L1 + z*(L2 + z*(... (L6 + z*L7)...))) + * + * See log__L() for the values of the coefficients. + * + * 3. Finally, log(1+x) = k*ln2 + log(1+f). + * + * Remarks 1. In step 3 n*ln2 will be stored in two floating point numbers + * n*ln2hi + n*ln2lo, where ln2hi is chosen such that the last + * 20 bits (for VAX D format), or the last 21 bits ( for IEEE + * double) is 0. This ensures n*ln2hi is exactly representable. + * 2. In step 1, f may not be representable. A correction term c + * for f is computed. It follows that the correction term for + * f - t (the leading term of log(1+f) in step 2) is c-c*x. We + * add this correction term to n*ln2lo to attenuate the error. + * + * + * Special cases: + * log1p(x) is NaN with signal if x < -1; log1p(NaN) is NaN with no signal; + * log1p(INF) is +INF; log1p(-1) is -INF with signal; + * only log1p(0)=0 is exact for finite argument. + * + * Accuracy: + * log1p(x) returns the exact log(1+x) nearly rounded. In a test run + * with 1,536,000 random arguments on a VAX, the maximum observed + * error was .846 ulps (units in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(ln2hi, 6.9314718055829871446E-1 ,7217,4031,0000,f7d0, 0, .B17217F7D00000) +vc(ln2lo, 1.6465949582897081279E-12 ,bcd5,2ce7,d9cc,e4f1, -39, .E7BCD5E4F1D9CC) +vc(sqrt2, 1.4142135623730950622E0 ,04f3,40b5,de65,33f9, 1, .B504F333F9DE65) + +ic(ln2hi, 6.9314718036912381649E-1, -1, 1.62E42FEE00000) +ic(ln2lo, 1.9082149292705877000E-10, -33, 1.A39EF35793C76) +ic(sqrt2, 1.4142135623730951455E0, 0, 1.6A09E667F3BCD) + +#ifdef vccast +#define ln2hi vccast(ln2hi) +#define ln2lo vccast(ln2lo) +#define sqrt2 vccast(sqrt2) +#endif + +double +log1p(double x) +{ + static const double zero=0.0, negone= -1.0, one=1.0, + half=1.0/2.0, small=1.0E-20; /* 1+small == 1 */ + double z,s,t,c; + int k; + +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + + if(finite(x)) { + if( x > negone ) { + + /* argument reduction */ + if(copysign(x,one)= sqrt2 ) + { k += 1 ; z *= half; t *= half; } + t += negone; x = z + t; + c = (t-x)+z ; /* correction term for x */ + + /* compute log(1+x) */ + s = x/(2+x); t = x*x*half; + c += (k*ln2lo-c*x); + z = c+s*(t+__log__L(s*s)); + x += (z - t) ; + + return(k*ln2hi+x); + } + /* end of if (x > negone) */ + + else { +#if defined(__vax__)||defined(tahoe) + if ( x == negone ) + return (infnan(-ERANGE)); /* -INF */ + else + return (infnan(EDOM)); /* NaN */ +#else /* defined(__vax__)||defined(tahoe) */ + /* x = -1, return -INF with signal */ + if ( x == negone ) return( negone/zero ); + + /* negative argument for log, return NaN with signal */ + else return ( zero / zero ); +#endif /* defined(__vax__)||defined(tahoe) */ + } + } + /* end of if (finite(x)) */ + + /* log(-INF) is NaN */ + else if(x<0) + return(zero/zero); + + /* log(+INF) is INF */ + else return(x); +} diff --git a/lib/nbsd_libm/noieee_src/n_log__L.c b/lib/nbsd_libm/noieee_src/n_log__L.c new file mode 100644 index 000000000..2c52242d7 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_log__L.c @@ -0,0 +1,110 @@ +/* $NetBSD: n_log__L.c,v 1.6 2003/08/07 16:44:52 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)log__L.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* log__L(Z) + * LOG(1+X) - 2S X + * RETURN --------------- WHERE Z = S*S, S = ------- , 0 <= Z <= .0294... + * S 2 + X + * + * DOUBLE PRECISION (VAX D FORMAT 56 bits or IEEE DOUBLE 53 BITS) + * KERNEL FUNCTION FOR LOG; TO BE USED IN LOG1P, LOG, AND POW FUNCTIONS + * CODED IN C BY K.C. NG, 1/19/85; + * REVISED BY K.C. Ng, 2/3/85, 4/16/85. + * + * Method : + * 1. Polynomial approximation: let s = x/(2+x). + * Based on log(1+x) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * + * (log(1+x) - 2s)/s is computed by + * + * z*(L1 + z*(L2 + z*(... (L7 + z*L8)...))) + * + * where z=s*s. (See the listing below for Lk's values.) The + * coefficients are obtained by a special Remez algorithm. + * + * Accuracy: + * Assuming no rounding error, the maximum magnitude of the approximation + * error (absolute) is 2**(-58.49) for IEEE double, and 2**(-63.63) + * for VAX D format. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "mathimpl.h" + +vc(L1, 6.6666666666666703212E-1 ,aaaa,402a,aac5,aaaa, 0, .AAAAAAAAAAAAC5) +vc(L2, 3.9999999999970461961E-1 ,cccc,3fcc,2684,cccc, -1, .CCCCCCCCCC2684) +vc(L3, 2.8571428579395698188E-1 ,4924,3f92,5782,92f8, -1, .92492492F85782) +vc(L4, 2.2222221233634724402E-1 ,8e38,3f63,af2c,39b7, -2, .E38E3839B7AF2C) +vc(L5, 1.8181879517064680057E-1 ,2eb4,3f3a,655e,cc39, -2, .BA2EB4CC39655E) +vc(L6, 1.5382888777946145467E-1 ,8551,3f1d,781d,e8c5, -2, .9D8551E8C5781D) +vc(L7, 1.3338356561139403517E-1 ,95b3,3f08,cd92,907f, -2, .8895B3907FCD92) +vc(L8, 1.2500000000000000000E-1 ,0000,3f00,0000,0000, -2, .80000000000000) + +ic(L1, 6.6666666666667340202E-1, -1, 1.5555555555592) +ic(L2, 3.9999999999416702146E-1, -2, 1.999999997FF24) +ic(L3, 2.8571428742008753154E-1, -2, 1.24924941E07B4) +ic(L4, 2.2222198607186277597E-1, -3, 1.C71C52150BEA6) +ic(L5, 1.8183562745289935658E-1, -3, 1.74663CC94342F) +ic(L6, 1.5314087275331442206E-1, -3, 1.39A1EC014045B) +ic(L7, 1.4795612545334174692E-1, -3, 1.2F039F0085122) + +#ifdef vccast +#define L1 vccast(L1) +#define L2 vccast(L2) +#define L3 vccast(L3) +#define L4 vccast(L4) +#define L5 vccast(L5) +#define L6 vccast(L6) +#define L7 vccast(L7) +#define L8 vccast(L8) +#endif + +double +__log__L(double z) +{ +#if defined(__vax__)||defined(tahoe) + return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*(L7+z*L8)))))))); +#else /* defined(__vax__)||defined(tahoe) */ + return(z*(L1+z*(L2+z*(L3+z*(L4+z*(L5+z*(L6+z*L7))))))); +#endif /* defined(__vax__)||defined(tahoe) */ +} diff --git a/lib/nbsd_libm/noieee_src/n_lround.c b/lib/nbsd_libm/noieee_src/n_lround.c new file mode 100644 index 000000000..bc35c891a --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_lround.c @@ -0,0 +1,53 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_lround.c,v 1.1 2010/12/09 22:52:59 abs Exp $"); +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_round.c,v 1.1 2004/06/07 08:05:36 das Exp $"); +#endif +#endif + +#include + +long +lround(double x) +{ + long t; + + if (x >= 0.0) { + t = ceil(x); + if (t - x > 0.5) + t -= 1.0; + return (t); + } else { + t = ceil(-x); + if (t + x > 0.5) + t -= 1.0; + return (-t); + } +} diff --git a/lib/nbsd_libm/noieee_src/n_lroundf.c b/lib/nbsd_libm/noieee_src/n_lroundf.c new file mode 100644 index 000000000..4bf4ec1e5 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_lroundf.c @@ -0,0 +1,53 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_lroundf.c,v 1.1 2010/12/09 22:52:59 abs Exp $"); +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_roundf.c,v 1.1 2004/06/07 08:05:36 das Exp $"); +#endif +#endif + +#include + +long +lroundf(float x) +{ + long t; + + if (x >= 0.0) { + t = ceilf(x); + if (t - x > 0.5) + t -= 1.0; + return (t); + } else { + t = ceilf(-x); + if (t + x > 0.5) + t -= 1.0; + return (-t); + } +} diff --git a/lib/nbsd_libm/noieee_src/n_pow.c b/lib/nbsd_libm/noieee_src/n_pow.c new file mode 100644 index 000000000..99fc0b875 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_pow.c @@ -0,0 +1,220 @@ +/* $NetBSD: n_pow.c,v 1.7 2003/08/07 16:44:52 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)pow.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* POW(X,Y) + * RETURN X**Y + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/8/85; + * REVISED BY K.C. NG on 7/10/85. + * KERNEL pow_P() REPLACED BY P. McILROY 7/22/92. + * Required system supported functions: + * scalb(x,n) + * logb(x) + * copysign(x,y) + * finite(x) + * drem(x,y) + * + * Required kernel functions: + * exp__D(a,c) exp(a + c) for |a| << |c| + * struct d_double dlog(x) r.a + r.b, |r.b| < |r.a| + * + * Method + * 1. Compute and return log(x) in three pieces: + * log(x) = n*ln2 + hi + lo, + * where n is an integer. + * 2. Perform y*log(x) by simulating muti-precision arithmetic and + * return the answer in three pieces: + * y*log(x) = m*ln2 + hi + lo, + * where m is an integer. + * 3. Return x**y = exp(y*log(x)) + * = 2^m * ( exp(hi+lo) ). + * + * Special cases: + * (anything) ** 0 is 1 ; + * (anything) ** 1 is itself; + * (anything) ** NaN is NaN; + * NaN ** (anything except 0) is NaN; + * +(anything > 1) ** +INF is +INF; + * -(anything > 1) ** +INF is NaN; + * +-(anything > 1) ** -INF is +0; + * +-(anything < 1) ** +INF is +0; + * +(anything < 1) ** -INF is +INF; + * -(anything < 1) ** -INF is NaN; + * +-1 ** +-INF is NaN and signal INVALID; + * +0 ** +(anything except 0, NaN) is +0; + * -0 ** +(anything except 0, NaN, odd integer) is +0; + * +0 ** -(anything except 0, NaN) is +INF and signal DIV-BY-ZERO; + * -0 ** -(anything except 0, NaN, odd integer) is +INF with signal; + * -0 ** (odd integer) = -( +0 ** (odd integer) ); + * +INF ** +(anything except 0,NaN) is +INF; + * +INF ** -(anything except 0,NaN) is +0; + * -INF ** (odd integer) = -( +INF ** (odd integer) ); + * -INF ** (even integer) = ( +INF ** (even integer) ); + * -INF ** -(anything except integer,NaN) is NaN with signal; + * -(x=anything) ** (k=integer) is (-1)**k * (x ** k); + * -(anything except 0) ** (non-integer) is NaN with signal; + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular, on a SUN, a VAX, + * and a Zilog Z8000, + * pow(integer,integer) + * always returns the correct integer provided it is representable. + * In a test run with 100,000 random arguments with 0 < x, y < 20.0 + * on a VAX, the maximum observed error was 1.79 ulps (units in the + * last place). + * + * Constants : + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include +#include + +#include "mathimpl.h" + +#if (defined(__vax__) || defined(tahoe)) +#define TRUNC(x) x = (double) (float) x +#define _IEEE 0 +#else +#define _IEEE 1 +#define endian (((*(int *) &one)) ? 1 : 0) +#define TRUNC(x) *(((int *) &x)+endian) &= 0xf8000000 +#define infnan(x) 0.0 +#endif /* __vax__ or tahoe */ + +static const double zero=0.0, one=1.0, two=2.0, negone= -1.0; + +static double pow_P (double, double); + +float +powf(float x, float y) +{ + return pow((double) x, (double) (y)); +} + +double +pow(double x, double y) +{ + double t; + if (y==zero) + return (one); + else if (y==one || (_IEEE && x != x)) + return (x); /* if x is NaN or y=1 */ + else if (_IEEE && y!=y) /* if y is NaN */ + return (y); + else if (!finite(y)) /* if y is INF */ + if ((t=fabs(x))==one) /* +-1 ** +-INF is NaN */ + return (y - y); + else if (t>one) + return ((y<0)? zero : ((x0)? zero : ((x<0)? y-y : -y)); + else if (y==two) + return (x*x); + else if (y==negone) + return (one/x); + /* x > 0, x == +0 */ + else if (copysign(one, x) == one) + return (pow_P(x, y)); + + /* sign(x)= -1 */ + /* if y is an even integer */ + else if ( (t=drem(y,two)) == zero) + return (pow_P(-x, y)); + + /* if y is an odd integer */ + else if (copysign(t,one) == one) + return (-pow_P(-x, y)); + + /* Henceforth y is not an integer */ + else if (x==zero) /* x is -0 */ + return ((y>zero)? -x : one/(-x)); + else if (_IEEE) + return (zero/zero); + else + return (infnan(EDOM)); +} + +/* kernel function for x >= 0 */ +static double +pow_P(double x, double y) +{ + struct Double s, t; + double huge = 1e300, tiny = 1e-300; + + if (x == zero) { + if (y > zero) + return (zero); + else if (_IEEE) + return (huge*huge); + else + return (infnan(ERANGE)); + } + if (x == one) + return (one); + if (!finite(x)) { + if (y < zero) + return (zero); + else if (_IEEE) + return (huge*huge); + else + return (infnan(ERANGE)); + } + if (y >= 7e18) { /* infinity */ + if (x < 1) + return(tiny*tiny); + else if (_IEEE) + return (huge*huge); + else + return (infnan(ERANGE)); + } + + /* Return exp(y*log(x)), using simulated extended */ + /* precision for the log and the multiply. */ + + s = __log__D(x); + t.a = y; + TRUNC(t.a); + t.b = y - t.a; + t.b = s.b*y + t.b*s.a; + t.a *= s.a; + s.a = t.a + t.b; + s.b = (t.a - s.a) + t.b; + return (__exp__D(s.a, s.b)); +} diff --git a/lib/nbsd_libm/noieee_src/n_round.c b/lib/nbsd_libm/noieee_src/n_round.c new file mode 100644 index 000000000..81823b30c --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_round.c @@ -0,0 +1,53 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_round.c,v 1.1 2006/01/17 13:16:08 is Exp $"); +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_round.c,v 1.1 2004/06/07 08:05:36 das Exp $"); +#endif +#endif + +#include + +double +round(double x) +{ + double t; + + if (x >= 0.0) { + t = ceil(x); + if (t - x > 0.5) + t -= 1.0; + return (t); + } else { + t = ceil(-x); + if (t + x > 0.5) + t -= 1.0; + return (-t); + } +} diff --git a/lib/nbsd_libm/noieee_src/n_roundf.c b/lib/nbsd_libm/noieee_src/n_roundf.c new file mode 100644 index 000000000..81a234ddb --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_roundf.c @@ -0,0 +1,53 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: n_roundf.c,v 1.1 2006/01/17 13:16:08 is Exp $"); +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_roundf.c,v 1.1 2004/06/07 08:05:36 das Exp $"); +#endif +#endif + +#include + +float +roundf(float x) +{ + float t; + + if (x >= 0.0) { + t = ceilf(x); + if (t - x > 0.5) + t -= 1.0; + return (t); + } else { + t = ceilf(-x); + if (t + x > 0.5) + t -= 1.0; + return (-t); + } +} diff --git a/lib/nbsd_libm/noieee_src/n_sincos.c b/lib/nbsd_libm/noieee_src/n_sincos.c new file mode 100644 index 000000000..8a2ed1a7a --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_sincos.c @@ -0,0 +1,110 @@ +/* $NetBSD: n_sincos.c,v 1.6 2003/08/07 16:44:52 agc Exp $ */ +/* + * Copyright (c) 1987, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)sincos.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +#define _LIBM_DECLARE +#include "mathimpl.h" +#include "trig.h" + +double +sin(double x) +{ + double a,c,z; + + if(!finite(x)) /* sin(NaN) and sin(INF) must be NaN */ + return x-x; + x=drem(x,PI2); /* reduce x into [-PI,PI] */ + a=copysign(x,__one); + if (a >= PIo4) { + if(a >= PI3o4) /* ... in [3PI/4,PI] */ + x = copysign((a = PI-a),x); + else { /* ... in [PI/4,3PI/4] */ + a = PIo2-a; /* rtn. sign(x)*C(PI/2-|x|) */ + z = a*a; + c = cos__C(z); + z *= __half; + a = (z >= thresh ? __half-((z-__half)-c) : __one-(z-c)); + return copysign(a,x); + } + } + + if (a < __small) { /* rtn. S(x) */ + z = __big+a; + return x; + } + return x+x*sin__S(x*x); +} + +float +sinf(float x) +{ + return sin(x); +} + +double +cos(double x) +{ + double a,c,z,s = 1.0; + + if(!finite(x)) /* cos(NaN) and cos(INF) must be NaN */ + return x-x; + x=drem(x,PI2); /* reduce x into [-PI,PI] */ + a=copysign(x,__one); + if (a >= PIo4) { + if (a >= PI3o4) { /* ... in [3PI/4,PI] */ + a = PI-a; + s = __negone; + } + else { /* ... in [PI/4,3PI/4] */ + a = PIo2-a; + return a+a*sin__S(a*a); /* rtn. S(PI/2-|x|) */ + } + } + if (a < __small) { + z = __big+a; + return s; /* rtn. s*C(a) */ + } + z = a*a; + c = cos__C(z); + z *= __half; + a = (z >= thresh ? __half-((z-__half)-c) : __one-(z-c)); + return copysign(a,s); +} + +float +cosf(float x) +{ + return cos(x); +} diff --git a/lib/nbsd_libm/noieee_src/n_sinh.c b/lib/nbsd_libm/noieee_src/n_sinh.c new file mode 100644 index 000000000..f4d3fd57c --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_sinh.c @@ -0,0 +1,133 @@ +/* $NetBSD: n_sinh.c,v 1.7 2008/03/20 16:41:26 mhitch Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)sinh.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* SINH(X) + * RETURN THE HYPERBOLIC SINE OF X + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/8/85; + * REVISED BY K.C. NG on 2/8/85, 3/7/85, 3/24/85, 4/16/85. + * + * Required system supported functions : + * copysign(x,y) + * scalb(x,N) + * + * Required kernel functions: + * expm1(x) ...return exp(x)-1 + * + * Method : + * 1. reduce x to non-negative by sinh(-x) = - sinh(x). + * 2. + * + * expm1(x) + expm1(x)/(expm1(x)+1) + * 0 <= x <= lnovfl : sinh(x) := -------------------------------- + * 2 + * lnovfl <= x <= lnovfl+ln2 : sinh(x) := expm1(x)/2 (avoid overflow) + * lnovfl+ln2 < x < INF : overflow to INF + * + * + * Special cases: + * sinh(x) is x if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite argument. + * + * Accuracy: + * sinh(x) returns the exact hyperbolic sine of x nearly rounded. In + * a test run with 1,024,000 random arguments on a VAX, the maximum + * observed error was 1.93 ulps (units in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#define _LIBM_STATIC +#include "../src/namespace.h" +#include "mathimpl.h" + +#ifdef __weak_alias +__weak_alias(sinh, _sinh); +__weak_alias(sinhf, _sinhf); +#endif + +vc(mln2hi, 8.8029691931113054792E1 ,0f33,43b0,2bdb,c7e2, 7, .B00F33C7E22BDB) +vc(mln2lo,-4.9650192275318476525E-16 ,1b60,a70f,582a,279e, -50,-.8F1B60279E582A) +vc(lnovfl, 8.8029691931113053016E1 ,0f33,43b0,2bda,c7e2, 7, .B00F33C7E22BDA) + +ic(mln2hi, 7.0978271289338397310E2, 10, 1.62E42FEFA39EF) +ic(mln2lo, 2.3747039373786107478E-14, -45, 1.ABC9E3B39803F) +ic(lnovfl, 7.0978271289338397310E2, 9, 1.62E42FEFA39EF) + +#ifdef vccast +#define mln2hi vccast(mln2hi) +#define mln2lo vccast(mln2lo) +#define lnovfl vccast(lnovfl) +#endif + +#if defined(__vax__)||defined(tahoe) +static const int max = 126 ; +#else /* defined(__vax__)||defined(tahoe) */ +static const int max = 1023 ; +#endif /* defined(__vax__)||defined(tahoe) */ + + +double +sinh(double x) +{ + static const double one=1.0, half=1.0/2.0 ; + double t, sign; +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + sign=copysign(one,x); + x=copysign(x,one); + if(x + static const unsigned short msign=0x7fff , mexp =0x7f80 ; + static const short prep1=57, gap=7, bias=129 ; + static const double novf=1.7E38, nunf=3.0E-39 ; +#else /* defined(__vax__)||defined(tahoe) */ + static const unsigned short msign=0x7fff, mexp =0x7ff0 ; + static const short prep1=54, gap=4, bias=1023 ; + static const double novf=1.7E308, nunf=3.0E-308; +#endif /* defined(__vax__)||defined(tahoe) */ + +double +scalb(double x, int N) +{ + int k; + +#ifdef national + unsigned short *px=(unsigned short *) &x + 3; +#else /* national */ + unsigned short *px=(unsigned short *) &x; +#endif /* national */ + + if( x == __zero ) return(x); + +#if defined(__vax__)||defined(tahoe) + if( (k= *px & mexp ) != ~msign ) { + if (N < -260) + return(nunf*nunf); + else if (N > 260) { + return(copysign(infnan(ERANGE),x)); + } +#else /* defined(__vax__)||defined(tahoe) */ + if( (k= *px & mexp ) != mexp ) { + if( N<-2100) return(nunf*nunf); else if(N>2100) return(novf+novf); + if( k == 0 ) { + x *= scalb(1.0,(int)prep1); N -= prep1; return(scalb(x,N));} +#endif /* defined(__vax__)||defined(tahoe) */ + + if((k = (k>>gap)+ N) > 0 ) + if( k < (mexp>>gap) ) *px = (*px&~mexp) | (k< -prep1 ) + /* gradual underflow */ + {*px=(*px&~mexp)|(short)(1<>gap)-bias); +#else /* defined(__vax__)||defined(tahoe) */ + if( (k= *px & mexp ) != mexp ) + if ( k != 0 ) + return ( (k>>gap) - bias ); + else if( x != __zero) + return ( -1022.0 ); + else + return(-(1.0/__zero)); + else if(x != x) + return(x); + else + {*px &= msign; return(x);} +#endif /* defined(__vax__)||defined(tahoe) */ +} + +int +finite(double x) +{ +#if defined(__vax__)||defined(tahoe) + return(1); +#else /* defined(__vax__)||defined(tahoe) */ +#ifdef national + return( (*((short *) &x+3 ) & mexp ) != mexp ); +#else /* national */ + return( (*((short *) &x ) & mexp ) != mexp ); +#endif /* national */ +#endif /* defined(__vax__)||defined(tahoe) */ +} + +double +drem(double x, double p) +{ + short sign; + double hp,dp,tmp; + unsigned short k; +#ifdef national + unsigned short + *px=(unsigned short *) &x +3, + *pp=(unsigned short *) &p +3, + *pd=(unsigned short *) &dp +3, + *pt=(unsigned short *) &tmp+3; +#else /* national */ + unsigned short + *px=(unsigned short *) &x , + *pp=(unsigned short *) &p , + *pd=(unsigned short *) &dp , + *pt=(unsigned short *) &tmp; +#endif /* national */ + + *pp &= msign ; + +#if defined(__vax__)||defined(tahoe) + if( ( *px & mexp ) == ~msign ) /* is x a reserved operand? */ +#else /* defined(__vax__)||defined(tahoe) */ + if( ( *px & mexp ) == mexp ) +#endif /* defined(__vax__)||defined(tahoe) */ + return (x-p)-(x-p); /* create nan if x is inf */ + if (p == __zero) { +#if defined(__vax__)||defined(tahoe) + return(infnan(EDOM)); +#else /* defined(__vax__)||defined(tahoe) */ + return __zero/__zero; +#endif /* defined(__vax__)||defined(tahoe) */ + } + +#if defined(__vax__)||defined(tahoe) + if( ( *pp & mexp ) == ~msign ) /* is p a reserved operand? */ +#else /* defined(__vax__)||defined(tahoe) */ + if( ( *pp & mexp ) == mexp ) +#endif /* defined(__vax__)||defined(tahoe) */ + { if (p != p) return p; else return x;} + + else if ( ((*pp & mexp)>>gap) <= 1 ) + /* subnormal p, or almost subnormal p */ + { double b; b=scalb(1.0,(int)prep1); + p *= b; x = drem(x,p); x *= b; return(drem(x,p)/b);} + else if ( p >= novf/2) + { p /= 2 ; x /= 2; return(drem(x,p)*2);} + else + { + dp=p+p; hp=p/2; + sign= *px & ~msign ; + *px &= msign ; + while ( x > dp ) + { + k=(*px & mexp) - (*pd & mexp) ; + tmp = dp ; + *pt += k ; + +#if defined(__vax__)||defined(tahoe) + if( x < tmp ) *pt -= 128 ; +#else /* defined(__vax__)||defined(tahoe) */ + if( x < tmp ) *pt -= 16 ; +#endif /* defined(__vax__)||defined(tahoe) */ + + x -= tmp ; + } + if ( x > hp ) + { x -= p ; if ( x >= hp ) x -= p ; } + +#if defined(__vax__)||defined(tahoe) + if (x) +#endif /* defined(__vax__)||defined(tahoe) */ + *px ^= sign; + return( x); + + } +} + + +double +sqrt(double x) +{ + double q,s,b,r; + double t; + int m,n,i; +#if defined(__vax__)||defined(tahoe) + int k=54; +#else /* defined(__vax__)||defined(tahoe) */ + int k=51; +#endif /* defined(__vax__)||defined(tahoe) */ + + /* sqrt(NaN) is NaN, sqrt(+-0) = +-0 */ + if(x!=x||x==__zero) return(x); + + /* sqrt(negative) is invalid */ + if(x<__zero) { +#if defined(__vax__)||defined(tahoe) + return (infnan(EDOM)); /* NaN */ +#else /* defined(__vax__)||defined(tahoe) */ + return(__zero/__zero); +#endif /* defined(__vax__)||defined(tahoe) */ + } + + /* sqrt(INF) is INF */ + if(!finite(x)) return(x); + + /* scale x to [1,4) */ + n=logb(x); + x=scalb(x,-n); + if((m=logb(x))!=0) x=scalb(x,-m); /* subnormal number */ + m += n; + n = m/2; + if((n+n)!=m) {x *= 2; m -=1; n=m/2;} + + /* generate sqrt(x) bit by bit (accumulating in q) */ + q=1.0; s=4.0; x -= 1.0; r=1; + for(i=1;i<=k;i++) { + t=s+1; x *= 4; r /= 2; + if(t<=x) { + s=t+t+2, x -= t; q += r;} + else + s *= 2; + } + + /* generate the last bit and determine the final rounding */ + r/=2; x *= 4; + if(x==__zero) goto end; 100+r; /* trigger inexact flag */ + if(s1.0) t=1; /* b>1 : Round-to-(+INF) */ + if(t>=0) q+=r; } /* else: Round-to-nearest */ + else { + s *= 2; x *= 4; + t = (x-s)-1; + b=1.0+3*r/4; if(b==1.0) goto end; + b=1.0+r/4; if(b>1.0) t=1; + if(t>=0) q+=r; } + +end: return(scalb(q,n)); +} + +#if 0 +/* DREM(X,Y) + * RETURN X REM Y =X-N*Y, N=[X/Y] ROUNDED (ROUNDED TO EVEN IN THE HALF WAY CASE) + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * INTENDED FOR ASSEMBLY LANGUAGE + * CODED IN C BY K.C. NG, 3/23/85, 4/8/85. + * + * Warning: this code should not get compiled in unless ALL of + * the following machine-dependent routines are supplied. + * + * Required machine dependent functions (not on a VAX): + * swapINX(i): save inexact flag and reset it to "i" + * swapENI(e): save inexact enable and reset it to "e" + */ + +double +drem(double x, double y) +{ + +#ifdef national /* order of words in floating point number */ + static const n0=3,n1=2,n2=1,n3=0; +#else /* VAX, SUN, ZILOG, TAHOE */ + static const n0=0,n1=1,n2=2,n3=3; +#endif + + static const unsigned short mexp =0x7ff0, m25 =0x0190, m57 =0x0390; + double hy,y1,t,t1; + short k; + long n; + int i,e; + unsigned short xexp,yexp, *px =(unsigned short *) &x , + nx,nf, *py =(unsigned short *) &y , + sign, *pt =(unsigned short *) &t , + *pt1 =(unsigned short *) &t1 ; + + xexp = px[n0] & mexp ; /* exponent of x */ + yexp = py[n0] & mexp ; /* exponent of y */ + sign = px[n0] &0x8000; /* sign of x */ + +/* return NaN if x is NaN, or y is NaN, or x is INF, or y is zero */ + if(x!=x) return(x); if(y!=y) return(y); /* x or y is NaN */ + if( xexp == mexp ) return(__zero/__zero); /* x is INF */ + if(y==__zero) return(y/y); + +/* save the inexact flag and inexact enable in i and e respectively + * and reset them to zero + */ + i=swapINX(0); e=swapENI(0); + +/* subnormal number */ + nx=0; + if(yexp==0) {t=1.0,pt[n0]+=m57; y*=t; nx=m57;} + +/* if y is tiny (biased exponent <= 57), scale up y to y*2**57 */ + if( yexp <= m57 ) {py[n0]+=m57; nx+=m57; yexp+=m57;} + + nf=nx; + py[n0] &= 0x7fff; + px[n0] &= 0x7fff; + +/* mask off the least significant 27 bits of y */ + t=y; pt[n3]=0; pt[n2]&=0xf800; y1=t; + +/* LOOP: argument reduction on x whenever x > y */ +loop: + while ( x > y ) + { + t=y; + t1=y1; + xexp=px[n0]&mexp; /* exponent of x */ + k=xexp-yexp-m25; + if(k>0) /* if x/y >= 2**26, scale up y so that x/y < 2**26 */ + {pt[n0]+=k;pt1[n0]+=k;} + n=x/t; x=(x-n*t1)-n*(t-t1); + } + /* end while (x > y) */ + + if(nx!=0) {t=1.0; pt[n0]+=nx; x*=t; nx=0; goto loop;} + +/* final adjustment */ + + hy=y/2.0; + if(x>hy||((x==hy)&&n%2==1)) x-=y; + px[n0] ^= sign; + if(nf!=0) { t=1.0; pt[n0]-=nf; x*=t;} + +/* restore inexact flag and inexact enable */ + swapINX(i); swapENI(e); + + return(x); +} +#endif + +#if 0 +/* SQRT + * RETURN CORRECTLY ROUNDED (ACCORDING TO THE ROUNDING MODE) SQRT + * FOR IEEE DOUBLE PRECISION ONLY, INTENDED FOR ASSEMBLY LANGUAGE + * CODED IN C BY K.C. NG, 3/22/85. + * + * Warning: this code should not get compiled in unless ALL of + * the following machine-dependent routines are supplied. + * + * Required machine dependent functions: + * swapINX(i) ...return the status of INEXACT flag and reset it to "i" + * swapRM(r) ...return the current Rounding Mode and reset it to "r" + * swapENI(e) ...return the status of inexact enable and reset it to "e" + * addc(t) ...perform t=t+1 regarding t as a 64 bit unsigned integer + * subc(t) ...perform t=t-1 regarding t as a 64 bit unsigned integer + */ + +static const unsigned long table[] = { +0, 1204, 3062, 5746, 9193, 13348, 18162, 23592, 29598, 36145, 43202, 50740, +58733, 67158, 75992, 85215, 83599, 71378, 60428, 50647, 41945, 34246, 27478, +21581, 16499, 12183, 8588, 5674, 3403, 1742, 661, 130, }; + +double +newsqrt(double x) +{ + double y,z,t,addc(),subc() + double const b54=134217728.*134217728.; /* b54=2**54 */ + long mx,scalx; + long const mexp=0x7ff00000; + int i,j,r,e,swapINX(),swapRM(),swapENI(); + unsigned long *py=(unsigned long *) &y , + *pt=(unsigned long *) &t , + *px=(unsigned long *) &x ; +#ifdef national /* ordering of word in a floating point number */ + const int n0=1, n1=0; +#else + const int n0=0, n1=1; +#endif +/* Rounding Mode: RN ...round-to-nearest + * RZ ...round-towards 0 + * RP ...round-towards +INF + * RM ...round-towards -INF + */ + const int RN=0,RZ=1,RP=2,RM=3; + /* machine dependent: work on a Zilog Z8070 + * and a National 32081 & 16081 + */ + +/* exceptions */ + if(x!=x||x==0.0) return(x); /* sqrt(NaN) is NaN, sqrt(+-0) = +-0 */ + if(x<0) return((x-x)/(x-x)); /* sqrt(negative) is invalid */ + if((mx=px[n0]&mexp)==mexp) return(x); /* sqrt(+INF) is +INF */ + +/* save, reset, initialize */ + e=swapENI(0); /* ...save and reset the inexact enable */ + i=swapINX(0); /* ...save INEXACT flag */ + r=swapRM(RN); /* ...save and reset the Rounding Mode to RN */ + scalx=0; + +/* subnormal number, scale up x to x*2**54 */ + if(mx==0) {x *= b54 ; scalx-=0x01b00000;} + +/* scale x to avoid intermediate over/underflow: + * if (x > 2**512) x=x/2**512; if (x < 2**-512) x=x*2**512 */ + if(mx>0x5ff00000) {px[n0] -= 0x20000000; scalx+= 0x10000000;} + if(mx<0x1ff00000) {px[n0] += 0x20000000; scalx-= 0x10000000;} + +/* magic initial approximation to almost 8 sig. bits */ + py[n0]=(px[n0]>>1)+0x1ff80000; + py[n0]=py[n0]-table[(py[n0]>>15)&31]; + +/* Heron's rule once with correction to improve y to almost 18 sig. bits */ + t=x/y; y=y+t; py[n0]=py[n0]-0x00100006; py[n1]=0; + +/* triple to almost 56 sig. bits; now y approx. sqrt(x) to within 1 ulp */ + t=y*y; z=t; pt[n0]+=0x00100000; t+=z; z=(x-z)*y; + t=z/(t+x) ; pt[n0]+=0x00100000; y+=t; + +/* twiddle last bit to force y correctly rounded */ + swapRM(RZ); /* ...set Rounding Mode to round-toward-zero */ + swapINX(0); /* ...clear INEXACT flag */ + swapENI(e); /* ...restore inexact enable status */ + t=x/y; /* ...chopped quotient, possibly inexact */ + j=swapINX(i); /* ...read and restore inexact flag */ + if(j==0) { if(t==y) goto end; else t=subc(t); } /* ...t=t-ulp */ + b54+0.1; /* ..trigger inexact flag, sqrt(x) is inexact */ + if(r==RN) t=addc(t); /* ...t=t+ulp */ + else if(r==RP) { t=addc(t);y=addc(y);}/* ...t=t+ulp;y=y+ulp; */ + y=y+t; /* ...chopped sum */ + py[n0]=py[n0]-0x00100000; /* ...correctly rounded sqrt(x) */ +end: py[n0]=py[n0]+scalx; /* ...scale back y */ + swapRM(r); /* ...restore Rounding Mode */ + return(y); +} +#endif diff --git a/lib/nbsd_libm/noieee_src/n_tan.c b/lib/nbsd_libm/noieee_src/n_tan.c new file mode 100644 index 000000000..3c0071a27 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_tan.c @@ -0,0 +1,73 @@ +/* $NetBSD: n_tan.c,v 1.5 2003/08/07 16:44:52 agc Exp $ */ +/* + * Copyright (c) 1987, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)tan.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +#include "mathimpl.h" +#include "trig.h" +double +tan(double x) +{ + double a,z,ss,cc,c; + int k; + + if(!finite(x)) /* tan(NaN) and tan(INF) must be NaN */ + return x-x; + x = drem(x,PI); /* reduce x into [-PI/2, PI/2] */ + a = copysign(x,__one); /* ... = abs(x) */ + if (a >= PIo4) { + k = 1; + x = copysign(PIo2-a,x); + } + else { + k = 0; + if (a < __small) { + z=__big+a; + return x; + } + } + z = x*x; + cc = cos__C(z); + ss = sin__S(z); + z *= __half; /* Next get c = cos(x) accurately */ + c = (z >= thresh ? __half-((z-__half)-cc) : __one-(z-cc)); + if (k == 0) + return x+(x*(z-(cc-ss)))/c; /* ... sin/cos */ +#ifdef national + else if (x == __zero) + return copysign(fmax,x); /* no inf on 32k */ +#endif /* national */ + else + return c/(x+x*ss); /* ... cos/sin */ +} diff --git a/lib/nbsd_libm/noieee_src/n_tanh.c b/lib/nbsd_libm/noieee_src/n_tanh.c new file mode 100644 index 000000000..5a8ab5ce5 --- /dev/null +++ b/lib/nbsd_libm/noieee_src/n_tanh.c @@ -0,0 +1,99 @@ +/* $NetBSD: n_tanh.c,v 1.6 2003/08/07 16:44:52 agc Exp $ */ +/* + * Copyright (c) 1985, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#ifndef lint +#if 0 +static char sccsid[] = "@(#)tanh.c 8.1 (Berkeley) 6/4/93"; +#endif +#endif /* not lint */ + +/* TANH(X) + * RETURN THE HYPERBOLIC TANGENT OF X + * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) + * CODED IN C BY K.C. NG, 1/8/85; + * REVISED BY K.C. NG on 2/8/85, 2/11/85, 3/7/85, 3/24/85. + * + * Required system supported functions : + * copysign(x,y) + * finite(x) + * + * Required kernel function: + * expm1(x) ...exp(x)-1 + * + * Method : + * 1. reduce x to non-negative by tanh(-x) = - tanh(x). + * 2. + * 0 < x <= 1.e-10 : tanh(x) := x + * -expm1(-2x) + * 1.e-10 < x <= 1 : tanh(x) := -------------- + * expm1(-2x) + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1 - --------------- + * expm1(2x) + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Note: 22 was chosen so that fl(1.0+2/(expm1(2*22)+2)) == 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + * + * Accuracy: + * tanh(x) returns the exact hyperbolic tangent of x nealy rounded. + * In a test run with 1,024,000 random arguments on a VAX, the maximum + * observed error was 2.22 ulps (units in the last place). + */ + +#include "mathimpl.h" + +double +tanh(double x) +{ + static const double one=1.0, two=2.0, small = 1.0e-10, big = 1.0e10; + double t, sign; + +#if !defined(__vax__)&&!defined(tahoe) + if(x!=x) return(x); /* x is NaN */ +#endif /* !defined(__vax__)&&!defined(tahoe) */ + + sign=copysign(one,x); + x=copysign(x,one); + if(x < 22.0) + if( x > one ) + return(copysign(one-two/(expm1(x+x)+two),sign)); + else if ( x > small ) + {t= -expm1(-(x+x)); return(copysign(t/(two-t),sign));} + else /* raise the INEXACT flag for non-zero x */ + { t = big+x; return(copysign(x,sign));} /* ??? -ragge */ + else if(finite(x)) + return (sign+1.0E-37); /* raise the INEXACT flag */ + else + return(sign); /* x is +- INF */ +} diff --git a/lib/nbsd_libm/noieee_src/trig.h b/lib/nbsd_libm/noieee_src/trig.h new file mode 100644 index 000000000..91f87f19a --- /dev/null +++ b/lib/nbsd_libm/noieee_src/trig.h @@ -0,0 +1,223 @@ +/* $NetBSD: trig.h,v 1.6 2003/08/07 16:44:53 agc Exp $ */ +/* + * Copyright (c) 1987, 1993 + * The Regents of the University of California. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * 3. Neither the name of the University nor the names of its contributors + * may be used to endorse or promote products derived from this software + * without specific prior written permission. + * + * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + * + * @(#)trig.h 8.1 (Berkeley) 6/4/93 + */ + +vc(thresh, 2.6117239648121182150E-1 ,b863,3f85,6ea0,6b02, -1, .85B8636B026EA0) +vc(PIo4, 7.8539816339744830676E-1 ,0fda,4049,68c2,a221, 0, .C90FDAA22168C2) +vc(PIo2, 1.5707963267948966135E0 ,0fda,40c9,68c2,a221, 1, .C90FDAA22168C2) +vc(PI3o4, 2.3561944901923449203E0 ,cbe3,4116,0e92,f999, 2, .96CBE3F9990E92) +vc(PI, 3.1415926535897932270E0 ,0fda,4149,68c2,a221, 2, .C90FDAA22168C2) +vc(PI2, 6.2831853071795864540E0 ,0fda,41c9,68c2,a221, 3, .C90FDAA22168C2) + +ic(thresh, 2.6117239648121182150E-1 , -2, 1.0B70C6D604DD4) +ic(PIo4, 7.8539816339744827900E-1 , -1, 1.921FB54442D18) +ic(PIo2, 1.5707963267948965580E0 , 0, 1.921FB54442D18) +ic(PI3o4, 2.3561944901923448370E0 , 1, 1.2D97C7F3321D2) +ic(PI, 3.1415926535897931160E0 , 1, 1.921FB54442D18) +ic(PI2, 6.2831853071795862320E0 , 2, 1.921FB54442D18) + +#ifdef vccast +#define thresh vccast(thresh) +#define PIo4 vccast(PIo4) +#define PIo2 vccast(PIo2) +#define PI3o4 vccast(PI3o4) +#define PI vccast(PI) +#define PI2 vccast(PI2) +#endif + +#ifdef national +static long fmaxx[] = { 0xffffffff, 0x7fefffff}; +#define fmax (*(double*)fmaxx) +#endif /* national */ + +#ifdef _LIBM_DECLARE +const double + __zero = 0, + __one = 1, + __negone = -1, + __half = 1.0/2.0, +#ifdef __vax__ + __small = 1E-9, /* 1+small**2 == 1; better values for small: + * small = 1.5E-9 for VAX D + * = 1.2E-8 for IEEE Double + * = 2.8E-10 for IEEE Extended + */ + __big = 1E18; /* big := 1/(small**2) */ +#else + __small = 1E-10, /* 1+small**2 == 1; better values for small: + * small = 1.5E-9 for VAX D + * = 1.2E-8 for IEEE Double + * = 2.8E-10 for IEEE Extended + */ + __big = 1E20; /* big := 1/(small**2) */ +#endif +#else +extern const double __zero, __one, __negone, __half, __small, __big; +#endif + +/* sin__S(x*x) ... re-implemented as a macro + * DOUBLE PRECISION (VAX D format 56 bits, IEEE DOUBLE 53 BITS) + * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) + * CODED IN C BY K.C. NG, 1/21/85; + * REVISED BY K.C. NG on 8/13/85. + * + * sin(x*k) - x + * RETURN --------------- on [-PI/4,PI/4] , where k=pi/PI, PI is the rounded + * x + * value of pi in machine precision: + * + * Decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * Hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 + * + * Method: + * 1. Let z=x*x. Create a polynomial approximation to + * (sin(k*x)-x)/x = z*(S0 + S1*z^1 + ... + S5*z^5). + * Then + * sin__S(x*x) = z*(S0 + S1*z^1 + ... + S5*z^5) + * + * The coefficient S's are obtained by a special Remez algorithm. + * + * Accuracy: + * In the absence of rounding error, the approximation has absolute error + * less than 2**(-61.11) for VAX D FORMAT, 2**(-57.45) for IEEE DOUBLE. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + * + */ + +vc(S0, -1.6666666666666646660E-1 ,aaaa,bf2a,aa71,aaaa, -2, -.AAAAAAAAAAAA71) +vc(S1, 8.3333333333297230413E-3 ,8888,3d08,477f,8888, -6, .8888888888477F) +vc(S2, -1.9841269838362403710E-4 ,0d00,ba50,1057,cf8a, -12, -.D00D00CF8A1057) +vc(S3, 2.7557318019967078930E-6 ,ef1c,3738,bedc,a326, -18, .B8EF1CA326BEDC) +vc(S4, -2.5051841873876551398E-8 ,3195,b3d7,e1d3,374c, -25, -.D73195374CE1D3) +vc(S5, 1.6028995389845827653E-10 ,3d9c,3030,cccc,6d26, -32, .B03D9C6D26CCCC) +vc(S6, -6.2723499671769283121E-13 ,8d0b,ac30,ea82,7561, -40, -.B08D0B7561EA82) + +ic(S0, -1.6666666666666463126E-1 , -3, -1.555555555550C) +ic(S1, 8.3333333332992771264E-3 , -7, 1.111111110C461) +ic(S2, -1.9841269816180999116E-4 , -13, -1.A01A019746345) +ic(S3, 2.7557309793219876880E-6 , -19, 1.71DE3209CDCD9) +ic(S4, -2.5050225177523807003E-8 , -26, -1.AE5C0E319A4EF) +ic(S5, 1.5868926979889205164E-10 , -33, 1.5CF61DF672B13) + +#ifdef vccast +#define S0 vccast(S0) +#define S1 vccast(S1) +#define S2 vccast(S2) +#define S3 vccast(S3) +#define S4 vccast(S4) +#define S5 vccast(S5) +#define S6 vccast(S6) +#endif + +#if defined(__vax__)||defined(tahoe) +# define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*(S5+z*S6))))))) +#else /* defined(__vax__)||defined(tahoe) */ +# define sin__S(z) (z*(S0+z*(S1+z*(S2+z*(S3+z*(S4+z*S5)))))) +#endif /* defined(__vax__)||defined(tahoe) */ + +/* cos__C(x*x) ... re-implemented as a macro + * DOUBLE PRECISION (VAX D FORMAT 56 BITS, IEEE DOUBLE 53 BITS) + * STATIC KERNEL FUNCTION OF SIN(X), COS(X), AND TAN(X) + * CODED IN C BY K.C. NG, 1/21/85; + * REVISED BY K.C. NG on 8/13/85. + * + * x*x + * RETURN cos(k*x) - 1 + ----- on [-PI/4,PI/4], where k = pi/PI, + * 2 + * PI is the rounded value of pi in machine precision : + * + * Decimal: + * pi = 3.141592653589793 23846264338327 ..... + * 53 bits PI = 3.141592653589793 115997963 ..... , + * 56 bits PI = 3.141592653589793 227020265 ..... , + * + * Hexadecimal: + * pi = 3.243F6A8885A308D313198A2E.... + * 53 bits PI = 3.243F6A8885A30 = 2 * 1.921FB54442D18 + * 56 bits PI = 3.243F6A8885A308 = 4 * .C90FDAA22168C2 + * + * + * Method: + * 1. Let z=x*x. Create a polynomial approximation to + * cos(k*x)-1+z/2 = z*z*(C0 + C1*z^1 + ... + C5*z^5) + * then + * cos__C(z) = z*z*(C0 + C1*z^1 + ... + C5*z^5) + * + * The coefficient C's are obtained by a special Remez algorithm. + * + * Accuracy: + * In the absence of rounding error, the approximation has absolute error + * less than 2**(-64) for VAX D FORMAT, 2**(-58.3) for IEEE DOUBLE. + * + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +vc(C0, 4.1666666666666504759E-2 ,aaaa,3e2a,a9f0,aaaa, -4, .AAAAAAAAAAA9F0) +vc(C1, -1.3888888888865302059E-3 ,0b60,bbb6,0cca,b60a, -9, -.B60B60B60A0CCA) +vc(C2, 2.4801587285601038265E-5 ,0d00,38d0,098f,cdcd, -15, .D00D00CDCD098F) +vc(C3, -2.7557313470902390219E-7 ,f27b,b593,e805,b593, -21, -.93F27BB593E805) +vc(C4, 2.0875623401082232009E-9 ,74c8,320f,3ff0,fa1e, -28, .8F74C8FA1E3FF0) +vc(C5, -1.1355178117642986178E-11 ,c32d,ae47,5a63,0a5c, -36, -.C7C32D0A5C5A63) + +ic(C0, 4.1666666666666504759E-2 , -5, 1.555555555553E) +ic(C1, -1.3888888888865301516E-3 , -10, -1.6C16C16C14199) +ic(C2, 2.4801587269650015769E-5 , -16, 1.A01A01971CAEB) +ic(C3, -2.7557304623183959811E-7 , -22, -1.27E4F1314AD1A) +ic(C4, 2.0873958177697780076E-9 , -29, 1.1EE3B60DDDC8C) +ic(C5, -1.1250289076471311557E-11 , -37, -1.8BD5986B2A52E) + +#ifdef vccast +#define C0 vccast(C0) +#define C1 vccast(C1) +#define C2 vccast(C2) +#define C3 vccast(C3) +#define C4 vccast(C4) +#define C5 vccast(C5) +#endif + +#define cos__C(z) (z*z*(C0+z*(C1+z*(C2+z*(C3+z*(C4+z*C5)))))) diff --git a/lib/nbsd_libm/shlib_version b/lib/nbsd_libm/shlib_version new file mode 100644 index 000000000..127db4625 --- /dev/null +++ b/lib/nbsd_libm/shlib_version @@ -0,0 +1,5 @@ +# $NetBSD: shlib_version,v 1.11 2010/01/11 16:28:39 christos Exp $ +# Remember to update distrib/sets/lists/base/shl.* when changing +# +major=0 +minor=8 diff --git a/lib/nbsd_libm/src/e_acos.c b/lib/nbsd_libm/src/e_acos.c new file mode 100644 index 000000000..5bec66416 --- /dev/null +++ b/lib/nbsd_libm/src/e_acos.c @@ -0,0 +1,104 @@ +/* @(#)e_acos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_acos.c,v 1.12 2002/05/26 22:01:47 wiz Exp $"); +#endif + +/* __ieee754_acos(x) + * Method : + * acos(x) = pi/2 - asin(x) + * acos(-x) = pi/2 + asin(x) + * For |x|<=0.5 + * acos(x) = pi/2 - (x + x*x^2*R(x^2)) (see asin.c) + * For x>0.5 + * acos(x) = pi/2 - (pi/2 - 2asin(sqrt((1-x)/2))) + * = 2asin(sqrt((1-x)/2)) + * = 2s + 2s*z*R(z) ...z=(1-x)/2, s=sqrt(z) + * = 2f + (2c + 2s*z*R(z)) + * where f=hi part of s, and c = (z-f*f)/(s+f) is the correction term + * for f so that f+c ~ sqrt(z). + * For x<-0.5 + * acos(x) = pi - 2asin(sqrt((1-|x|)/2)) + * = pi - 0.5*(s+s*z*R(z)), where z=(1-|x|)/2,s=sqrt(z) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + * Function needed: __ieee754_sqrt + */ + +#include "math.h" +#include "math_private.h" + +static const double +one= 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +double +__ieee754_acos(double x) +{ + double z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x3ff00000) { /* |x| >= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+2.0*pio2_lo; /* acos(-1)= pi */ + } + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3fe00000) { /* |x| < 0.5 */ + if(ix<=0x3c600000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = __ieee754_sqrt(z); + r = p/q; + w = r*s-pio2_lo; + return pi - 2.0*(s+w); + } else { /* x > 0.5 */ + z = (one-x)*0.5; + s = __ieee754_sqrt(z); + df = s; + SET_LOW_WORD(df,0); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return 2.0*(df+w); + } +} diff --git a/lib/nbsd_libm/src/e_acosf.c b/lib/nbsd_libm/src/e_acosf.c new file mode 100644 index 000000000..5c7d34470 --- /dev/null +++ b/lib/nbsd_libm/src/e_acosf.c @@ -0,0 +1,82 @@ +/* e_acosf.c -- float version of e_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_acosf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +float +__ieee754_acosf(float x) +{ + float z,p,q,r,w,s,c,df; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { /* |x|==1 */ + if(hx>0) return 0.0; /* acos(1) = 0 */ + else return pi+(float)2.0*pio2_lo; /* acos(-1)= pi */ + } else if(ix>0x3f800000) { /* |x| >= 1 */ + return (x-x)/(x-x); /* acos(|x|>1) is NaN */ + } + if(ix<0x3f000000) { /* |x| < 0.5 */ + if(ix<=0x23000000) return pio2_hi+pio2_lo;/*if|x|<2**-57*/ + z = x*x; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + return pio2_hi - (x - (pio2_lo-x*r)); + } else if (hx<0) { /* x < -0.5 */ + z = (one+x)*(float)0.5; + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + s = __ieee754_sqrtf(z); + r = p/q; + w = r*s-pio2_lo; + return pi - (float)2.0*(s+w); + } else { /* x > 0.5 */ + int32_t idf; + z = (one-x)*(float)0.5; + s = __ieee754_sqrtf(z); + df = s; + GET_FLOAT_WORD(idf,df); + SET_FLOAT_WORD(df,idf&0xfffff000); + c = (z-df*df)/(s+df); + p = z*(pS0+z*(pS1+z*(pS2+z*(pS3+z*(pS4+z*pS5))))); + q = one+z*(qS1+z*(qS2+z*(qS3+z*qS4))); + r = p/q; + w = r*s+c; + return (float)2.0*(df+w); + } +} diff --git a/lib/nbsd_libm/src/e_acosh.c b/lib/nbsd_libm/src/e_acosh.c new file mode 100644 index 000000000..8259394e4 --- /dev/null +++ b/lib/nbsd_libm/src/e_acosh.c @@ -0,0 +1,62 @@ +/* @(#)e_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_acosh.c,v 1.12 2002/05/26 22:01:48 wiz Exp $"); +#endif + +/* __ieee754_acosh(x) + * Method : + * Based on + * acosh(x) = log [ x + sqrt(x*x-1) ] + * we have + * acosh(x) := log(x)+ln2, if x is large; else + * acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x>2; else + * acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t=x-1. + * + * Special cases: + * acosh(x) is NaN with signal if x<1. + * acosh(NaN) is NaN without signal. + */ + +#include "math.h" +#include "math_private.h" + +static const double +one = 1.0, +ln2 = 6.93147180559945286227e-01; /* 0x3FE62E42, 0xFEFA39EF */ + +double +__ieee754_acosh(double x) +{ + double t; + int32_t hx; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + if(hx<0x3ff00000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x41b00000) { /* x > 2**28 */ + if(hx >=0x7ff00000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_log(x)+ln2; /* acosh(huge)=log(2x) */ + } else if(((hx-0x3ff00000)|lx)==0) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_log(2.0*x-one/(x+__ieee754_sqrt(t-one))); + } else { /* 1 +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_acoshf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +one = 1.0, +ln2 = 6.9314718246e-01; /* 0x3f317218 */ + +float +__ieee754_acoshf(float x) +{ + float t; + int32_t hx; + GET_FLOAT_WORD(hx,x); + if(hx<0x3f800000) { /* x < 1 */ + return (x-x)/(x-x); + } else if(hx >=0x4d800000) { /* x > 2**28 */ + if(hx >=0x7f800000) { /* x is inf of NaN */ + return x+x; + } else + return __ieee754_logf(x)+ln2; /* acosh(huge)=log(2x) */ + } else if (hx==0x3f800000) { + return 0.0; /* acosh(1) = 0 */ + } else if (hx > 0x40000000) { /* 2**28 > x > 2 */ + t=x*x; + return __ieee754_logf((float)2.0*x-one/(x+__ieee754_sqrtf(t-one))); + } else { /* 1 +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_asin.c,v 1.12 2002/05/26 22:01:48 wiz Exp $"); +#endif + +/* __ieee754_asin(x) + * Method : + * Since asin(x) = x + x^3/6 + x^5*3/40 + x^7*15/336 + ... + * we approximate asin(x) on [0,0.5] by + * asin(x) = x + x*x^2*R(x^2) + * where + * R(x^2) is a rational approximation of (asin(x)-x)/x^3 + * and its remez error is bounded by + * |(asin(x)-x)/x^3 - R(x^2)| < 2^(-58.75) + * + * For x in [0.5,1] + * asin(x) = pi/2-2*asin(sqrt((1-x)/2)) + * Let y = (1-x), z = y/2, s := sqrt(z), and pio2_hi+pio2_lo=pi/2; + * then for x>0.98 + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio2_hi - (2*(s+s*z*R(z)) - pio2_lo) + * For x<=0.98, let pio4_hi = pio2_hi/2, then + * f = hi part of s; + * c = sqrt(z) - f = (z-f*f)/(s+f) ...f+c=sqrt(z) + * and + * asin(x) = pi/2 - 2*(s+s*z*R(z)) + * = pio4_hi+(pio4-2s)-(2s*z*R(z)-pio2_lo) + * = pio4_hi+(pio4-2f)-(2s*z*R(z)-(pio2_lo+2c)) + * + * Special cases: + * if x is NaN, return x itself; + * if |x|>1, return NaN with invalid signal. + * + */ + + +#include "math.h" +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +huge = 1.000e+300, +pio2_hi = 1.57079632679489655800e+00, /* 0x3FF921FB, 0x54442D18 */ +pio2_lo = 6.12323399573676603587e-17, /* 0x3C91A626, 0x33145C07 */ +pio4_hi = 7.85398163397448278999e-01, /* 0x3FE921FB, 0x54442D18 */ + /* coefficient for R(x^2) */ +pS0 = 1.66666666666666657415e-01, /* 0x3FC55555, 0x55555555 */ +pS1 = -3.25565818622400915405e-01, /* 0xBFD4D612, 0x03EB6F7D */ +pS2 = 2.01212532134862925881e-01, /* 0x3FC9C155, 0x0E884455 */ +pS3 = -4.00555345006794114027e-02, /* 0xBFA48228, 0xB5688F3B */ +pS4 = 7.91534994289814532176e-04, /* 0x3F49EFE0, 0x7501B288 */ +pS5 = 3.47933107596021167570e-05, /* 0x3F023DE1, 0x0DFDF709 */ +qS1 = -2.40339491173441421878e+00, /* 0xC0033A27, 0x1C8A2D4B */ +qS2 = 2.02094576023350569471e+00, /* 0x40002AE5, 0x9C598AC8 */ +qS3 = -6.88283971605453293030e-01, /* 0xBFE6066C, 0x1B8D0159 */ +qS4 = 7.70381505559019352791e-02; /* 0x3FB3B8C5, 0xB12E9282 */ + +double +__ieee754_asin(double x) +{ + double t,w,p,q,c,r,s; + int32_t hx,ix; + + t = 0; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>= 0x3ff00000) { /* |x|>= 1 */ + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((ix-0x3ff00000)|lx)==0) + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3fe00000) { /* |x|<0.5 */ + if(ix<0x3e400000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabs(x); + t = w*0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = __ieee754_sqrt(t); + if(ix>=0x3FEF3333) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-(2.0*(s+s*w)-pio2_lo); + } else { + w = s; + SET_LOW_WORD(w,0); + c = (t-w*w)/(s+w); + r = p/q; + p = 2.0*s*r-(pio2_lo-2.0*c); + q = pio4_hi-2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/lib/nbsd_libm/src/e_asinf.c b/lib/nbsd_libm/src/e_asinf.c new file mode 100644 index 000000000..859e83ee1 --- /dev/null +++ b/lib/nbsd_libm/src/e_asinf.c @@ -0,0 +1,87 @@ +/* e_asinf.c -- float version of e_asin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_asinf.c,v 1.8 2002/05/26 22:01:48 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +huge = 1.000e+30, +pio2_hi = 1.5707962513e+00, /* 0x3fc90fda */ +pio2_lo = 7.5497894159e-08, /* 0x33a22168 */ +pio4_hi = 7.8539818525e-01, /* 0x3f490fdb */ + /* coefficient for R(x^2) */ +pS0 = 1.6666667163e-01, /* 0x3e2aaaab */ +pS1 = -3.2556581497e-01, /* 0xbea6b090 */ +pS2 = 2.0121252537e-01, /* 0x3e4e0aa8 */ +pS3 = -4.0055535734e-02, /* 0xbd241146 */ +pS4 = 7.9153501429e-04, /* 0x3a4f7f04 */ +pS5 = 3.4793309169e-05, /* 0x3811ef08 */ +qS1 = -2.4033949375e+00, /* 0xc019d139 */ +qS2 = 2.0209457874e+00, /* 0x4001572d */ +qS3 = -6.8828397989e-01, /* 0xbf303361 */ +qS4 = 7.7038154006e-02; /* 0x3d9dc62e */ + +float +__ieee754_asinf(float x) +{ + float t,w,p,q,c,r,s; + int32_t hx,ix; + + t = 0; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix==0x3f800000) { + /* asin(1)=+-pi/2 with inexact */ + return x*pio2_hi+x*pio2_lo; + } else if(ix> 0x3f800000) { /* |x|>= 1 */ + return (x-x)/(x-x); /* asin(|x|>1) is NaN */ + } else if (ix<0x3f000000) { /* |x|<0.5 */ + if(ix<0x32000000) { /* if |x| < 2**-27 */ + if(huge+x>one) return x;/* return x with inexact if x!=0*/ + } else + t = x*x; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + w = p/q; + return x+x*w; + } + /* 1> |x|>= 0.5 */ + w = one-fabsf(x); + t = w*(float)0.5; + p = t*(pS0+t*(pS1+t*(pS2+t*(pS3+t*(pS4+t*pS5))))); + q = one+t*(qS1+t*(qS2+t*(qS3+t*qS4))); + s = __ieee754_sqrtf(t); + if(ix>=0x3F79999A) { /* if |x| > 0.975 */ + w = p/q; + t = pio2_hi-((float)2.0*(s+s*w)-pio2_lo); + } else { + int32_t iw; + w = s; + GET_FLOAT_WORD(iw,w); + SET_FLOAT_WORD(w,iw&0xfffff000); + c = (t-w*w)/(s+w); + r = p/q; + p = (float)2.0*s*r-(pio2_lo-(float)2.0*c); + q = pio4_hi-(float)2.0*w; + t = pio4_hi-(p-q); + } + if(hx>0) return t; else return -t; +} diff --git a/lib/nbsd_libm/src/e_atan2.c b/lib/nbsd_libm/src/e_atan2.c new file mode 100644 index 000000000..08d8f06da --- /dev/null +++ b/lib/nbsd_libm/src/e_atan2.c @@ -0,0 +1,123 @@ +/* @(#)e_atan2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_atan2.c,v 1.12 2002/05/26 22:01:48 wiz Exp $"); +#endif + +/* __ieee754_atan2(y,x) + * Method : + * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x). + * 2. Reduce x to positive by (if x and y are unexceptional): + * ARG (x+iy) = arctan(y/x) ... if x > 0, + * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0, + * + * Special cases: + * + * ATAN2((anything), NaN ) is NaN; + * ATAN2(NAN , (anything) ) is NaN; + * ATAN2(+-0, +(anything but NaN)) is +-0 ; + * ATAN2(+-0, -(anything but NaN)) is +-pi ; + * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2; + * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ; + * ATAN2(+-(anything but INF and NaN), -INF) is +-pi; + * ATAN2(+-INF,+INF ) is +-pi/4 ; + * ATAN2(+-INF,-INF ) is +-3pi/4; + * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2; + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +static const double +tiny = 1.0e-300, +zero = 0.0, +pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */ +pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */ +pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */ +pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */ + +double +__ieee754_atan2(double y, double x) +{ + double z; + int32_t k,m,hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + EXTRACT_WORDS(hy,ly,y); + iy = hy&0x7fffffff; + if(((ix|((lx|-lx)>>31))>0x7ff00000)|| + ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */ + return x+y; + if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if((iy|ly)==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7ff00000) { + if(iy==0x7ff00000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>20; + if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atan(fabs(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_HIGH_WORD(zh,z); + SET_HIGH_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/lib/nbsd_libm/src/e_atan2f.c b/lib/nbsd_libm/src/e_atan2f.c new file mode 100644 index 000000000..3dbd3b6cc --- /dev/null +++ b/lib/nbsd_libm/src/e_atan2f.c @@ -0,0 +1,98 @@ +/* e_atan2f.c -- float version of e_atan2.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_atan2f.c,v 1.7 2002/05/26 22:01:49 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +tiny = 1.0e-30, +zero = 0.0, +pi_o_4 = 7.8539818525e-01, /* 0x3f490fdb */ +pi_o_2 = 1.5707963705e+00, /* 0x3fc90fdb */ +pi = 3.1415925026e+00, /* 0x40490fda */ +pi_lo = 1.5099578832e-07; /* 0x34222168 */ + +float +__ieee754_atan2f(float y, float x) +{ + float z; + int32_t k,m,hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + GET_FLOAT_WORD(hy,y); + iy = hy&0x7fffffff; + if((ix>0x7f800000)|| + (iy>0x7f800000)) /* x or y is NaN */ + return x+y; + if(hx==0x3f800000) return atanf(y); /* x=1.0 */ + m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */ + + /* when y = 0 */ + if(iy==0) { + switch(m) { + case 0: + case 1: return y; /* atan(+-0,+anything)=+-0 */ + case 2: return pi+tiny;/* atan(+0,-anything) = pi */ + case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */ + } + } + /* when x = 0 */ + if(ix==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* when x is INF */ + if(ix==0x7f800000) { + if(iy==0x7f800000) { + switch(m) { + case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */ + case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */ + case 2: return (float)3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/ + case 3: return (float)-3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/ + } + } else { + switch(m) { + case 0: return zero ; /* atan(+...,+INF) */ + case 1: return -zero ; /* atan(-...,+INF) */ + case 2: return pi+tiny ; /* atan(+...,-INF) */ + case 3: return -pi-tiny ; /* atan(-...,-INF) */ + } + } + } + /* when y is INF */ + if(iy==0x7f800000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny; + + /* compute y/x */ + k = (iy-ix)>>23; + if(k > 60) z=pi_o_2+(float)0.5*pi_lo; /* |y/x| > 2**60 */ + else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */ + else z=atanf(fabsf(y/x)); /* safe to do y/x */ + switch (m) { + case 0: return z ; /* atan(+,+) */ + case 1: { + u_int32_t zh; + GET_FLOAT_WORD(zh,z); + SET_FLOAT_WORD(z,zh ^ 0x80000000); + } + return z ; /* atan(-,+) */ + case 2: return pi-(z-pi_lo);/* atan(+,-) */ + default: /* case 3 */ + return (z-pi_lo)-pi;/* atan(-,-) */ + } +} diff --git a/lib/nbsd_libm/src/e_atanh.c b/lib/nbsd_libm/src/e_atanh.c new file mode 100644 index 000000000..6c0f33159 --- /dev/null +++ b/lib/nbsd_libm/src/e_atanh.c @@ -0,0 +1,63 @@ +/* @(#)e_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_atanh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $"); +#endif + +/* __ieee754_atanh(x) + * Method : + * 1.Reduced x to positive by atanh(-x) = -atanh(x) + * 2.For x>=0.5 + * 1 2x x + * atanh(x) = --- * log(1 + -------) = 0.5 * log1p(2 * --------) + * 2 1 - x 1 - x + * + * For x<0.5 + * atanh(x) = 0.5*log1p(2x+2x*x/(1-x)) + * + * Special cases: + * atanh(x) is NaN if |x| > 1 with signal; + * atanh(NaN) is that NaN with no signal; + * atanh(+-1) is +-INF with signal. + * + */ + +#include "math.h" +#include "math_private.h" + +static const double one = 1.0, huge = 1e300; + +static const double zero = 0.0; + +double +__ieee754_atanh(double x) +{ + double t; + int32_t hx,ix; + u_int32_t lx; + EXTRACT_WORDS(hx,lx,x); + ix = hx&0x7fffffff; + if ((ix|((lx|(-lx))>>31))>0x3ff00000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3ff00000) + return x/zero; + if(ix<0x3e300000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_HIGH_WORD(x,ix); + if(ix<0x3fe00000) { /* x < 0.5 */ + t = x+x; + t = 0.5*log1p(t+t*x/(one-x)); + } else + t = 0.5*log1p((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/lib/nbsd_libm/src/e_atanhf.c b/lib/nbsd_libm/src/e_atanhf.c new file mode 100644 index 000000000..5f225f24d --- /dev/null +++ b/lib/nbsd_libm/src/e_atanhf.c @@ -0,0 +1,47 @@ +/* e_atanhf.c -- float version of e_atanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_atanhf.c,v 1.7 2002/05/26 22:01:49 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float one = 1.0, huge = 1e30; + +static const float zero = 0.0; + +float +__ieee754_atanhf(float x) +{ + float t; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if (ix>0x3f800000) /* |x|>1 */ + return (x-x)/(x-x); + if(ix==0x3f800000) + return x/zero; + if(ix<0x31800000&&(huge+x)>zero) return x; /* x<2**-28 */ + SET_FLOAT_WORD(x,ix); + if(ix<0x3f000000) { /* x < 0.5 */ + t = x+x; + t = (float)0.5*log1pf(t+t*x/(one-x)); + } else + t = (float)0.5*log1pf((x+x)/(one-x)); + if(hx>=0) return t; else return -t; +} diff --git a/lib/nbsd_libm/src/e_cosh.c b/lib/nbsd_libm/src/e_cosh.c new file mode 100644 index 000000000..1e1a8df6e --- /dev/null +++ b/lib/nbsd_libm/src/e_cosh.c @@ -0,0 +1,86 @@ +/* @(#)e_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_cosh.c,v 1.11 2002/05/26 22:01:49 wiz Exp $"); +#endif + +/* __ieee754_cosh(x) + * Method : + * mathematically cosh(x) if defined to be (exp(x)+exp(-x))/2 + * 1. Replace x by |x| (cosh(x) = cosh(-x)). + * 2. + * [ exp(x) - 1 ]^2 + * 0 <= x <= ln2/2 : cosh(x) := 1 + ------------------- + * 2*exp(x) + * + * exp(x) + 1/exp(x) + * ln2/2 <= x <= 22 : cosh(x) := ------------------- + * 2 + * 22 <= x <= lnovft : cosh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: cosh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : cosh(x) := huge*huge (overflow) + * + * Special cases: + * cosh(x) is |x| if x is +INF, -INF, or NaN. + * only cosh(0)=1 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +static const double one = 1.0, half=0.5, huge = 1.0e300; + +double +__ieee754_cosh(double x) +{ + double t,w; + int32_t ix; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3fd62e43) { + t = expm1(fabs(x)); + w = one+t; + if (ix<0x3c800000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x40360000) { + t = __ieee754_exp(fabs(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x40862E42) return half*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || + ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = __ieee754_exp(half*fabs(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/lib/nbsd_libm/src/e_coshf.c b/lib/nbsd_libm/src/e_coshf.c new file mode 100644 index 000000000..32d64c7c1 --- /dev/null +++ b/lib/nbsd_libm/src/e_coshf.c @@ -0,0 +1,65 @@ +/* e_coshf.c -- float version of e_cosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_coshf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e30; +static const float one = 1.0, half=0.5; + +float +__ieee754_coshf(float x) +{ + float t,w; + int32_t ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x*x; + + /* |x| in [0,0.5*ln2], return 1+expm1(|x|)^2/(2*exp(|x|)) */ + if(ix<0x3eb17218) { + t = expm1f(fabsf(x)); + w = one+t; + if (ix<0x24000000) return w; /* cosh(tiny) = 1 */ + return one+(t*t)/(w+w); + } + + /* |x| in [0.5*ln2,22], return (exp(|x|)+1/exp(|x|)/2; */ + if (ix < 0x41b00000) { + t = __ieee754_expf(fabsf(x)); + return half*t+half/t; + } + + /* |x| in [22, log(maxdouble)] return half*exp(|x|) */ + if (ix < 0x42b17180) return half*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf(half*fabsf(x)); + t = half*w; + return t*w; + } + + /* |x| > overflowthresold, cosh(x) overflow */ + return huge*huge; +} diff --git a/lib/nbsd_libm/src/e_exp.c b/lib/nbsd_libm/src/e_exp.c new file mode 100644 index 000000000..5c28dd6be --- /dev/null +++ b/lib/nbsd_libm/src/e_exp.c @@ -0,0 +1,162 @@ +/* @(#)e_exp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_exp.c,v 1.11 2002/05/26 22:01:49 wiz Exp $"); +#endif + +/* __ieee754_exp(x) + * Returns the exponential of x. + * + * Method + * 1. Argument reduction: + * Reduce x to an r so that |r| <= 0.5*ln2 ~ 0.34658. + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2. + * + * Here r will be represented as r = hi-lo for better + * accuracy. + * + * 2. Approximation of exp(r) by a special rational function on + * the interval [0,0.34658]: + * Write + * R(r**2) = r*(exp(r)+1)/(exp(r)-1) = 2 + r*r/6 - r**4/360 + ... + * We use a special Reme algorithm on [0,0.34658] to generate + * a polynomial of degree 5 to approximate R. The maximum error + * of this polynomial approximation is bounded by 2**-59. In + * other words, + * R(z) ~ 2.0 + P1*z + P2*z**2 + P3*z**3 + P4*z**4 + P5*z**5 + * (where z=r*r, and the values of P1 to P5 are listed below) + * and + * | 5 | -59 + * | 2.0+P1*z+...+P5*z - R(z) | <= 2 + * | | + * The computation of exp(r) thus becomes + * 2*r + * exp(r) = 1 + ------- + * R - r + * r*R1(r) + * = 1 + r + ----------- (for better accuracy) + * 2 - R1(r) + * where + * 2 4 10 + * R1(r) = r - (P1*r + P2*r + ... + P5*r ). + * + * 3. Scale back to obtain exp(x): + * From step 1, we have + * exp(x) = 2^k * exp(r) + * + * Special cases: + * exp(INF) is INF, exp(NaN) is NaN; + * exp(-INF) is 0, and + * for finite argument, only exp(0)=1 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then exp(x) overflow + * if x < -7.45133219101941108420e+02 then exp(x) underflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +static const double +one = 1.0, +halF[2] = {0.5,-0.5,}, +huge = 1.0e+300, +twom1000= 9.33263618503218878990e-302, /* 2**-1000=0x01700000,0*/ +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02, /* 0xc0874910, 0xD52D3051 */ +ln2HI[2] ={ 6.93147180369123816490e-01, /* 0x3fe62e42, 0xfee00000 */ + -6.93147180369123816490e-01,},/* 0xbfe62e42, 0xfee00000 */ +ln2LO[2] ={ 1.90821492927058770002e-10, /* 0x3dea39ef, 0x35793c76 */ + -1.90821492927058770002e-10,},/* 0xbdea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00, /* 0x3ff71547, 0x652b82fe */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08; /* 0x3E663769, 0x72BEA4D0 */ + + +double +__ieee754_exp(double x) /* default IEEE double exp */ +{ + double y,hi,lo,c,t; + int32_t k,xsb; + u_int32_t hx; + + hi = lo = 0; + k = 0; + GET_HIGH_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t lx; + GET_LOW_WORD(lx,x); + if(((hx&0xfffff)|lx)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom1000*twom1000; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = invln2*x+halF[xsb]; + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + x = hi - lo; + } + else if(hx < 0x3e300000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-2.0)-x); + else y = one-((lo-(x*c)/(2.0-c))-hi); + if(k >= -1021) { + u_int32_t hy; + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(y,hy+(k<<20)); /* add k to y's exponent */ + return y; + } else { + u_int32_t hy; + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(y,hy+((k+1000)<<20)); /* add k to y's exponent */ + return y*twom1000; + } +} diff --git a/lib/nbsd_libm/src/e_expf.c b/lib/nbsd_libm/src/e_expf.c new file mode 100644 index 000000000..d598d4ecf --- /dev/null +++ b/lib/nbsd_libm/src/e_expf.c @@ -0,0 +1,99 @@ +/* e_expf.c -- float version of e_exp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_expf.c,v 1.9 2002/05/26 22:01:49 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e+30; + +static const float +one = 1.0, +halF[2] = {0.5,-0.5,}, +twom100 = 7.8886090522e-31, /* 2**-100=0x0d800000 */ +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02, /* 0xc2cff1b5 */ +ln2HI[2] ={ 6.9313812256e-01, /* 0x3f317180 */ + -6.9313812256e-01,}, /* 0xbf317180 */ +ln2LO[2] ={ 9.0580006145e-06, /* 0x3717f7d1 */ + -9.0580006145e-06,}, /* 0xb717f7d1 */ +invln2 = 1.4426950216e+00, /* 0x3fb8aa3b */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08; /* 0x3331bb4c */ + +float +__ieee754_expf(float x) /* default IEEE double exp */ +{ + float y,hi,lo,c,t; + int32_t k,xsb; + u_int32_t hx; + + hi = lo = 0; + k = 0; + GET_FLOAT_WORD(hx,x); + xsb = (hx>>31)&1; /* sign bit of x */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out non-finite argument */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:0.0; /* exp(+-inf)={inf,0} */ + if(x > o_threshold) return huge*huge; /* overflow */ + if(x < u_threshold) return twom100*twom100; /* underflow */ + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + hi = x-ln2HI[xsb]; lo=ln2LO[xsb]; k = 1-xsb-xsb; + } else { + k = invln2*x+halF[xsb]; + t = k; + hi = x - t*ln2HI[0]; /* t*ln2HI is exact here */ + lo = t*ln2LO[0]; + } + x = hi - lo; + } + else if(hx < 0x31800000) { /* when |x|<2**-28 */ + if(huge+x>one) return one+x;/* trigger inexact */ + } + else k = 0; + + /* x is now in primary range */ + t = x*x; + c = x - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + if(k==0) return one-((x*c)/(c-(float)2.0)-x); + else y = one-((lo-(x*c)/((float)2.0-c))-hi); + if(k >= -125) { + u_int32_t hy; + GET_FLOAT_WORD(hy,y); + SET_FLOAT_WORD(y,hy+(k<<23)); /* add k to y's exponent */ + return y; + } else { + u_int32_t hy; + GET_FLOAT_WORD(hy,y); + SET_FLOAT_WORD(y,hy+((k+100)<<23)); /* add k to y's exponent */ + return y*twom100; + } +} diff --git a/lib/nbsd_libm/src/e_fmod.c b/lib/nbsd_libm/src/e_fmod.c new file mode 100644 index 000000000..dfbc4da09 --- /dev/null +++ b/lib/nbsd_libm/src/e_fmod.c @@ -0,0 +1,133 @@ +/* @(#)e_fmod.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_fmod.c,v 1.11 2002/05/26 22:01:49 wiz Exp $"); +#endif + +/* + * __ieee754_fmod(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include "math.h" +#include "math_private.h" + +static const double one = 1.0, Zero[] = {0.0, -0.0,}; + +double +__ieee754_fmod(double x, double y) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + u_int32_t lx,ly,lz; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ + ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx<=hy) { + if((hx>31]; /* |x|=|y| return x*0*/ + } + + /* determine ix = ilogb(x) */ + if(hx<0x00100000) { /* subnormal x */ + if(hx==0) { + for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; + } else { + for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; + } + } else ix = (hx>>20)-1023; + + /* determine iy = ilogb(y) */ + if(hy<0x00100000) { /* subnormal y */ + if(hy==0) { + for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; + } else { + for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; + } + } else iy = (hy>>20)-1023; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -1022) + hx = 0x00100000|(0x000fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -1022-ix; + if(n<=31) { + hx = (hx<>(32-n)); + lx <<= n; + } else { + hx = lx<<(n-32); + lx = 0; + } + } + if(iy >= -1022) + hy = 0x00100000|(0x000fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -1022-iy; + if(n<=31) { + hy = (hy<>(32-n)); + ly <<= n; + } else { + hy = ly<<(n-32); + ly = 0; + } + } + + /* fix point fmod */ + n = ix - iy; + while(n--) { + hz=hx-hy;lz=lx-ly; if(lx>31); lx = lx+lx;} + else { + if((hz|lz)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + hx = hz+hz+(lz>>31); lx = lz+lz; + } + } + hz=hx-hy;lz=lx-ly; if(lx=0) {hx=hz;lx=lz;} + + /* convert back to floating value and restore the sign */ + if((hx|lx)==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00100000) { /* normalize x */ + hx = hx+hx+(lx>>31); lx = lx+lx; + iy -= 1; + } + if(iy>= -1022) { /* normalize output */ + hx = ((hx-0x00100000)|((iy+1023)<<20)); + INSERT_WORDS(x,hx|sx,lx); + } else { /* subnormal output */ + n = -1022 - iy; + if(n<=20) { + lx = (lx>>n)|((u_int32_t)hx<<(32-n)); + hx >>= n; + } else if (n<=31) { + lx = (hx<<(32-n))|(lx>>n); hx = sx; + } else { + lx = hx>>(n-32); hx = sx; + } + INSERT_WORDS(x,hx|sx,lx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/lib/nbsd_libm/src/e_fmodf.c b/lib/nbsd_libm/src/e_fmodf.c new file mode 100644 index 000000000..5bc02a433 --- /dev/null +++ b/lib/nbsd_libm/src/e_fmodf.c @@ -0,0 +1,106 @@ +/* e_fmodf.c -- float version of e_fmod.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_fmodf.c,v 1.7 2002/05/26 22:01:49 wiz Exp $"); +#endif + +/* + * __ieee754_fmodf(x,y) + * Return x mod y in exact arithmetic + * Method: shift and subtract + */ + +#include "math.h" +#include "math_private.h" + +static const float one = 1.0, Zero[] = {0.0, -0.0,}; + +float +__ieee754_fmodf(float x, float y) +{ + int32_t n,hx,hy,hz,ix,iy,sx,i; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + sx = hx&0x80000000; /* sign of x */ + hx ^=sx; /* |x| */ + hy &= 0x7fffffff; /* |y| */ + + /* purge off exception values */ + if(hy==0||(hx>=0x7f800000)|| /* y=0,or x not finite */ + (hy>0x7f800000)) /* or y is NaN */ + return (x*y)/(x*y); + if(hx>31]; /* |x|=|y| return x*0*/ + + /* determine ix = ilogb(x) */ + if(hx<0x00800000) { /* subnormal x */ + for (ix = -126,i=(hx<<8); i>0; i<<=1) ix -=1; + } else ix = (hx>>23)-127; + + /* determine iy = ilogb(y) */ + if(hy<0x00800000) { /* subnormal y */ + for (iy = -126,i=(hy<<8); i>=0; i<<=1) iy -=1; + } else iy = (hy>>23)-127; + + /* set up {hx,lx}, {hy,ly} and align y to x */ + if(ix >= -126) + hx = 0x00800000|(0x007fffff&hx); + else { /* subnormal x, shift x to normal */ + n = -126-ix; + hx = hx<= -126) + hy = 0x00800000|(0x007fffff&hy); + else { /* subnormal y, shift y to normal */ + n = -126-iy; + hy = hy<>31]; + hx = hz+hz; + } + } + hz=hx-hy; + if(hz>=0) {hx=hz;} + + /* convert back to floating value and restore the sign */ + if(hx==0) /* return sign(x)*0 */ + return Zero[(u_int32_t)sx>>31]; + while(hx<0x00800000) { /* normalize x */ + hx = hx+hx; + iy -= 1; + } + if(iy>= -126) { /* normalize output */ + hx = ((hx-0x00800000)|((iy+127)<<23)); + SET_FLOAT_WORD(x,hx|sx); + } else { /* subnormal output */ + n = -126 - iy; + hx >>= n; + SET_FLOAT_WORD(x,hx|sx); + x *= one; /* create necessary signal */ + } + return x; /* exact output */ +} diff --git a/lib/nbsd_libm/src/e_hypot.c b/lib/nbsd_libm/src/e_hypot.c new file mode 100644 index 000000000..130c37d23 --- /dev/null +++ b/lib/nbsd_libm/src/e_hypot.c @@ -0,0 +1,125 @@ +/* @(#)e_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_hypot.c,v 1.13 2008/04/25 22:21:53 christos Exp $"); +#endif + +/* __ieee754_hypot(x,y) + * + * Method : + * If (assume round-to-nearest) z=x*x+y*y + * has error less than sqrt(2)/2 ulp, than + * sqrt(z) has error less than 1 ulp (exercise). + * + * So, compute sqrt(x*x+y*y) with some care as + * follows to get the error below 1 ulp: + * + * Assume x>y>0; + * (if possible, set rounding to round-to-nearest) + * 1. if x > 2y use + * x1*x1+(y*y+(x2*(x+x1))) for x*x+y*y + * where x1 = x with lower 32 bits cleared, x2 = x-x1; else + * 2. if x <= 2y use + * t1*yy1+((x-y)*(x-y)+(t1*y2+t2*y)) + * where t1 = 2x with lower 32 bits cleared, t2 = 2x-t1, + * yy1= y with lower 32 bits chopped, y2 = y-yy1. + * + * NOTE: scaling may be necessary if some argument is too + * large or too tiny + * + * Special cases: + * hypot(x,y) is INF if x or y is +INF or -INF; else + * hypot(x,y) is NAN if x or y is NAN. + * + * Accuracy: + * hypot(x,y) returns sqrt(x^2+y^2) with error less + * than 1 ulps (units in the last place) + */ + +#include "math.h" +#include "math_private.h" + +double +__ieee754_hypot(double x, double y) +{ + double a=x,b=y,t1,t2,yy1,y2,w; + int32_t j,k,ha,hb; + + GET_HIGH_WORD(ha,x); + ha &= 0x7fffffff; + GET_HIGH_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_HIGH_WORD(a,ha); /* a <- |a| */ + SET_HIGH_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0x3c00000) {return a+b;} /* x/y > 2**60 */ + k=0; + if(ha > 0x5f300000) { /* a>2**500 */ + if(ha >= 0x7ff00000) { /* Inf or NaN */ + u_int32_t low; + w = a+b; /* for sNaN */ + GET_LOW_WORD(low,a); + if(((ha&0xfffff)|low)==0) w = a; + GET_LOW_WORD(low,b); + if(((hb^0x7ff00000)|low)==0) w = b; + return w; + } + /* scale a and b by 2**-600 */ + ha -= 0x25800000; hb -= 0x25800000; k += 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + if(hb < 0x20b00000) { /* b < 2**-500 */ + if(hb <= 0x000fffff) { /* subnormal b or 0 */ + u_int32_t low; + GET_LOW_WORD(low,b); + if((hb|low)==0) return a; + t1=0; + SET_HIGH_WORD(t1,0x7fd00000); /* t1=2^1022 */ + b *= t1; + a *= t1; + k -= 1022; + } else { /* scale a and b by 2^600 */ + ha += 0x25800000; /* a *= 2^600 */ + hb += 0x25800000; /* b *= 2^600 */ + k -= 600; + SET_HIGH_WORD(a,ha); + SET_HIGH_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + t1 = 0; + SET_HIGH_WORD(t1,ha); + t2 = a-t1; + w = __ieee754_sqrt(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + yy1 = 0; + SET_HIGH_WORD(yy1,hb); + y2 = b - yy1; + t1 = 0; + SET_HIGH_WORD(t1,ha+0x00100000); + t2 = a - t1; + w = __ieee754_sqrt(t1*yy1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + u_int32_t high; + t1 = 1.0; + GET_HIGH_WORD(high,t1); + SET_HIGH_WORD(t1,high+(k<<20)); + return t1*w; + } else return w; +} diff --git a/lib/nbsd_libm/src/e_hypotf.c b/lib/nbsd_libm/src/e_hypotf.c new file mode 100644 index 000000000..23906617d --- /dev/null +++ b/lib/nbsd_libm/src/e_hypotf.c @@ -0,0 +1,84 @@ +/* e_hypotf.c -- float version of e_hypot.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_hypotf.c,v 1.9 2008/04/25 22:21:53 christos Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +__ieee754_hypotf(float x, float y) +{ + float a=x,b=y,t1,t2,yy1,y2,w; + int32_t j,k,ha,hb; + + GET_FLOAT_WORD(ha,x); + ha &= 0x7fffffff; + GET_FLOAT_WORD(hb,y); + hb &= 0x7fffffff; + if(hb > ha) {a=y;b=x;j=ha; ha=hb;hb=j;} else {a=x;b=y;} + SET_FLOAT_WORD(a,ha); /* a <- |a| */ + SET_FLOAT_WORD(b,hb); /* b <- |b| */ + if((ha-hb)>0xf000000) {return a+b;} /* x/y > 2**30 */ + k=0; + if(ha > 0x58800000) { /* a>2**50 */ + if(ha >= 0x7f800000) { /* Inf or NaN */ + w = a+b; /* for sNaN */ + if(ha == 0x7f800000) w = a; + if(hb == 0x7f800000) w = b; + return w; + } + /* scale a and b by 2**-60 */ + ha -= 0x5d800000; hb -= 0x5d800000; k += 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + if(hb < 0x26800000) { /* b < 2**-50 */ + if(hb <= 0x007fffff) { /* subnormal b or 0 */ + if(hb==0) return a; + SET_FLOAT_WORD(t1,0x3f000000); /* t1=2^126 */ + b *= t1; + a *= t1; + k -= 126; + } else { /* scale a and b by 2^60 */ + ha += 0x5d800000; /* a *= 2^60 */ + hb += 0x5d800000; /* b *= 2^60 */ + k -= 60; + SET_FLOAT_WORD(a,ha); + SET_FLOAT_WORD(b,hb); + } + } + /* medium size a and b */ + w = a-b; + if (w>b) { + SET_FLOAT_WORD(t1,ha&0xfffff000); + t2 = a-t1; + w = __ieee754_sqrtf(t1*t1-(b*(-b)-t2*(a+t1))); + } else { + a = a+a; + SET_FLOAT_WORD(yy1,hb&0xfffff000); + y2 = b - yy1; + SET_FLOAT_WORD(t1,ha+0x00800000); + t2 = a - t1; + w = __ieee754_sqrtf(t1*yy1-(w*(-w)-(t1*y2+t2*b))); + } + if(k!=0) { + SET_FLOAT_WORD(t1,0x3f800000+(k<<23)); + return t1*w; + } else return w; +} diff --git a/lib/nbsd_libm/src/e_j0.c b/lib/nbsd_libm/src/e_j0.c new file mode 100644 index 000000000..96ade957c --- /dev/null +++ b/lib/nbsd_libm/src/e_j0.c @@ -0,0 +1,389 @@ +/* @(#)e_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_j0.c,v 1.12 2007/08/20 16:01:38 drochner Exp $"); +#endif + +/* __ieee754_j0(x), __ieee754_y0(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j0(x): + * 1. For tiny x, we use j0(x) = 1 - x^2/4 + x^4/64 - ... + * 2. Reduce x to |x| since j0(x)=j0(-x), and + * for x in (0,2) + * j0(x) = 1-z/4+ z^2*R0/S0, where z = x*x; + * (precision: |j0-1+z/4-z^2R0/S0 |<2**-63.67 ) + * for x in (2,inf) + * j0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)-q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * as follow: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (cos(x) + sin(x)) + * sin(x0) = sin(x)cos(pi/4)-cos(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j0(nan)= nan + * j0(0) = 1 + * j0(inf) = 0 + * + * Method -- y0(x): + * 1. For x<2. + * Since + * y0(x) = 2/pi*(j0(x)*(ln(x/2)+Euler) + x^2/4 - ...) + * therefore y0(x)-2/pi*j0(x)*ln(x) is an even function. + * We use the following function to approximate y0, + * y0(x) = U(z)/V(z) + (2/pi)*(j0(x)*ln(x)), z= x^2 + * where + * U(z) = u00 + u01*z + ... + u06*z^6 + * V(z) = 1 + v01*z + ... + v04*z^4 + * with absolute approximation error bounded by 2**-72. + * Note: For tiny x, U/V = u0 and j0(x)~1, hence + * y0(tiny) = u0 + (2/pi)*ln(tiny), (choose tiny<2**-27) + * 2. For x>=2. + * y0(x) = sqrt(2/(pi*x))*(p0(x)*cos(x0)+q0(x)*sin(x0)) + * where x0 = x-pi/4. It is better to compute sin(x0),cos(x0) + * by the method mentioned above. + * 3. Special cases: y0(0)=-inf, y0(x<0)=NaN, y0(inf)=0. + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static double pzero(double), qzero(double); + +static const double +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.56249999999999947958e-02, /* 0x3F8FFFFF, 0xFFFFFFFD */ +R03 = -1.89979294238854721751e-04, /* 0xBF28E6A5, 0xB61AC6E9 */ +R04 = 1.82954049532700665670e-06, /* 0x3EBEB1D1, 0x0C503919 */ +R05 = -4.61832688532103189199e-09, /* 0xBE33D5E7, 0x73D63FCE */ +S01 = 1.56191029464890010492e-02, /* 0x3F8FFCE8, 0x82C8C2A4 */ +S02 = 1.16926784663337450260e-04, /* 0x3F1EA6D2, 0xDD57DBF4 */ +S03 = 5.13546550207318111446e-07, /* 0x3EA13B54, 0xCE84D5A9 */ +S04 = 1.16614003333790000205e-09; /* 0x3E1408BC, 0xF4745D8F */ + +static const double zero = 0.0; + +double +__ieee754_j0(double x) +{ + double z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/(x*x); + x = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*cc)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*cc-v*ss)/sqrt(x); + } + return z; + } + if(ix<0x3f200000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x3e400000) return one; /* |x|<2**-27 */ + else return one - 0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3FF00000) { /* |x| < 1.00 */ + return one + z*(-0.25+(r/s)); + } else { + u = 0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +static const double +u00 = -7.38042951086872317523e-02, /* 0xBFB2E4D6, 0x99CBD01F */ +u01 = 1.76666452509181115538e-01, /* 0x3FC69D01, 0x9DE9E3FC */ +u02 = -1.38185671945596898896e-02, /* 0xBF8C4CE8, 0xB16CFA97 */ +u03 = 3.47453432093683650238e-04, /* 0x3F36C54D, 0x20B29B6B */ +u04 = -3.81407053724364161125e-06, /* 0xBECFFEA7, 0x73D25CAD */ +u05 = 1.95590137035022920206e-08, /* 0x3E550057, 0x3B4EABD4 */ +u06 = -3.98205194132103398453e-11, /* 0xBDC5E43D, 0x693FB3C8 */ +v01 = 1.27304834834123699328e-02, /* 0x3F8A1270, 0x91C9C71A */ +v02 = 7.60068627350353253702e-05, /* 0x3F13ECBB, 0xF578C6C1 */ +v03 = 2.59150851840457805467e-07, /* 0x3E91642D, 0x7FF202FD */ +v04 = 4.41110311332675467403e-10; /* 0x3DFE5018, 0x3BD6D9EF */ + +double +__ieee754_y0(double x) +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sin(x); + c = cos(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = -cos(x+x); + if ((s*c)0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pzero(x); v = qzero(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3e400000) { /* x < 2**-27 */ + return(u00 + tpi*__ieee754_log(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0(x)*__ieee754_log(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const double pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -7.03124999999900357484e-02, /* 0xBFB1FFFF, 0xFFFFFD32 */ + -8.08167041275349795626e+00, /* 0xC02029D0, 0xB44FA779 */ + -2.57063105679704847262e+02, /* 0xC0701102, 0x7B19E863 */ + -2.48521641009428822144e+03, /* 0xC0A36A6E, 0xCD4DCAFC */ + -5.25304380490729545272e+03, /* 0xC0B4850B, 0x36CC643D */ +}; +static const double pS8[5] = { + 1.16534364619668181717e+02, /* 0x405D2233, 0x07A96751 */ + 3.83374475364121826715e+03, /* 0x40ADF37D, 0x50596938 */ + 4.05978572648472545552e+04, /* 0x40E3D2BB, 0x6EB6B05F */ + 1.16752972564375915681e+05, /* 0x40FC810F, 0x8F9FA9BD */ + 4.76277284146730962675e+04, /* 0x40E74177, 0x4F2C49DC */ +}; + +static const double pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.14125464691894502584e-11, /* 0xBDA918B1, 0x47E495CC */ + -7.03124940873599280078e-02, /* 0xBFB1FFFF, 0xE69AFBC6 */ + -4.15961064470587782438e+00, /* 0xC010A370, 0xF90C6BBF */ + -6.76747652265167261021e+01, /* 0xC050EB2F, 0x5A7D1783 */ + -3.31231299649172967747e+02, /* 0xC074B3B3, 0x6742CC63 */ + -3.46433388365604912451e+02, /* 0xC075A6EF, 0x28A38BD7 */ +}; +static const double pS5[5] = { + 6.07539382692300335975e+01, /* 0x404E6081, 0x0C98C5DE */ + 1.05125230595704579173e+03, /* 0x40906D02, 0x5C7E2864 */ + 5.97897094333855784498e+03, /* 0x40B75AF8, 0x8FBE1D60 */ + 9.62544514357774460223e+03, /* 0x40C2CCB8, 0xFA76FA38 */ + 2.40605815922939109441e+03, /* 0x40A2CC1D, 0xC70BE864 */ +}; + +static const double pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.54704601771951915620e-09, /* 0xBE25E103, 0x6FE1AA86 */ + -7.03119616381481654654e-02, /* 0xBFB1FFF6, 0xF7C0E24B */ + -2.40903221549529611423e+00, /* 0xC00345B2, 0xAEA48074 */ + -2.19659774734883086467e+01, /* 0xC035F74A, 0x4CB94E14 */ + -5.80791704701737572236e+01, /* 0xC04D0A22, 0x420A1A45 */ + -3.14479470594888503854e+01, /* 0xC03F72AC, 0xA892D80F */ +}; +static const double pS3[5] = { + 3.58560338055209726349e+01, /* 0x4041ED92, 0x84077DD3 */ + 3.61513983050303863820e+02, /* 0x40769839, 0x464A7C0E */ + 1.19360783792111533330e+03, /* 0x4092A66E, 0x6D1061D6 */ + 1.12799679856907414432e+03, /* 0x40919FFC, 0xB8C39B7E */ + 1.73580930813335754692e+02, /* 0x4065B296, 0xFC379081 */ +}; + +static const double pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.87534333032526411254e-08, /* 0xBE77D316, 0xE927026D */ + -7.03030995483624743247e-02, /* 0xBFB1FF62, 0x495E1E42 */ + -1.45073846780952986357e+00, /* 0xBFF73639, 0x8A24A843 */ + -7.63569613823527770791e+00, /* 0xC01E8AF3, 0xEDAFA7F3 */ + -1.11931668860356747786e+01, /* 0xC02662E6, 0xC5246303 */ + -3.23364579351335335033e+00, /* 0xC009DE81, 0xAF8FE70F */ +}; +static const double pS2[5] = { + 2.22202997532088808441e+01, /* 0x40363865, 0x908B5959 */ + 1.36206794218215208048e+02, /* 0x4061069E, 0x0EE8878F */ + 2.70470278658083486789e+02, /* 0x4070E786, 0x42EA079B */ + 1.53875394208320329881e+02, /* 0x40633C03, 0x3AB6FAFF */ + 1.46576176948256193810e+01, /* 0x402D50B3, 0x44391809 */ +}; + +static double +pzero(double x) +{ + const double *p,*q; + double z,r,s; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pR8; q= pS8;} + else if(ix>=0x40122E8B){p = pR5; q= pS5;} + else if(ix>=0x4006DB6D){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const double qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 7.32421874999935051953e-02, /* 0x3FB2BFFF, 0xFFFFFE2C */ + 1.17682064682252693899e+01, /* 0x40278952, 0x5BB334D6 */ + 5.57673380256401856059e+02, /* 0x40816D63, 0x15301825 */ + 8.85919720756468632317e+03, /* 0x40C14D99, 0x3E18F46D */ + 3.70146267776887834771e+04, /* 0x40E212D4, 0x0E901566 */ +}; +static const double qS8[6] = { + 1.63776026895689824414e+02, /* 0x406478D5, 0x365B39BC */ + 8.09834494656449805916e+03, /* 0x40BFA258, 0x4E6B0563 */ + 1.42538291419120476348e+05, /* 0x41016652, 0x54D38C3F */ + 8.03309257119514397345e+05, /* 0x412883DA, 0x83A52B43 */ + 8.40501579819060512818e+05, /* 0x4129A66B, 0x28DE0B3D */ + -3.43899293537866615225e+05, /* 0xC114FD6D, 0x2C9530C5 */ +}; + +static const double qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.84085963594515531381e-11, /* 0x3DB43D8F, 0x29CC8CD9 */ + 7.32421766612684765896e-02, /* 0x3FB2BFFF, 0xD172B04C */ + 5.83563508962056953777e+00, /* 0x401757B0, 0xB9953DD3 */ + 1.35111577286449829671e+02, /* 0x4060E392, 0x0A8788E9 */ + 1.02724376596164097464e+03, /* 0x40900CF9, 0x9DC8C481 */ + 1.98997785864605384631e+03, /* 0x409F17E9, 0x53C6E3A6 */ +}; +static const double qS5[6] = { + 8.27766102236537761883e+01, /* 0x4054B1B3, 0xFB5E1543 */ + 2.07781416421392987104e+03, /* 0x40A03BA0, 0xDA21C0CE */ + 1.88472887785718085070e+04, /* 0x40D267D2, 0x7B591E6D */ + 5.67511122894947329769e+04, /* 0x40EBB5E3, 0x97E02372 */ + 3.59767538425114471465e+04, /* 0x40E19118, 0x1F7A54A0 */ + -5.35434275601944773371e+03, /* 0xC0B4EA57, 0xBEDBC609 */ +}; + +static const double qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.37741014089738620906e-09, /* 0x3E32CD03, 0x6ADECB82 */ + 7.32411180042911447163e-02, /* 0x3FB2BFEE, 0x0E8D0842 */ + 3.34423137516170720929e+00, /* 0x400AC0FC, 0x61149CF5 */ + 4.26218440745412650017e+01, /* 0x40454F98, 0x962DAEDD */ + 1.70808091340565596283e+02, /* 0x406559DB, 0xE25EFD1F */ + 1.66733948696651168575e+02, /* 0x4064D77C, 0x81FA21E0 */ +}; +static const double qS3[6] = { + 4.87588729724587182091e+01, /* 0x40486122, 0xBFE343A6 */ + 7.09689221056606015736e+02, /* 0x40862D83, 0x86544EB3 */ + 3.70414822620111362994e+03, /* 0x40ACF04B, 0xE44DFC63 */ + 6.46042516752568917582e+03, /* 0x40B93C6C, 0xD7C76A28 */ + 2.51633368920368957333e+03, /* 0x40A3A8AA, 0xD94FB1C0 */ + -1.49247451836156386662e+02, /* 0xC062A7EB, 0x201CF40F */ +}; + +static const double qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.50444444886983272379e-07, /* 0x3E84313B, 0x54F76BDB */ + 7.32234265963079278272e-02, /* 0x3FB2BEC5, 0x3E883E34 */ + 1.99819174093815998816e+00, /* 0x3FFFF897, 0xE727779C */ + 1.44956029347885735348e+01, /* 0x402CFDBF, 0xAAF96FE5 */ + 3.16662317504781540833e+01, /* 0x403FAA8E, 0x29FBDC4A */ + 1.62527075710929267416e+01, /* 0x403040B1, 0x71814BB4 */ +}; +static const double qS2[6] = { + 3.03655848355219184498e+01, /* 0x403E5D96, 0xF7C07AED */ + 2.69348118608049844624e+02, /* 0x4070D591, 0xE4D14B40 */ + 8.44783757595320139444e+02, /* 0x408A6645, 0x22B3BF22 */ + 8.82935845112488550512e+02, /* 0x408B977C, 0x9C5CC214 */ + 2.12666388511798828631e+02, /* 0x406A9553, 0x0E001365 */ + -5.31095493882666946917e+00, /* 0xC0153E6A, 0xF8B32931 */ +}; + +static double +qzero(double x) +{ + const double *p,*q; + double s,r,z; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qR8; q= qS8;} + else if(ix>=0x40122E8B){p = qR5; q= qS5;} + else if(ix>=0x4006DB6D){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-.125 + r/s)/x; +} diff --git a/lib/nbsd_libm/src/e_j0f.c b/lib/nbsd_libm/src/e_j0f.c new file mode 100644 index 000000000..96d3a95b5 --- /dev/null +++ b/lib/nbsd_libm/src/e_j0f.c @@ -0,0 +1,352 @@ +/* e_j0f.c -- float version of e_j0.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_j0f.c,v 1.10 2007/08/20 16:01:38 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static float pzerof(float), qzerof(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0, 2.00] */ +R02 = 1.5625000000e-02, /* 0x3c800000 */ +R03 = -1.8997929874e-04, /* 0xb947352e */ +R04 = 1.8295404516e-06, /* 0x35f58e88 */ +R05 = -4.6183270541e-09, /* 0xb19eaf3c */ +S01 = 1.5619102865e-02, /* 0x3c7fe744 */ +S02 = 1.1692678527e-04, /* 0x38f53697 */ +S03 = 5.1354652442e-07, /* 0x3509daa6 */ +S04 = 1.1661400734e-09; /* 0x30a045e8 */ + +static const float zero = 0.0; + +float +__ieee754_j0f(float x) +{ + float z, s,c,ss,cc,r,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/(x*x); + x = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)0x80000000) z = (invsqrtpi*cc)/sqrtf(x); + else +#endif + { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*cc-v*ss)/sqrtf(x); + } + return z; + } + if(ix<0x39000000) { /* |x| < 2**-13 */ + if(huge+x>one) { /* raise inexact if x != 0 */ + if(ix<0x32000000) return one; /* |x|<2**-27 */ + else return one - (float)0.25*x*x; + } + } + z = x*x; + r = z*(R02+z*(R03+z*(R04+z*R05))); + s = one+z*(S01+z*(S02+z*(S03+z*S04))); + if(ix < 0x3F800000) { /* |x| < 1.00 */ + return one + z*((float)-0.25+(r/s)); + } else { + u = (float)0.5*x; + return((one+u)*(one-u)+z*(r/s)); + } +} + +static const float +u00 = -7.3804296553e-02, /* 0xbd9726b5 */ +u01 = 1.7666645348e-01, /* 0x3e34e80d */ +u02 = -1.3818567619e-02, /* 0xbc626746 */ +u03 = 3.4745343146e-04, /* 0x39b62a69 */ +u04 = -3.8140706238e-06, /* 0xb67ff53c */ +u05 = 1.9559013964e-08, /* 0x32a802ba */ +u06 = -3.9820518410e-11, /* 0xae2f21eb */ +v01 = 1.2730483897e-02, /* 0x3c509385 */ +v02 = 7.6006865129e-05, /* 0x389f65e0 */ +v03 = 2.5915085189e-07, /* 0x348b216c */ +v04 = 4.4111031494e-10; /* 0x2ff280c2 */ + +float +__ieee754_y0f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* Y0(NaN) is NaN, y0(-inf) is Nan, y0(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + /* y0(x) = sqrt(2/(pi*x))*(p0(x)*sin(x0)+q0(x)*cos(x0)) + * where x0 = x-pi/4 + * Better formula: + * cos(x0) = cos(x)cos(pi/4)+sin(x)sin(pi/4) + * = 1/sqrt(2) * (sin(x) + cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + s = sinf(x); + c = cosf(x); + ss = s-c; + cc = s+c; + /* + * j0(x) = 1/sqrt(pi) * (P(0,x)*cc - Q(0,x)*ss) / sqrt(x) + * y0(x) = 1/sqrt(pi) * (P(0,x)*ss + Q(0,x)*cc) / sqrt(x) + */ + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = -cosf(x+x); + if ((s*c)0x80000000) z = (invsqrtpi*ss)/sqrtf(x); + else +#endif + { + u = pzerof(x); v = qzerof(x); + z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); + } + return z; + } + if(ix<=0x32000000) { /* x < 2**-27 */ + return(u00 + tpi*__ieee754_logf(x)); + } + z = x*x; + u = u00+z*(u01+z*(u02+z*(u03+z*(u04+z*(u05+z*u06))))); + v = one+z*(v01+z*(v02+z*(v03+z*v04))); + return(u/v + tpi*(__ieee754_j0f(x)*__ieee754_logf(x))); +} + +/* The asymptotic expansions of pzero is + * 1 - 9/128 s^2 + 11025/98304 s^4 - ..., where s = 1/x. + * For x >= 2, We approximate pzero by + * pzero(x) = 1 + (R/S) + * where R = pR0 + pR1*s^2 + pR2*s^4 + ... + pR5*s^10 + * S = 1 + pS0*s^2 + ... + pS4*s^10 + * and + * | pzero(x)-1-R/S | <= 2 ** ( -60.26) + */ +static const float pR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -7.0312500000e-02, /* 0xbd900000 */ + -8.0816707611e+00, /* 0xc1014e86 */ + -2.5706311035e+02, /* 0xc3808814 */ + -2.4852163086e+03, /* 0xc51b5376 */ + -5.2530439453e+03, /* 0xc5a4285a */ +}; +static const float pS8[5] = { + 1.1653436279e+02, /* 0x42e91198 */ + 3.8337448730e+03, /* 0x456f9beb */ + 4.0597855469e+04, /* 0x471e95db */ + 1.1675296875e+05, /* 0x47e4087c */ + 4.7627726562e+04, /* 0x473a0bba */ +}; +static const float pR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -1.1412546255e-11, /* 0xad48c58a */ + -7.0312492549e-02, /* 0xbd8fffff */ + -4.1596107483e+00, /* 0xc0851b88 */ + -6.7674766541e+01, /* 0xc287597b */ + -3.3123129272e+02, /* 0xc3a59d9b */ + -3.4643338013e+02, /* 0xc3ad3779 */ +}; +static const float pS5[5] = { + 6.0753936768e+01, /* 0x42730408 */ + 1.0512523193e+03, /* 0x44836813 */ + 5.9789707031e+03, /* 0x45bad7c4 */ + 9.6254453125e+03, /* 0x461665c8 */ + 2.4060581055e+03, /* 0x451660ee */ +}; + +static const float pR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + -2.5470459075e-09, /* 0xb12f081b */ + -7.0311963558e-02, /* 0xbd8fffb8 */ + -2.4090321064e+00, /* 0xc01a2d95 */ + -2.1965976715e+01, /* 0xc1afba52 */ + -5.8079170227e+01, /* 0xc2685112 */ + -3.1447946548e+01, /* 0xc1fb9565 */ +}; +static const float pS3[5] = { + 3.5856033325e+01, /* 0x420f6c94 */ + 3.6151397705e+02, /* 0x43b4c1ca */ + 1.1936077881e+03, /* 0x44953373 */ + 1.1279968262e+03, /* 0x448cffe6 */ + 1.7358093262e+02, /* 0x432d94b8 */ +}; + +static const float pR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -8.8753431271e-08, /* 0xb3be98b7 */ + -7.0303097367e-02, /* 0xbd8ffb12 */ + -1.4507384300e+00, /* 0xbfb9b1cc */ + -7.6356959343e+00, /* 0xc0f4579f */ + -1.1193166733e+01, /* 0xc1331736 */ + -3.2336456776e+00, /* 0xc04ef40d */ +}; +static const float pS2[5] = { + 2.2220300674e+01, /* 0x41b1c32d */ + 1.3620678711e+02, /* 0x430834f0 */ + 2.7047027588e+02, /* 0x43873c32 */ + 1.5387539673e+02, /* 0x4319e01a */ + 1.4657617569e+01, /* 0x416a859a */ +}; + +static float +pzerof(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pR8; q= pS8;} + else if(ix>=0x40f71c58){p = pR5; q= pS5;} + else if(ix>=0x4036db68){p = pR3; q= pS3;} + else if(ix>=0x40000000){p = pR2; q= pS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qzero is + * -1/8 s + 75/1024 s^3 - ..., where s = 1/x. + * We approximate pzero by + * qzero(x) = s*(-1.25 + (R/S)) + * where R = qR0 + qR1*s^2 + qR2*s^4 + ... + qR5*s^10 + * S = 1 + qS0*s^2 + ... + qS5*s^12 + * and + * | qzero(x)/s +1.25-R/S | <= 2 ** ( -61.22) + */ +static const float qR8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 7.3242187500e-02, /* 0x3d960000 */ + 1.1768206596e+01, /* 0x413c4a93 */ + 5.5767340088e+02, /* 0x440b6b19 */ + 8.8591972656e+03, /* 0x460a6cca */ + 3.7014625000e+04, /* 0x471096a0 */ +}; +static const float qS8[6] = { + 1.6377603149e+02, /* 0x4323c6aa */ + 8.0983447266e+03, /* 0x45fd12c2 */ + 1.4253829688e+05, /* 0x480b3293 */ + 8.0330925000e+05, /* 0x49441ed4 */ + 8.4050156250e+05, /* 0x494d3359 */ + -3.4389928125e+05, /* 0xc8a7eb69 */ +}; + +static const float qR5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.8408595828e-11, /* 0x2da1ec79 */ + 7.3242180049e-02, /* 0x3d95ffff */ + 5.8356351852e+00, /* 0x40babd86 */ + 1.3511157227e+02, /* 0x43071c90 */ + 1.0272437744e+03, /* 0x448067cd */ + 1.9899779053e+03, /* 0x44f8bf4b */ +}; +static const float qS5[6] = { + 8.2776611328e+01, /* 0x42a58da0 */ + 2.0778142090e+03, /* 0x4501dd07 */ + 1.8847289062e+04, /* 0x46933e94 */ + 5.6751113281e+04, /* 0x475daf1d */ + 3.5976753906e+04, /* 0x470c88c1 */ + -5.3543427734e+03, /* 0xc5a752be */ +}; + +static const float qR3[6] = {/* for x in [4.547,2.8571]=1/[0.2199,0.35001] */ + 4.3774099900e-09, /* 0x3196681b */ + 7.3241114616e-02, /* 0x3d95ff70 */ + 3.3442313671e+00, /* 0x405607e3 */ + 4.2621845245e+01, /* 0x422a7cc5 */ + 1.7080809021e+02, /* 0x432acedf */ + 1.6673394775e+02, /* 0x4326bbe4 */ +}; +static const float qS3[6] = { + 4.8758872986e+01, /* 0x42430916 */ + 7.0968920898e+02, /* 0x44316c1c */ + 3.7041481934e+03, /* 0x4567825f */ + 6.4604252930e+03, /* 0x45c9e367 */ + 2.5163337402e+03, /* 0x451d4557 */ + -1.4924745178e+02, /* 0xc3153f59 */ +}; + +static const float qR2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.5044444979e-07, /* 0x342189db */ + 7.3223426938e-02, /* 0x3d95f62a */ + 1.9981917143e+00, /* 0x3fffc4bf */ + 1.4495602608e+01, /* 0x4167edfd */ + 3.1666231155e+01, /* 0x41fd5471 */ + 1.6252708435e+01, /* 0x4182058c */ +}; +static const float qS2[6] = { + 3.0365585327e+01, /* 0x41f2ecb8 */ + 2.6934811401e+02, /* 0x4386ac8f */ + 8.4478375244e+02, /* 0x44533229 */ + 8.8293585205e+02, /* 0x445cbbe5 */ + 2.1266638184e+02, /* 0x4354aa98 */ + -5.3109550476e+00, /* 0xc0a9f358 */ +}; + +static float +qzerof(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = qR8; q= qS8;} + else if(ix>=0x40f71c58){p = qR5; q= qS5;} + else if(ix>=0x4036db68){p = qR3; q= qS3;} + else if(ix>=0x40000000){p = qR2; q= qS2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (-(float).125 + r/s)/x; +} diff --git a/lib/nbsd_libm/src/e_j1.c b/lib/nbsd_libm/src/e_j1.c new file mode 100644 index 000000000..e29b397c8 --- /dev/null +++ b/lib/nbsd_libm/src/e_j1.c @@ -0,0 +1,384 @@ +/* @(#)e_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_j1.c,v 1.12 2007/08/20 16:01:38 drochner Exp $"); +#endif + +/* __ieee754_j1(x), __ieee754_y1(x) + * Bessel function of the first and second kinds of order zero. + * Method -- j1(x): + * 1. For tiny x, we use j1(x) = x/2 - x^3/16 + x^5/384 - ... + * 2. Reduce x to |x| since j1(x)=-j1(-x), and + * for x in (0,2) + * j1(x) = x/2 + x*z*R0/S0, where z = x*x; + * (precision: |j1/x - 1/2 - R0/S0 |<2**-61.51 ) + * for x in (2,inf) + * j1(x) = sqrt(2/(pi*x))*(p1(x)*cos(x1)-q1(x)*sin(x1)) + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * as follow: + * cos(x1) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x1) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (sin(x) + cos(x)) + * (To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one.) + * + * 3 Special cases + * j1(nan)= nan + * j1(0) = 0 + * j1(inf) = 0 + * + * Method -- y1(x): + * 1. screen out x<=0 cases: y1(0)=-inf, y1(x<0)=NaN + * 2. For x<2. + * Since + * y1(x) = 2/pi*(j1(x)*(ln(x/2)+Euler)-1/x-x/2+5/64*x^3-...) + * therefore y1(x)-2/pi*j1(x)*ln(x)-1/x is an odd function. + * We use the following function to approximate y1, + * y1(x) = x*U(z)/V(z) + (2/pi)*(j1(x)*ln(x)-1/x), z= x^2 + * where for x in [0,2] (abs err less than 2**-65.89) + * U(z) = U0[0] + U0[1]*z + ... + U0[4]*z^4 + * V(z) = 1 + v0[0]*z + ... + v0[4]*z^5 + * Note: For tiny x, 1/x dominate y1 and hence + * y1(tiny) = -2/pi/tiny, (choose tiny<2**-54) + * 3. For x>=2. + * y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x1)+q1(x)*cos(x1)) + * where x1 = x-3*pi/4. It is better to compute sin(x1),cos(x1) + * by method mentioned above. + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static double pone(double), qone(double); + +static const double +huge = 1e300, +one = 1.0, +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +tpi = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ + /* R0/S0 on [0,2] */ +r00 = -6.25000000000000000000e-02, /* 0xBFB00000, 0x00000000 */ +r01 = 1.40705666955189706048e-03, /* 0x3F570D9F, 0x98472C61 */ +r02 = -1.59955631084035597520e-05, /* 0xBEF0C5C6, 0xBA169668 */ +r03 = 4.96727999609584448412e-08, /* 0x3E6AAAFA, 0x46CA0BD9 */ +s01 = 1.91537599538363460805e-02, /* 0x3F939D0B, 0x12637E53 */ +s02 = 1.85946785588630915560e-04, /* 0x3F285F56, 0xB9CDF664 */ +s03 = 1.17718464042623683263e-06, /* 0x3EB3BFF8, 0x333F8498 */ +s04 = 5.04636257076217042715e-09, /* 0x3E35AC88, 0xC97DFF2C */ +s05 = 1.23542274426137913908e-11; /* 0x3DAB2ACF, 0xCFB97ED8 */ + +static const double zero = 0.0; + +double +__ieee754_j1(double x) +{ + double z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return one/x; + y = fabs(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(y); + c = cos(y); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure y+y not overflow */ + z = cos(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ + if(ix>0x48000000) z = (invsqrtpi*cc)/sqrt(y); + else { + u = pone(y); v = qone(y); + z = invsqrtpi*(u*cc-v*ss)/sqrt(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x3e400000) { /* |x|<2**-27 */ + if(huge+x>one) return 0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*0.5+r/s); +} + +static const double U0[5] = { + -1.96057090646238940668e-01, /* 0xBFC91866, 0x143CBC8A */ + 5.04438716639811282616e-02, /* 0x3FA9D3C7, 0x76292CD1 */ + -1.91256895875763547298e-03, /* 0xBF5F55E5, 0x4844F50F */ + 2.35252600561610495928e-05, /* 0x3EF8AB03, 0x8FA6B88E */ + -9.19099158039878874504e-08, /* 0xBE78AC00, 0x569105B8 */ +}; +static const double V0[5] = { + 1.99167318236649903973e-02, /* 0x3F94650D, 0x3F4DA9F0 */ + 2.02552581025135171496e-04, /* 0x3F2A8C89, 0x6C257764 */ + 1.35608801097516229404e-06, /* 0x3EB6C05A, 0x894E8CA6 */ + 6.22741452364621501295e-09, /* 0x3E3ABF1D, 0x5BA69A86 */ + 1.66559246207992079114e-11, /* 0x3DB25039, 0xDACA772A */ +}; + +double +__ieee754_y1(double x) +{ + double z, s,c,ss,cc,u,v; + int32_t hx,ix,lx; + + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7ff00000) return one/(x+x*x); + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sin(x); + c = cos(x); + ss = -s-c; + cc = s-c; + if(ix<0x7fe00000) { /* make sure x+x not overflow */ + z = cos(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/sqrt(x); + else { + u = pone(x); v = qone(x); + z = invsqrtpi*(u*ss+v*cc)/sqrt(x); + } + return z; + } + if(ix<=0x3c900000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1(x)*__ieee754_log(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const double pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + 1.17187499999988647970e-01, /* 0x3FBDFFFF, 0xFFFFFCCE */ + 1.32394806593073575129e+01, /* 0x402A7A9D, 0x357F7FCE */ + 4.12051854307378562225e+02, /* 0x4079C0D4, 0x652EA590 */ + 3.87474538913960532227e+03, /* 0x40AE457D, 0xA3A532CC */ + 7.91447954031891731574e+03, /* 0x40BEEA7A, 0xC32782DD */ +}; +static const double ps8[5] = { + 1.14207370375678408436e+02, /* 0x405C8D45, 0x8E656CAC */ + 3.65093083420853463394e+03, /* 0x40AC85DC, 0x964D274F */ + 3.69562060269033463555e+04, /* 0x40E20B86, 0x97C5BB7F */ + 9.76027935934950801311e+04, /* 0x40F7D42C, 0xB28F17BB */ + 3.08042720627888811578e+04, /* 0x40DE1511, 0x697A0B2D */ +}; + +static const double pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.31990519556243522749e-11, /* 0x3DAD0667, 0xDAE1CA7D */ + 1.17187493190614097638e-01, /* 0x3FBDFFFF, 0xE2C10043 */ + 6.80275127868432871736e+00, /* 0x401B3604, 0x6E6315E3 */ + 1.08308182990189109773e+02, /* 0x405B13B9, 0x452602ED */ + 5.17636139533199752805e+02, /* 0x40802D16, 0xD052D649 */ + 5.28715201363337541807e+02, /* 0x408085B8, 0xBB7E0CB7 */ +}; +static const double ps5[5] = { + 5.92805987221131331921e+01, /* 0x404DA3EA, 0xA8AF633D */ + 9.91401418733614377743e+02, /* 0x408EFB36, 0x1B066701 */ + 5.35326695291487976647e+03, /* 0x40B4E944, 0x5706B6FB */ + 7.84469031749551231769e+03, /* 0x40BEA4B0, 0xB8A5BB15 */ + 1.50404688810361062679e+03, /* 0x40978030, 0x036F5E51 */ +}; + +static const double pr3[6] = { + 3.02503916137373618024e-09, /* 0x3E29FC21, 0xA7AD9EDD */ + 1.17186865567253592491e-01, /* 0x3FBDFFF5, 0x5B21D17B */ + 3.93297750033315640650e+00, /* 0x400F76BC, 0xE85EAD8A */ + 3.51194035591636932736e+01, /* 0x40418F48, 0x9DA6D129 */ + 9.10550110750781271918e+01, /* 0x4056C385, 0x4D2C1837 */ + 4.85590685197364919645e+01, /* 0x4048478F, 0x8EA83EE5 */ +}; +static const double ps3[5] = { + 3.47913095001251519989e+01, /* 0x40416549, 0xA134069C */ + 3.36762458747825746741e+02, /* 0x40750C33, 0x07F1A75F */ + 1.04687139975775130551e+03, /* 0x40905B7C, 0x5037D523 */ + 8.90811346398256432622e+02, /* 0x408BD67D, 0xA32E31E9 */ + 1.03787932439639277504e+02, /* 0x4059F26D, 0x7C2EED53 */ +}; + +static const double pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.07710830106873743082e-07, /* 0x3E7CE9D4, 0xF65544F4 */ + 1.17176219462683348094e-01, /* 0x3FBDFF42, 0xBE760D83 */ + 2.36851496667608785174e+00, /* 0x4002F2B7, 0xF98FAEC0 */ + 1.22426109148261232917e+01, /* 0x40287C37, 0x7F71A964 */ + 1.76939711271687727390e+01, /* 0x4031B1A8, 0x177F8EE2 */ + 5.07352312588818499250e+00, /* 0x40144B49, 0xA574C1FE */ +}; +static const double ps2[5] = { + 2.14364859363821409488e+01, /* 0x40356FBD, 0x8AD5ECDC */ + 1.25290227168402751090e+02, /* 0x405F5293, 0x14F92CD5 */ + 2.32276469057162813669e+02, /* 0x406D08D8, 0xD5A2DBD9 */ + 1.17679373287147100768e+02, /* 0x405D6B7A, 0xDA1884A9 */ + 8.36463893371618283368e+00, /* 0x4020BAB1, 0xF44E5192 */ +}; + +static double +pone(double x) +{ + const double *p,*q; + double z,r,s; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = pr8; q= ps8;} + else if(ix>=0x40122E8B){p = pr5; q= ps5;} + else if(ix>=0x4006DB6D){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const double qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ + -1.02539062499992714161e-01, /* 0xBFBA3FFF, 0xFFFFFDF3 */ + -1.62717534544589987888e+01, /* 0xC0304591, 0xA26779F7 */ + -7.59601722513950107896e+02, /* 0xC087BCD0, 0x53E4B576 */ + -1.18498066702429587167e+04, /* 0xC0C724E7, 0x40F87415 */ + -4.84385124285750353010e+04, /* 0xC0E7A6D0, 0x65D09C6A */ +}; +static const double qs8[6] = { + 1.61395369700722909556e+02, /* 0x40642CA6, 0xDE5BCDE5 */ + 7.82538599923348465381e+03, /* 0x40BE9162, 0xD0D88419 */ + 1.33875336287249578163e+05, /* 0x4100579A, 0xB0B75E98 */ + 7.19657723683240939863e+05, /* 0x4125F653, 0x72869C19 */ + 6.66601232617776375264e+05, /* 0x412457D2, 0x7719AD5C */ + -2.94490264303834643215e+05, /* 0xC111F969, 0x0EA5AA18 */ +}; + +static const double qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.08979931141764104297e-11, /* 0xBDB6FA43, 0x1AA1A098 */ + -1.02539050241375426231e-01, /* 0xBFBA3FFF, 0xCB597FEF */ + -8.05644828123936029840e+00, /* 0xC0201CE6, 0xCA03AD4B */ + -1.83669607474888380239e+02, /* 0xC066F56D, 0x6CA7B9B0 */ + -1.37319376065508163265e+03, /* 0xC09574C6, 0x6931734F */ + -2.61244440453215656817e+03, /* 0xC0A468E3, 0x88FDA79D */ +}; +static const double qs5[6] = { + 8.12765501384335777857e+01, /* 0x405451B2, 0xFF5A11B2 */ + 1.99179873460485964642e+03, /* 0x409F1F31, 0xE77BF839 */ + 1.74684851924908907677e+04, /* 0x40D10F1F, 0x0D64CE29 */ + 4.98514270910352279316e+04, /* 0x40E8576D, 0xAABAD197 */ + 2.79480751638918118260e+04, /* 0x40DB4B04, 0xCF7C364B */ + -4.71918354795128470869e+03, /* 0xC0B26F2E, 0xFCFFA004 */ +}; + +static const double qr3[6] = { + -5.07831226461766561369e-09, /* 0xBE35CFA9, 0xD38FC84F */ + -1.02537829820837089745e-01, /* 0xBFBA3FEB, 0x51AEED54 */ + -4.61011581139473403113e+00, /* 0xC01270C2, 0x3302D9FF */ + -5.78472216562783643212e+01, /* 0xC04CEC71, 0xC25D16DA */ + -2.28244540737631695038e+02, /* 0xC06C87D3, 0x4718D55F */ + -2.19210128478909325622e+02, /* 0xC06B66B9, 0x5F5C1BF6 */ +}; +static const double qs3[6] = { + 4.76651550323729509273e+01, /* 0x4047D523, 0xCCD367E4 */ + 6.73865112676699709482e+02, /* 0x40850EEB, 0xC031EE3E */ + 3.38015286679526343505e+03, /* 0x40AA684E, 0x448E7C9A */ + 5.54772909720722782367e+03, /* 0x40B5ABBA, 0xA61D54A6 */ + 1.90311919338810798763e+03, /* 0x409DBC7A, 0x0DD4DF4B */ + -1.35201191444307340817e+02, /* 0xC060E670, 0x290A311F */ +}; + +static const double qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.78381727510958865572e-07, /* 0xBE87F126, 0x44C626D2 */ + -1.02517042607985553460e-01, /* 0xBFBA3E8E, 0x9148B010 */ + -2.75220568278187460720e+00, /* 0xC0060484, 0x69BB4EDA */ + -1.96636162643703720221e+01, /* 0xC033A9E2, 0xC168907F */ + -4.23253133372830490089e+01, /* 0xC04529A3, 0xDE104AAA */ + -2.13719211703704061733e+01, /* 0xC0355F36, 0x39CF6E52 */ +}; +static const double qs2[6] = { + 2.95333629060523854548e+01, /* 0x403D888A, 0x78AE64FF */ + 2.52981549982190529136e+02, /* 0x406F9F68, 0xDB821CBA */ + 7.57502834868645436472e+02, /* 0x4087AC05, 0xCE49A0F7 */ + 7.39393205320467245656e+02, /* 0x40871B25, 0x48D4C029 */ + 1.55949003336666123687e+02, /* 0x40637E5E, 0x3C3ED8D4 */ + -4.95949898822628210127e+00, /* 0xC013D686, 0xE71BE86B */ +}; + +static double +qone(double x) +{ + const double *p,*q; + double s,r,z; + int32_t ix; + + p = q = 0; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x40200000) {p = qr8; q= qs8;} + else if(ix>=0x40122E8B){p = qr5; q= qs5;} + else if(ix>=0x4006DB6D){p = qr3; q= qs3;} + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return (.375 + r/s)/x; +} diff --git a/lib/nbsd_libm/src/e_j1f.c b/lib/nbsd_libm/src/e_j1f.c new file mode 100644 index 000000000..aef9fe653 --- /dev/null +++ b/lib/nbsd_libm/src/e_j1f.c @@ -0,0 +1,349 @@ +/* e_j1f.c -- float version of e_j1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_j1f.c,v 1.11 2007/08/20 16:01:38 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static float ponef(float), qonef(float); + +static const float +huge = 1e30, +one = 1.0, +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +tpi = 6.3661974669e-01, /* 0x3f22f983 */ + /* R0/S0 on [0,2] */ +r00 = -6.2500000000e-02, /* 0xbd800000 */ +r01 = 1.4070566976e-03, /* 0x3ab86cfd */ +r02 = -1.5995563444e-05, /* 0xb7862e36 */ +r03 = 4.9672799207e-08, /* 0x335557d2 */ +s01 = 1.9153760746e-02, /* 0x3c9ce859 */ +s02 = 1.8594678841e-04, /* 0x3942fab6 */ +s03 = 1.1771846857e-06, /* 0x359dffc2 */ +s04 = 5.0463624390e-09, /* 0x31ad6446 */ +s05 = 1.2354227016e-11; /* 0x2d59567e */ + +static const float zero = 0.0; + +float +__ieee754_j1f(float x) +{ + float z, s,c,ss,cc,r,u,v,y; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return one/x; + y = fabsf(x); + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(y); + c = cosf(y); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure y+y not overflow */ + z = cosf(y+y); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* + * j1(x) = 1/sqrt(pi) * (P(1,x)*cc - Q(1,x)*ss) / sqrt(x) + * y1(x) = 1/sqrt(pi) * (P(1,x)*ss + Q(1,x)*cc) / sqrt(x) + */ +#ifdef DEAD_CODE + if(ix>0x80000000) z = (invsqrtpi*cc)/sqrtf(y); + else +#endif + { + u = ponef(y); v = qonef(y); + z = invsqrtpi*(u*cc-v*ss)/sqrtf(y); + } + if(hx<0) return -z; + else return z; + } + if(ix<0x32000000) { /* |x|<2**-27 */ + if(huge+x>one) return (float)0.5*x;/* inexact if x!=0 necessary */ + } + z = x*x; + r = z*(r00+z*(r01+z*(r02+z*r03))); + s = one+z*(s01+z*(s02+z*(s03+z*(s04+z*s05)))); + r *= x; + return(x*(float)0.5+r/s); +} + +static const float U0[5] = { + -1.9605709612e-01, /* 0xbe48c331 */ + 5.0443872809e-02, /* 0x3d4e9e3c */ + -1.9125689287e-03, /* 0xbafaaf2a */ + 2.3525259166e-05, /* 0x37c5581c */ + -9.1909917899e-08, /* 0xb3c56003 */ +}; +static const float V0[5] = { + 1.9916731864e-02, /* 0x3ca3286a */ + 2.0255257550e-04, /* 0x3954644b */ + 1.3560879779e-06, /* 0x35b602d4 */ + 6.2274145840e-09, /* 0x31d5f8eb */ + 1.6655924903e-11, /* 0x2d9281cf */ +}; + +float +__ieee754_y1f(float x) +{ + float z, s,c,ss,cc,u,v; + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y1(NaN) is NaN, Y1(-inf) is NaN, Y1(inf) is 0 */ + if(ix>=0x7f800000) return one/(x+x*x); + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + if(ix >= 0x40000000) { /* |x| >= 2.0 */ + s = sinf(x); + c = cosf(x); + ss = -s-c; + cc = s-c; + if(ix<0x7f000000) { /* make sure x+x not overflow */ + z = cosf(x+x); + if ((s*c)>zero) cc = z/ss; + else ss = z/cc; + } + /* y1(x) = sqrt(2/(pi*x))*(p1(x)*sin(x0)+q1(x)*cos(x0)) + * where x0 = x-3pi/4 + * Better formula: + * cos(x0) = cos(x)cos(3pi/4)+sin(x)sin(3pi/4) + * = 1/sqrt(2) * (sin(x) - cos(x)) + * sin(x0) = sin(x)cos(3pi/4)-cos(x)sin(3pi/4) + * = -1/sqrt(2) * (cos(x) + sin(x)) + * To avoid cancellation, use + * sin(x) +- cos(x) = -cos(2x)/(sin(x) -+ cos(x)) + * to compute the worse one. + */ + if(ix>0x48000000) z = (invsqrtpi*ss)/sqrtf(x); + else { + u = ponef(x); v = qonef(x); + z = invsqrtpi*(u*ss+v*cc)/sqrtf(x); + } + return z; + } + if(ix<=0x24800000) { /* x < 2**-54 */ + return(-tpi/x); + } + z = x*x; + u = U0[0]+z*(U0[1]+z*(U0[2]+z*(U0[3]+z*U0[4]))); + v = one+z*(V0[0]+z*(V0[1]+z*(V0[2]+z*(V0[3]+z*V0[4])))); + return(x*(u/v) + tpi*(__ieee754_j1f(x)*__ieee754_logf(x)-one/x)); +} + +/* For x >= 8, the asymptotic expansions of pone is + * 1 + 15/128 s^2 - 4725/2^15 s^4 - ..., where s = 1/x. + * We approximate pone by + * pone(x) = 1 + (R/S) + * where R = pr0 + pr1*s^2 + pr2*s^4 + ... + pr5*s^10 + * S = 1 + ps0*s^2 + ... + ps4*s^10 + * and + * | pone(x)-1-R/S | <= 2 ** ( -60.06) + */ + +static const float pr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + 1.1718750000e-01, /* 0x3df00000 */ + 1.3239480972e+01, /* 0x4153d4ea */ + 4.1205184937e+02, /* 0x43ce06a3 */ + 3.8747453613e+03, /* 0x45722bed */ + 7.9144794922e+03, /* 0x45f753d6 */ +}; +static const float ps8[5] = { + 1.1420736694e+02, /* 0x42e46a2c */ + 3.6509309082e+03, /* 0x45642ee5 */ + 3.6956207031e+04, /* 0x47105c35 */ + 9.7602796875e+04, /* 0x47bea166 */ + 3.0804271484e+04, /* 0x46f0a88b */ +}; + +static const float pr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + 1.3199052094e-11, /* 0x2d68333f */ + 1.1718749255e-01, /* 0x3defffff */ + 6.8027510643e+00, /* 0x40d9b023 */ + 1.0830818176e+02, /* 0x42d89dca */ + 5.1763616943e+02, /* 0x440168b7 */ + 5.2871520996e+02, /* 0x44042dc6 */ +}; +static const float ps5[5] = { + 5.9280597687e+01, /* 0x426d1f55 */ + 9.9140142822e+02, /* 0x4477d9b1 */ + 5.3532670898e+03, /* 0x45a74a23 */ + 7.8446904297e+03, /* 0x45f52586 */ + 1.5040468750e+03, /* 0x44bc0180 */ +}; + +static const float pr3[6] = { + 3.0250391081e-09, /* 0x314fe10d */ + 1.1718686670e-01, /* 0x3defffab */ + 3.9329774380e+00, /* 0x407bb5e7 */ + 3.5119403839e+01, /* 0x420c7a45 */ + 9.1055007935e+01, /* 0x42b61c2a */ + 4.8559066772e+01, /* 0x42423c7c */ +}; +static const float ps3[5] = { + 3.4791309357e+01, /* 0x420b2a4d */ + 3.3676245117e+02, /* 0x43a86198 */ + 1.0468714600e+03, /* 0x4482dbe3 */ + 8.9081134033e+02, /* 0x445eb3ed */ + 1.0378793335e+02, /* 0x42cf936c */ +}; + +static const float pr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + 1.0771083225e-07, /* 0x33e74ea8 */ + 1.1717621982e-01, /* 0x3deffa16 */ + 2.3685150146e+00, /* 0x401795c0 */ + 1.2242610931e+01, /* 0x4143e1bc */ + 1.7693971634e+01, /* 0x418d8d41 */ + 5.0735230446e+00, /* 0x40a25a4d */ +}; +static const float ps2[5] = { + 2.1436485291e+01, /* 0x41ab7dec */ + 1.2529022980e+02, /* 0x42fa9499 */ + 2.3227647400e+02, /* 0x436846c7 */ + 1.1767937469e+02, /* 0x42eb5bd7 */ + 8.3646392822e+00, /* 0x4105d590 */ +}; + +static float +ponef(float x) +{ + const float *p,*q; + float z,r,s; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + if(ix>=0x41000000) {p = pr8; q= ps8;} + else if(ix>=0x40f71c58){p = pr5; q= ps5;} + else if(ix>=0x4036db68){p = pr3; q= ps3;} + else if(ix>=0x40000000){p = pr2; q= ps2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*q[4])))); + return one+ r/s; +} + + +/* For x >= 8, the asymptotic expansions of qone is + * 3/8 s - 105/1024 s^3 - ..., where s = 1/x. + * We approximate pone by + * qone(x) = s*(0.375 + (R/S)) + * where R = qr1*s^2 + qr2*s^4 + ... + qr5*s^10 + * S = 1 + qs1*s^2 + ... + qs6*s^12 + * and + * | qone(x)/s -0.375-R/S | <= 2 ** ( -61.13) + */ + +static const float qr8[6] = { /* for x in [inf, 8]=1/[0,0.125] */ + 0.0000000000e+00, /* 0x00000000 */ + -1.0253906250e-01, /* 0xbdd20000 */ + -1.6271753311e+01, /* 0xc1822c8d */ + -7.5960174561e+02, /* 0xc43de683 */ + -1.1849806641e+04, /* 0xc639273a */ + -4.8438511719e+04, /* 0xc73d3683 */ +}; +static const float qs8[6] = { + 1.6139537048e+02, /* 0x43216537 */ + 7.8253862305e+03, /* 0x45f48b17 */ + 1.3387534375e+05, /* 0x4802bcd6 */ + 7.1965775000e+05, /* 0x492fb29c */ + 6.6660125000e+05, /* 0x4922be94 */ + -2.9449025000e+05, /* 0xc88fcb48 */ +}; + +static const float qr5[6] = { /* for x in [8,4.5454]=1/[0.125,0.22001] */ + -2.0897993405e-11, /* 0xadb7d219 */ + -1.0253904760e-01, /* 0xbdd1fffe */ + -8.0564479828e+00, /* 0xc100e736 */ + -1.8366960144e+02, /* 0xc337ab6b */ + -1.3731937256e+03, /* 0xc4aba633 */ + -2.6124443359e+03, /* 0xc523471c */ +}; +static const float qs5[6] = { + 8.1276550293e+01, /* 0x42a28d98 */ + 1.9917987061e+03, /* 0x44f8f98f */ + 1.7468484375e+04, /* 0x468878f8 */ + 4.9851425781e+04, /* 0x4742bb6d */ + 2.7948074219e+04, /* 0x46da5826 */ + -4.7191835938e+03, /* 0xc5937978 */ +}; + +static const float qr3[6] = { /* for x in [4.5454,2.8570]=1/[0.22001,0.3499] */ + -5.0783124372e-09, /* 0xb1ae7d4f */ + -1.0253783315e-01, /* 0xbdd1ff5b */ + -4.6101160049e+00, /* 0xc0938612 */ + -5.7847221375e+01, /* 0xc267638e */ + -2.2824453735e+02, /* 0xc3643e9a */ + -2.1921012878e+02, /* 0xc35b35cb */ +}; +static const float qs3[6] = { + 4.7665153503e+01, /* 0x423ea91e */ + 6.7386511230e+02, /* 0x4428775e */ + 3.3801528320e+03, /* 0x45534272 */ + 5.5477290039e+03, /* 0x45ad5dd5 */ + 1.9031191406e+03, /* 0x44ede3d0 */ + -1.3520118713e+02, /* 0xc3073381 */ +}; + +static const float qr2[6] = {/* for x in [2.8570,2]=1/[0.3499,0.5] */ + -1.7838172539e-07, /* 0xb43f8932 */ + -1.0251704603e-01, /* 0xbdd1f475 */ + -2.7522056103e+00, /* 0xc0302423 */ + -1.9663616180e+01, /* 0xc19d4f16 */ + -4.2325313568e+01, /* 0xc2294d1f */ + -2.1371921539e+01, /* 0xc1aaf9b2 */ +}; +static const float qs2[6] = { + 2.9533363342e+01, /* 0x41ec4454 */ + 2.5298155212e+02, /* 0x437cfb47 */ + 7.5750280762e+02, /* 0x443d602e */ + 7.3939318848e+02, /* 0x4438d92a */ + 1.5594900513e+02, /* 0x431bf2f2 */ + -4.9594988823e+00, /* 0xc09eb437 */ +}; + +static float +qonef(float x) +{ + const float *p,*q; + float s,r,z; + int32_t ix; + + p = q = 0; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + /* [inf, 8] (8 41000000) */ + if(ix>=0x41000000) {p = qr8; q= qs8;} + /* [8, 4.5454] (4.5454 409173eb) */ + else if(ix>=0x409173eb){p = qr5; q= qs5;} + /* [4.5454, 2.8570] (2.8570 4036d917) */ + else if(ix>=0x4036d917){p = qr3; q= qs3;} + /* [2.8570, 2] (2 40000000) */ + else if(ix>=0x40000000){p = qr2; q= qs2;} + z = one/(x*x); + r = p[0]+z*(p[1]+z*(p[2]+z*(p[3]+z*(p[4]+z*p[5])))); + s = one+z*(q[0]+z*(q[1]+z*(q[2]+z*(q[3]+z*(q[4]+z*q[5]))))); + return ((float).375 + r/s)/x; +} diff --git a/lib/nbsd_libm/src/e_jn.c b/lib/nbsd_libm/src/e_jn.c new file mode 100644 index 000000000..07d963a25 --- /dev/null +++ b/lib/nbsd_libm/src/e_jn.c @@ -0,0 +1,274 @@ +/* @(#)e_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_jn.c,v 1.14 2010/11/29 15:10:06 drochner Exp $"); +#endif + +/* + * __ieee754_jn(n, x), __ieee754_yn(n, x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for nx, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static const double +invsqrtpi= 5.64189583547756279280e-01, /* 0x3FE20DD7, 0x50429B6D */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ +one = 1.00000000000000000000e+00; /* 0x3FF00000, 0x00000000 */ + +static const double zero = 0.00000000000000000000e+00; + +double +__ieee754_jn(int n, double x) +{ + int32_t i,hx,ix,lx, sgn; + double a, b, temp, di; + double z, w; + + temp = 0; + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0(x)); + if(n==1) return(__ieee754_j1(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabs(x); + if((ix|lx)==0||ix>=0x7ff00000) /* if x is 0 or inf */ + b = zero; + else if((double)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = cos(x)+sin(x); break; + case 1: temp = -cos(x)+sin(x); break; + case 2: temp = -cos(x)-sin(x); break; + case 3: temp = cos(x)-sin(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + a = __ieee754_j0(x); + b = __ieee754_j1(x); + for(i=1;i33) /* underflow */ + b = zero; + else { + temp = x*0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (double)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + double t,v; + double q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(double)x; h = 2.0/(double)x; + q0 = w; z = w+h; q1 = w*z - 1.0; k=1; + while(q1<1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_log(fabs(v*tmp)); + if(tmp<7.09782712893383973096e+02) { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(double)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>1e100) { + a /= b; + t /= b; + b = one; + } + } + } + z = __ieee754_j0(x); + w = __ieee754_j1(x); + if (fabs(z) >= fabs(w)) + b = (t*z/b); + else + b = (t*w/a); + } + } + if(sgn==1) return -b; else return b; +} + +double +__ieee754_yn(int n, double x) +{ + int32_t i,hx,ix,lx; + int32_t sign; + double a, b, temp; + + temp = 0; + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if((ix|((u_int32_t)(lx|-lx))>>31)>0x7ff00000) return x+x; + if((ix|lx)==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0(x)); + if(n==1) return(sign*__ieee754_y1(x)); + if(ix==0x7ff00000) return zero; + if(ix>=0x52D00000) { /* x > 2**302 */ + /* (x >> n**2) + * Jn(x) = cos(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Yn(x) = sin(x-(2n+1)*pi/4)*sqrt(2/x*pi) + * Let s=sin(x), c=cos(x), + * xn=x-(2n+1)*pi/4, sqt2 = sqrt(2),then + * + * n sin(xn)*sqt2 cos(xn)*sqt2 + * ---------------------------------- + * 0 s-c c+s + * 1 -s-c -c+s + * 2 -s+c -c-s + * 3 s+c c-s + */ + switch(n&3) { + case 0: temp = sin(x)-cos(x); break; + case 1: temp = -sin(x)-cos(x); break; + case 2: temp = -sin(x)+cos(x); break; + case 3: temp = sin(x)+cos(x); break; + } + b = invsqrtpi*temp/sqrt(x); + } else { + u_int32_t high; + a = __ieee754_y0(x); + b = __ieee754_y1(x); + /* quit if b is -inf */ + GET_HIGH_WORD(high,b); + for(i=1;i0) return b; else return -b; +} diff --git a/lib/nbsd_libm/src/e_jnf.c b/lib/nbsd_libm/src/e_jnf.c new file mode 100644 index 000000000..9263cdfb4 --- /dev/null +++ b/lib/nbsd_libm/src/e_jnf.c @@ -0,0 +1,204 @@ +/* e_jnf.c -- float version of e_jn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_jnf.c,v 1.11 2010/11/29 15:10:06 drochner Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +#if 0 +invsqrtpi= 5.6418961287e-01, /* 0x3f106ebb */ +#endif +two = 2.0000000000e+00, /* 0x40000000 */ +one = 1.0000000000e+00; /* 0x3F800000 */ + +static const float zero = 0.0000000000e+00; + +float +__ieee754_jnf(int n, float x) +{ + int32_t i,hx,ix, sgn; + float a, b, temp, di; + float z, w; + + /* J(-n,x) = (-1)^n * J(n, x), J(n, -x) = (-1)^n * J(n, x) + * Thus, J(-n,x) = J(n,-x) + */ + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if J(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(n<0){ + n = -n; + x = -x; + hx ^= 0x80000000; + } + if(n==0) return(__ieee754_j0f(x)); + if(n==1) return(__ieee754_j1f(x)); + sgn = (n&1)&(hx>>31); /* even n -- 0, odd n -- sign(x) */ + x = fabsf(x); + if(ix==0||ix>=0x7f800000) /* if x is 0 or inf */ + b = zero; + else if((float)n<=x) { + /* Safe to use J(n+1,x)=2n/x *J(n,x)-J(n-1,x) */ + a = __ieee754_j0f(x); + b = __ieee754_j1f(x); + for(i=1;i33) /* underflow */ + b = zero; + else { + temp = x*(float)0.5; b = temp; + for (a=one,i=2;i<=n;i++) { + a *= (float)i; /* a = n! */ + b *= temp; /* b = (x/2)^n */ + } + b = b/a; + } + } else { + /* use backward recurrence */ + /* x x^2 x^2 + * J(n,x)/J(n-1,x) = ---- ------ ------ ..... + * 2n - 2(n+1) - 2(n+2) + * + * 1 1 1 + * (for large x) = ---- ------ ------ ..... + * 2n 2(n+1) 2(n+2) + * -- - ------ - ------ - + * x x x + * + * Let w = 2n/x and h=2/x, then the above quotient + * is equal to the continued fraction: + * 1 + * = ----------------------- + * 1 + * w - ----------------- + * 1 + * w+h - --------- + * w+2h - ... + * + * To determine how many terms needed, let + * Q(0) = w, Q(1) = w(w+h) - 1, + * Q(k) = (w+k*h)*Q(k-1) - Q(k-2), + * When Q(k) > 1e4 good for single + * When Q(k) > 1e9 good for double + * When Q(k) > 1e17 good for quadruple + */ + /* determine k */ + float t,v; + float q0,q1,h,tmp; int32_t k,m; + w = (n+n)/(float)x; h = (float)2.0/(float)x; + q0 = w; z = w+h; q1 = w*z - (float)1.0; k=1; + while(q1<(float)1.0e9) { + k += 1; z += h; + tmp = z*q1 - q0; + q0 = q1; + q1 = tmp; + } + m = n+n; + for(t=zero, i = 2*(n+k); i>=m; i -= 2) t = one/(i/x-t); + a = t; + b = one; + /* estimate log((2/x)^n*n!) = n*log(2/x)+n*ln(n) + * Hence, if n*(log(2n/x)) > ... + * single 8.8722839355e+01 + * double 7.09782712893383973096e+02 + * long double 1.1356523406294143949491931077970765006170e+04 + * then recurrent value may overflow and the result is + * likely underflow to zero + */ + tmp = n; + v = two/x; + tmp = tmp*__ieee754_logf(fabsf(v*tmp)); + if(tmp<(float)8.8721679688e+01) { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + } + } else { + for(i=n-1,di=(float)(i+i);i>0;i--){ + temp = b; + b *= di; + b = b/x - a; + a = temp; + di -= two; + /* scale b to avoid spurious overflow */ + if(b>(float)1e10) { + a /= b; + t /= b; + b = one; + } + } + } + z = __ieee754_j0f(x); + w = __ieee754_j1f(x); + if (fabsf(z) >= fabsf(w)) + b = (t*z/b); + else + b = (t*w/a); + } + } + if(sgn==1) return -b; else return b; +} + +float +__ieee754_ynf(int n, float x) +{ + int32_t i,hx,ix,ib; + int32_t sign; + float a, b, temp; + + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + /* if Y(n,NaN) is NaN */ + if(ix>0x7f800000) return x+x; + if(ix==0) return -one/zero; + if(hx<0) return zero/zero; + sign = 1; + if(n<0){ + n = -n; + sign = 1 - ((n&1)<<1); + } + if(n==0) return(__ieee754_y0f(x)); + if(n==1) return(sign*__ieee754_y1f(x)); + if(ix==0x7f800000) return zero; + + a = __ieee754_y0f(x); + b = __ieee754_y1f(x); + /* quit if b is -inf */ + GET_FLOAT_WORD(ib,b); + for(i=1;i0) return b; else return -b; +} diff --git a/lib/nbsd_libm/src/e_lgamma_r.c b/lib/nbsd_libm/src/e_lgamma_r.c new file mode 100644 index 000000000..9e70adbaa --- /dev/null +++ b/lib/nbsd_libm/src/e_lgamma_r.c @@ -0,0 +1,298 @@ +/* @(#)er_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_lgamma_r.c,v 1.10 2002/05/26 22:01:51 wiz Exp $"); +#endif + +/* __ieee754_lgamma_r(x, signgamp) + * Reentrant version of the logarithm of the Gamma function + * with user provide pointer for the sign of Gamma(x). + * + * Method: + * 1. Argument Reduction for 0 < x <= 8 + * Since gamma(1+s)=s*gamma(s), for x in [0,8], we may + * reduce x to a number in [1.5,2.5] by + * lgamma(1+s) = log(s) + lgamma(s) + * for example, + * lgamma(7.3) = log(6.3) + lgamma(6.3) + * = log(6.3*5.3) + lgamma(5.3) + * = log(6.3*5.3*4.3*3.3*2.3) + lgamma(2.3) + * 2. Polynomial approximation of lgamma around its + * minimun ymin=1.461632144968362245 to maintain monotonicity. + * On [ymin-0.23, ymin+0.27] (i.e., [1.23164,1.73163]), use + * Let z = x-ymin; + * lgamma(x) = -1.214862905358496078218 + z^2*poly(z) + * where + * poly(z) is a 14 degree polynomial. + * 2. Rational approximation in the primary interval [2,3] + * We use the following approximation: + * s = x-2.0; + * lgamma(x) = 0.5*s + s*P(s)/Q(s) + * with accuracy + * |P/Q - (lgamma(x)-0.5s)| < 2**-61.71 + * Our algorithms are based on the following observation + * + * zeta(2)-1 2 zeta(3)-1 3 + * lgamma(2+s) = s*(1-Euler) + --------- * s - --------- * s + ... + * 2 3 + * + * where Euler = 0.5771... is the Euler constant, which is very + * close to 0.5. + * + * 3. For x>=8, we have + * lgamma(x)~(x-0.5)log(x)-x+0.5*log(2pi)+1/(12x)-1/(360x**3)+.... + * (better formula: + * lgamma(x)~(x-0.5)*(log(x)-1)-.5*(log(2pi)-1) + ...) + * Let z = 1/x, then we approximation + * f(z) = lgamma(x) - (x-0.5)(log(x)-1) + * by + * 3 5 11 + * w = w0 + w1*z + w2*z + w3*z + ... + w6*z + * where + * |w - f(z)| < 2**-58.74 + * + * 4. For negative x, since (G is gamma function) + * -x*G(-x)*G(x) = pi/sin(pi*x), + * we have + * G(x) = pi/(sin(pi*x)*(-x)*G(-x)) + * since G(-x) is positive, sign(G(x)) = sign(sin(pi*x)) for x<0 + * Hence, for x<0, signgam = sign(sin(pi*x)) and + * lgamma(x) = log(|Gamma(x)|) + * = log(pi/(|x*sin(pi*x)|)) - lgamma(-x); + * Note: one should avoid compute pi*(-x) directly in the + * computation of sin(pi*(-x)). + * + * 5. Special Cases + * lgamma(2+s) ~ s*(1-Euler) for tiny s + * lgamma(1)=lgamma(2)=0 + * lgamma(x) ~ -log(x) for tiny x + * lgamma(0) = lgamma(inf) = inf + * lgamma(-integer) = +-inf + * + */ + +#include "math.h" +#include "math_private.h" + +static const double +two52= 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +pi = 3.14159265358979311600e+00, /* 0x400921FB, 0x54442D18 */ +a0 = 7.72156649015328655494e-02, /* 0x3FB3C467, 0xE37DB0C8 */ +a1 = 3.22467033424113591611e-01, /* 0x3FD4A34C, 0xC4A60FAD */ +a2 = 6.73523010531292681824e-02, /* 0x3FB13E00, 0x1A5562A7 */ +a3 = 2.05808084325167332806e-02, /* 0x3F951322, 0xAC92547B */ +a4 = 7.38555086081402883957e-03, /* 0x3F7E404F, 0xB68FEFE8 */ +a5 = 2.89051383673415629091e-03, /* 0x3F67ADD8, 0xCCB7926B */ +a6 = 1.19270763183362067845e-03, /* 0x3F538A94, 0x116F3F5D */ +a7 = 5.10069792153511336608e-04, /* 0x3F40B6C6, 0x89B99C00 */ +a8 = 2.20862790713908385557e-04, /* 0x3F2CF2EC, 0xED10E54D */ +a9 = 1.08011567247583939954e-04, /* 0x3F1C5088, 0x987DFB07 */ +a10 = 2.52144565451257326939e-05, /* 0x3EFA7074, 0x428CFA52 */ +a11 = 4.48640949618915160150e-05, /* 0x3F07858E, 0x90A45837 */ +tc = 1.46163214496836224576e+00, /* 0x3FF762D8, 0x6356BE3F */ +tf = -1.21486290535849611461e-01, /* 0xBFBF19B9, 0xBCC38A42 */ +/* tt = -(tail of tf) */ +tt = -3.63867699703950536541e-18, /* 0xBC50C7CA, 0xA48A971F */ +t0 = 4.83836122723810047042e-01, /* 0x3FDEF72B, 0xC8EE38A2 */ +t1 = -1.47587722994593911752e-01, /* 0xBFC2E427, 0x8DC6C509 */ +t2 = 6.46249402391333854778e-02, /* 0x3FB08B42, 0x94D5419B */ +t3 = -3.27885410759859649565e-02, /* 0xBFA0C9A8, 0xDF35B713 */ +t4 = 1.79706750811820387126e-02, /* 0x3F9266E7, 0x970AF9EC */ +t5 = -1.03142241298341437450e-02, /* 0xBF851F9F, 0xBA91EC6A */ +t6 = 6.10053870246291332635e-03, /* 0x3F78FCE0, 0xE370E344 */ +t7 = -3.68452016781138256760e-03, /* 0xBF6E2EFF, 0xB3E914D7 */ +t8 = 2.25964780900612472250e-03, /* 0x3F6282D3, 0x2E15C915 */ +t9 = -1.40346469989232843813e-03, /* 0xBF56FE8E, 0xBF2D1AF1 */ +t10 = 8.81081882437654011382e-04, /* 0x3F4CDF0C, 0xEF61A8E9 */ +t11 = -5.38595305356740546715e-04, /* 0xBF41A610, 0x9C73E0EC */ +t12 = 3.15632070903625950361e-04, /* 0x3F34AF6D, 0x6C0EBBF7 */ +t13 = -3.12754168375120860518e-04, /* 0xBF347F24, 0xECC38C38 */ +t14 = 3.35529192635519073543e-04, /* 0x3F35FD3E, 0xE8C2D3F4 */ +u0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +u1 = 6.32827064025093366517e-01, /* 0x3FE4401E, 0x8B005DFF */ +u2 = 1.45492250137234768737e+00, /* 0x3FF7475C, 0xD119BD6F */ +u3 = 9.77717527963372745603e-01, /* 0x3FEF4976, 0x44EA8450 */ +u4 = 2.28963728064692451092e-01, /* 0x3FCD4EAE, 0xF6010924 */ +u5 = 1.33810918536787660377e-02, /* 0x3F8B678B, 0xBF2BAB09 */ +v1 = 2.45597793713041134822e+00, /* 0x4003A5D7, 0xC2BD619C */ +v2 = 2.12848976379893395361e+00, /* 0x40010725, 0xA42B18F5 */ +v3 = 7.69285150456672783825e-01, /* 0x3FE89DFB, 0xE45050AF */ +v4 = 1.04222645593369134254e-01, /* 0x3FBAAE55, 0xD6537C88 */ +v5 = 3.21709242282423911810e-03, /* 0x3F6A5ABB, 0x57D0CF61 */ +s0 = -7.72156649015328655494e-02, /* 0xBFB3C467, 0xE37DB0C8 */ +s1 = 2.14982415960608852501e-01, /* 0x3FCB848B, 0x36E20878 */ +s2 = 3.25778796408930981787e-01, /* 0x3FD4D98F, 0x4F139F59 */ +s3 = 1.46350472652464452805e-01, /* 0x3FC2BB9C, 0xBEE5F2F7 */ +s4 = 2.66422703033638609560e-02, /* 0x3F9B481C, 0x7E939961 */ +s5 = 1.84028451407337715652e-03, /* 0x3F5E26B6, 0x7368F239 */ +s6 = 3.19475326584100867617e-05, /* 0x3F00BFEC, 0xDD17E945 */ +r1 = 1.39200533467621045958e+00, /* 0x3FF645A7, 0x62C4AB74 */ +r2 = 7.21935547567138069525e-01, /* 0x3FE71A18, 0x93D3DCDC */ +r3 = 1.71933865632803078993e-01, /* 0x3FC601ED, 0xCCFBDF27 */ +r4 = 1.86459191715652901344e-02, /* 0x3F9317EA, 0x742ED475 */ +r5 = 7.77942496381893596434e-04, /* 0x3F497DDA, 0xCA41A95B */ +r6 = 7.32668430744625636189e-06, /* 0x3EDEBAF7, 0xA5B38140 */ +w0 = 4.18938533204672725052e-01, /* 0x3FDACFE3, 0x90C97D69 */ +w1 = 8.33333333333329678849e-02, /* 0x3FB55555, 0x5555553B */ +w2 = -2.77777777728775536470e-03, /* 0xBF66C16C, 0x16B02E5C */ +w3 = 7.93650558643019558500e-04, /* 0x3F4A019F, 0x98CF38B6 */ +w4 = -5.95187557450339963135e-04, /* 0xBF4380CB, 0x8C0FE741 */ +w5 = 8.36339918996282139126e-04, /* 0x3F4B67BA, 0x4CDAD5D1 */ +w6 = -1.63092934096575273989e-03; /* 0xBF5AB89D, 0x0B9E43E4 */ + +static const double zero= 0.00000000000000000000e+00; + +static +double sin_pi(double x) +{ + double y,z; + int n,ix; + + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3fd00000) return __kernel_sin(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floor(y); + if(z!=y) { /* inexact anyway */ + y *= 0.5; + y = 2.0*(y - floor(y)); /* y = |x| mod 2.0 */ + n = (int) (y*4.0); + } else { + if(ix>=0x43400000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x43300000) z = y+two52; /* exact */ + GET_LOW_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sin(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cos(pi*(0.5-y),zero); break; + case 3: + case 4: y = __kernel_sin(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cos(pi*(y-1.5),zero); break; + default: y = __kernel_sin(pi*(y-2.0),zero,0); break; + } + return -y; +} + + +double +__ieee754_lgamma_r(double x, int *signgamp) +{ + double t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,lx,ix; + + nadj = 0; + EXTRACT_WORDS(hx,lx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x*x; + if((ix|lx)==0) return one/zero; + if(ix<0x3b900000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_log(-x); + } else return -__ieee754_log(x); + } + if(hx<0) { + if(ix>=0x43300000) /* |x|>=2**52, must be -integer */ + return one/zero; + t = sin_pi(x); + if(t==zero) return one/zero; /* -integer */ + nadj = __ieee754_log(pi/fabs(t*x)); + if(t=0x3FE76944) {y = one-x; i= 0;} + else if(ix>=0x3FCDA661) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3FFBB4C3) {y=2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3FF3B4C4) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-0.5*y + p1/p2); + } + } + else if(ix<0x40200000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(double)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+6.0); /* FALLTHRU */ + case 6: z *= (y+5.0); /* FALLTHRU */ + case 5: z *= (y+4.0); /* FALLTHRU */ + case 4: z *= (y+3.0); /* FALLTHRU */ + case 3: z *= (y+2.0); /* FALLTHRU */ + r += __ieee754_log(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x43900000) { + t = __ieee754_log(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_log(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/lib/nbsd_libm/src/e_lgammaf_r.c b/lib/nbsd_libm/src/e_lgammaf_r.c new file mode 100644 index 000000000..36d890b21 --- /dev/null +++ b/lib/nbsd_libm/src/e_lgammaf_r.c @@ -0,0 +1,234 @@ +/* e_lgammaf_r.c -- float version of e_lgamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_lgammaf_r.c,v 1.6 2002/05/26 22:01:51 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +two23= 8.3886080000e+06, /* 0x4b000000 */ +half= 5.0000000000e-01, /* 0x3f000000 */ +one = 1.0000000000e+00, /* 0x3f800000 */ +pi = 3.1415927410e+00, /* 0x40490fdb */ +a0 = 7.7215664089e-02, /* 0x3d9e233f */ +a1 = 3.2246702909e-01, /* 0x3ea51a66 */ +a2 = 6.7352302372e-02, /* 0x3d89f001 */ +a3 = 2.0580807701e-02, /* 0x3ca89915 */ +a4 = 7.3855509982e-03, /* 0x3bf2027e */ +a5 = 2.8905137442e-03, /* 0x3b3d6ec6 */ +a6 = 1.1927076848e-03, /* 0x3a9c54a1 */ +a7 = 5.1006977446e-04, /* 0x3a05b634 */ +a8 = 2.2086278477e-04, /* 0x39679767 */ +a9 = 1.0801156895e-04, /* 0x38e28445 */ +a10 = 2.5214456400e-05, /* 0x37d383a2 */ +a11 = 4.4864096708e-05, /* 0x383c2c75 */ +tc = 1.4616321325e+00, /* 0x3fbb16c3 */ +tf = -1.2148628384e-01, /* 0xbdf8cdcd */ +/* tt = -(tail of tf) */ +tt = 6.6971006518e-09, /* 0x31e61c52 */ +t0 = 4.8383611441e-01, /* 0x3ef7b95e */ +t1 = -1.4758771658e-01, /* 0xbe17213c */ +t2 = 6.4624942839e-02, /* 0x3d845a15 */ +t3 = -3.2788541168e-02, /* 0xbd064d47 */ +t4 = 1.7970675603e-02, /* 0x3c93373d */ +t5 = -1.0314224288e-02, /* 0xbc28fcfe */ +t6 = 6.1005386524e-03, /* 0x3bc7e707 */ +t7 = -3.6845202558e-03, /* 0xbb7177fe */ +t8 = 2.2596477065e-03, /* 0x3b141699 */ +t9 = -1.4034647029e-03, /* 0xbab7f476 */ +t10 = 8.8108185446e-04, /* 0x3a66f867 */ +t11 = -5.3859531181e-04, /* 0xba0d3085 */ +t12 = 3.1563205994e-04, /* 0x39a57b6b */ +t13 = -3.1275415677e-04, /* 0xb9a3f927 */ +t14 = 3.3552918467e-04, /* 0x39afe9f7 */ +u0 = -7.7215664089e-02, /* 0xbd9e233f */ +u1 = 6.3282704353e-01, /* 0x3f2200f4 */ +u2 = 1.4549225569e+00, /* 0x3fba3ae7 */ +u3 = 9.7771751881e-01, /* 0x3f7a4bb2 */ +u4 = 2.2896373272e-01, /* 0x3e6a7578 */ +u5 = 1.3381091878e-02, /* 0x3c5b3c5e */ +v1 = 2.4559779167e+00, /* 0x401d2ebe */ +v2 = 2.1284897327e+00, /* 0x4008392d */ +v3 = 7.6928514242e-01, /* 0x3f44efdf */ +v4 = 1.0422264785e-01, /* 0x3dd572af */ +v5 = 3.2170924824e-03, /* 0x3b52d5db */ +s0 = -7.7215664089e-02, /* 0xbd9e233f */ +s1 = 2.1498242021e-01, /* 0x3e5c245a */ +s2 = 3.2577878237e-01, /* 0x3ea6cc7a */ +s3 = 1.4635047317e-01, /* 0x3e15dce6 */ +s4 = 2.6642270386e-02, /* 0x3cda40e4 */ +s5 = 1.8402845599e-03, /* 0x3af135b4 */ +s6 = 3.1947532989e-05, /* 0x3805ff67 */ +r1 = 1.3920053244e+00, /* 0x3fb22d3b */ +r2 = 7.2193557024e-01, /* 0x3f38d0c5 */ +r3 = 1.7193385959e-01, /* 0x3e300f6e */ +r4 = 1.8645919859e-02, /* 0x3c98bf54 */ +r5 = 7.7794247773e-04, /* 0x3a4beed6 */ +r6 = 7.3266842264e-06, /* 0x36f5d7bd */ +w0 = 4.1893854737e-01, /* 0x3ed67f1d */ +w1 = 8.3333335817e-02, /* 0x3daaaaab */ +w2 = -2.7777778450e-03, /* 0xbb360b61 */ +w3 = 7.9365057172e-04, /* 0x3a500cfd */ +w4 = -5.9518753551e-04, /* 0xba1c065c */ +w5 = 8.3633989561e-04, /* 0x3a5b3dd2 */ +w6 = -1.6309292987e-03; /* 0xbad5c4e8 */ + +static const float zero= 0.0000000000e+00; + +static float +sin_pif(float x) +{ + float y,z; + int n,ix; + + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + + if(ix<0x3e800000) return __kernel_sinf(pi*x,zero,0); + y = -x; /* x is assume negative */ + + /* + * argument reduction, make sure inexact flag not raised if input + * is an integer + */ + z = floorf(y); + if(z!=y) { /* inexact anyway */ + y *= (float)0.5; + y = (float)2.0*(y - floorf(y)); /* y = |x| mod 2.0 */ + n = (int) (y*(float)4.0); + } else { + if(ix>=0x4b800000) { + y = zero; n = 0; /* y must be even */ + } else { + if(ix<0x4b000000) z = y+two23; /* exact */ + GET_FLOAT_WORD(n,z); + n &= 1; + y = n; + n<<= 2; + } + } + switch (n) { + case 0: y = __kernel_sinf(pi*y,zero,0); break; + case 1: + case 2: y = __kernel_cosf(pi*((float)0.5-y),zero); break; + case 3: + case 4: y = __kernel_sinf(pi*(one-y),zero,0); break; + case 5: + case 6: y = -__kernel_cosf(pi*(y-(float)1.5),zero); break; + default: y = __kernel_sinf(pi*(y-(float)2.0),zero,0); break; + } + return -y; +} + + +float +__ieee754_lgammaf_r(float x, int *signgamp) +{ + float t,y,z,nadj,p,p1,p2,p3,q,r,w; + int i,hx,ix; + + nadj = 0; + GET_FLOAT_WORD(hx,x); + + /* purge off +-inf, NaN, +-0, and negative arguments */ + *signgamp = 1; + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x*x; + if(ix==0) return one/zero; + if(ix<0x1c800000) { /* |x|<2**-70, return -log(|x|) */ + if(hx<0) { + *signgamp = -1; + return -__ieee754_logf(-x); + } else return -__ieee754_logf(x); + } + if(hx<0) { + if(ix>=0x4b000000) /* |x|>=2**23, must be -integer */ + return one/zero; + t = sin_pif(x); + if(t==zero) return one/zero; /* -integer */ + nadj = __ieee754_logf(pi/fabsf(t*x)); + if(t=0x3f3b4a20) {y = one-x; i= 0;} + else if(ix>=0x3e6d3308) {y= x-(tc-one); i=1;} + else {y = x; i=2;} + } else { + r = zero; + if(ix>=0x3fdda618) {y=(float)2.0-x;i=0;} /* [1.7316,2] */ + else if(ix>=0x3F9da620) {y=x-tc;i=1;} /* [1.23,1.73] */ + else {y=x-one;i=2;} + } + switch(i) { + case 0: + z = y*y; + p1 = a0+z*(a2+z*(a4+z*(a6+z*(a8+z*a10)))); + p2 = z*(a1+z*(a3+z*(a5+z*(a7+z*(a9+z*a11))))); + p = y*p1+p2; + r += (p-(float)0.5*y); break; + case 1: + z = y*y; + w = z*y; + p1 = t0+w*(t3+w*(t6+w*(t9 +w*t12))); /* parallel comp */ + p2 = t1+w*(t4+w*(t7+w*(t10+w*t13))); + p3 = t2+w*(t5+w*(t8+w*(t11+w*t14))); + p = z*p1-(tt-w*(p2+y*p3)); + r += (tf + p); break; + case 2: + p1 = y*(u0+y*(u1+y*(u2+y*(u3+y*(u4+y*u5))))); + p2 = one+y*(v1+y*(v2+y*(v3+y*(v4+y*v5)))); + r += (-(float)0.5*y + p1/p2); + } + } + else if(ix<0x41000000) { /* x < 8.0 */ + i = (int)x; + t = zero; + y = x-(float)i; + p = y*(s0+y*(s1+y*(s2+y*(s3+y*(s4+y*(s5+y*s6)))))); + q = one+y*(r1+y*(r2+y*(r3+y*(r4+y*(r5+y*r6))))); + r = half*y+p/q; + z = one; /* lgamma(1+s) = log(s) + lgamma(s) */ + switch(i) { + case 7: z *= (y+(float)6.0); /* FALLTHRU */ + case 6: z *= (y+(float)5.0); /* FALLTHRU */ + case 5: z *= (y+(float)4.0); /* FALLTHRU */ + case 4: z *= (y+(float)3.0); /* FALLTHRU */ + case 3: z *= (y+(float)2.0); /* FALLTHRU */ + r += __ieee754_logf(z); break; + } + /* 8.0 <= x < 2**58 */ + } else if (ix < 0x5c800000) { + t = __ieee754_logf(x); + z = one/x; + y = z*z; + w = w0+z*(w1+y*(w2+y*(w3+y*(w4+y*(w5+y*w6))))); + r = (x-half)*(t-one)+w; + } else + /* 2**58 <= x <= inf */ + r = x*(__ieee754_logf(x)-one); + if(hx<0) r = nadj - r; + return r; +} diff --git a/lib/nbsd_libm/src/e_log.c b/lib/nbsd_libm/src/e_log.c new file mode 100644 index 000000000..c1dbace9a --- /dev/null +++ b/lib/nbsd_libm/src/e_log.c @@ -0,0 +1,136 @@ +/* @(#)e_log.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_log.c,v 1.12 2002/05/26 22:01:51 wiz Exp $"); +#endif + +/* __ieee754_log(x) + * Return the logrithm of x + * + * Method : + * 1. Argument Reduction: find k and f such that + * x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * 2. Approximation of log(1+f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lg1*s +Lg2*s +Lg3*s +Lg4*s +Lg5*s +Lg6*s +Lg7*s + * (the values of Lg1 to Lg7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lg1*s +...+Lg7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log(1+f) = f - s*(f - R) (if f is not too large) + * log(1+f) = f - (hfsq - s*(hfsq+R)). (better accuracy) + * + * 3. Finally, log(x) = k*ln2 + log(1+f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log(x) is NaN with signal if x < 0 (including -INF) ; + * log(+INF) is +INF; log(0) is -INF with signal; + * log(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +__ieee754_log(double x) +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; else {dk=(double)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*(0.5-0.33333333333333333*f); + if(k==0) return f-R; else {dk=(double)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/(2.0+f); + dk = (double)k; + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/lib/nbsd_libm/src/e_log10.c b/lib/nbsd_libm/src/e_log10.c new file mode 100644 index 000000000..84cfbabbc --- /dev/null +++ b/lib/nbsd_libm/src/e_log10.c @@ -0,0 +1,87 @@ +/* @(#)e_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_log10.c,v 1.12 2002/05/26 22:01:51 wiz Exp $"); +#endif + +/* __ieee754_log10(x) + * Return the base 10 logarithm of x + * + * Method : + * Let log10_2hi = leading 40 bits of log10(2) and + * log10_2lo = log10(2) - log10_2hi, + * ivln10 = 1/log(10) rounded. + * Then + * n = ilogb(x), + * if(n<0) n = n+1; + * x = scalbn(x,-n); + * log10(x) := n*log10_2hi + (n*log10_2lo + ivln10*log(x)) + * + * Note 1: + * To guarantee log10(10**n)=n, where 10**n is normal, the rounding + * mode must set to Round-to-Nearest. + * Note 2: + * [1/log(10)] rounded to 53 bits has error .198 ulps; + * log10 is monotonic at all binary break points. + * + * Special cases: + * log10(x) is NaN with signal if x < 0; + * log10(+INF) is +INF with no signal; log10(0) is -INF with signal; + * log10(NaN) is that NaN with no signal; + * log10(10**N) = N for N=0,1,...,22. + * + * Constants: + * The hexadecimal values are the intended ones for the following constants. + * The decimal values may be used, provided that the compiler will convert + * from decimal to binary accurately enough to produce the hexadecimal values + * shown. + */ + +#include "math.h" +#include "math_private.h" + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +ivln10 = 4.34294481903251816668e-01, /* 0x3FDBCB7B, 0x1526E50E */ +log10_2hi = 3.01029995663611771306e-01, /* 0x3FD34413, 0x509F6000 */ +log10_2lo = 3.69423907715893078616e-13; /* 0x3D59FEF3, 0x11F12B36 */ + +static const double zero = 0.0; + +double +__ieee754_log10(double x) +{ + double y,z; + int32_t i,k,hx; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x000fffff)|((0x3ff-i)<<20); + y = (double)(k+i); + SET_HIGH_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_log(x); + return z+y*log10_2hi; +} diff --git a/lib/nbsd_libm/src/e_log10f.c b/lib/nbsd_libm/src/e_log10f.c new file mode 100644 index 000000000..1969a63ce --- /dev/null +++ b/lib/nbsd_libm/src/e_log10f.c @@ -0,0 +1,56 @@ +/* e_log10f.c -- float version of e_log10.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_log10f.c,v 1.8 2002/05/26 22:01:51 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +two25 = 3.3554432000e+07, /* 0x4c000000 */ +ivln10 = 4.3429449201e-01, /* 0x3ede5bd9 */ +log10_2hi = 3.0102920532e-01, /* 0x3e9a2080 */ +log10_2lo = 7.9034151668e-07; /* 0x355427db */ + +static const float zero = 0.0; + +float +__ieee754_log10f(float x) +{ + float y,z; + int32_t i,k,hx; + + GET_FLOAT_WORD(hx,x); + + k=0; + if (hx < 0x00800000) { /* x < 2**-126 */ + if ((hx&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(hx,x); + } + if (hx >= 0x7f800000) return x+x; + k += (hx>>23)-127; + i = ((u_int32_t)k&0x80000000)>>31; + hx = (hx&0x007fffff)|((0x7f-i)<<23); + y = (float)(k+i); + SET_FLOAT_WORD(x,hx); + z = y*log10_2lo + ivln10*__ieee754_logf(x); + return z+y*log10_2hi; +} diff --git a/lib/nbsd_libm/src/e_log2.c b/lib/nbsd_libm/src/e_log2.c new file mode 100644 index 000000000..46da3ca24 --- /dev/null +++ b/lib/nbsd_libm/src/e_log2.c @@ -0,0 +1,80 @@ + +/* @(#)e_log.c 1.3 95/01/18 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunSoft, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_log2.c,v 1.1 2005/07/21 12:55:58 christos Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const double +ln2 = 0.6931471805599452862268, +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lg1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lg2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lg3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lg4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lg5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lg6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lg7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +__ieee754_log2(double x) +{ + double hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,hx,i,j; + u_int32_t lx; + + EXTRACT_WORDS(hx,lx,x); + + k=0; + if (hx < 0x00100000) { /* x < 2**-1022 */ + if (((hx&0x7fffffff)|lx)==0) + return -two54/zero; /* log(+-0)=-inf */ + if (hx<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 54; x *= two54; /* subnormal number, scale up x */ + GET_HIGH_WORD(hx,x); + } + if (hx >= 0x7ff00000) return x+x; + k += (hx>>20)-1023; + hx &= 0x000fffff; + i = (hx+0x95f64)&0x100000; + SET_HIGH_WORD(x,hx|(i^0x3ff00000)); /* normalize x or x/2 */ + k += (i>>20); + f = x-1.0; + dk = (double)k; + if((0x000fffff&(2+hx))<3) { /* |f| < 2**-20 */ + if (f==zero) + return (dk); + R = f*f*(0.5-0.33333333333333333*f); + return (dk-(R-f)/ln2); + } + s = f/(2.0+f); + z = s*s; + i = hx-0x6147a; + w = z*z; + j = 0x6b851-hx; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=0.5*f*f; + return (dk-(hfsq-s*(hfsq+R)-f)/ln2); + } else + return (dk-((s*(f-R))-f)/ln2); +} diff --git a/lib/nbsd_libm/src/e_log2f.c b/lib/nbsd_libm/src/e_log2f.c new file mode 100644 index 000000000..c521d7b20 --- /dev/null +++ b/lib/nbsd_libm/src/e_log2f.c @@ -0,0 +1,81 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_log2f.c,v 1.1 2005/07/21 12:55:58 christos Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +ln2 = 0.6931471805599452862268, +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +__ieee754_log2f(float x) +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + dk = (float)k; + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if (f==zero) + return (dk); + R = f*f*((float)0.5-(float)0.33333333333333333*f); + return (dk-(R-f)/ln2); + } + s = f/((float)2.0+f); + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + return (dk-(hfsq-s*(hfsq+R)-f)/ln2); + } else + return (dk-((s*(f-R))-f)/ln2); +} diff --git a/lib/nbsd_libm/src/e_logf.c b/lib/nbsd_libm/src/e_logf.c new file mode 100644 index 000000000..d40f0d659 --- /dev/null +++ b/lib/nbsd_libm/src/e_logf.c @@ -0,0 +1,87 @@ +/* e_logf.c -- float version of e_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_logf.c,v 1.8 2002/05/26 22:01:51 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lg1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lg2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lg3 = 2.8571429849e-01, /* 3E924925 */ +Lg4 = 2.2222198546e-01, /* 3E638E29 */ +Lg5 = 1.8183572590e-01, /* 3E3A3325 */ +Lg6 = 1.5313838422e-01, /* 3E1CD04F */ +Lg7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +__ieee754_logf(float x) +{ + float hfsq,f,s,z,R,w,t1,t2,dk; + int32_t k,ix,i,j; + + GET_FLOAT_WORD(ix,x); + + k=0; + if (ix < 0x00800000) { /* x < 2**-126 */ + if ((ix&0x7fffffff)==0) + return -two25/zero; /* log(+-0)=-inf */ + if (ix<0) return (x-x)/zero; /* log(-#) = NaN */ + k -= 25; x *= two25; /* subnormal number, scale up x */ + GET_FLOAT_WORD(ix,x); + } + if (ix >= 0x7f800000) return x+x; + k += (ix>>23)-127; + ix &= 0x007fffff; + i = (ix+(0x95f64<<3))&0x800000; + SET_FLOAT_WORD(x,ix|(i^0x3f800000)); /* normalize x or x/2 */ + k += (i>>23); + f = x-(float)1.0; + if((0x007fffff&(15+ix))<16) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; else {dk=(float)k; + return dk*ln2_hi+dk*ln2_lo;} + } + R = f*f*((float)0.5-(float)0.33333333333333333*f); + if(k==0) return f-R; else {dk=(float)k; + return dk*ln2_hi-((R-dk*ln2_lo)-f);} + } + s = f/((float)2.0+f); + dk = (float)k; + z = s*s; + i = ix-(0x6147a<<3); + w = z*z; + j = (0x6b851<<3)-ix; + t1= w*(Lg2+w*(Lg4+w*Lg6)); + t2= z*(Lg1+w*(Lg3+w*(Lg5+w*Lg7))); + i |= j; + R = t2+t1; + if(i>0) { + hfsq=(float)0.5*f*f; + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return dk*ln2_hi-((hfsq-(s*(hfsq+R)+dk*ln2_lo))-f); + } else { + if(k==0) return f-s*(f-R); else + return dk*ln2_hi-((s*(f-R)-dk*ln2_lo)-f); + } +} diff --git a/lib/nbsd_libm/src/e_pow.c b/lib/nbsd_libm/src/e_pow.c new file mode 100644 index 000000000..b9e2a6322 --- /dev/null +++ b/lib/nbsd_libm/src/e_pow.c @@ -0,0 +1,303 @@ +/* @(#)e_pow.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_pow.c,v 1.16 2010/04/23 19:17:07 drochner Exp $"); +#endif + +/* __ieee754_pow(x,y) return x**y + * + * n + * Method: Let x = 2 * (1+f) + * 1. Compute and return log2(x) in two pieces: + * log2(x) = w1 + w2, + * where w1 has 53-24 = 29 bit trailing zeros. + * 2. Perform y*log2(x) = n+y' by simulating multi-precision + * arithmetic, where |y'|<=0.5. + * 3. Return x**y = 2**n*exp(y'*log2) + * + * Special cases: + * 1. (anything) ** 0 is 1 + * 2. (anything) ** 1 is itself + * 3. (anything) ** NAN is NAN + * 4. NAN ** (anything except 0) is NAN + * 5. +-(|x| > 1) ** +INF is +INF + * 6. +-(|x| > 1) ** -INF is +0 + * 7. +-(|x| < 1) ** +INF is +0 + * 8. +-(|x| < 1) ** -INF is +INF + * 9. +-1 ** +-INF is NAN + * 10. +0 ** (+anything except 0, NAN) is +0 + * 11. -0 ** (+anything except 0, NAN, odd integer) is +0 + * 12. +0 ** (-anything except 0, NAN) is +INF + * 13. -0 ** (-anything except 0, NAN, odd integer) is +INF + * 14. -0 ** (odd integer) = -( +0 ** (odd integer) ) + * 15. +INF ** (+anything except 0,NAN) is +INF + * 16. +INF ** (-anything except 0,NAN) is +0 + * 17. -INF ** (anything) = -0 ** (-anything) + * 18. (-anything) ** (integer) is (-1)**(integer)*(+anything**integer) + * 19. (-anything except 0 and inf) ** (non-integer) is NAN + * + * Accuracy: + * pow(x,y) returns x**y nearly rounded. In particular + * pow(integer,integer) + * always returns the correct integer provided it is + * representable. + * + * Constants : + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static const double +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84962487220764160156e-01,}, /* 0x3FE2B803, 0x40000000 */ +dp_l[] = { 0.0, 1.35003920212974897128e-08,}, /* 0x3E4CFDEB, 0x43CFD006 */ +zero = 0.0, +one = 1.0, +two = 2.0, +two53 = 9007199254740992.0, /* 0x43400000, 0x00000000 */ +huge = 1.0e300, +tiny = 1.0e-300, + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 5.99999999999994648725e-01, /* 0x3FE33333, 0x33333303 */ +L2 = 4.28571428578550184252e-01, /* 0x3FDB6DB6, 0xDB6FABFF */ +L3 = 3.33333329818377432918e-01, /* 0x3FD55555, 0x518F264D */ +L4 = 2.72728123808534006489e-01, /* 0x3FD17460, 0xA91D4101 */ +L5 = 2.30660745775561754067e-01, /* 0x3FCD864A, 0x93C9DB65 */ +L6 = 2.06975017800338417784e-01, /* 0x3FCA7E28, 0x4A454EEF */ +P1 = 1.66666666666666019037e-01, /* 0x3FC55555, 0x5555553E */ +P2 = -2.77777777770155933842e-03, /* 0xBF66C16C, 0x16BEBD93 */ +P3 = 6.61375632143793436117e-05, /* 0x3F11566A, 0xAF25DE2C */ +P4 = -1.65339022054652515390e-06, /* 0xBEBBBD41, 0xC5D26BF1 */ +P5 = 4.13813679705723846039e-08, /* 0x3E663769, 0x72BEA4D0 */ +lg2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +lg2_h = 6.93147182464599609375e-01, /* 0x3FE62E43, 0x00000000 */ +lg2_l = -1.90465429995776804525e-09, /* 0xBE205C61, 0x0CA86C39 */ +ovt = 8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */ +cp = 9.61796693925975554329e-01, /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */ +cp_h = 9.61796700954437255859e-01, /* 0x3FEEC709, 0xE0000000 =(float)cp */ +cp_l = -7.02846165095275826516e-09, /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/ +ivln2 = 1.44269504088896338700e+00, /* 0x3FF71547, 0x652B82FE =1/ln2 */ +ivln2_h = 1.44269502162933349609e+00, /* 0x3FF71547, 0x60000000 =24b 1/ln2*/ +ivln2_l = 1.92596299112661746887e-08; /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/ + +double +__ieee754_pow(double x, double y) +{ + double z,ax,z_h,z_l,p_h,p_l; + double yy1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if((iy|ly)==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7ff00000 || ((ix==0x7ff00000)&&(lx!=0)) || + iy > 0x7ff00000 || ((iy==0x7ff00000)&&(ly!=0))) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x43400000) yisint = 2; /* even integer y */ + else if(iy>=0x3ff00000) { + k = (iy>>20)-0x3ff; /* exponent */ + if(k>20) { + j = ly>>(52-k); + if((uint32_t)(j<<(52-k))==ly) yisint = 2-(j&1); + } else if(ly==0) { + j = iy>>(20-k); + if((j<<(20-k))==iy) yisint = 2-(j&1); + } + } + } + + /* special value of y */ + if(ly==0) { + if (iy==0x7ff00000) { /* y is +-inf */ + if(((ix-0x3ff00000)|lx)==0) + return y - y; /* inf**+-1 is NaN */ + else if (ix >= 0x3ff00000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3ff00000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3fe00000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrt(x); + } + } + + ax = fabs(x); + /* special value of x */ + if(lx==0) { + if(ix==0x7ff00000||ix==0||ix==0x3ff00000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3ff00000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + } + + n = (hx>>31)+1; + + /* (x<0)**(non-int) is NaN */ + if((n|yisint)==0) return (x-x)/(x-x); + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if((n|(yisint-1))==0) s = -one;/* (-ve)**(odd int) */ + + /* |y| is huge */ + if(iy>0x41e00000) { /* if |y| > 2**31 */ + if(iy>0x43f00000){ /* if |y| > 2**64, must o/uflow */ + if(ix<=0x3fefffff) return (hy<0)? huge*huge:tiny*tiny; + if(ix>=0x3ff00000) return (hy>0)? huge*huge:tiny*tiny; + } + /* over/underflow if x is not close to one */ + if(ix<0x3fefffff) return (hy<0)? s*huge*huge:s*tiny*tiny; + if(ix>0x3ff00000) return (hy>0)? s*huge*huge:s*tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-one; /* t has 20 trailing zeros */ + w = (t*t)*(0.5-t*(0.3333333333333333333333-t*0.25)); + u = ivln2_h*t; /* ivln2_h has 21 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + SET_LOW_WORD(t1,0); + t2 = v-(t1-u); + } else { + double ss,s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00100000) + {ax *= two53; n -= 53; GET_HIGH_WORD(ix,ax); } + n += ((ix)>>20)-0x3ff; + j = ix&0x000fffff; + /* determine interval */ + ix = j|0x3ff00000; /* normalize ix */ + if(j<=0x3988E) k=0; /* |x|>1)|0x20000000)+0x00080000+(k<<18)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = ss*ss; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+ss); + s2 = s_h*s_h; + t_h = 3.0+s2+r; + SET_LOW_WORD(t_h,0); + t_l = r-((t_h-3.0)-s2); + /* u+v = ss*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*ss; + /* 2/(3log2)*(ss+...) */ + p_h = u+v; + SET_LOW_WORD(p_h,0); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (ss+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (double)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + SET_LOW_WORD(t1,0); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + /* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */ + yy1 = y; + SET_LOW_WORD(yy1,0); + p_l = (y-yy1)*t1+y*t2; + p_h = yy1*t1; + z = p_l+p_h; + EXTRACT_WORDS(j,i,z); + if (j>=0x40900000) { /* z >= 1024 */ + if(((j-0x40900000)|i)!=0) /* if z > 1024 */ + return s*huge*huge; /* overflow */ + else { + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + } else if((j&0x7fffffff)>=0x4090cc00 ) { /* z <= -1075 */ + if(((j-0xc090cc00)|i)!=0) /* z < -1075 */ + return s*tiny*tiny; /* underflow */ + else { + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + } + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>20)-0x3ff; + n = 0; + if(i>0x3fe00000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00100000>>(k+1)); + k = ((n&0x7fffffff)>>20)-0x3ff; /* new k for n */ + t = zero; + SET_HIGH_WORD(t,n&~(0x000fffff>>k)); + n = ((n&0x000fffff)|0x00100000)>>(20-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + SET_LOW_WORD(t,0); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_HIGH_WORD(j,z); + j += (n<<20); + if((j>>20)<=0) z = scalbn(z,n); /* subnormal output */ + else SET_HIGH_WORD(z,j); + return s*z; +} diff --git a/lib/nbsd_libm/src/e_powf.c b/lib/nbsd_libm/src/e_powf.c new file mode 100644 index 000000000..b4894e0fb --- /dev/null +++ b/lib/nbsd_libm/src/e_powf.c @@ -0,0 +1,247 @@ +/* e_powf.c -- float version of e_pow.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_powf.c,v 1.15 2010/04/23 19:17:07 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e+30, tiny = 1.0e-30; + +static const float +bp[] = {1.0, 1.5,}, +dp_h[] = { 0.0, 5.84960938e-01,}, /* 0x3f15c000 */ +dp_l[] = { 0.0, 1.56322085e-06,}, /* 0x35d1cfdc */ +zero = 0.0, +one = 1.0, +two = 2.0, +two24 = 16777216.0, /* 0x4b800000 */ + /* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */ +L1 = 6.0000002384e-01, /* 0x3f19999a */ +L2 = 4.2857143283e-01, /* 0x3edb6db7 */ +L3 = 3.3333334327e-01, /* 0x3eaaaaab */ +L4 = 2.7272811532e-01, /* 0x3e8ba305 */ +L5 = 2.3066075146e-01, /* 0x3e6c3255 */ +L6 = 2.0697501302e-01, /* 0x3e53f142 */ +P1 = 1.6666667163e-01, /* 0x3e2aaaab */ +P2 = -2.7777778450e-03, /* 0xbb360b61 */ +P3 = 6.6137559770e-05, /* 0x388ab355 */ +P4 = -1.6533901999e-06, /* 0xb5ddea0e */ +P5 = 4.1381369442e-08, /* 0x3331bb4c */ +lg2 = 6.9314718246e-01, /* 0x3f317218 */ +lg2_h = 6.93145752e-01, /* 0x3f317200 */ +lg2_l = 1.42860654e-06, /* 0x35bfbe8c */ +ovt = 4.2995665694e-08, /* -(128-log2(ovfl+.5ulp)) */ +cp = 9.6179670095e-01, /* 0x3f76384f =2/(3ln2) */ +cp_h = 9.6179199219e-01, /* 0x3f763800 =head of cp */ +cp_l = 4.7017383622e-06, /* 0x369dc3a0 =tail of cp_h */ +ivln2 = 1.4426950216e+00, /* 0x3fb8aa3b =1/ln2 */ +ivln2_h = 1.4426879883e+00, /* 0x3fb8aa00 =16b 1/ln2*/ +ivln2_l = 7.0526075433e-06; /* 0x36eca570 =1/ln2 tail*/ + +float +__ieee754_powf(float x, float y) +{ + float z,ax,z_h,z_l,p_h,p_l; + float yy1,t1,t2,r,s,t,u,v,w; + int32_t i,j,k,yisint,n; + int32_t hx,hy,ix,iy,is; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; iy = hy&0x7fffffff; + + /* y==zero: x**0 = 1 */ + if(iy==0) return one; + + /* +-NaN return x+y */ + if(ix > 0x7f800000 || + iy > 0x7f800000) + return x+y; + + /* determine if y is an odd int when x < 0 + * yisint = 0 ... y is not an integer + * yisint = 1 ... y is an odd int + * yisint = 2 ... y is an even int + */ + yisint = 0; + if(hx<0) { + if(iy>=0x4b800000) yisint = 2; /* even integer y */ + else if(iy>=0x3f800000) { + k = (iy>>23)-0x7f; /* exponent */ + j = iy>>(23-k); + if((j<<(23-k))==iy) yisint = 2-(j&1); + } + } + + /* special value of y */ + if (iy==0x7f800000) { /* y is +-inf */ + if (ix==0x3f800000) + return y - y; /* inf**+-1 is NaN */ + else if (ix > 0x3f800000)/* (|x|>1)**+-inf = inf,0 */ + return (hy>=0)? y: zero; + else /* (|x|<1)**-,+inf = inf,0 */ + return (hy<0)?-y: zero; + } + if(iy==0x3f800000) { /* y is +-1 */ + if(hy<0) return one/x; else return x; + } + if(hy==0x40000000) return x*x; /* y is 2 */ + if(hy==0x3f000000) { /* y is 0.5 */ + if(hx>=0) /* x >= +0 */ + return __ieee754_sqrtf(x); + } + + ax = fabsf(x); + /* special value of x */ + if(ix==0x7f800000||ix==0||ix==0x3f800000){ + z = ax; /*x is +-0,+-inf,+-1*/ + if(hy<0) z = one/z; /* z = (1/|x|) */ + if(hx<0) { + if(((ix-0x3f800000)|yisint)==0) { + z = (z-z)/(z-z); /* (-1)**non-int is NaN */ + } else if(yisint==1) + z = -z; /* (x<0)**odd = -(|x|**odd) */ + } + return z; + } + + /* (x<0)**(non-int) is NaN */ + if(((((u_int32_t)hx>>31)-1)|yisint)==0) return (x-x)/(x-x); + + /* |y| is huge */ + if(iy>0x4d000000) { /* if |y| > 2**27 */ + /* over/underflow if x is not close to one */ + if(ix<0x3f7ffff8) return (hy<0)? huge*huge:tiny*tiny; + if(ix>0x3f800007) return (hy>0)? huge*huge:tiny*tiny; + /* now |1-x| is tiny <= 2**-20, suffice to compute + log(x) by x-x^2/2+x^3/3-x^4/4 */ + t = ax-one; /* t has 20 trailing zeros */ + w = (t*t)*((float)0.5-t*((float)0.333333333333-t*(float)0.25)); + u = ivln2_h*t; /* ivln2_h has 16 sig. bits */ + v = t*ivln2_l-w*ivln2; + t1 = u+v; + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = v-(t1-u); + } else { + float s2,s_h,s_l,t_h,t_l; + n = 0; + /* take care subnormal number */ + if(ix<0x00800000) + {ax *= two24; n -= 24; GET_FLOAT_WORD(ix,ax); } + n += ((ix)>>23)-0x7f; + j = ix&0x007fffff; + /* determine interval */ + ix = j|0x3f800000; /* normalize ix */ + if(j<=0x1cc471) k=0; /* |x|>1)|0x20000000)+0x0040000+(k<<21)); + t_l = ax - (t_h-bp[k]); + s_l = v*((u-s_h*t_h)-s_h*t_l); + /* compute log(ax) */ + s2 = s*s; + r = s2*s2*(L1+s2*(L2+s2*(L3+s2*(L4+s2*(L5+s2*L6))))); + r += s_l*(s_h+s); + s2 = s_h*s_h; + t_h = (float)3.0+s2+r; + GET_FLOAT_WORD(is,t_h); + SET_FLOAT_WORD(t_h,is&0xfffff000); + t_l = r-((t_h-(float)3.0)-s2); + /* u+v = s*(1+...) */ + u = s_h*t_h; + v = s_l*t_h+t_l*s; + /* 2/(3log2)*(s+...) */ + p_h = u+v; + GET_FLOAT_WORD(is,p_h); + SET_FLOAT_WORD(p_h,is&0xfffff000); + p_l = v-(p_h-u); + z_h = cp_h*p_h; /* cp_h+cp_l = 2/(3*log2) */ + z_l = cp_l*p_h+p_l*cp+dp_l[k]; + /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */ + t = (float)n; + t1 = (((z_h+z_l)+dp_h[k])+t); + GET_FLOAT_WORD(is,t1); + SET_FLOAT_WORD(t1,is&0xfffff000); + t2 = z_l-(((t1-t)-dp_h[k])-z_h); + } + + s = one; /* s (sign of result -ve**odd) = -1 else = 1 */ + if(((((u_int32_t)hx>>31)-1)|(yisint-1))==0) + s = -one; /* (-ve)**(odd int) */ + + /* split up y into yy1+y2 and compute (yy1+y2)*(t1+t2) */ + GET_FLOAT_WORD(is,y); + SET_FLOAT_WORD(yy1,is&0xfffff000); + p_l = (y-yy1)*t1+y*t2; + p_h = yy1*t1; + z = p_l+p_h; + GET_FLOAT_WORD(j,z); + if (j>0x43000000) /* if z > 128 */ + return s*huge*huge; /* overflow */ + else if (j==0x43000000) { /* if z == 128 */ + if(p_l+ovt>z-p_h) return s*huge*huge; /* overflow */ + } + else if ((uint32_t)j==0xc3160000){ /* z == -150 */ + if(p_l<=z-p_h) return s*tiny*tiny; /* underflow */ + } + else if ((j&0x7fffffff)>0x43160000) /* z <= -150 */ + return s*tiny*tiny; /* underflow */ + /* + * compute 2**(p_h+p_l) + */ + i = j&0x7fffffff; + k = (i>>23)-0x7f; + n = 0; + if(i>0x3f000000) { /* if |z| > 0.5, set n = [z+0.5] */ + n = j+(0x00800000>>(k+1)); + k = ((n&0x7fffffff)>>23)-0x7f; /* new k for n */ + SET_FLOAT_WORD(t,n&~(0x007fffff>>k)); + n = ((n&0x007fffff)|0x00800000)>>(23-k); + if(j<0) n = -n; + p_h -= t; + } + t = p_l+p_h; + GET_FLOAT_WORD(is,t); + SET_FLOAT_WORD(t,is&0xfffff000); + u = t*lg2_h; + v = (p_l-(t-p_h))*lg2+t*lg2_l; + z = u+v; + w = v-(z-u); + t = z*z; + t1 = z - t*(P1+t*(P2+t*(P3+t*(P4+t*P5)))); + r = (z*t1)/(t1-two)-(w+z*w); + z = one-(r-z); + GET_FLOAT_WORD(j,z); + j += (n<<23); + if((j>>23)<=0) z = scalbnf(z,n); /* subnormal output */ + else SET_FLOAT_WORD(z,j); + return s*z; +} diff --git a/lib/nbsd_libm/src/e_rem_pio2.c b/lib/nbsd_libm/src/e_rem_pio2.c new file mode 100644 index 000000000..466e0ba78 --- /dev/null +++ b/lib/nbsd_libm/src/e_rem_pio2.c @@ -0,0 +1,169 @@ +/* @(#)e_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_rem_pio2.c,v 1.11 2002/05/26 22:01:52 wiz Exp $"); +#endif + +/* __ieee754_rem_pio2(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2() + */ + +#include "math.h" +#include "math_private.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +0xA2F983, 0x6E4E44, 0x1529FC, 0x2757D1, 0xF534DD, 0xC0DB62, +0x95993C, 0x439041, 0xFE5163, 0xABDEBB, 0xC561B7, 0x246E3A, +0x424DD2, 0xE00649, 0x2EEA09, 0xD1921C, 0xFE1DEB, 0x1CB129, +0xA73EE8, 0x8235F5, 0x2EBB44, 0x84E99C, 0x7026B4, 0x5F7E41, +0x3991D6, 0x398353, 0x39F49C, 0x845F8B, 0xBDF928, 0x3B1FF8, +0x97FFDE, 0x05980F, 0xEF2F11, 0x8B5A0A, 0x6D1F6D, 0x367ECF, +0x27CB09, 0xB74F46, 0x3F669E, 0x5FEA2D, 0x7527BA, 0xC7EBE5, +0xF17B3D, 0x0739F7, 0x8A5292, 0xEA6BFB, 0x5FB11F, 0x8D5D08, +0x560330, 0x46FC7B, 0x6BABF0, 0xCFBC20, 0x9AF436, 0x1DA9E3, +0x91615E, 0xE61B08, 0x659985, 0x5F14A0, 0x68408D, 0xFFD880, +0x4D7327, 0x310606, 0x1556CA, 0x73A8C9, 0x60E27B, 0xC08C6B, +}; + +static const int32_t npio2_hw[] = { +0x3FF921FB, 0x400921FB, 0x4012D97C, 0x401921FB, 0x401F6A7A, 0x4022D97C, +0x4025FDBB, 0x402921FB, 0x402C463A, 0x402F6A7A, 0x4031475C, 0x4032D97C, +0x40346B9C, 0x4035FDBB, 0x40378FDB, 0x403921FB, 0x403AB41B, 0x403C463A, +0x403DD85A, 0x403F6A7A, 0x40407E4C, 0x4041475C, 0x4042106C, 0x4042D97C, +0x4043A28C, 0x40446B9C, 0x404534AC, 0x4045FDBB, 0x4046C6CB, 0x40478FDB, +0x404858EB, 0x404921FB, +}; + +/* + * invpio2: 53 bits of 2/pi + * pio2_1: first 33 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 33 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 33 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const double +zero = 0.00000000000000000000e+00, /* 0x00000000, 0x00000000 */ +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +invpio2 = 6.36619772367581382433e-01, /* 0x3FE45F30, 0x6DC9C883 */ +pio2_1 = 1.57079632673412561417e+00, /* 0x3FF921FB, 0x54400000 */ +pio2_1t = 6.07710050650619224932e-11, /* 0x3DD0B461, 0x1A626331 */ +pio2_2 = 6.07710050630396597660e-11, /* 0x3DD0B461, 0x1A600000 */ +pio2_2t = 2.02226624879595063154e-21, /* 0x3BA3198A, 0x2E037073 */ +pio2_3 = 2.02226624871116645580e-21, /* 0x3BA3198A, 0x2E000000 */ +pio2_3t = 8.47842766036889956997e-32; /* 0x397B839A, 0x252049C1 */ + +int32_t +__ieee754_rem_pio2(double x, double *y) +{ + double z,w,t,r,fn; + double tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + u_int32_t low; + + z = 0; + GET_HIGH_WORD(hx,x); /* high word of x */ + ix = hx&0x7fffffff; + if(ix<=0x3fe921fb) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4002d97c) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if(ix!=0x3ff921fb) { /* 33+53 bit pi is good enough */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 33+33+53 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x413921fb) { /* |x| ~<= 2^19*(pi/2), medium size */ + t = fabs(x); + n = (int32_t) (t*invpio2+half); + fn = (double)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 85 bit */ + if(n<32&&ix!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>20; + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>16) { /* 2nd iteration needed, good to 118 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_HIGH_WORD(high,y[0]); + i = j-((high>>20)&0x7ff); + if(i>49) { /* 3rd iteration need, 151 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7ff00000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-23) */ + GET_LOW_WORD(low,x); + SET_LOW_WORD(z,low); + e0 = (ix>>20)-1046; /* e0 = ilogb(z)-23; */ + SET_HIGH_WORD(z, ix - ((int32_t)(e0<<20))); + for(i=0;i<2;i++) { + tx[i] = (double)((int32_t)(z)); + z = (z-tx[i])*two24; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/lib/nbsd_libm/src/e_rem_pio2f.c b/lib/nbsd_libm/src/e_rem_pio2f.c new file mode 100644 index 000000000..c22ad5279 --- /dev/null +++ b/lib/nbsd_libm/src/e_rem_pio2f.c @@ -0,0 +1,181 @@ +/* e_rem_pio2f.c -- float version of e_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_rem_pio2f.c,v 1.9 2009/01/19 06:00:30 lukem Exp $"); +#endif + +/* __ieee754_rem_pio2f(x,y) + * + * return the remainder of x rem pi/2 in y[0]+y[1] + * use __kernel_rem_pio2f() + */ + +#include "math.h" +#include "math_private.h" + +/* + * Table of constants for 2/pi, 396 Hex digits (476 decimal) of 2/pi + */ +static const int32_t two_over_pi[] = { +0xA2, 0xF9, 0x83, 0x6E, 0x4E, 0x44, 0x15, 0x29, 0xFC, +0x27, 0x57, 0xD1, 0xF5, 0x34, 0xDD, 0xC0, 0xDB, 0x62, +0x95, 0x99, 0x3C, 0x43, 0x90, 0x41, 0xFE, 0x51, 0x63, +0xAB, 0xDE, 0xBB, 0xC5, 0x61, 0xB7, 0x24, 0x6E, 0x3A, +0x42, 0x4D, 0xD2, 0xE0, 0x06, 0x49, 0x2E, 0xEA, 0x09, +0xD1, 0x92, 0x1C, 0xFE, 0x1D, 0xEB, 0x1C, 0xB1, 0x29, +0xA7, 0x3E, 0xE8, 0x82, 0x35, 0xF5, 0x2E, 0xBB, 0x44, +0x84, 0xE9, 0x9C, 0x70, 0x26, 0xB4, 0x5F, 0x7E, 0x41, +0x39, 0x91, 0xD6, 0x39, 0x83, 0x53, 0x39, 0xF4, 0x9C, +0x84, 0x5F, 0x8B, 0xBD, 0xF9, 0x28, 0x3B, 0x1F, 0xF8, +0x97, 0xFF, 0xDE, 0x05, 0x98, 0x0F, 0xEF, 0x2F, 0x11, +0x8B, 0x5A, 0x0A, 0x6D, 0x1F, 0x6D, 0x36, 0x7E, 0xCF, +0x27, 0xCB, 0x09, 0xB7, 0x4F, 0x46, 0x3F, 0x66, 0x9E, +0x5F, 0xEA, 0x2D, 0x75, 0x27, 0xBA, 0xC7, 0xEB, 0xE5, +0xF1, 0x7B, 0x3D, 0x07, 0x39, 0xF7, 0x8A, 0x52, 0x92, +0xEA, 0x6B, 0xFB, 0x5F, 0xB1, 0x1F, 0x8D, 0x5D, 0x08, +0x56, 0x03, 0x30, 0x46, 0xFC, 0x7B, 0x6B, 0xAB, 0xF0, +0xCF, 0xBC, 0x20, 0x9A, 0xF4, 0x36, 0x1D, 0xA9, 0xE3, +0x91, 0x61, 0x5E, 0xE6, 0x1B, 0x08, 0x65, 0x99, 0x85, +0x5F, 0x14, 0xA0, 0x68, 0x40, 0x8D, 0xFF, 0xD8, 0x80, +0x4D, 0x73, 0x27, 0x31, 0x06, 0x06, 0x15, 0x56, 0xCA, +0x73, 0xA8, 0xC9, 0x60, 0xE2, 0x7B, 0xC0, 0x8C, 0x6B, +}; + +/* This array is like the one in e_rem_pio2.c, but the numbers are + single precision and the last 8 bits are forced to 0. */ +static const int32_t npio2_hw[] = { +0x3fc90f00, 0x40490f00, 0x4096cb00, 0x40c90f00, 0x40fb5300, 0x4116cb00, +0x412fed00, 0x41490f00, 0x41623100, 0x417b5300, 0x418a3a00, 0x4196cb00, +0x41a35c00, 0x41afed00, 0x41bc7e00, 0x41c90f00, 0x41d5a000, 0x41e23100, +0x41eec200, 0x41fb5300, 0x4203f200, 0x420a3a00, 0x42108300, 0x4216cb00, +0x421d1400, 0x42235c00, 0x4229a500, 0x422fed00, 0x42363600, 0x423c7e00, +0x4242c700, 0x42490f00 +}; + +/* + * invpio2: 24 bits of 2/pi + * pio2_1: first 17 bit of pi/2 + * pio2_1t: pi/2 - pio2_1 + * pio2_2: second 17 bit of pi/2 + * pio2_2t: pi/2 - (pio2_1+pio2_2) + * pio2_3: third 17 bit of pi/2 + * pio2_3t: pi/2 - (pio2_1+pio2_2+pio2_3) + */ + +static const float +zero = 0.0000000000e+00, /* 0x00000000 */ +half = 5.0000000000e-01, /* 0x3f000000 */ +two8 = 2.5600000000e+02, /* 0x43800000 */ +invpio2 = 6.3661980629e-01, /* 0x3f22f984 */ +pio2_1 = 1.5707855225e+00, /* 0x3fc90f80 */ +pio2_1t = 1.0804334124e-05, /* 0x37354443 */ +pio2_2 = 1.0804273188e-05, /* 0x37354400 */ +pio2_2t = 6.0770999344e-11, /* 0x2e85a308 */ +pio2_3 = 6.0770943833e-11, /* 0x2e85a300 */ +pio2_3t = 6.1232342629e-17; /* 0x248d3132 */ + +int32_t +__ieee754_rem_pio2f(float x, float *y) +{ + float z,w,t,r,fn; + float tx[3]; + int32_t e0,i,j,nx,n,ix,hx; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix<=0x3f490fd8) /* |x| ~<= pi/4 , no need for reduction */ + {y[0] = x; y[1] = 0; return 0;} + if(ix<0x4016cbe4) { /* |x| < 3pi/4, special case with n=+-1 */ + if(hx>0) { + z = x - pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z - pio2_1t; + y[1] = (z-y[0])-pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z -= pio2_2; + y[0] = z - pio2_2t; + y[1] = (z-y[0])-pio2_2t; + } + return 1; + } else { /* negative x */ + z = x + pio2_1; + if((ix&0xfffffff0)!=0x3fc90fd0) { /* 24+24 bit pi OK */ + y[0] = z + pio2_1t; + y[1] = (z-y[0])+pio2_1t; + } else { /* near pi/2, use 24+24+24 bit pi */ + z += pio2_2; + y[0] = z + pio2_2t; + y[1] = (z-y[0])+pio2_2t; + } + return -1; + } + } + if(ix<=0x43490f80) { /* |x| ~<= 2^7*(pi/2), medium size */ + t = fabsf(x); + n = (int32_t) (t*invpio2+half); + fn = (float)n; + r = t-fn*pio2_1; + w = fn*pio2_1t; /* 1st round good to 40 bit */ + if(n<32&&(int32_t)(ix&0xffffff00)!=npio2_hw[n-1]) { + y[0] = r-w; /* quick check no cancellation */ + } else { + u_int32_t high; + j = ix>>23; + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>8) { /* 2nd iteration needed, good to 57 */ + t = r; + w = fn*pio2_2; + r = t-w; + w = fn*pio2_2t-((t-r)-w); + y[0] = r-w; + GET_FLOAT_WORD(high,y[0]); + i = j-((high>>23)&0xff); + if(i>25) { /* 3rd iteration need, 74 bits acc */ + t = r; /* will cover all possible cases */ + w = fn*pio2_3; + r = t-w; + w = fn*pio2_3t-((t-r)-w); + y[0] = r-w; + } + } + } + y[1] = (r-y[0])-w; + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + else return n; + } + /* + * all other (large) arguments + */ + if(ix>=0x7f800000) { /* x is inf or NaN */ + y[0]=y[1]=x-x; return 0; + } + /* set z = scalbn(|x|,ilogb(x)-7) */ + e0 = (ix>>23)-134; /* e0 = ilogb(z)-7; */ + SET_FLOAT_WORD(z, ix - ((int32_t)(e0<<23))); + for(i=0;i<2;i++) { + tx[i] = (float)((int32_t)(z)); + z = (z-tx[i])*two8; + } + tx[2] = z; + nx = 3; + while(tx[nx-1]==zero) nx--; /* skip zero term */ + n = __kernel_rem_pio2f(tx,y,e0,nx,2,two_over_pi); + if(hx<0) {y[0] = -y[0]; y[1] = -y[1]; return -n;} + return n; +} diff --git a/lib/nbsd_libm/src/e_remainder.c b/lib/nbsd_libm/src/e_remainder.c new file mode 100644 index 000000000..34e0e062c --- /dev/null +++ b/lib/nbsd_libm/src/e_remainder.c @@ -0,0 +1,73 @@ +/* @(#)e_remainder.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_remainder.c,v 1.11 2002/05/26 22:01:52 wiz Exp $"); +#endif + +/* __ieee754_remainder(x,p) + * Return : + * returns x REM p = x - [x/p]*p as if in infinite + * precise arithmetic, where [x/p] is the (infinite bit) + * integer nearest x/p (in half way case choose the even one). + * Method : + * Based on fmod() return x-[x/p]chopped*p exactlp. + */ + +#include "math.h" +#include "math_private.h" + +static const double zero = 0.0; + + +double +__ieee754_remainder(double x, double p) +{ + int32_t hx,hp; + u_int32_t sx,lx,lp; + double p_half; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hp,lp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if((hp|lp)==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7ff00000)|| /* x not finite */ + ((hp>=0x7ff00000)&& /* p is NaN */ + (((hp-0x7ff00000)|lp)!=0))) + return (x*p)/(x*p); + + + if (hp<=0x7fdfffff) x = __ieee754_fmod(x,p+p); /* now x < 2p */ + if (((hx-hp)|(lx-lp))==0) return zero*x; + x = fabs(x); + p = fabs(p); + if (hp<0x00200000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = 0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_HIGH_WORD(hx,x); + SET_HIGH_WORD(x,hx^sx); + return x; +} diff --git a/lib/nbsd_libm/src/e_remainderf.c b/lib/nbsd_libm/src/e_remainderf.c new file mode 100644 index 000000000..f56fb3096 --- /dev/null +++ b/lib/nbsd_libm/src/e_remainderf.c @@ -0,0 +1,66 @@ +/* e_remainderf.c -- float version of e_remainder.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_remainderf.c,v 1.7 2002/05/26 22:01:52 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float zero = 0.0; + + +float +__ieee754_remainderf(float x, float p) +{ + int32_t hx,hp; + u_int32_t sx; + float p_half; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hp,p); + sx = hx&0x80000000; + hp &= 0x7fffffff; + hx &= 0x7fffffff; + + /* purge off exception values */ + if(hp==0) return (x*p)/(x*p); /* p = 0 */ + if((hx>=0x7f800000)|| /* x not finite */ + ((hp>0x7f800000))) /* p is NaN */ + return (x*p)/(x*p); + + + if (hp<=0x7effffff) x = __ieee754_fmodf(x,p+p); /* now x < 2p */ + if ((hx-hp)==0) return zero*x; + x = fabsf(x); + p = fabsf(p); + if (hp<0x01000000) { + if(x+x>p) { + x-=p; + if(x+x>=p) x -= p; + } + } else { + p_half = (float)0.5*p; + if(x>p_half) { + x-=p; + if(x>=p_half) x -= p; + } + } + GET_FLOAT_WORD(hx,x); + SET_FLOAT_WORD(x,hx^sx); + return x; +} diff --git a/lib/nbsd_libm/src/e_scalb.c b/lib/nbsd_libm/src/e_scalb.c new file mode 100644 index 000000000..b3859f3b5 --- /dev/null +++ b/lib/nbsd_libm/src/e_scalb.c @@ -0,0 +1,49 @@ +/* @(#)e_scalb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_scalb.c,v 1.10 2010/04/23 19:17:07 drochner Exp $"); +#endif + +/* + * __ieee754_scalb(x, fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef _SCALB_INT +double +__ieee754_scalb(double x, int fn) +#else +double +__ieee754_scalb(double x, double fn) +#endif +{ +#ifdef _SCALB_INT + return scalbn(x,fn); +#else + if (isnan(x)||isnan(fn)) return x*fn; + if (!finite(fn)) { + if(fn>0.0) return x*fn; + else return x/(-fn); + } + if (rint(fn)!=fn) return (fn-fn)/(fn-fn); + if ( fn > 65000.0) return scalbn(x, 65000); + if (-fn > 65000.0) return scalbn(x,-65000); + return scalbn(x,(int)fn); +#endif +} diff --git a/lib/nbsd_libm/src/e_scalbf.c b/lib/nbsd_libm/src/e_scalbf.c new file mode 100644 index 000000000..1dfa37254 --- /dev/null +++ b/lib/nbsd_libm/src/e_scalbf.c @@ -0,0 +1,46 @@ +/* e_scalbf.c -- float version of e_scalb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_scalbf.c,v 1.7 2010/04/23 19:17:07 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef _SCALB_INT +float +__ieee754_scalbf(float x, int fn) +#else +float +__ieee754_scalbf(float x, float fn) +#endif +{ +#ifdef _SCALB_INT + return scalbnf(x,fn); +#else + if (isnanf(x)||isnanf(fn)) return x*fn; + if (!finitef(fn)) { + if(fn>(float)0.0) return x*fn; + else return x/(-fn); + } + if (rintf(fn)!=fn) return (fn-fn)/(fn-fn); + if ( fn > (float)65000.0) return scalbnf(x, 65000); + if (-fn > (float)65000.0) return scalbnf(x,-65000); + return scalbnf(x,(int)fn); +#endif +} diff --git a/lib/nbsd_libm/src/e_sinh.c b/lib/nbsd_libm/src/e_sinh.c new file mode 100644 index 000000000..12c9003d6 --- /dev/null +++ b/lib/nbsd_libm/src/e_sinh.c @@ -0,0 +1,79 @@ +/* @(#)e_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_sinh.c,v 1.11 2002/05/26 22:01:52 wiz Exp $"); +#endif + +/* __ieee754_sinh(x) + * Method : + * mathematically sinh(x) if defined to be (exp(x)-exp(-x))/2 + * 1. Replace x by |x| (sinh(-x) = -sinh(x)). + * 2. + * E + E/(E+1) + * 0 <= x <= 22 : sinh(x) := --------------, E=expm1(x) + * 2 + * + * 22 <= x <= lnovft : sinh(x) := exp(x)/2 + * lnovft <= x <= ln2ovft: sinh(x) := exp(x/2)/2 * exp(x/2) + * ln2ovft < x : sinh(x) := x*shuge (overflow) + * + * Special cases: + * sinh(x) is |x| if x is +INF, -INF, or NaN. + * only sinh(0)=0 is exact for finite x. + */ + +#include "math.h" +#include "math_private.h" + +static const double one = 1.0, shuge = 1.0e307; + +double +__ieee754_sinh(double x) +{ + double t,w,h; + int32_t ix,jx; + u_int32_t lx; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3e300000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1(fabs(x)); + if(ix<0x3ff00000) return h*(2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x40862E42) return h*__ieee754_exp(fabs(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + GET_LOW_WORD(lx,x); + if (ix<0x408633CE || ((ix==0x408633ce)&&(lx<=(u_int32_t)0x8fb9f87d))) { + w = __ieee754_exp(0.5*fabs(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/lib/nbsd_libm/src/e_sinhf.c b/lib/nbsd_libm/src/e_sinhf.c new file mode 100644 index 000000000..639de1562 --- /dev/null +++ b/lib/nbsd_libm/src/e_sinhf.c @@ -0,0 +1,61 @@ +/* e_sinhf.c -- float version of e_sinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_sinhf.c,v 1.7 2002/05/26 22:01:52 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float one = 1.0, shuge = 1.0e37; + +float +__ieee754_sinhf(float x) +{ + float t,w,h; + int32_t ix,jx; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) return x+x; + + h = 0.5; + if (jx<0) h = -h; + /* |x| in [0,22], return sign(x)*0.5*(E+E/(E+1))) */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix<0x31800000) /* |x|<2**-28 */ + if(shuge+x>one) return x;/* sinh(tiny) = tiny with inexact */ + t = expm1f(fabsf(x)); + if(ix<0x3f800000) return h*((float)2.0*t-t*t/(t+one)); + return h*(t+t/(t+one)); + } + + /* |x| in [22, log(maxdouble)] return 0.5*exp(|x|) */ + if (ix < 0x42b17180) return h*__ieee754_expf(fabsf(x)); + + /* |x| in [log(maxdouble), overflowthresold] */ + if (ix<=0x42b2d4fc) { + w = __ieee754_expf((float)0.5*fabsf(x)); + t = h*w; + return t*w; + } + + /* |x| > overflowthresold, sinh(x) overflow */ + return x*shuge; +} diff --git a/lib/nbsd_libm/src/e_sqrt.c b/lib/nbsd_libm/src/e_sqrt.c new file mode 100644 index 000000000..c49d31b04 --- /dev/null +++ b/lib/nbsd_libm/src/e_sqrt.c @@ -0,0 +1,446 @@ +/* @(#)e_sqrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_sqrt.c,v 1.13 2009/02/16 01:19:34 lukem Exp $"); +#endif + +/* __ieee754_sqrt(x) + * Return correctly rounded sqrt. + * ------------------------------------------ + * | Use the hardware sqrt if you have one | + * ------------------------------------------ + * Method: + * Bit by bit method using integer arithmetic. (Slow, but portable) + * 1. Normalization + * Scale x to y in [1,4) with even powers of 2: + * find an integer k such that 1 <= (y=x*2^(2k)) < 4, then + * sqrt(x) = 2^k * sqrt(y) + * 2. Bit by bit computation + * Let q = sqrt(y) truncated to i bit after binary point (q = 1), + * i 0 + * i+1 2 + * s = 2*q , and y = 2 * ( y - q ). (1) + * i i i i + * + * To compute q from q , one checks whether + * i+1 i + * + * -(i+1) 2 + * (q + 2 ) <= y. (2) + * i + * -(i+1) + * If (2) is false, then q = q ; otherwise q = q + 2 . + * i+1 i i+1 i + * + * With some algebric manipulation, it is not difficult to see + * that (2) is equivalent to + * -(i+1) + * s + 2 <= y (3) + * i i + * + * The advantage of (3) is that s and y can be computed by + * i i + * the following recurrence formula: + * if (3) is false + * + * s = s , y = y ; (4) + * i+1 i i+1 i + * + * otherwise, + * -i -(i+1) + * s = s + 2 , y = y - s - 2 (5) + * i+1 i i+1 i i + * + * One may easily use induction to prove (4) and (5). + * Note. Since the left hand side of (3) contain only i+2 bits, + * it does not necessary to do a full (53-bit) comparison + * in (3). + * 3. Final rounding + * After generating the 53 bits result, we compute one more bit. + * Together with the remainder, we can decide whether the + * result is exact, bigger than 1/2ulp, or less than 1/2ulp + * (it will never equal to 1/2ulp). + * The rounding mode can be detected by checking whether + * huge + tiny is equal to huge, and whether huge - tiny is + * equal to huge for some floating point number "huge" and "tiny". + * + * Special cases: + * sqrt(+-0) = +-0 ... exact + * sqrt(inf) = inf + * sqrt(-ve) = NaN ... with invalid signal + * sqrt(NaN) = NaN ... with invalid signal for signaling NaN + * + * Other methods : see the appended file at the end of the program below. + *--------------- + */ + +#include "math.h" +#include "math_private.h" + +static const double one = 1.0, tiny=1.0e-300; + +double +__ieee754_sqrt(double x) +{ + double z; + int32_t sign = (int)0x80000000; + int32_t ix0,s0,q,m,t,i; + u_int32_t r,t1,s1,ix1,q1; + + EXTRACT_WORDS(ix0,ix1,x); + + /* take care of Inf and NaN */ + if((ix0&0x7ff00000)==0x7ff00000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix0<=0) { + if(((ix0&(~sign))|ix1)==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix0<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix0>>20); + if(m==0) { /* subnormal x */ + while(ix0==0) { + m -= 21; + ix0 |= (ix1>>11); ix1 <<= 21; + } + for(i=0;(ix0&0x00100000)==0;i++) ix0<<=1; + m -= i-1; + ix0 |= (ix1>>(32-i)); + ix1 <<= i; + } + m -= 1023; /* unbias exponent */ + ix0 = (ix0&0x000fffff)|0x00100000; + if(m&1){ /* odd m, double x to make it even */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + } + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + q = q1 = s0 = s1 = 0; /* [q,q1] = sqrt(x) */ + r = 0x00200000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s0+r; + if(t<=ix0) { + s0 = t+r; + ix0 -= t; + q += r; + } + ix0 += ix0 + ((ix1&sign)>>31); + ix1 += ix1; + r>>=1; + } + + r = sign; + while(r!=0) { + t1 = s1+r; + t = s0; + if((t>31); + ix1 += ix1; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if((ix0|ix1)!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (q1==(u_int32_t)0xffffffff) { q1=0; q += 1;} + else if (z>one) { + if (q1==(u_int32_t)0xfffffffe) q+=1; + q1+=2; + } else + q1 += (q1&1); + } + } + ix0 = (q>>1)+0x3fe00000; + ix1 = q1>>1; + if ((q&1)==1) ix1 |= sign; + ix0 += (m <<20); + INSERT_WORDS(z,ix0,ix1); + return z; +} + +/* +Other methods (use floating-point arithmetic) +------------- +(This is a copy of a drafted paper by Prof W. Kahan +and K.C. Ng, written in May, 1986) + + Two algorithms are given here to implement sqrt(x) + (IEEE double precision arithmetic) in software. + Both supply sqrt(x) correctly rounded. The first algorithm (in + Section A) uses newton iterations and involves four divisions. + The second one uses reciproot iterations to avoid division, but + requires more multiplications. Both algorithms need the ability + to chop results of arithmetic operations instead of round them, + and the INEXACT flag to indicate when an arithmetic operation + is executed exactly with no roundoff error, all part of the + standard (IEEE 754-1985). The ability to perform shift, add, + subtract and logical AND operations upon 32-bit words is needed + too, though not part of the standard. + +A. sqrt(x) by Newton Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + + 1 11 52 ...widths + ------------------------------------------------------ + x: |s| e | f | + ------------------------------------------------------ + msb lsb msb lsb ...order + + + ------------------------ ------------------------ + x0: |s| e | f1 | x1: | f2 | + ------------------------ ------------------------ + + By performing shifts and subtracts on x0 and x1 (both regarded + as integers), we obtain an 8-bit approximation of sqrt(x) as + follows. + + k := (x0>>1) + 0x1ff80000; + y0 := k - T1[31&(k>>15)]. ... y ~ sqrt(x) to 8 bits + Here k is a 32-bit integer and T1[] is an integer array containing + correction terms. Now magically the floating value of y (y's + leading 32-bit word is y0, the value of its trailing word is 0) + approximates sqrt(x) to almost 8-bit. + + Value of T1: + static int T1[32]= { + 0, 1024, 3062, 5746, 9193, 13348, 18162, 23592, + 29598, 36145, 43202, 50740, 58733, 67158, 75992, 85215, + 83599, 71378, 60428, 50647, 41945, 34246, 27478, 21581, + 16499, 12183, 8588, 5674, 3403, 1742, 661, 130,}; + + (2) Iterative refinement + + Apply Heron's rule three times to y, we have y approximates + sqrt(x) to within 1 ulp (Unit in the Last Place): + + y := (y+x/y)/2 ... almost 17 sig. bits + y := (y+x/y)/2 ... almost 35 sig. bits + y := y-(y-x/y)/2 ... within 1 ulp + + + Remark 1. + Another way to improve y to within 1 ulp is: + + y := (y+x/y) ... almost 17 sig. bits to 2*sqrt(x) + y := y - 0x00100006 ... almost 18 sig. bits to sqrt(x) + + 2 + (x-y )*y + y := y + 2* ---------- ...within 1 ulp + 2 + 3y + x + + + This formula has one division fewer than the one above; however, + it requires more multiplications and additions. Also x must be + scaled in advance to avoid spurious overflow in evaluating the + expression 3y*y+x. Hence it is not recommended uless division + is slow. If division is very slow, then one should use the + reciproot algorithm given in section B. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + I := FALSE; ... reset INEXACT flag I + R := RZ; ... set rounding mode to round-toward-zero + z := x/y; ... chopped quotient, possibly inexact + If(not I) then { ... if the quotient is exact + if(z=y) { + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + } else { + z := z - ulp; ... special rounding + } + } + i := TRUE; ... sqrt(x) is inexact + If (r=RN) then z=z+ulp ... rounded-to-nearest + If (r=RP) then { ... round-toward-+inf + y = y+ulp; z=z+ulp; + } + y := y+z; ... chopped sum + y0:=y0-0x00100000; ... y := y/2 is correctly rounded. + I := i; ... restore inexact flag + R := r; ... restore rounded mode + return sqrt(x):=y. + + (4) Special cases + + Square root of +inf, +-0, or NaN is itself; + Square root of a negative number is NaN with invalid signal. + + +B. sqrt(x) by Reciproot Iteration + + (1) Initial approximation + + Let x0 and x1 be the leading and the trailing 32-bit words of + a floating point number x (in IEEE double format) respectively + (see section A). By performing shifs and subtracts on x0 and y0, + we obtain a 7.8-bit approximation of 1/sqrt(x) as follows. + + k := 0x5fe80000 - (x0>>1); + y0:= k - T2[63&(k>>14)]. ... y ~ 1/sqrt(x) to 7.8 bits + + Here k is a 32-bit integer and T2[] is an integer array + containing correction terms. Now magically the floating + value of y (y's leading 32-bit word is y0, the value of + its trailing word y1 is set to zero) approximates 1/sqrt(x) + to almost 7.8-bit. + + Value of T2: + static int T2[64]= { + 0x1500, 0x2ef8, 0x4d67, 0x6b02, 0x87be, 0xa395, 0xbe7a, 0xd866, + 0xf14a, 0x1091b,0x11fcd,0x13552,0x14999,0x15c98,0x16e34,0x17e5f, + 0x18d03,0x19a01,0x1a545,0x1ae8a,0x1b5c4,0x1bb01,0x1bfde,0x1c28d, + 0x1c2de,0x1c0db,0x1ba73,0x1b11c,0x1a4b5,0x1953d,0x18266,0x16be0, + 0x1683e,0x179d8,0x18a4d,0x19992,0x1a789,0x1b445,0x1bf61,0x1c989, + 0x1d16d,0x1d77b,0x1dddf,0x1e2ad,0x1e5bf,0x1e6e8,0x1e654,0x1e3cd, + 0x1df2a,0x1d635,0x1cb16,0x1be2c,0x1ae4e,0x19bde,0x1868e,0x16e2e, + 0x1527f,0x1334a,0x11051,0xe951, 0xbe01, 0x8e0d, 0x5924, 0x1edd,}; + + (2) Iterative refinement + + Apply Reciproot iteration three times to y and multiply the + result by x to get an approximation z that matches sqrt(x) + to about 1 ulp. To be exact, we will have + -1ulp < sqrt(x)-z<1.0625ulp. + + ... set rounding mode to Round-to-nearest + y := y*(1.5-0.5*x*y*y) ... almost 15 sig. bits to 1/sqrt(x) + y := y*((1.5-2^-30)+0.5*x*y*y)... about 29 sig. bits to 1/sqrt(x) + ... special arrangement for better accuracy + z := x*y ... 29 bits to sqrt(x), with z*y<1 + z := z + 0.5*z*(1-z*y) ... about 1 ulp to sqrt(x) + + Remark 2. The constant 1.5-2^-30 is chosen to bias the error so that + (a) the term z*y in the final iteration is always less than 1; + (b) the error in the final result is biased upward so that + -1 ulp < sqrt(x) - z < 1.0625 ulp + instead of |sqrt(x)-z|<1.03125ulp. + + (3) Final adjustment + + By twiddling y's last bit it is possible to force y to be + correctly rounded according to the prevailing rounding mode + as follows. Let r and i be copies of the rounding mode and + inexact flag before entering the square root program. Also we + use the expression y+-ulp for the next representable floating + numbers (up and down) of y. Note that y+-ulp = either fixed + point y+-1, or multiply y by nextafter(1,+-inf) in chopped + mode. + + R := RZ; ... set rounding mode to round-toward-zero + switch(r) { + case RN: ... round-to-nearest + if(x<= z*(z-ulp)...chopped) z = z - ulp; else + if(x<= z*(z+ulp)...chopped) z = z; else z = z+ulp; + break; + case RZ:case RM: ... round-to-zero or round-to--inf + R:=RP; ... reset rounding mod to round-to-+inf + if(x=(z+ulp)*(z+ulp) ...rounded up) z = z+ulp; + break; + case RP: ... round-to-+inf + if(x>(z+ulp)*(z+ulp)...chopped) z = z+2*ulp; else + if(x>z*z ...chopped) z = z+ulp; + break; + } + + Remark 3. The above comparisons can be done in fixed point. For + example, to compare x and w=z*z chopped, it suffices to compare + x1 and w1 (the trailing parts of x and w), regarding them as + two's complement integers. + + ...Is z an exact square root? + To determine whether z is an exact square root of x, let z1 be the + trailing part of z, and also let x0 and x1 be the leading and + trailing parts of x. + + If ((z1&0x03ffffff)!=0) ... not exact if trailing 26 bits of z!=0 + I := 1; ... Raise Inexact flag: z is not exact + else { + j := 1 - [(x0>>20)&1] ... j = logb(x) mod 2 + k := z1 >> 26; ... get z's 25-th and 26-th + fraction bits + I := i or (k&j) or ((k&(j+j+1))!=(x1&3)); + } + R:= r ... restore rounded mode + return sqrt(x):=z. + + If multiplication is cheaper than the foregoing red tape, the + Inexact flag can be evaluated by + + I := i; + I := (z*z!=x) or I. + + Note that z*z can overwrite I; this value must be sensed if it is + True. + + Remark 4. If z*z = x exactly, then bit 25 to bit 0 of z1 must be + zero. + + -------------------- + z1: | f2 | + -------------------- + bit 31 bit 0 + + Further more, bit 27 and 26 of z1, bit 0 and 1 of x1, and the odd + or even of logb(x) have the following relations: + + ------------------------------------------------- + bit 27,26 of z1 bit 1,0 of x1 logb(x) + ------------------------------------------------- + 00 00 odd and even + 01 01 even + 10 10 odd + 10 00 even + 11 01 even + ------------------------------------------------- + + (4) Special cases (see (4) of Section A). + + */ + diff --git a/lib/nbsd_libm/src/e_sqrtf.c b/lib/nbsd_libm/src/e_sqrtf.c new file mode 100644 index 000000000..3bd705d83 --- /dev/null +++ b/lib/nbsd_libm/src/e_sqrtf.c @@ -0,0 +1,90 @@ +/* e_sqrtf.c -- float version of e_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: e_sqrtf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float one = 1.0, tiny=1.0e-30; + +float +__ieee754_sqrtf(float x) +{ + float z; + int32_t sign = (int)0x80000000; + int32_t ix,s,q,m,t,i; + u_int32_t r; + + GET_FLOAT_WORD(ix,x); + + /* take care of Inf and NaN */ + if((ix&0x7f800000)==0x7f800000) { + return x*x+x; /* sqrt(NaN)=NaN, sqrt(+inf)=+inf + sqrt(-inf)=sNaN */ + } + /* take care of zero */ + if(ix<=0) { + if((ix&(~sign))==0) return x;/* sqrt(+-0) = +-0 */ + else if(ix<0) + return (x-x)/(x-x); /* sqrt(-ve) = sNaN */ + } + /* normalize x */ + m = (ix>>23); + if(m==0) { /* subnormal x */ + for(i=0;(ix&0x00800000)==0;i++) ix<<=1; + m -= i-1; + } + m -= 127; /* unbias exponent */ + ix = (ix&0x007fffff)|0x00800000; + if(m&1) /* odd m, double x to make it even */ + ix += ix; + m >>= 1; /* m = [m/2] */ + + /* generate sqrt(x) bit by bit */ + ix += ix; + q = s = 0; /* q = sqrt(x) */ + r = 0x01000000; /* r = moving bit from right to left */ + + while(r!=0) { + t = s+r; + if(t<=ix) { + s = t+r; + ix -= t; + q += r; + } + ix += ix; + r>>=1; + } + + /* use floating add to find out rounding direction */ + if(ix!=0) { + z = one-tiny; /* trigger inexact flag */ + if (z>=one) { + z = one+tiny; + if (z>one) + q += 2; + else + q += (q&1); + } + } + ix = (q>>1)+0x3f000000; + ix += (m <<23); + SET_FLOAT_WORD(z,ix); + return z; +} diff --git a/lib/nbsd_libm/src/k_cos.c b/lib/nbsd_libm/src/k_cos.c new file mode 100644 index 000000000..3d5c17536 --- /dev/null +++ b/lib/nbsd_libm/src/k_cos.c @@ -0,0 +1,89 @@ +/* @(#)k_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_cos.c,v 1.11 2002/05/26 22:01:53 wiz Exp $"); +#endif + +/* + * __kernel_cos( x, y ) + * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * + * Algorithm + * 1. Since cos(-x) = cos(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0. + * 3. cos(x) is approximated by a polynomial of degree 14 on + * [0,pi/4] + * 4 14 + * cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x + * where the remez error is + * + * | 2 4 6 8 10 12 14 | -58 + * |cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x +C6*x )| <= 2 + * | | + * + * 4 6 8 10 12 14 + * 4. let r = C1*x +C2*x +C3*x +C4*x +C5*x +C6*x , then + * cos(x) = 1 - x*x/2 + r + * since cos(x+y) ~ cos(x) - sin(x)*y + * ~ cos(x) - x*y, + * a correction term is necessary in cos(x) and hence + * cos(x+y) = 1 - (x*x/2 - (r - x*y)) + * For better accuracy when x > 0.3, let qx = |x|/4 with + * the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125. + * Then + * cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)). + * Note that 1-qx and (x*x/2-qx) is EXACT here, and the + * magnitude of the latter is at least a quarter of x*x/2, + * thus, reducing the rounding error in the subtraction. + */ + +#include "math.h" +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +C1 = 4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */ +C2 = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */ +C3 = 2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */ +C4 = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */ +C5 = 2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */ +C6 = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */ + +double +__kernel_cos(double x, double y) +{ + double a,hz,z,r,qx; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x3e400000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3FD33333) /* if |x| < 0.3 */ + return one - (0.5*z - (z*r - x*y)); + else { + if(ix > 0x3fe90000) { /* x > 0.78125 */ + qx = 0.28125; + } else { + INSERT_WORDS(qx,ix-0x00200000,0); /* x/4 */ + } + hz = 0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/lib/nbsd_libm/src/k_cosf.c b/lib/nbsd_libm/src/k_cosf.c new file mode 100644 index 000000000..5fc6f8c25 --- /dev/null +++ b/lib/nbsd_libm/src/k_cosf.c @@ -0,0 +1,57 @@ +/* k_cosf.c -- float version of k_cos.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_cosf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3f800000 */ +C1 = 4.1666667908e-02, /* 0x3d2aaaab */ +C2 = -1.3888889225e-03, /* 0xbab60b61 */ +C3 = 2.4801587642e-05, /* 0x37d00d01 */ +C4 = -2.7557314297e-07, /* 0xb493f27c */ +C5 = 2.0875723372e-09, /* 0x310f74f6 */ +C6 = -1.1359647598e-11; /* 0xad47d74e */ + +float +__kernel_cosf(float x, float y) +{ + float a,hz,z,r,qx; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* ix = |x|'s high word*/ + if(ix<0x32000000) { /* if x < 2**27 */ + if(((int)x)==0) return one; /* generate inexact */ + } + z = x*x; + r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6))))); + if(ix < 0x3e99999a) /* if |x| < 0.3 */ + return one - ((float)0.5*z - (z*r - x*y)); + else { + if(ix > 0x3f480000) { /* x > 0.78125 */ + qx = (float)0.28125; + } else { + SET_FLOAT_WORD(qx,ix-0x01000000); /* x/4 */ + } + hz = (float)0.5*z-qx; + a = one-qx; + return a - (hz - (z*r-x*y)); + } +} diff --git a/lib/nbsd_libm/src/k_rem_pio2.c b/lib/nbsd_libm/src/k_rem_pio2.c new file mode 100644 index 000000000..f19370d8d --- /dev/null +++ b/lib/nbsd_libm/src/k_rem_pio2.c @@ -0,0 +1,306 @@ +/* @(#)k_rem_pio2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_rem_pio2.c,v 1.12 2010/04/23 19:17:07 drochner Exp $"); +#endif + +/* + * __kernel_rem_pio2(x,y,e0,nx,prec,ipio2) + * double x[],y[]; int e0,nx,prec; int ipio2[]; + * + * __kernel_rem_pio2 return the last three digits of N with + * y = x - N*pi/2 + * so that |y| < pi/2. + * + * The method is to compute the integer (mod 8) and fraction parts of + * (2/pi)*x without doing the full multiplication. In general we + * skip the part of the product that are known to be a huge integer ( + * more accurately, = 0 mod 8 ). Thus the number of operations are + * independent of the exponent of the input. + * + * (2/pi) is represented by an array of 24-bit integers in ipio2[]. + * + * Input parameters: + * x[] The input value (must be positive) is broken into nx + * pieces of 24-bit integers in double precision format. + * x[i] will be the i-th 24 bit of x. The scaled exponent + * of x[0] is given in input parameter e0 (i.e., x[0]*2^e0 + * match x's up to 24 bits. + * + * Example of breaking a double positive z into x[0]+x[1]+x[2]: + * e0 = ilogb(z)-23 + * z = scalbn(z,-e0) + * for i = 0,1,2 + * x[i] = floor(z) + * z = (z-x[i])*2**24 + * + * + * y[] output result in an array of double precision numbers. + * The dimension of y[] is: + * 24-bit precision 1 + * 53-bit precision 2 + * 64-bit precision 2 + * 113-bit precision 3 + * The actual value is the sum of them. Thus for 113-bit + * precison, one may have to do something like: + * + * long double t,w,r_head, r_tail; + * t = (long double)y[2] + (long double)y[1]; + * w = (long double)y[0]; + * r_head = t+w; + * r_tail = w - (r_head - t); + * + * e0 The exponent of x[0] + * + * nx dimension of x[] + * + * prec an integer indicating the precision: + * 0 24 bits (single) + * 1 53 bits (double) + * 2 64 bits (extended) + * 3 113 bits (quad) + * + * ipio2[] + * integer array, contains the (24*i)-th to (24*i+23)-th + * bit of 2/pi after binary point. The corresponding + * floating value is + * + * ipio2[i] * 2^(-24(i+1)). + * + * External function: + * double scalbn(), floor(); + * + * + * Here is the description of some local variables: + * + * jk jk+1 is the initial number of terms of ipio2[] needed + * in the computation. The recommended value is 2,3,4, + * 6 for single, double, extended,and quad. + * + * jz local integer variable indicating the number of + * terms of ipio2[] used. + * + * jx nx - 1 + * + * jv index for pointing to the suitable ipio2[] for the + * computation. In general, we want + * ( 2^e0*x[0] * ipio2[jv-1]*2^(-24jv) )/8 + * is an integer. Thus + * e0-3-24*jv >= 0 or (e0-3)/24 >= jv + * Hence jv = max(0,(e0-3)/24). + * + * jp jp+1 is the number of terms in PIo2[] needed, jp = jk. + * + * q[] double array with integral value, representing the + * 24-bits chunk of the product of x and 2/pi. + * + * q0 the corresponding exponent of q[0]. Note that the + * exponent for q[i] would be q0-24*i. + * + * PIo2[] double precision array, obtained by cutting pi/2 + * into 24 bits chunks. + * + * f[] ipio2[] in floating point + * + * iq[] integer array by breaking up q[] in 24-bits chunk. + * + * fq[] final product of x*(2/pi) in fq[0],..,fq[jk] + * + * ih integer. If >0 it indicates q[] is >= 0.5, hence + * it also indicates the *sign* of the result. + * + */ + + +/* + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +static const int init_jk[] = {2,3,4,6}; /* initial value for jk */ + +static const double PIo2[] = { + 1.57079625129699707031e+00, /* 0x3FF921FB, 0x40000000 */ + 7.54978941586159635335e-08, /* 0x3E74442D, 0x00000000 */ + 5.39030252995776476554e-15, /* 0x3CF84698, 0x80000000 */ + 3.28200341580791294123e-22, /* 0x3B78CC51, 0x60000000 */ + 1.27065575308067607349e-29, /* 0x39F01B83, 0x80000000 */ + 1.22933308981111328932e-36, /* 0x387A2520, 0x40000000 */ + 2.73370053816464559624e-44, /* 0x36E38222, 0x80000000 */ + 2.16741683877804819444e-51, /* 0x3569F31D, 0x00000000 */ +}; + +static const double +zero = 0.0, +one = 1.0, +two24 = 1.67772160000000000000e+07, /* 0x41700000, 0x00000000 */ +twon24 = 5.96046447753906250000e-08; /* 0x3E700000, 0x00000000 */ + +int +__kernel_rem_pio2(double *x, double *y, int e0, int nx, int prec, const int32_t *ipio2) +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + double z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/24; if(jv<0) jv=0; + q0 = e0-24*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (double) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (double)((int32_t)(twon24* z)); + iq[i] = (int32_t)(z-two24*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbn(z,q0); /* actual value of z */ + z -= 8.0*floor(z*0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (double)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(24-q0)); n += i; + iq[jz-1] -= i<<(24-q0); + ih = iq[jz-1]>>(23-q0); + } + else if(q0==0) ih = iq[jz-1]>>23; + else if(z>=0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7fffff; break; + case 2: + iq[jz-1] &= 0x3fffff; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbn(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (double) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==0.0) { + jz -= 1; q0 -= 24; + while(iq[jz]==0) { jz--; q0-=24;} + } else { /* break z into 24-bit if necessary */ + z = scalbn(z,-q0); + if(z>=two24) { + fw = (double)((int32_t)(twon24*z)); + iq[jz] = (int32_t)(z-two24*fw); + jz += 1; q0 += 24; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbn(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(double)iq[i]; fw*=twon24; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/lib/nbsd_libm/src/k_rem_pio2f.c b/lib/nbsd_libm/src/k_rem_pio2f.c new file mode 100644 index 000000000..b5ad2d6eb --- /dev/null +++ b/lib/nbsd_libm/src/k_rem_pio2f.c @@ -0,0 +1,199 @@ +/* k_rem_pio2f.c -- float version of k_rem_pio2.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_rem_pio2f.c,v 1.8 2010/04/23 19:17:07 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +/* In the float version, the input parameter x contains 8 bit + integers, not 24 bit integers. 113 bit precision is not supported. */ + +static const int init_jk[] = {4,7,9}; /* initial value for jk */ + +static const float PIo2[] = { + 1.5703125000e+00, /* 0x3fc90000 */ + 4.5776367188e-04, /* 0x39f00000 */ + 2.5987625122e-05, /* 0x37da0000 */ + 7.5437128544e-08, /* 0x33a20000 */ + 6.0026650317e-11, /* 0x2e840000 */ + 7.3896444519e-13, /* 0x2b500000 */ + 5.3845816694e-15, /* 0x27c20000 */ + 5.6378512969e-18, /* 0x22d00000 */ + 8.3009228831e-20, /* 0x1fc40000 */ + 3.2756352257e-22, /* 0x1bc60000 */ + 6.3331015649e-25, /* 0x17440000 */ +}; + +static const float +zero = 0.0, +one = 1.0, +two8 = 2.5600000000e+02, /* 0x43800000 */ +twon8 = 3.9062500000e-03; /* 0x3b800000 */ + +int +__kernel_rem_pio2f(float *x, float *y, int e0, int nx, int prec, const int32_t *ipio2) +{ + int32_t jz,jx,jv,jp,jk,carry,n,iq[20],i,j,k,m,q0,ih; + float z,fw,f[20],fq[20],q[20]; + + /* initialize jk*/ + jk = init_jk[prec]; + jp = jk; + + /* determine jx,jv,q0, note that 3>q0 */ + jx = nx-1; + jv = (e0-3)/8; if(jv<0) jv=0; + q0 = e0-8*(jv+1); + + /* set up f[0] to f[jx+jk] where f[jx+jk] = ipio2[jv+jk] */ + j = jv-jx; m = jx+jk; + for(i=0;i<=m;i++,j++) f[i] = (j<0)? zero : (float) ipio2[j]; + + /* compute q[0],q[1],...q[jk] */ + for (i=0;i<=jk;i++) { + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; q[i] = fw; + } + + jz = jk; +recompute: + /* distill q[] into iq[] reversingly */ + for(i=0,j=jz,z=q[jz];j>0;i++,j--) { + fw = (float)((int32_t)(twon8* z)); + iq[i] = (int32_t)(z-two8*fw); + z = q[j-1]+fw; + } + + /* compute n */ + z = scalbnf(z,q0); /* actual value of z */ + z -= (float)8.0*floorf(z*(float)0.125); /* trim off integer >= 8 */ + n = (int32_t) z; + z -= (float)n; + ih = 0; + if(q0>0) { /* need iq[jz-1] to determine n */ + i = (iq[jz-1]>>(8-q0)); n += i; + iq[jz-1] -= i<<(8-q0); + ih = iq[jz-1]>>(7-q0); + } + else if(q0==0) ih = iq[jz-1]>>8; + else if(z>=(float)0.5) ih=2; + + if(ih>0) { /* q > 0.5 */ + n += 1; carry = 0; + for(i=0;i0) { /* rare case: chance is 1 in 12 */ + switch(q0) { + case 1: + iq[jz-1] &= 0x7f; break; + case 2: + iq[jz-1] &= 0x3f; break; + } + } + if(ih==2) { + z = one - z; + if(carry!=0) z -= scalbnf(one,q0); + } + } + + /* check if recomputation is needed */ + if(z==zero) { + j = 0; + for (i=jz-1;i>=jk;i--) j |= iq[i]; + if(j==0) { /* need recomputation */ + for(k=1;iq[jk-k]==0;k++); /* k = no. of terms needed */ + + for(i=jz+1;i<=jz+k;i++) { /* add q[jz+1] to q[jz+k] */ + f[jx+i] = (float) ipio2[jv+i]; + for(j=0,fw=0.0;j<=jx;j++) fw += x[j]*f[jx+i-j]; + q[i] = fw; + } + jz += k; + goto recompute; + } + } + + /* chop off zero terms */ + if(z==(float)0.0) { + jz -= 1; q0 -= 8; + while(iq[jz]==0) { jz--; q0-=8;} + } else { /* break z into 8-bit if necessary */ + z = scalbnf(z,-q0); + if(z>=two8) { + fw = (float)((int32_t)(twon8*z)); + iq[jz] = (int32_t)(z-two8*fw); + jz += 1; q0 += 8; + iq[jz] = (int32_t) fw; + } else iq[jz] = (int32_t) z ; + } + + /* convert integer "bit" chunk to floating-point value */ + fw = scalbnf(one,q0); + for(i=jz;i>=0;i--) { + q[i] = fw*(float)iq[i]; fw*=twon8; + } + + /* compute PIo2[0,...,jp]*q[jz,...,0] */ + for(i=jz;i>=0;i--) { + for(fw=0.0,k=0;k<=jp&&k<=jz-i;k++) fw += PIo2[k]*q[i+k]; + fq[jz-i] = fw; + } + + /* compress fq[] into y[] */ + switch(prec) { + case 0: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + break; + case 1: + case 2: + fw = 0.0; + for (i=jz;i>=0;i--) fw += fq[i]; + y[0] = (ih==0)? fw: -fw; + fw = fq[0]-fw; + for (i=1;i<=jz;i++) fw += fq[i]; + y[1] = (ih==0)? fw: -fw; + break; + case 3: /* painful */ + for (i=jz;i>0;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (i=jz;i>1;i--) { + fw = fq[i-1]+fq[i]; + fq[i] += fq[i-1]-fw; + fq[i-1] = fw; + } + for (fw=0.0,i=jz;i>=2;i--) fw += fq[i]; + if(ih==0) { + y[0] = fq[0]; y[1] = fq[1]; y[2] = fw; + } else { + y[0] = -fq[0]; y[1] = -fq[1]; y[2] = -fw; + } + } + return n&7; +} diff --git a/lib/nbsd_libm/src/k_sin.c b/lib/nbsd_libm/src/k_sin.c new file mode 100644 index 000000000..cb229226d --- /dev/null +++ b/lib/nbsd_libm/src/k_sin.c @@ -0,0 +1,72 @@ +/* @(#)k_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_sin.c,v 1.11 2002/05/26 22:01:53 wiz Exp $"); +#endif + +/* __kernel_sin( x, y, iy) + * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). + * + * Algorithm + * 1. Since sin(-x) = -sin(x), we need only to consider positive x. + * 2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0. + * 3. sin(x) is approximated by a polynomial of degree 13 on + * [0,pi/4] + * 3 13 + * sin(x) ~ x + S1*x + ... + S6*x + * where + * + * |sin(x) 2 4 6 8 10 12 | -58 + * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 + * | x | + * + * 4. sin(x+y) = sin(x) + sin'(x')*y + * ~ sin(x) + (1-x*x/2)*y + * For better accuracy, let + * 3 2 2 2 2 + * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) + * then 3 2 + * sin(x) = x + (S1*x + (x *(r-y/2)+y)) + */ + +#include "math.h" +#include "math_private.h" + +static const double +half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ +S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ +S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ +S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ +S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ +S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ + +double +__kernel_sin(double x, double y, int iy) +{ + double z,r,v; + int32_t ix; + GET_HIGH_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x3e400000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/lib/nbsd_libm/src/k_sinf.c b/lib/nbsd_libm/src/k_sinf.c new file mode 100644 index 000000000..906da3b3f --- /dev/null +++ b/lib/nbsd_libm/src/k_sinf.c @@ -0,0 +1,47 @@ +/* k_sinf.c -- float version of k_sin.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_sinf.c,v 1.7 2002/05/26 22:01:53 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +half = 5.0000000000e-01,/* 0x3f000000 */ +S1 = -1.6666667163e-01, /* 0xbe2aaaab */ +S2 = 8.3333337680e-03, /* 0x3c088889 */ +S3 = -1.9841270114e-04, /* 0xb9500d01 */ +S4 = 2.7557314297e-06, /* 0x3638ef1b */ +S5 = -2.5050759689e-08, /* 0xb2d72f34 */ +S6 = 1.5896910177e-10; /* 0x2f2ec9d3 */ + +float +__kernel_sinf(float x, float y, int iy) +{ + float z,r,v; + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high word of x */ + if(ix<0x32000000) /* |x| < 2**-27 */ + {if((int)x==0) return x;} /* generate inexact */ + z = x*x; + v = z*x; + r = S2+z*(S3+z*(S4+z*(S5+z*S6))); + if(iy==0) return x+v*(S1+z*r); + else return x-((z*(half*y-v*r)-y)-v*S1); +} diff --git a/lib/nbsd_libm/src/k_standard.c b/lib/nbsd_libm/src/k_standard.c new file mode 100644 index 000000000..caf4bd2a7 --- /dev/null +++ b/lib/nbsd_libm/src/k_standard.c @@ -0,0 +1,815 @@ +/* @(#)k_standard.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_standard.c,v 1.16 2010/09/01 10:44:28 drochner Exp $"); +#endif + +#include "math.h" +#include "math_private.h" +#include + +#ifndef _USE_WRITE +#include /* fputs(), stderr */ +#define WRITE2(u,v) fputs(u, stderr) +#else /* !defined(_USE_WRITE) */ +#include /* write */ +#define WRITE2(u,v) write(2, u, v) +#undef fflush +#endif /* !defined(_USE_WRITE) */ + +static const double zero = 0.0; /* used as const */ + +/* + * Standard conformance (non-IEEE) on exception cases. + * Mapping: + * 1 -- acos(|x|>1) + * 2 -- asin(|x|>1) + * 3 -- atan2(+-0,+-0) + * 4 -- hypot overflow + * 5 -- cosh overflow + * 6 -- exp overflow + * 7 -- exp underflow + * 8 -- y0(0) + * 9 -- y0(-ve) + * 10-- y1(0) + * 11-- y1(-ve) + * 12-- yn(0) + * 13-- yn(-ve) + * 14-- lgamma(finite) overflow + * 15-- lgamma(-integer) + * 16-- log(0) + * 17-- log(x<0) + * 18-- log10(0) + * 19-- log10(x<0) + * 20-- pow(0.0,0.0) + * 21-- pow(x,y) overflow + * 22-- pow(x,y) underflow + * 23-- pow(0,negative) + * 24-- pow(neg,non-integral) + * 25-- sinh(finite) overflow + * 26-- sqrt(negative) + * 27-- fmod(x,0) + * 28-- remainder(x,0) + * 29-- acosh(x<1) + * 30-- atanh(|x|>1) + * 31-- atanh(|x|=1) + * 32-- scalb overflow + * 33-- scalb underflow + * 34-- j0(|x|>X_TLOSS) + * 35-- y0(x>X_TLOSS) + * 36-- j1(|x|>X_TLOSS) + * 37-- y1(x>X_TLOSS) + * 38-- jn(|x|>X_TLOSS, n) + * 39-- yn(x>X_TLOSS, n) + * 40-- gamma(finite) overflow + * 41-- gamma(-integer) + * 42-- pow(NaN,0.0) + * 48-- log2(0) + * 49-- log2(x<0) + */ + + +double +__kernel_standard(double x, double y, int type) +{ + struct exception exc; +#ifndef HUGE_VAL /* this is the only routine that uses HUGE_VAL */ +#define HUGE_VAL inf + double inf = 0.0; + + SET_HIGH_WORD(inf,0x7ff00000); /* set inf to infinite */ +#endif + +#ifdef _USE_WRITE + (void) fflush(stdout); +#endif + exc.arg1 = x; + exc.arg2 = y; + switch(type) { + case 1: + case 101: + /* acos(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acos" : "acosf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) { + exc.retval = zero/zero; + errno = EDOM; + } else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("acos: DOMAIN error\n", 19); + } + errno = EDOM; + } + break; + case 2: + case 102: + /* asin(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "asin" : "asinf"; + exc.retval = zero; + if(_LIB_VERSION == _POSIX_) { + exc.retval = zero/zero; + errno = EDOM; + } else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("asin: DOMAIN error\n", 19); + } + errno = EDOM; + } + break; + case 3: + case 103: + /* atan2(+-0,+-0) */ + exc.arg1 = y; + exc.arg2 = x; + exc.type = DOMAIN; + exc.name = type < 100 ? "atan2" : "atan2f"; + exc.retval = zero; + if(_LIB_VERSION == _POSIX_) { + exc.retval = copysign(signbit(y) ? M_PI : zero, x); + } else if (!matherr(&exc)) { + if(_LIB_VERSION == _SVID_) { + (void) WRITE2("atan2: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 4: + case 104: + /* hypot(finite,finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "hypot" : "hypotf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 5: + case 105: + /* cosh(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "cosh" : "coshf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 6: + case 106: + /* exp(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "exp" : "expf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 7: + case 107: + /* exp(finite) underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "exp" : "expf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 8: + case 108: + /* y0(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y0" : "y0f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 9: + case 109: + /* y0(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y0" : "y0f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y0: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 10: + case 110: + /* y1(0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "y1" : "y1f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 11: + case 111: + /* y1(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "y1" : "y1f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("y1: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 12: + case 112: + /* yn(n,0) = -inf */ + exc.type = DOMAIN; /* should be SING for IEEE */ + exc.name = type < 100 ? "yn" : "ynf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 13: + case 113: + /* yn(x<0) = NaN */ + exc.type = DOMAIN; + exc.name = type < 100 ? "yn" : "ynf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("yn: DOMAIN error\n", 17); + } + errno = EDOM; + } + break; + case 14: + case 114: + /* lgamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "lgamma" : "lgammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 15: + case 115: + /* lgamma(-integer) or lgamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "lgamma" : "lgammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("lgamma: SING error\n", 19); + } + errno = EDOM; + } + break; + case 16: + case 116: + /* log(0) */ + exc.type = SING; + exc.name = type < 100 ? "log" : "logf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: SING error\n", 16); + } + errno = EDOM; + } + break; + case 17: + case 117: + /* log(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log" : "logf"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log: DOMAIN error\n", 18); + } + errno = EDOM; + } + break; + case 18: + case 118: + /* log10(0) */ + exc.type = SING; + exc.name = type < 100 ? "log10" : "log10f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: SING error\n", 18); + } + errno = EDOM; + } + break; + case 19: + case 119: + /* log10(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log10" : "log10f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log10: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 20: + case 120: + /* pow(0.0,0.0) */ + /* error only if _LIB_VERSION == _SVID_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + exc.retval = zero; + if (_LIB_VERSION != _SVID_) exc.retval = 1.0; + else if (!matherr(&exc)) { + (void) WRITE2("pow(0,0): DOMAIN error\n", 23); + errno = EDOM; + } + break; + case 21: + case 121: + /* pow(x,y) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "pow" : "powf"; + if (_LIB_VERSION == _SVID_) { + exc.retval = HUGE; + y *= 0.5; + if(xzero) ? HUGE : -HUGE); + else + exc.retval = ( (x>zero) ? HUGE_VAL : -HUGE_VAL); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 26: + case 126: + /* sqrt(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "sqrt" : "sqrtf"; + if (_LIB_VERSION == _SVID_) + exc.retval = zero; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("sqrt: DOMAIN error\n", 19); + } + errno = EDOM; + } + break; + case 27: + case 127: + /* fmod(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "fmod" : "fmodf"; + if (_LIB_VERSION == _SVID_) + exc.retval = x; + else + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("fmod: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 28: + case 128: + /* remainder(x,0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "remainder" : "remainderf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("remainder: DOMAIN error\n", 24); + } + errno = EDOM; + } + break; + case 29: + case 129: + /* acosh(x<1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "acosh" : "acoshf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("acosh: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 30: + case 130: + /* atanh(|x|>1) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "atanh" : "atanhf"; + exc.retval = zero/zero; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + case 31: + case 131: + /* atanh(|x|=1) */ + exc.type = SING; + exc.name = type < 100 ? "atanh" : "atanhf"; + exc.retval = x/zero; /* sign(x)*inf */ + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("atanh: SING error\n", 18); + } + errno = EDOM; + } + break; + case 32: + case 132: + /* scalb overflow; SVID also returns +-HUGE_VAL */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "scalb" : "scalbf"; + exc.retval = x > zero ? HUGE_VAL : -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 33: + case 133: + /* scalb underflow */ + exc.type = UNDERFLOW; + exc.name = type < 100 ? "scalb" : "scalbf"; + exc.retval = copysign(zero,x); + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 34: + case 134: + /* j0(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j0" : "j0f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 35: + case 135: + /* y0(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y0" : "y0f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 36: + case 136: + /* j1(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "j1" : "j1f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 37: + case 137: + /* y1(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "y1" : "y1f"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 38: + case 138: + /* jn(|x|>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "jn" : "jnf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 39: + case 139: + /* yn(x>X_TLOSS) */ + exc.type = TLOSS; + exc.name = type < 100 ? "yn" : "ynf"; + exc.retval = zero; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2(exc.name, 2); + (void) WRITE2(": TLOSS error\n", 14); + } + errno = ERANGE; + } + break; + case 40: + case 140: + /* gamma(finite) overflow */ + exc.type = OVERFLOW; + exc.name = type < 100 ? "gamma" : "gammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + errno = ERANGE; + } + break; + case 41: + case 141: + /* gamma(-integer) or gamma(0) */ + exc.type = SING; + exc.name = type < 100 ? "gamma" : "gammaf"; + if (_LIB_VERSION == _SVID_) + exc.retval = HUGE; + else + exc.retval = HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("gamma: SING error\n", 18); + } + errno = EDOM; + } + break; + case 42: + case 142: + /* pow(NaN,0.0) */ + /* error only if _LIB_VERSION == _SVID_ & _XOPEN_ */ + exc.type = DOMAIN; + exc.name = type < 100 ? "pow" : "powf"; + exc.retval = x; + if (_LIB_VERSION == _IEEE_ || + _LIB_VERSION == _POSIX_) exc.retval = 1.0; + else if (!matherr(&exc)) { + errno = EDOM; + } + break; + case 48: + case 148: + /* log2(0) */ + exc.type = SING; + exc.name = type < 100 ? "log2" : "log2f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = ERANGE; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log2: SING error\n", 18); + } + errno = EDOM; + } + break; + case 49: + case 149: + /* log2(x<0) */ + exc.type = DOMAIN; + exc.name = type < 100 ? "log2" : "log2f"; + if (_LIB_VERSION == _SVID_) + exc.retval = -HUGE; + else + exc.retval = -HUGE_VAL; + if (_LIB_VERSION == _POSIX_) + errno = EDOM; + else if (!matherr(&exc)) { + if (_LIB_VERSION == _SVID_) { + (void) WRITE2("log2: DOMAIN error\n", 20); + } + errno = EDOM; + } + break; + } + return exc.retval; +} diff --git a/lib/nbsd_libm/src/k_tan.c b/lib/nbsd_libm/src/k_tan.c new file mode 100644 index 000000000..5bed57a80 --- /dev/null +++ b/lib/nbsd_libm/src/k_tan.c @@ -0,0 +1,156 @@ +/* @(#)k_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_tan.c,v 1.12 2004/07/22 18:24:09 drochner Exp $"); +#endif + +/* __kernel_tan( x, y, k ) + * kernel tan function on [-pi/4, pi/4], pi/4 ~ 0.7854 + * Input x is assumed to be bounded by ~pi/4 in magnitude. + * Input y is the tail of x. + * Input k indicates whether tan (if k=1) or + * -1/tan (if k= -1) is returned. + * + * Algorithm + * 1. Since tan(-x) = -tan(x), we need only to consider positive x. + * 2. if x < 2^-28 (hx<0x3e300000 0), return x with inexact if x!=0. + * 3. tan(x) is approximated by a odd polynomial of degree 27 on + * [0,0.67434] + * 3 27 + * tan(x) ~ x + T1*x + ... + T13*x + * where + * + * |tan(x) 2 4 26 | -59.2 + * |----- - (1+T1*x +T2*x +.... +T13*x )| <= 2 + * | x | + * + * Note: tan(x+y) = tan(x) + tan'(x)*y + * ~ tan(x) + (1+x*x)*y + * Therefore, for better accuracy in computing tan(x+y), let + * 3 2 2 2 2 + * r = x *(T2+x *(T3+x *(...+x *(T12+x *T13)))) + * then + * 3 2 + * tan(x+y) = x + (T1*x + (x *(r+y)+y)) + * + * 4. For x in [0.67434,pi/4], let y = pi/4 - x, then + * tan(x) = tan(pi/4-y) = (1-tan(y))/(1+tan(y)) + * = 1 - 2*(tan(y) - (tan(y)^2)/(1+tan(y))) + */ + +#include "math.h" +#include "math_private.h" + +static const double xxx[] = { + 3.33333333333334091986e-01, /* 3FD55555, 55555563 */ + 1.33333333333201242699e-01, /* 3FC11111, 1110FE7A */ + 5.39682539762260521377e-02, /* 3FABA1BA, 1BB341FE */ + 2.18694882948595424599e-02, /* 3F9664F4, 8406D637 */ + 8.86323982359930005737e-03, /* 3F8226E3, E96E8493 */ + 3.59207910759131235356e-03, /* 3F6D6D22, C9560328 */ + 1.45620945432529025516e-03, /* 3F57DBC8, FEE08315 */ + 5.88041240820264096874e-04, /* 3F4344D8, F2F26501 */ + 2.46463134818469906812e-04, /* 3F3026F7, 1A8D1068 */ + 7.81794442939557092300e-05, /* 3F147E88, A03792A6 */ + 7.14072491382608190305e-05, /* 3F12B80F, 32F0A7E9 */ + -1.85586374855275456654e-05, /* BEF375CB, DB605373 */ + 2.59073051863633712884e-05, /* 3EFB2A70, 74BF7AD4 */ +/* one */ 1.00000000000000000000e+00, /* 3FF00000, 00000000 */ +/* pio4 */ 7.85398163397448278999e-01, /* 3FE921FB, 54442D18 */ +/* pio4lo */ 3.06161699786838301793e-17 /* 3C81A626, 33145C07 */ +}; +#define one xxx[13] +#define pio4 xxx[14] +#define pio4lo xxx[15] +#define T xxx + +double +__kernel_tan(double x, double y, int iy) +{ + double z, r, v, w, s; + int32_t ix, hx; + + GET_HIGH_WORD(hx, x); /* high word of x */ + ix = hx & 0x7fffffff; /* high word of |x| */ + if (ix < 0x3e300000) { /* x < 2**-28 */ + if ((int) x == 0) { /* generate inexact */ + u_int32_t low; + GET_LOW_WORD(low, x); + if(((ix | low) | (iy + 1)) == 0) + return one / fabs(x); + else { + if (iy == 1) + return x; + else { /* compute -1 / (x+y) carefully */ + double a, t; + + z = w = x + y; + SET_LOW_WORD(z, 0); + v = y - (z - x); + t = a = -one / w; + SET_LOW_WORD(t, 0); + s = one + t * z; + return t + a * (s + t * v); + } + } + } + } + if (ix >= 0x3FE59428) { /* |x| >= 0.6744 */ + if (hx < 0) { + x = -x; + y = -y; + } + z = pio4 - x; + w = pio4lo - y; + x = z + w; + y = 0.0; + } + z = x * x; + w = z * z; + /* + * Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1] + w * (T[3] + w * (T[5] + w * (T[7] + w * (T[9] + + w * T[11])))); + v = z * (T[2] + w * (T[4] + w * (T[6] + w * (T[8] + w * (T[10] + + w * T[12]))))); + s = z * x; + r = y + z * (s * (r + v) + y); + r += T[0] * s; + w = x + r; + if (ix >= 0x3FE59428) { + v = (double) iy; + return (double) (1 - ((hx >> 30) & 2)) * + (v - 2.0 * (x - (w * w / (w + v) - r))); + } + if (iy == 1) + return w; + else { + /* + * if allow error up to 2 ulp, simply return + * -1.0 / (x+r) here + */ + /* compute -1.0 / (x+r) accurately */ + double a, t; + z = w; + SET_LOW_WORD(z, 0); + v = r - (z - x); /* z+v = r+x */ + t = a = -1.0 / w; /* a = -1.0/w */ + SET_LOW_WORD(t, 0); + s = 1.0 + t * z; + return t + a * (s + t * v); + } +} diff --git a/lib/nbsd_libm/src/k_tanf.c b/lib/nbsd_libm/src/k_tanf.c new file mode 100644 index 000000000..a3703a409 --- /dev/null +++ b/lib/nbsd_libm/src/k_tanf.c @@ -0,0 +1,94 @@ +/* k_tanf.c -- float version of k_tan.c + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: k_tanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" +static const float +one = 1.0000000000e+00, /* 0x3f800000 */ +pio4 = 7.8539812565e-01, /* 0x3f490fda */ +pio4lo= 3.7748947079e-08, /* 0x33222168 */ +T[] = { + 3.3333334327e-01, /* 0x3eaaaaab */ + 1.3333334029e-01, /* 0x3e088889 */ + 5.3968254477e-02, /* 0x3d5d0dd1 */ + 2.1869488060e-02, /* 0x3cb327a4 */ + 8.8632395491e-03, /* 0x3c11371f */ + 3.5920790397e-03, /* 0x3b6b6916 */ + 1.4562094584e-03, /* 0x3abede48 */ + 5.8804126456e-04, /* 0x3a1a26c8 */ + 2.4646313977e-04, /* 0x398137b9 */ + 7.8179444245e-05, /* 0x38a3f445 */ + 7.1407252108e-05, /* 0x3895c07a */ + -1.8558637748e-05, /* 0xb79bae5f */ + 2.5907305826e-05, /* 0x37d95384 */ +}; + +float +__kernel_tanf(float x, float y, int iy) +{ + float z,r,v,w,s; + int32_t ix,hx; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; /* high word of |x| */ + if(ix<0x31800000) /* x < 2**-28 */ + {if((int)x==0) { /* generate inexact */ + if((ix|(iy+1))==0) return one/fabsf(x); + else return (iy==1)? x: -one/x; + } + } + if(ix>=0x3f2ca140) { /* |x|>=0.6744 */ + if(hx<0) {x = -x; y = -y;} + z = pio4-x; + w = pio4lo-y; + x = z+w; y = 0.0; + } + z = x*x; + w = z*z; + /* Break x^5*(T[1]+x^2*T[2]+...) into + * x^5(T[1]+x^4*T[3]+...+x^20*T[11]) + + * x^5(x^2*(T[2]+x^4*T[4]+...+x^22*[T12])) + */ + r = T[1]+w*(T[3]+w*(T[5]+w*(T[7]+w*(T[9]+w*T[11])))); + v = z*(T[2]+w*(T[4]+w*(T[6]+w*(T[8]+w*(T[10]+w*T[12]))))); + s = z*x; + r = y + z*(s*(r+v)+y); + r += T[0]*s; + w = x+r; + if(ix>=0x3f2ca140) { + v = (float)iy; + return (float)(1-((hx>>30)&2))*(v-(float)2.0*(x-(w*w/(w+v)-r))); + } + if(iy==1) return w; + else { /* if allow error up to 2 ulp, + simply return -1.0/(x+r) here */ + /* compute -1.0/(x+r) accurately */ + float a,t; + int32_t i; + z = w; + GET_FLOAT_WORD(i,z); + SET_FLOAT_WORD(z,i&0xfffff000); + v = r-(z - x); /* z+v = r+x */ + t = a = -(float)1.0/w; /* a = -1.0/w */ + GET_FLOAT_WORD(i,t); + SET_FLOAT_WORD(t,i&0xfffff000); + s = (float)1.0+t*z; + return t+a*(s+t*v); + } +} diff --git a/lib/nbsd_libm/src/llrint.c b/lib/nbsd_libm/src/llrint.c new file mode 100644 index 000000000..dba6ae90b --- /dev/null +++ b/lib/nbsd_libm/src/llrint.c @@ -0,0 +1,13 @@ +/* $NetBSD: llrint.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#define LRINTNAME llrint +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lrint.c" diff --git a/lib/nbsd_libm/src/llrintf.c b/lib/nbsd_libm/src/llrintf.c new file mode 100644 index 000000000..6a16426ca --- /dev/null +++ b/lib/nbsd_libm/src/llrintf.c @@ -0,0 +1,13 @@ +/* $NetBSD: llrintf.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#define LRINTNAME llrintf +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lrintf.c" diff --git a/lib/nbsd_libm/src/llround.c b/lib/nbsd_libm/src/llround.c new file mode 100644 index 000000000..4dc34a48e --- /dev/null +++ b/lib/nbsd_libm/src/llround.c @@ -0,0 +1,13 @@ +/* $NetBSD: llround.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#define LROUNDNAME llround +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lround.c" diff --git a/lib/nbsd_libm/src/llroundf.c b/lib/nbsd_libm/src/llroundf.c new file mode 100644 index 000000000..bc9dd430b --- /dev/null +++ b/lib/nbsd_libm/src/llroundf.c @@ -0,0 +1,13 @@ +/* $NetBSD: llroundf.c,v 1.2 2004/10/13 15:18:32 drochner Exp $ */ + +/* + * Written by Matthias Drochner . + * Public domain. + */ + +#define LROUNDNAME llroundf +#define RESTYPE long long int +#define RESTYPE_MIN LLONG_MIN +#define RESTYPE_MAX LLONG_MAX + +#include "lroundf.c" diff --git a/lib/nbsd_libm/src/lrint.c b/lib/nbsd_libm/src/lrint.c new file mode 100644 index 000000000..9b8113261 --- /dev/null +++ b/lib/nbsd_libm/src/lrint.c @@ -0,0 +1,92 @@ +/* $NetBSD: lrint.c,v 1.4 2008/04/26 23:49:50 christos Exp $ */ + +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LRINTNAME +#define LRINTNAME lrint +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +RESTYPE +LRINTNAME(double x) +{ + u_int32_t i0, i1; + int e, s, shift; + RESTYPE res; + + GET_HIGH_WORD(i0, x); + e = i0 >> 20; + s = (uint32_t)e >> DBL_EXPBITS; + e = (e & 0x7ff) - DBL_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^52 is already an exact integer */ + if (e < DBL_FRACBITS) { + /* round, using current direction */ + x += TWO52[s]; + x -= TWO52[s]; + } + + EXTRACT_WORDS(i0, i1, x); + e = ((i0 >> 20) & 0x7ff) - DBL_EXP_BIAS; + i0 &= 0xfffff; + i0 |= (1 << 20); + + shift = e - DBL_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i1 << shift : 0); + else + res = (shift > -32 ? i1 >> -shift : 0); + shift += 32; + if (shift >=0) + res |= (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res |= (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/nbsd_libm/src/lrintf.c b/lib/nbsd_libm/src/lrintf.c new file mode 100644 index 000000000..929854cbf --- /dev/null +++ b/lib/nbsd_libm/src/lrintf.c @@ -0,0 +1,91 @@ +/* $NetBSD: lrintf.c,v 1.5 2008/04/26 23:49:50 christos Exp $ */ + +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LRINTNAME +#define LRINTNAME lrintf +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +RESTYPE +LRINTNAME(float x) +{ + u_int32_t i0; + int e, s, shift; + RESTYPE res; +#ifdef __i386__ /* XXX gcc4 will omit the rounding otherwise */ + volatile +#endif + float w; + + GET_FLOAT_WORD(i0, x); + e = i0 >> SNG_FRACBITS; + s = (uint32_t)e >> SNG_EXPBITS; + e = (e & 0xff) - SNG_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^23 is already an exact integer */ + if (e < SNG_FRACBITS) { + /* round, using current direction */ + w = TWO23[s] + x; + x = w - TWO23[s]; + } + + GET_FLOAT_WORD(i0, x); + e = ((i0 >> SNG_FRACBITS) & 0xff) - SNG_EXP_BIAS; + i0 &= 0x7fffff; + i0 |= (1 << SNG_FRACBITS); + + shift = e - SNG_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res = (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/nbsd_libm/src/lround.c b/lib/nbsd_libm/src/lround.c new file mode 100644 index 000000000..ab7194418 --- /dev/null +++ b/lib/nbsd_libm/src/lround.c @@ -0,0 +1,85 @@ +/* $NetBSD: lround.c,v 1.3 2008/04/26 23:49:50 christos Exp $ */ + +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LROUNDNAME +#define LROUNDNAME lround +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +RESTYPE +LROUNDNAME(double x) +{ + u_int32_t i0, i1; + int e, s, shift; + RESTYPE res; + + GET_HIGH_WORD(i0, x); + e = i0 >> 20; + s = (uint32_t)e >> DBL_EXPBITS; + e = (e & 0x7ff) - DBL_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^52 is already an exact integer */ + if (e < DBL_FRACBITS) { + /* add 0.5, extraction below will truncate */ + x += (s ? -0.5 : 0.5); + } + + EXTRACT_WORDS(i0, i1, x); + e = ((i0 >> 20) & 0x7ff) - DBL_EXP_BIAS; + i0 &= 0xfffff; + i0 |= (1 << 20); + + shift = e - DBL_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i1 << shift : 0); + else + res = (shift > -32 ? i1 >> -shift : 0); + shift += 32; + if (shift >=0) + res |= (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res |= (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/nbsd_libm/src/lroundf.c b/lib/nbsd_libm/src/lroundf.c new file mode 100644 index 000000000..75fb0299e --- /dev/null +++ b/lib/nbsd_libm/src/lroundf.c @@ -0,0 +1,80 @@ +/* $NetBSD: lroundf.c,v 1.3 2008/04/26 23:49:50 christos Exp $ */ + +/*- + * Copyright (c) 2004 + * Matthias Drochner. All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +#include +#include +#include "math_private.h" + +#ifndef LROUNDNAME +#define LROUNDNAME lroundf +#define RESTYPE long int +#define RESTYPE_MIN LONG_MIN +#define RESTYPE_MAX LONG_MAX +#endif + +#define RESTYPE_BITS (sizeof(RESTYPE) * 8) + +RESTYPE +LROUNDNAME(float x) +{ + u_int32_t i0; + int e, s, shift; + RESTYPE res; + + GET_FLOAT_WORD(i0, x); + e = i0 >> SNG_FRACBITS; + s = (uint32_t)e >> SNG_EXPBITS; + e = (e & 0xff) - SNG_EXP_BIAS; + + /* 1.0 x 2^-1 is the smallest number which can be rounded to 1 */ + if (e < -1) + return (0); + /* 1.0 x 2^31 (or 2^63) is already too large */ + if (e >= (int)RESTYPE_BITS - 1) + return (s ? RESTYPE_MIN : RESTYPE_MAX); /* ??? unspecified */ + + /* >= 2^23 is already an exact integer */ + if (e < SNG_FRACBITS) { + /* add 0.5, extraction below will truncate */ + x += (s ? -0.5 : 0.5); + } + + GET_FLOAT_WORD(i0, x); + e = ((i0 >> SNG_FRACBITS) & 0xff) - SNG_EXP_BIAS; + i0 &= 0x7fffff; + i0 |= (1 << SNG_FRACBITS); + + shift = e - SNG_FRACBITS; + if (shift >=0) + res = (shift < 32 ? (RESTYPE)i0 << shift : 0); + else + res = (shift > -32 ? i0 >> -shift : 0); + + return (s ? -res : res); +} diff --git a/lib/nbsd_libm/src/math_private.h b/lib/nbsd_libm/src/math_private.h new file mode 100644 index 000000000..684f81adb --- /dev/null +++ b/lib/nbsd_libm/src/math_private.h @@ -0,0 +1,278 @@ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +/* + * from: @(#)fdlibm.h 5.1 93/09/24 + * $NetBSD: math_private.h,v 1.16 2010/09/16 20:39:50 drochner Exp $ + */ + +#ifndef _MATH_PRIVATE_H_ +#define _MATH_PRIVATE_H_ + +#include + +/* The original fdlibm code used statements like: + n0 = ((*(int*)&one)>>29)^1; * index of high word * + ix0 = *(n0+(int*)&x); * high word of x * + ix1 = *((1-n0)+(int*)&x); * low word of x * + to dig two 32 bit words out of the 64 bit IEEE floating point + value. That is non-ANSI, and, moreover, the gcc instruction + scheduler gets it wrong. We instead use the following macros. + Unlike the original code, we determine the endianness at compile + time, not at run time; I don't see much benefit to selecting + endianness at run time. */ + +/* A union which permits us to convert between a double and two 32 bit + ints. */ + +/* + * The ARM ports are little endian except for the FPA word order which is + * big endian. + */ + +#if (BYTE_ORDER == BIG_ENDIAN) || (defined(__arm__) && !defined(__VFP_FP__)) + +typedef union +{ + double value; + struct + { + u_int32_t msw; + u_int32_t lsw; + } parts; +} ieee_double_shape_type; + +#endif + +#if (BYTE_ORDER == LITTLE_ENDIAN) && \ + !(defined(__arm__) && !defined(__VFP_FP__)) + +typedef union +{ + double value; + struct + { + u_int32_t lsw; + u_int32_t msw; + } parts; +} ieee_double_shape_type; + +#endif + +/* Get two 32 bit ints from a double. */ + +#define EXTRACT_WORDS(ix0,ix1,d) \ +do { \ + ieee_double_shape_type ew_u; \ + ew_u.value = (d); \ + (ix0) = ew_u.parts.msw; \ + (ix1) = ew_u.parts.lsw; \ +} while (/*CONSTCOND*/0) + +/* Get the more significant 32 bit int from a double. */ + +#define GET_HIGH_WORD(i,d) \ +do { \ + ieee_double_shape_type gh_u; \ + gh_u.value = (d); \ + (i) = gh_u.parts.msw; \ +} while (/*CONSTCOND*/0) + +/* Get the less significant 32 bit int from a double. */ + +#define GET_LOW_WORD(i,d) \ +do { \ + ieee_double_shape_type gl_u; \ + gl_u.value = (d); \ + (i) = gl_u.parts.lsw; \ +} while (/*CONSTCOND*/0) + +/* Set a double from two 32 bit ints. */ + +#define INSERT_WORDS(d,ix0,ix1) \ +do { \ + ieee_double_shape_type iw_u; \ + iw_u.parts.msw = (ix0); \ + iw_u.parts.lsw = (ix1); \ + (d) = iw_u.value; \ +} while (/*CONSTCOND*/0) + +/* Set the more significant 32 bits of a double from an int. */ + +#define SET_HIGH_WORD(d,v) \ +do { \ + ieee_double_shape_type sh_u; \ + sh_u.value = (d); \ + sh_u.parts.msw = (v); \ + (d) = sh_u.value; \ +} while (/*CONSTCOND*/0) + +/* Set the less significant 32 bits of a double from an int. */ + +#define SET_LOW_WORD(d,v) \ +do { \ + ieee_double_shape_type sl_u; \ + sl_u.value = (d); \ + sl_u.parts.lsw = (v); \ + (d) = sl_u.value; \ +} while (/*CONSTCOND*/0) + +/* A union which permits us to convert between a float and a 32 bit + int. */ + +typedef union +{ + float value; + u_int32_t word; +} ieee_float_shape_type; + +/* Get a 32 bit int from a float. */ + +#define GET_FLOAT_WORD(i,d) \ +do { \ + ieee_float_shape_type gf_u; \ + gf_u.value = (d); \ + (i) = gf_u.word; \ +} while (/*CONSTCOND*/0) + +/* Set a float from a 32 bit int. */ + +#define SET_FLOAT_WORD(d,i) \ +do { \ + ieee_float_shape_type sf_u; \ + sf_u.word = (i); \ + (d) = sf_u.value; \ +} while (/*CONSTCOND*/0) + +/* + * Attempt to get strict C99 semantics for assignment with non-C99 compilers. + */ +#if FLT_EVAL_METHOD == 0 || __GNUC__ == 0 +#define STRICT_ASSIGN(type, lval, rval) ((lval) = (rval)) +#else +#define STRICT_ASSIGN(type, lval, rval) do { \ + volatile type __lval; \ + \ + if (sizeof(type) >= sizeof(double)) \ + (lval) = (rval); \ + else { \ + __lval = (rval); \ + (lval) = __lval; \ + } \ +} while (/*CONSTCOND*/0) +#endif + +#ifdef _COMPLEX_H + +/* + * Quoting from ISO/IEC 9899:TC2: + * + * 6.2.5.13 Types + * Each complex type has the same representation and alignment requirements as + * an array type containing exactly two elements of the corresponding real type; + * the first element is equal to the real part, and the second element to the + * imaginary part, of the complex number. + */ +typedef union { + float complex z; + float parts[2]; +} float_complex; + +typedef union { + double complex z; + double parts[2]; +} double_complex; + +typedef union { + long double complex z; + long double parts[2]; +} long_double_complex; + +#define REAL_PART(z) ((z).parts[0]) +#define IMAG_PART(z) ((z).parts[1]) + +#endif /* _COMPLEX_H */ + +/* ieee style elementary functions */ +extern double __ieee754_sqrt __P((double)); +extern double __ieee754_acos __P((double)); +extern double __ieee754_acosh __P((double)); +extern double __ieee754_log __P((double)); +extern double __ieee754_atanh __P((double)); +extern double __ieee754_asin __P((double)); +extern double __ieee754_atan2 __P((double,double)); +extern double __ieee754_exp __P((double)); +extern double __ieee754_cosh __P((double)); +extern double __ieee754_fmod __P((double,double)); +extern double __ieee754_pow __P((double,double)); +extern double __ieee754_lgamma_r __P((double,int *)); +extern double __ieee754_gamma_r __P((double,int *)); +extern double __ieee754_lgamma __P((double)); +extern double __ieee754_gamma __P((double)); +extern double __ieee754_log10 __P((double)); +extern double __ieee754_log2 __P((double)); +extern double __ieee754_sinh __P((double)); +extern double __ieee754_hypot __P((double,double)); +extern double __ieee754_j0 __P((double)); +extern double __ieee754_j1 __P((double)); +extern double __ieee754_y0 __P((double)); +extern double __ieee754_y1 __P((double)); +extern double __ieee754_jn __P((int,double)); +extern double __ieee754_yn __P((int,double)); +extern double __ieee754_remainder __P((double,double)); +extern int __ieee754_rem_pio2 __P((double,double*)); +extern double __ieee754_scalb __P((double,double)); + +/* fdlibm kernel function */ +extern double __kernel_standard __P((double,double,int)); +extern double __kernel_sin __P((double,double,int)); +extern double __kernel_cos __P((double,double)); +extern double __kernel_tan __P((double,double,int)); +extern int __kernel_rem_pio2 __P((double*,double*,int,int,int,const int*)); + + +/* ieee style elementary float functions */ +extern float __ieee754_sqrtf __P((float)); +extern float __ieee754_acosf __P((float)); +extern float __ieee754_acoshf __P((float)); +extern float __ieee754_logf __P((float)); +extern float __ieee754_atanhf __P((float)); +extern float __ieee754_asinf __P((float)); +extern float __ieee754_atan2f __P((float,float)); +extern float __ieee754_expf __P((float)); +extern float __ieee754_coshf __P((float)); +extern float __ieee754_fmodf __P((float,float)); +extern float __ieee754_powf __P((float,float)); +extern float __ieee754_lgammaf_r __P((float,int *)); +extern float __ieee754_gammaf_r __P((float,int *)); +extern float __ieee754_lgammaf __P((float)); +extern float __ieee754_gammaf __P((float)); +extern float __ieee754_log10f __P((float)); +extern float __ieee754_log2f __P((float)); +extern float __ieee754_sinhf __P((float)); +extern float __ieee754_hypotf __P((float,float)); +extern float __ieee754_j0f __P((float)); +extern float __ieee754_j1f __P((float)); +extern float __ieee754_y0f __P((float)); +extern float __ieee754_y1f __P((float)); +extern float __ieee754_jnf __P((int,float)); +extern float __ieee754_ynf __P((int,float)); +extern float __ieee754_remainderf __P((float,float)); +extern int __ieee754_rem_pio2f __P((float,float*)); +extern float __ieee754_scalbf __P((float,float)); + +/* float versions of fdlibm kernel functions */ +extern float __kernel_sinf __P((float,float,int)); +extern float __kernel_cosf __P((float,float)); +extern float __kernel_tanf __P((float,float,int)); +extern int __kernel_rem_pio2f __P((float*,float*,int,int,int,const int*)); + +#endif /* _MATH_PRIVATE_H_ */ diff --git a/lib/nbsd_libm/src/namespace.h b/lib/nbsd_libm/src/namespace.h new file mode 100644 index 000000000..a2d39e479 --- /dev/null +++ b/lib/nbsd_libm/src/namespace.h @@ -0,0 +1,34 @@ +/* $NetBSD: namespace.h,v 1.3 2010/04/23 19:17:07 drochner Exp $ */ + +#define atan2 _atan2 +#define atan2f _atan2f +#define hypot _hypot +#define hypotf _hypotf + +#define exp _exp +#define expf _expf +#define log _log +#define logf _logf + +#if 0 /* not yet - need to review use in machdep code first */ +#define sin _sin +#define sinf _sinf +#define cos _cos +#define cosf _cosf +#define finite _finite +#define finitef _finitef +#endif /* notyet */ +#define sinh _sinh +#define sinhf _sinhf +#define cosh _cosh +#define coshf _coshf +#define asin _asin +#define asinf _asinf + +#define casin _casin +#define casinf _casinf +#define catan _catan +#define catanf _catanf + +#define scalbn _scalbn +#define scalbnf _scalbnf diff --git a/lib/nbsd_libm/src/s_asinh.c b/lib/nbsd_libm/src/s_asinh.c new file mode 100644 index 000000000..01ef74c5d --- /dev/null +++ b/lib/nbsd_libm/src/s_asinh.c @@ -0,0 +1,58 @@ +/* @(#)s_asinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_asinh.c,v 1.12 2002/05/26 22:01:54 wiz Exp $"); +#endif + +/* asinh(x) + * Method : + * Based on + * asinh(x) = sign(x) * log [ |x| + sqrt(x*x+1) ] + * we have + * asinh(x) := x if 1+x*x=1, + * := sign(x)*(log(x)+ln2)) for large |x|, else + * := sign(x)*log(2|x|+1/(|x|+sqrt(x*x+1))) if|x|>2, else + * := sign(x)*log1p(|x| + x^2/(1 + sqrt(1+x^2))) + */ + +#include "math.h" +#include "math_private.h" + +static const double +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +ln2 = 6.93147180559945286227e-01, /* 0x3FE62E42, 0xFEFA39EF */ +huge= 1.00000000000000000000e+300; + +double +asinh(double x) +{ + double t,w; + int32_t hx,ix; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) return x+x; /* x is inf or NaN */ + if(ix< 0x3e300000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x41b00000) { /* |x| > 2**28 */ + w = __ieee754_log(fabs(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabs(x); + w = __ieee754_log(2.0*t+one/(__ieee754_sqrt(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1p(fabs(x)+t/(one+__ieee754_sqrt(one+t))); + } + if(hx>0) return w; else return -w; +} diff --git a/lib/nbsd_libm/src/s_asinhf.c b/lib/nbsd_libm/src/s_asinhf.c new file mode 100644 index 000000000..060e7cac9 --- /dev/null +++ b/lib/nbsd_libm/src/s_asinhf.c @@ -0,0 +1,50 @@ +/* s_asinhf.c -- float version of s_asinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_asinhf.c,v 1.8 2002/05/26 22:01:54 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +one = 1.0000000000e+00, /* 0x3F800000 */ +ln2 = 6.9314718246e-01, /* 0x3f317218 */ +huge= 1.0000000000e+30; + +float +asinhf(float x) +{ + float t,w; + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) return x+x; /* x is inf or NaN */ + if(ix< 0x31800000) { /* |x|<2**-28 */ + if(huge+x>one) return x; /* return x inexact except 0 */ + } + if(ix>0x4d800000) { /* |x| > 2**28 */ + w = __ieee754_logf(fabsf(x))+ln2; + } else if (ix>0x40000000) { /* 2**28 > |x| > 2.0 */ + t = fabsf(x); + w = __ieee754_logf((float)2.0*t+one/(__ieee754_sqrtf(x*x+one)+t)); + } else { /* 2.0 > |x| > 2**-28 */ + t = x*x; + w =log1pf(fabsf(x)+t/(one+__ieee754_sqrtf(one+t))); + } + if(hx>0) return w; else return -w; +} diff --git a/lib/nbsd_libm/src/s_atan.c b/lib/nbsd_libm/src/s_atan.c new file mode 100644 index 000000000..18a97e5fd --- /dev/null +++ b/lib/nbsd_libm/src/s_atan.c @@ -0,0 +1,120 @@ +/* @(#)s_atan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_atan.c,v 1.11 2002/05/26 22:01:54 wiz Exp $"); +#endif + +/* atan(x) + * Method + * 1. Reduce x to positive by atan(x) = -atan(-x). + * 2. According to the integer k=4t+0.25 chopped, t=x, the argument + * is further reduced to one of the following intervals and the + * arctangent of t is evaluated by the corresponding formula: + * + * [0,7/16] atan(x) = t-t^3*(a1+t^2*(a2+...(a10+t^2*a11)...) + * [7/16,11/16] atan(x) = atan(1/2) + atan( (t-0.5)/(1+t/2) ) + * [11/16.19/16] atan(x) = atan( 1 ) + atan( (t-1)/(1+t) ) + * [19/16,39/16] atan(x) = atan(3/2) + atan( (t-1.5)/(1+1.5t) ) + * [39/16,INF] atan(x) = atan(INF) + atan( -1/t ) + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +static const double atanhi[] = { + 4.63647609000806093515e-01, /* atan(0.5)hi 0x3FDDAC67, 0x0561BB4F */ + 7.85398163397448278999e-01, /* atan(1.0)hi 0x3FE921FB, 0x54442D18 */ + 9.82793723247329054082e-01, /* atan(1.5)hi 0x3FEF730B, 0xD281F69B */ + 1.57079632679489655800e+00, /* atan(inf)hi 0x3FF921FB, 0x54442D18 */ +}; + +static const double atanlo[] = { + 2.26987774529616870924e-17, /* atan(0.5)lo 0x3C7A2B7F, 0x222F65E2 */ + 3.06161699786838301793e-17, /* atan(1.0)lo 0x3C81A626, 0x33145C07 */ + 1.39033110312309984516e-17, /* atan(1.5)lo 0x3C700788, 0x7AF0CBBD */ + 6.12323399573676603587e-17, /* atan(inf)lo 0x3C91A626, 0x33145C07 */ +}; + +static const double aT[] = { + 3.33333333333329318027e-01, /* 0x3FD55555, 0x5555550D */ + -1.99999999998764832476e-01, /* 0xBFC99999, 0x9998EBC4 */ + 1.42857142725034663711e-01, /* 0x3FC24924, 0x920083FF */ + -1.11111104054623557880e-01, /* 0xBFBC71C6, 0xFE231671 */ + 9.09088713343650656196e-02, /* 0x3FB745CD, 0xC54C206E */ + -7.69187620504482999495e-02, /* 0xBFB3B0F2, 0xAF749A6D */ + 6.66107313738753120669e-02, /* 0x3FB10D66, 0xA0D03D51 */ + -5.83357013379057348645e-02, /* 0xBFADDE2D, 0x52DEFD9A */ + 4.97687799461593236017e-02, /* 0x3FA97B4B, 0x24760DEB */ + -3.65315727442169155270e-02, /* 0xBFA2B444, 0x2C6A6C2F */ + 1.62858201153657823623e-02, /* 0x3F90AD3A, 0xE322DA11 */ +}; + + static const double +one = 1.0, +huge = 1.0e300; + +double +atan(double x) +{ + double w,s1,s2,z; + int32_t ix,hx,id; + + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x44100000) { /* if |x| >= 2^66 */ + u_int32_t low; + GET_LOW_WORD(low,x); + if(ix>0x7ff00000|| + (ix==0x7ff00000&&(low!=0))) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3fdc0000) { /* |x| < 0.4375 */ + if (ix < 0x3e200000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabs(x); + if (ix < 0x3ff30000) { /* |x| < 1.1875 */ + if (ix < 0x3fe60000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = (2.0*x-one)/(2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x40038000) { /* |x| < 2.4375 */ + id = 2; x = (x-1.5)/(one+1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/lib/nbsd_libm/src/s_atanf.c b/lib/nbsd_libm/src/s_atanf.c new file mode 100644 index 000000000..5874ed1c4 --- /dev/null +++ b/lib/nbsd_libm/src/s_atanf.c @@ -0,0 +1,100 @@ +/* s_atanf.c -- float version of s_atan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_atanf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float atanhi[] = { + 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ + 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ + 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ + 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ +}; + +static const float atanlo[] = { + 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ + 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ + 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ + 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ +}; + +static const float aT[] = { + 3.3333334327e-01, /* 0x3eaaaaaa */ + -2.0000000298e-01, /* 0xbe4ccccd */ + 1.4285714924e-01, /* 0x3e124925 */ + -1.1111110449e-01, /* 0xbde38e38 */ + 9.0908870101e-02, /* 0x3dba2e6e */ + -7.6918758452e-02, /* 0xbd9d8795 */ + 6.6610731184e-02, /* 0x3d886b35 */ + -5.8335702866e-02, /* 0xbd6ef16b */ + 4.9768779427e-02, /* 0x3d4bda59 */ + -3.6531571299e-02, /* 0xbd15a221 */ + 1.6285819933e-02, /* 0x3c8569d7 */ +}; + +static const float +one = 1.0, +huge = 1.0e30; + +float +atanf(float x) +{ + float w,s1,s2,z; + int32_t ix,hx,id; + + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x50800000) { /* if |x| >= 2^34 */ + if(ix>0x7f800000) + return x+x; /* NaN */ + if(hx>0) return atanhi[3]+atanlo[3]; + else return -atanhi[3]-atanlo[3]; + } if (ix < 0x3ee00000) { /* |x| < 0.4375 */ + if (ix < 0x31000000) { /* |x| < 2^-29 */ + if(huge+x>one) return x; /* raise inexact */ + } + id = -1; + } else { + x = fabsf(x); + if (ix < 0x3f980000) { /* |x| < 1.1875 */ + if (ix < 0x3f300000) { /* 7/16 <=|x|<11/16 */ + id = 0; x = ((float)2.0*x-one)/((float)2.0+x); + } else { /* 11/16<=|x|< 19/16 */ + id = 1; x = (x-one)/(x+one); + } + } else { + if (ix < 0x401c0000) { /* |x| < 2.4375 */ + id = 2; x = (x-(float)1.5)/(one+(float)1.5*x); + } else { /* 2.4375 <= |x| < 2^66 */ + id = 3; x = -(float)1.0/x; + } + }} + /* end of argument reduction */ + z = x*x; + w = z*z; + /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ + s1 = z*(aT[0]+w*(aT[2]+w*(aT[4]+w*(aT[6]+w*(aT[8]+w*aT[10]))))); + s2 = w*(aT[1]+w*(aT[3]+w*(aT[5]+w*(aT[7]+w*aT[9])))); + if (id<0) return x - x*(s1+s2); + else { + z = atanhi[id] - ((x*(s1+s2) - atanlo[id]) - x); + return (hx<0)? -z:z; + } +} diff --git a/lib/nbsd_libm/src/s_cbrt.c b/lib/nbsd_libm/src/s_cbrt.c new file mode 100644 index 000000000..2e0f88ab7 --- /dev/null +++ b/lib/nbsd_libm/src/s_cbrt.c @@ -0,0 +1,82 @@ +/* @(#)s_cbrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_cbrt.c,v 1.11 2002/05/26 22:01:54 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +/* cbrt(x) + * Return cube root of x + */ +static const u_int32_t + B1 = 715094163, /* B1 = (682-0.03306235651)*2**20 */ + B2 = 696219795; /* B2 = (664-0.03306235651)*2**20 */ + +static const double +C = 5.42857142857142815906e-01, /* 19/35 = 0x3FE15F15, 0xF15F15F1 */ +D = -7.05306122448979611050e-01, /* -864/1225 = 0xBFE691DE, 0x2532C834 */ +E = 1.41428571428571436819e+00, /* 99/70 = 0x3FF6A0EA, 0x0EA0EA0F */ +F = 1.60714285714285720630e+00, /* 45/28 = 0x3FF9B6DB, 0x6DB6DB6E */ +G = 3.57142857142857150787e-01; /* 5/14 = 0x3FD6DB6D, 0xB6DB6DB7 */ + +double +cbrt(double x) +{ + int32_t hx; + double r,s,t=0.0,w; + u_int32_t sign; + u_int32_t high,low; + + GET_HIGH_WORD(hx,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7ff00000) return(x+x); /* cbrt(NaN,INF) is itself */ + GET_LOW_WORD(low,x); + if((hx|low)==0) + return(x); /* cbrt(0) is itself */ + + SET_HIGH_WORD(x,hx); /* x <- |x| */ + /* rough cbrt to 5 bits */ + if(hx<0x00100000) /* subnormal number */ + {SET_HIGH_WORD(t,0x43500000); /* set t= 2**54 */ + t*=x; GET_HIGH_WORD(high,t); SET_HIGH_WORD(t,high/3+B2); + } + else + SET_HIGH_WORD(t,hx/3+B1); + + + /* new cbrt to 23 bits, may be implemented in single precision */ + r=t*t/x; + s=C+r*t; + t*=G+F/(s+E+D/s); + + /* chopped to 20 bits and make it larger than cbrt(x) */ + GET_HIGH_WORD(high,t); + INSERT_WORDS(t,high+0x00000001,0); + + + /* one step newton iteration to 53 bits with error less than 0.667 ulps */ + s=t*t; /* t*t is exact */ + r=x/s; + w=t+t; + r=(r-t)/(w+r); /* r-s is exact */ + t=t+t*r; + + /* retore the sign bit */ + GET_HIGH_WORD(high,t); + SET_HIGH_WORD(t,high|sign); + return(t); +} diff --git a/lib/nbsd_libm/src/s_cbrtf.c b/lib/nbsd_libm/src/s_cbrtf.c new file mode 100644 index 000000000..83acbde3b --- /dev/null +++ b/lib/nbsd_libm/src/s_cbrtf.c @@ -0,0 +1,72 @@ +/* s_cbrtf.c -- float version of s_cbrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_cbrtf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +/* cbrtf(x) + * Return cube root of x + */ +static const unsigned + B1 = 709958130, /* B1 = (84+2/3-0.03306235651)*2**23 */ + B2 = 642849266; /* B2 = (76+2/3-0.03306235651)*2**23 */ + +static const float +C = 5.4285717010e-01, /* 19/35 = 0x3f0af8b0 */ +D = -7.0530611277e-01, /* -864/1225 = 0xbf348ef1 */ +E = 1.4142856598e+00, /* 99/70 = 0x3fb50750 */ +F = 1.6071428061e+00, /* 45/28 = 0x3fcdb6db */ +G = 3.5714286566e-01; /* 5/14 = 0x3eb6db6e */ + +float +cbrtf(float x) +{ + float r,s,t; + int32_t hx; + u_int32_t sign; + u_int32_t high; + + GET_FLOAT_WORD(hx,x); + sign=hx&0x80000000; /* sign= sign(x) */ + hx ^=sign; + if(hx>=0x7f800000) return(x+x); /* cbrt(NaN,INF) is itself */ + if(hx==0) + return(x); /* cbrt(0) is itself */ + + SET_FLOAT_WORD(x,hx); /* x <- |x| */ + /* rough cbrt to 5 bits */ + if(hx<0x00800000) /* subnormal number */ + {SET_FLOAT_WORD(t,0x4b800000); /* set t= 2**24 */ + t*=x; GET_FLOAT_WORD(high,t); SET_FLOAT_WORD(t,high/3+B2); + } + else + SET_FLOAT_WORD(t,hx/3+B1); + + + /* new cbrt to 23 bits */ + r=t*t/x; + s=C+r*t; + t*=G+F/(s+E+D/s); + + /* retore the sign bit */ + GET_FLOAT_WORD(high,t); + SET_FLOAT_WORD(t,high|sign); + return(t); +} diff --git a/lib/nbsd_libm/src/s_ceil.c b/lib/nbsd_libm/src/s_ceil.c new file mode 100644 index 000000000..48d900b60 --- /dev/null +++ b/lib/nbsd_libm/src/s_ceil.c @@ -0,0 +1,73 @@ +/* @(#)s_ceil.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_ceil.c,v 1.13 2009/02/16 01:22:18 lukem Exp $"); +#endif + +/* + * ceil(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to ceil(x). + */ + +#include "math.h" +#include "math_private.h" + +static const double huge = 1.0e300; + +double +ceil(double x) +{ + int32_t i0,i1,jj0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + jj0 = ((i0>>20)&0x7ff)-0x3ff; + if(jj0<20) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;i1=0;} + else if((i0|i1)!=0) { i0=0x3ff00000;i1=0;} + } + } else { + i = (0x000fffff)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00100000)>>jj0; + i0 &= (~i); i1=0; + } + } + } else if (jj0>51) { + if(jj0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(jj0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0>0) { + if(jj0==20) i0+=1; + else { + j = i1 + (1<<(52-jj0)); + if(j<(u_int32_t)i1) i0+=1; /* got a carry */ + i1 = j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} diff --git a/lib/nbsd_libm/src/s_ceilf.c b/lib/nbsd_libm/src/s_ceilf.c new file mode 100644 index 000000000..81cf80ea5 --- /dev/null +++ b/lib/nbsd_libm/src/s_ceilf.c @@ -0,0 +1,54 @@ +/* s_ceilf.c -- float version of s_ceil.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_ceilf.c,v 1.8 2008/04/25 22:21:53 christos Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e30; + +float +ceilf(float x) +{ + int32_t i0,jj0; + u_int32_t i; + + GET_FLOAT_WORD(i0,x); + jj0 = ((i0>>23)&0xff)-0x7f; + if(jj0<23) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0<0) {i0=0x80000000;} + else if(i0!=0) { i0=0x3f800000;} + } + } else { + i = (0x007fffff)>>jj0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0>0) i0 += (0x00800000)>>jj0; + i0 &= (~i); + } + } + } else { + if(jj0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/lib/nbsd_libm/src/s_copysign.c b/lib/nbsd_libm/src/s_copysign.c new file mode 100644 index 000000000..aec947740 --- /dev/null +++ b/lib/nbsd_libm/src/s_copysign.c @@ -0,0 +1,35 @@ +/* @(#)s_copysign.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_copysign.c,v 1.11 2002/05/26 22:01:54 wiz Exp $"); +#endif + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +double +copysign(double x, double y) +{ + u_int32_t hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; +} diff --git a/lib/nbsd_libm/src/s_copysignf.c b/lib/nbsd_libm/src/s_copysignf.c new file mode 100644 index 000000000..f7e1b596c --- /dev/null +++ b/lib/nbsd_libm/src/s_copysignf.c @@ -0,0 +1,38 @@ +/* s_copysignf.c -- float version of s_copysign.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_copysignf.c,v 1.7 2002/05/26 22:01:54 wiz Exp $"); +#endif + +/* + * copysignf(float x, float y) + * copysignf(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +float +copysignf(float x, float y) +{ + u_int32_t ix,iy; + GET_FLOAT_WORD(ix,x); + GET_FLOAT_WORD(iy,y); + SET_FLOAT_WORD(x,(ix&0x7fffffff)|(iy&0x80000000)); + return x; +} diff --git a/lib/nbsd_libm/src/s_copysignl.c b/lib/nbsd_libm/src/s_copysignl.c new file mode 100644 index 000000000..c347e1d53 --- /dev/null +++ b/lib/nbsd_libm/src/s_copysignl.c @@ -0,0 +1,51 @@ +/* $NetBSD: s_copysignl.c,v 1.2 2010/09/17 20:39:39 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: s_copysignl.c,v 1.2 2010/09/17 20:39:39 christos Exp $"); + +#include +#include + +/* + * copysignl(long double x, long double y) + * This function returns a value with the magnitude of x and the sign of y. + */ +#ifdef EXT_EXP_INFNAN +long double +copysignl(long double x, long double y) +{ + union ieee_ext_u ux, uy; + + ux.extu_ld = x; + uy.extu_ld = y; + + ux.extu_ext.ext_sign = uy.extu_ext.ext_sign; + + return (ux.extu_ld); +} +#endif diff --git a/lib/nbsd_libm/src/s_cos.c b/lib/nbsd_libm/src/s_cos.c new file mode 100644 index 000000000..f1f19db8a --- /dev/null +++ b/lib/nbsd_libm/src/s_cos.c @@ -0,0 +1,86 @@ +/* @(#)s_cos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_cos.c,v 1.11 2007/08/20 16:01:39 drochner Exp $"); +#endif + +/* cos(x) + * Return cosine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cosine function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#if 0 /* notyet */ +#ifdef __weak_alias +__weak_alias(cos, _cos) +#endif +#endif + +double +cos(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_cos(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_cos(y[0],y[1]); + case 1: return -__kernel_sin(y[0],y[1],1); + case 2: return -__kernel_cos(y[0],y[1]); + default: + return __kernel_sin(y[0],y[1],1); + } + } +} diff --git a/lib/nbsd_libm/src/s_cosf.c b/lib/nbsd_libm/src/s_cosf.c new file mode 100644 index 000000000..b23623c1c --- /dev/null +++ b/lib/nbsd_libm/src/s_cosf.c @@ -0,0 +1,61 @@ +/* s_cosf.c -- float version of s_cos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_cosf.c,v 1.9 2007/08/20 16:01:39 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#if 0 /* notyet */ +#ifdef __weak_alias +__weak_alias(cosf, _cosf) +#endif +#endif + +#if 0 +static const float one=1.0; +#endif + +float +cosf(float x) +{ + float y[2],z=0.0; + int32_t n,ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_cosf(x,z); + + /* cos(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_cosf(y[0],y[1]); + case 1: return -__kernel_sinf(y[0],y[1],1); + case 2: return -__kernel_cosf(y[0],y[1]); + default: + return __kernel_sinf(y[0],y[1],1); + } + } +} diff --git a/lib/nbsd_libm/src/s_erf.c b/lib/nbsd_libm/src/s_erf.c new file mode 100644 index 000000000..87743ea6f --- /dev/null +++ b/lib/nbsd_libm/src/s_erf.c @@ -0,0 +1,303 @@ +/* @(#)s_erf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_erf.c,v 1.11 2002/05/26 22:01:55 wiz Exp $"); +#endif + +/* double erf(double x) + * double erfc(double x) + * x + * 2 |\ + * erf(x) = --------- | exp(-t*t)dt + * sqrt(pi) \| + * 0 + * + * erfc(x) = 1-erf(x) + * Note that + * erf(-x) = -erf(x) + * erfc(-x) = 2 - erfc(x) + * + * Method: + * 1. For |x| in [0, 0.84375] + * erf(x) = x + x*R(x^2) + * erfc(x) = 1 - erf(x) if x in [-.84375,0.25] + * = 0.5 + ((0.5-x)-x*R) if x in [0.25,0.84375] + * where R = P/Q where P is an odd poly of degree 8 and + * Q is an odd poly of degree 10. + * -57.90 + * | R - (erf(x)-x)/x | <= 2 + * + * + * Remark. The formula is derived by noting + * erf(x) = (2/sqrt(pi))*(x - x^3/3 + x^5/10 - x^7/42 + ....) + * and that + * 2/sqrt(pi) = 1.128379167095512573896158903121545171688 + * is close to one. The interval is chosen because the fix + * point of erf(x) is near 0.6174 (i.e., erf(x)=x when x is + * near 0.6174), and by some experiment, 0.84375 is chosen to + * guarantee the error is less than one ulp for erf. + * + * 2. For |x| in [0.84375,1.25], let s = |x| - 1, and + * c = 0.84506291151 rounded to single (24 bits) + * erf(x) = sign(x) * (c + P1(s)/Q1(s)) + * erfc(x) = (1-c) - P1(s)/Q1(s) if x > 0 + * 1+(c+P1(s)/Q1(s)) if x < 0 + * |P1/Q1 - (erf(|x|)-c)| <= 2**-59.06 + * Remark: here we use the taylor series expansion at x=1. + * erf(1+s) = erf(1) + s*Poly(s) + * = 0.845.. + P1(s)/Q1(s) + * That is, we use rational approximation to approximate + * erf(1+s) - (c = (single)0.84506291151) + * Note that |P1/Q1|< 0.078 for x in [0.84375,1.25] + * where + * P1(s) = degree 6 poly in s + * Q1(s) = degree 6 poly in s + * + * 3. For x in [1.25,1/0.35(~2.857143)], + * erfc(x) = (1/x)*exp(-x*x-0.5625+R1/S1) + * erf(x) = 1 - erfc(x) + * where + * R1(z) = degree 7 poly in z, (z=1/x^2) + * S1(z) = degree 8 poly in z + * + * 4. For x in [1/0.35,28] + * erfc(x) = (1/x)*exp(-x*x-0.5625+R2/S2) if x > 0 + * = 2.0 - (1/x)*exp(-x*x-0.5625+R2/S2) if -6 x >= 28 + * erf(x) = sign(x) *(1 - tiny) (raise inexact) + * erfc(x) = tiny*tiny (raise underflow) if x > 0 + * = 2 - tiny if x<0 + * + * 7. Special case: + * erf(0) = 0, erf(inf) = 1, erf(-inf) = -1, + * erfc(0) = 1, erfc(inf) = 0, erfc(-inf) = 2, + * erfc/erf(NaN) is NaN + */ + + +#include "math.h" +#include "math_private.h" + +static const double +tiny = 1e-300, +half= 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ +one = 1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */ +two = 2.00000000000000000000e+00, /* 0x40000000, 0x00000000 */ + /* c = (float)0.84506291151 */ +erx = 8.45062911510467529297e-01, /* 0x3FEB0AC1, 0x60000000 */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.28379167095512586316e-01, /* 0x3FC06EBA, 0x8214DB69 */ +efx8= 1.02703333676410069053e+00, /* 0x3FF06EBA, 0x8214DB69 */ +pp0 = 1.28379167095512558561e-01, /* 0x3FC06EBA, 0x8214DB68 */ +pp1 = -3.25042107247001499370e-01, /* 0xBFD4CD7D, 0x691CB913 */ +pp2 = -2.84817495755985104766e-02, /* 0xBF9D2A51, 0xDBD7194F */ +pp3 = -5.77027029648944159157e-03, /* 0xBF77A291, 0x236668E4 */ +pp4 = -2.37630166566501626084e-05, /* 0xBEF8EAD6, 0x120016AC */ +qq1 = 3.97917223959155352819e-01, /* 0x3FD97779, 0xCDDADC09 */ +qq2 = 6.50222499887672944485e-02, /* 0x3FB0A54C, 0x5536CEBA */ +qq3 = 5.08130628187576562776e-03, /* 0x3F74D022, 0xC4D36B0F */ +qq4 = 1.32494738004321644526e-04, /* 0x3F215DC9, 0x221C1A10 */ +qq5 = -3.96022827877536812320e-06, /* 0xBED09C43, 0x42A26120 */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.36211856075265944077e-03, /* 0xBF6359B8, 0xBEF77538 */ +pa1 = 4.14856118683748331666e-01, /* 0x3FDA8D00, 0xAD92B34D */ +pa2 = -3.72207876035701323847e-01, /* 0xBFD7D240, 0xFBB8C3F1 */ +pa3 = 3.18346619901161753674e-01, /* 0x3FD45FCA, 0x805120E4 */ +pa4 = -1.10894694282396677476e-01, /* 0xBFBC6398, 0x3D3E28EC */ +pa5 = 3.54783043256182359371e-02, /* 0x3FA22A36, 0x599795EB */ +pa6 = -2.16637559486879084300e-03, /* 0xBF61BF38, 0x0A96073F */ +qa1 = 1.06420880400844228286e-01, /* 0x3FBB3E66, 0x18EEE323 */ +qa2 = 5.40397917702171048937e-01, /* 0x3FE14AF0, 0x92EB6F33 */ +qa3 = 7.18286544141962662868e-02, /* 0x3FB2635C, 0xD99FE9A7 */ +qa4 = 1.26171219808761642112e-01, /* 0x3FC02660, 0xE763351F */ +qa5 = 1.36370839120290507362e-02, /* 0x3F8BEDC2, 0x6B51DD1C */ +qa6 = 1.19844998467991074170e-02, /* 0x3F888B54, 0x5735151D */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.86494403484714822705e-03, /* 0xBF843412, 0x600D6435 */ +ra1 = -6.93858572707181764372e-01, /* 0xBFE63416, 0xE4BA7360 */ +ra2 = -1.05586262253232909814e+01, /* 0xC0251E04, 0x41B0E726 */ +ra3 = -6.23753324503260060396e+01, /* 0xC04F300A, 0xE4CBA38D */ +ra4 = -1.62396669462573470355e+02, /* 0xC0644CB1, 0x84282266 */ +ra5 = -1.84605092906711035994e+02, /* 0xC067135C, 0xEBCCABB2 */ +ra6 = -8.12874355063065934246e+01, /* 0xC0545265, 0x57E4D2F2 */ +ra7 = -9.81432934416914548592e+00, /* 0xC023A0EF, 0xC69AC25C */ +sa1 = 1.96512716674392571292e+01, /* 0x4033A6B9, 0xBD707687 */ +sa2 = 1.37657754143519042600e+02, /* 0x4061350C, 0x526AE721 */ +sa3 = 4.34565877475229228821e+02, /* 0x407B290D, 0xD58A1A71 */ +sa4 = 6.45387271733267880336e+02, /* 0x40842B19, 0x21EC2868 */ +sa5 = 4.29008140027567833386e+02, /* 0x407AD021, 0x57700314 */ +sa6 = 1.08635005541779435134e+02, /* 0x405B28A3, 0xEE48AE2C */ +sa7 = 6.57024977031928170135e+00, /* 0x401A47EF, 0x8E484A93 */ +sa8 = -6.04244152148580987438e-02, /* 0xBFAEEFF2, 0xEE749A62 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.86494292470009928597e-03, /* 0xBF843412, 0x39E86F4A */ +rb1 = -7.99283237680523006574e-01, /* 0xBFE993BA, 0x70C285DE */ +rb2 = -1.77579549177547519889e+01, /* 0xC031C209, 0x555F995A */ +rb3 = -1.60636384855821916062e+02, /* 0xC064145D, 0x43C5ED98 */ +rb4 = -6.37566443368389627722e+02, /* 0xC083EC88, 0x1375F228 */ +rb5 = -1.02509513161107724954e+03, /* 0xC0900461, 0x6A2E5992 */ +rb6 = -4.83519191608651397019e+02, /* 0xC07E384E, 0x9BDC383F */ +sb1 = 3.03380607434824582924e+01, /* 0x403E568B, 0x261D5190 */ +sb2 = 3.25792512996573918826e+02, /* 0x40745CAE, 0x221B9F0A */ +sb3 = 1.53672958608443695994e+03, /* 0x409802EB, 0x189D5118 */ +sb4 = 3.19985821950859553908e+03, /* 0x40A8FFB7, 0x688C246A */ +sb5 = 2.55305040643316442583e+03, /* 0x40A3F219, 0xCEDF3BE6 */ +sb6 = 4.74528541206955367215e+02, /* 0x407DA874, 0xE79FE763 */ +sb7 = -2.24409524465858183362e+01; /* 0xC03670E2, 0x42712D62 */ + +double +erf(double x) +{ + int32_t hx,ix,i; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (double)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3e300000) { /* |x|<2**-28 */ + if (ix < 0x00800000) + return 0.125*(8.0*x+efx8*x); /*avoid underflow */ + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40180000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)*__ieee754_exp((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +double +erfc(double x) +{ + int32_t hx,ix; + double R,S,P,Q,s,y,z,r; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7ff00000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (double)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3feb0000) { /* |x|<0.84375 */ + if(ix < 0x3c700000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3fd00000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3ff40000) { /* 0.84375 <= |x| < 1.25 */ + s = fabs(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x403c0000) { /* |x|<28 */ + x = fabs(x); + s = one/(x*x); + if(ix< 0x4006DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40180000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + z = x; + SET_LOW_WORD(z,0); + r = __ieee754_exp(-z*z-0.5625)* + __ieee754_exp((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} diff --git a/lib/nbsd_libm/src/s_erff.c b/lib/nbsd_libm/src/s_erff.c new file mode 100644 index 000000000..b20393134 --- /dev/null +++ b/lib/nbsd_libm/src/s_erff.c @@ -0,0 +1,212 @@ +/* s_erff.c -- float version of s_erf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_erff.c,v 1.7 2002/05/26 22:01:55 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +tiny = 1e-30, +half= 5.0000000000e-01, /* 0x3F000000 */ +one = 1.0000000000e+00, /* 0x3F800000 */ +two = 2.0000000000e+00, /* 0x40000000 */ + /* c = (subfloat)0.84506291151 */ +erx = 8.4506291151e-01, /* 0x3f58560b */ +/* + * Coefficients for approximation to erf on [0,0.84375] + */ +efx = 1.2837916613e-01, /* 0x3e0375d4 */ +efx8= 1.0270333290e+00, /* 0x3f8375d4 */ +pp0 = 1.2837916613e-01, /* 0x3e0375d4 */ +pp1 = -3.2504209876e-01, /* 0xbea66beb */ +pp2 = -2.8481749818e-02, /* 0xbce9528f */ +pp3 = -5.7702702470e-03, /* 0xbbbd1489 */ +pp4 = -2.3763017452e-05, /* 0xb7c756b1 */ +qq1 = 3.9791721106e-01, /* 0x3ecbbbce */ +qq2 = 6.5022252500e-02, /* 0x3d852a63 */ +qq3 = 5.0813062117e-03, /* 0x3ba68116 */ +qq4 = 1.3249473704e-04, /* 0x390aee49 */ +qq5 = -3.9602282413e-06, /* 0xb684e21a */ +/* + * Coefficients for approximation to erf in [0.84375,1.25] + */ +pa0 = -2.3621185683e-03, /* 0xbb1acdc6 */ +pa1 = 4.1485610604e-01, /* 0x3ed46805 */ +pa2 = -3.7220788002e-01, /* 0xbebe9208 */ +pa3 = 3.1834661961e-01, /* 0x3ea2fe54 */ +pa4 = -1.1089469492e-01, /* 0xbde31cc2 */ +pa5 = 3.5478305072e-02, /* 0x3d1151b3 */ +pa6 = -2.1663755178e-03, /* 0xbb0df9c0 */ +qa1 = 1.0642088205e-01, /* 0x3dd9f331 */ +qa2 = 5.4039794207e-01, /* 0x3f0a5785 */ +qa3 = 7.1828655899e-02, /* 0x3d931ae7 */ +qa4 = 1.2617121637e-01, /* 0x3e013307 */ +qa5 = 1.3637083583e-02, /* 0x3c5f6e13 */ +qa6 = 1.1984500103e-02, /* 0x3c445aa3 */ +/* + * Coefficients for approximation to erfc in [1.25,1/0.35] + */ +ra0 = -9.8649440333e-03, /* 0xbc21a093 */ +ra1 = -6.9385856390e-01, /* 0xbf31a0b7 */ +ra2 = -1.0558626175e+01, /* 0xc128f022 */ +ra3 = -6.2375331879e+01, /* 0xc2798057 */ +ra4 = -1.6239666748e+02, /* 0xc322658c */ +ra5 = -1.8460508728e+02, /* 0xc3389ae7 */ +ra6 = -8.1287437439e+01, /* 0xc2a2932b */ +ra7 = -9.8143291473e+00, /* 0xc11d077e */ +sa1 = 1.9651271820e+01, /* 0x419d35ce */ +sa2 = 1.3765776062e+02, /* 0x4309a863 */ +sa3 = 4.3456588745e+02, /* 0x43d9486f */ +sa4 = 6.4538726807e+02, /* 0x442158c9 */ +sa5 = 4.2900814819e+02, /* 0x43d6810b */ +sa6 = 1.0863500214e+02, /* 0x42d9451f */ +sa7 = 6.5702495575e+00, /* 0x40d23f7c */ +sa8 = -6.0424413532e-02, /* 0xbd777f97 */ +/* + * Coefficients for approximation to erfc in [1/.35,28] + */ +rb0 = -9.8649431020e-03, /* 0xbc21a092 */ +rb1 = -7.9928326607e-01, /* 0xbf4c9dd4 */ +rb2 = -1.7757955551e+01, /* 0xc18e104b */ +rb3 = -1.6063638306e+02, /* 0xc320a2ea */ +rb4 = -6.3756646729e+02, /* 0xc41f6441 */ +rb5 = -1.0250950928e+03, /* 0xc480230b */ +rb6 = -4.8351919556e+02, /* 0xc3f1c275 */ +sb1 = 3.0338060379e+01, /* 0x41f2b459 */ +sb2 = 3.2579251099e+02, /* 0x43a2e571 */ +sb3 = 1.5367296143e+03, /* 0x44c01759 */ +sb4 = 3.1998581543e+03, /* 0x4547fdbb */ +sb5 = 2.5530502930e+03, /* 0x451f90ce */ +sb6 = 4.7452853394e+02, /* 0x43ed43a7 */ +sb7 = -2.2440952301e+01; /* 0xc1b38712 */ + +float +erff(float x) +{ + int32_t hx,ix,i; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erf(nan)=nan */ + i = ((u_int32_t)hx>>31)<<1; + return (float)(1-i)+one/x; /* erf(+-inf)=+-1 */ + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x31800000) { /* |x|<2**-28 */ + if (ix < 0x04000000) + /*avoid underflow */ + return (float)0.125*((float)8.0*x+efx8*x); + return x + efx*x; + } + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + return x + x*y; + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) return erx + P/Q; else return -erx - P/Q; + } + if (ix >= 0x40c00000) { /* inf>|x|>=6 */ + if(hx>=0) return one-tiny; else return tiny-one; + } + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6E) { /* |x| < 1/0.35 */ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/0.35 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = __ieee754_expf(-z*z-(float)0.5625)*__ieee754_expf((z-x)*(z+x)+R/S); + if(hx>=0) return one-r/x; else return r/x-one; +} + +float +erfcf(float x) +{ + int32_t hx,ix; + float R,S,P,Q,s,y,z,r; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + if(ix>=0x7f800000) { /* erfc(nan)=nan */ + /* erfc(+-inf)=0,2 */ + return (float)(((u_int32_t)hx>>31)<<1)+one/x; + } + + if(ix < 0x3f580000) { /* |x|<0.84375 */ + if(ix < 0x23800000) /* |x|<2**-56 */ + return one-x; + z = x*x; + r = pp0+z*(pp1+z*(pp2+z*(pp3+z*pp4))); + s = one+z*(qq1+z*(qq2+z*(qq3+z*(qq4+z*qq5)))); + y = r/s; + if(hx < 0x3e800000) { /* x<1/4 */ + return one-(x+x*y); + } else { + r = x*y; + r += (x-half); + return half - r ; + } + } + if(ix < 0x3fa00000) { /* 0.84375 <= |x| < 1.25 */ + s = fabsf(x)-one; + P = pa0+s*(pa1+s*(pa2+s*(pa3+s*(pa4+s*(pa5+s*pa6))))); + Q = one+s*(qa1+s*(qa2+s*(qa3+s*(qa4+s*(qa5+s*qa6))))); + if(hx>=0) { + z = one-erx; return z - P/Q; + } else { + z = erx+P/Q; return one+z; + } + } + if (ix < 0x41e00000) { /* |x|<28 */ + x = fabsf(x); + s = one/(x*x); + if(ix< 0x4036DB6D) { /* |x| < 1/.35 ~ 2.857143*/ + R=ra0+s*(ra1+s*(ra2+s*(ra3+s*(ra4+s*( + ra5+s*(ra6+s*ra7)))))); + S=one+s*(sa1+s*(sa2+s*(sa3+s*(sa4+s*( + sa5+s*(sa6+s*(sa7+s*sa8))))))); + } else { /* |x| >= 1/.35 ~ 2.857143 */ + if(hx<0&&ix>=0x40c00000) return two-tiny;/* x < -6 */ + R=rb0+s*(rb1+s*(rb2+s*(rb3+s*(rb4+s*( + rb5+s*rb6))))); + S=one+s*(sb1+s*(sb2+s*(sb3+s*(sb4+s*( + sb5+s*(sb6+s*sb7)))))); + } + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(z,ix&0xfffff000); + r = __ieee754_expf(-z*z-(float)0.5625)* + __ieee754_expf((z-x)*(z+x)+R/S); + if(hx>0) return r/x; else return two-r/x; + } else { + if(hx>0) return tiny*tiny; else return two-tiny; + } +} diff --git a/lib/nbsd_libm/src/s_exp2.c b/lib/nbsd_libm/src/s_exp2.c new file mode 100644 index 000000000..8d3d2907c --- /dev/null +++ b/lib/nbsd_libm/src/s_exp2.c @@ -0,0 +1,401 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_exp2.c,v 1.2 2010/01/11 23:38:24 christos Exp $"); +#ifdef __FBSDID +__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2.c,v 1.7 2008/02/22 02:27:34 das Exp $"); +#endif + +#include + +#include "math.h" +#include "math_private.h" + +#define TBLBITS 8 +#define TBLSIZE (1 << TBLBITS) + +static const double + huge = 0x1p1000, + redux = 0x1.8p52 / TBLSIZE, + P1 = 0x1.62e42fefa39efp-1, + P2 = 0x1.ebfbdff82c575p-3, + P3 = 0x1.c6b08d704a0a6p-5, + P4 = 0x1.3b2ab88f70400p-7, + P5 = 0x1.5d88003875c74p-10; + +static volatile double twom1000 = 0x1p-1000; + +static const double tbl[TBLSIZE * 2] = { +/* exp2(z + eps) eps */ + 0x1.6a09e667f3d5dp-1, 0x1.9880p-44, + 0x1.6b052fa751744p-1, 0x1.8000p-50, + 0x1.6c012750bd9fep-1, -0x1.8780p-45, + 0x1.6cfdcddd476bfp-1, 0x1.ec00p-46, + 0x1.6dfb23c651a29p-1, -0x1.8000p-50, + 0x1.6ef9298593ae3p-1, -0x1.c000p-52, + 0x1.6ff7df9519386p-1, -0x1.fd80p-45, + 0x1.70f7466f42da3p-1, -0x1.c880p-45, + 0x1.71f75e8ec5fc3p-1, 0x1.3c00p-46, + 0x1.72f8286eacf05p-1, -0x1.8300p-44, + 0x1.73f9a48a58152p-1, -0x1.0c00p-47, + 0x1.74fbd35d7ccfcp-1, 0x1.f880p-45, + 0x1.75feb564267f1p-1, 0x1.3e00p-47, + 0x1.77024b1ab6d48p-1, -0x1.7d00p-45, + 0x1.780694fde5d38p-1, -0x1.d000p-50, + 0x1.790b938ac1d00p-1, 0x1.3000p-49, + 0x1.7a11473eb0178p-1, -0x1.d000p-49, + 0x1.7b17b0976d060p-1, 0x1.0400p-45, + 0x1.7c1ed0130c133p-1, 0x1.0000p-53, + 0x1.7d26a62ff8636p-1, -0x1.6900p-45, + 0x1.7e2f336cf4e3bp-1, -0x1.2e00p-47, + 0x1.7f3878491c3e8p-1, -0x1.4580p-45, + 0x1.80427543e1b4ep-1, 0x1.3000p-44, + 0x1.814d2add1071ap-1, 0x1.f000p-47, + 0x1.82589994ccd7ep-1, -0x1.1c00p-45, + 0x1.8364c1eb942d0p-1, 0x1.9d00p-45, + 0x1.8471a4623cab5p-1, 0x1.7100p-43, + 0x1.857f4179f5bbcp-1, 0x1.2600p-45, + 0x1.868d99b4491afp-1, -0x1.2c40p-44, + 0x1.879cad931a395p-1, -0x1.3000p-45, + 0x1.88ac7d98a65b8p-1, -0x1.a800p-45, + 0x1.89bd0a4785800p-1, -0x1.d000p-49, + 0x1.8ace5422aa223p-1, 0x1.3280p-44, + 0x1.8be05bad619fap-1, 0x1.2b40p-43, + 0x1.8cf3216b54383p-1, -0x1.ed00p-45, + 0x1.8e06a5e08664cp-1, -0x1.0500p-45, + 0x1.8f1ae99157807p-1, 0x1.8280p-45, + 0x1.902fed0282c0ep-1, -0x1.cb00p-46, + 0x1.9145b0b91ff96p-1, -0x1.5e00p-47, + 0x1.925c353aa2ff9p-1, 0x1.5400p-48, + 0x1.93737b0cdc64ap-1, 0x1.7200p-46, + 0x1.948b82b5f98aep-1, -0x1.9000p-47, + 0x1.95a44cbc852cbp-1, 0x1.5680p-45, + 0x1.96bdd9a766f21p-1, -0x1.6d00p-44, + 0x1.97d829fde4e2ap-1, -0x1.1000p-47, + 0x1.98f33e47a23a3p-1, 0x1.d000p-45, + 0x1.9a0f170ca0604p-1, -0x1.8a40p-44, + 0x1.9b2bb4d53ff89p-1, 0x1.55c0p-44, + 0x1.9c49182a3f15bp-1, 0x1.6b80p-45, + 0x1.9d674194bb8c5p-1, -0x1.c000p-49, + 0x1.9e86319e3238ep-1, 0x1.7d00p-46, + 0x1.9fa5e8d07f302p-1, 0x1.6400p-46, + 0x1.a0c667b5de54dp-1, -0x1.5000p-48, + 0x1.a1e7aed8eb8f6p-1, 0x1.9e00p-47, + 0x1.a309bec4a2e27p-1, 0x1.ad80p-45, + 0x1.a42c980460a5dp-1, -0x1.af00p-46, + 0x1.a5503b23e259bp-1, 0x1.b600p-47, + 0x1.a674a8af46213p-1, 0x1.8880p-44, + 0x1.a799e1330b3a7p-1, 0x1.1200p-46, + 0x1.a8bfe53c12e8dp-1, 0x1.6c00p-47, + 0x1.a9e6b5579fcd2p-1, -0x1.9b80p-45, + 0x1.ab0e521356fb8p-1, 0x1.b700p-45, + 0x1.ac36bbfd3f381p-1, 0x1.9000p-50, + 0x1.ad5ff3a3c2780p-1, 0x1.4000p-49, + 0x1.ae89f995ad2a3p-1, -0x1.c900p-45, + 0x1.afb4ce622f367p-1, 0x1.6500p-46, + 0x1.b0e07298db790p-1, 0x1.fd40p-45, + 0x1.b20ce6c9a89a9p-1, 0x1.2700p-46, + 0x1.b33a2b84f1a4bp-1, 0x1.d470p-43, + 0x1.b468415b747e7p-1, -0x1.8380p-44, + 0x1.b59728de5593ap-1, 0x1.8000p-54, + 0x1.b6c6e29f1c56ap-1, 0x1.ad00p-47, + 0x1.b7f76f2fb5e50p-1, 0x1.e800p-50, + 0x1.b928cf22749b2p-1, -0x1.4c00p-47, + 0x1.ba5b030a10603p-1, -0x1.d700p-47, + 0x1.bb8e0b79a6f66p-1, 0x1.d900p-47, + 0x1.bcc1e904bc1ffp-1, 0x1.2a00p-47, + 0x1.bdf69c3f3a16fp-1, -0x1.f780p-46, + 0x1.bf2c25bd71db8p-1, -0x1.0a00p-46, + 0x1.c06286141b2e9p-1, -0x1.1400p-46, + 0x1.c199bdd8552e0p-1, 0x1.be00p-47, + 0x1.c2d1cd9fa64eep-1, -0x1.9400p-47, + 0x1.c40ab5fffd02fp-1, -0x1.ed00p-47, + 0x1.c544778fafd15p-1, 0x1.9660p-44, + 0x1.c67f12e57d0cbp-1, -0x1.a100p-46, + 0x1.c7ba88988c1b6p-1, -0x1.8458p-42, + 0x1.c8f6d9406e733p-1, -0x1.a480p-46, + 0x1.ca3405751c4dfp-1, 0x1.b000p-51, + 0x1.cb720dcef9094p-1, 0x1.1400p-47, + 0x1.ccb0f2e6d1689p-1, 0x1.0200p-48, + 0x1.cdf0b555dc412p-1, 0x1.3600p-48, + 0x1.cf3155b5bab3bp-1, -0x1.6900p-47, + 0x1.d072d4a0789bcp-1, 0x1.9a00p-47, + 0x1.d1b532b08c8fap-1, -0x1.5e00p-46, + 0x1.d2f87080d8a85p-1, 0x1.d280p-46, + 0x1.d43c8eacaa203p-1, 0x1.1a00p-47, + 0x1.d5818dcfba491p-1, 0x1.f000p-50, + 0x1.d6c76e862e6a1p-1, -0x1.3a00p-47, + 0x1.d80e316c9834ep-1, -0x1.cd80p-47, + 0x1.d955d71ff6090p-1, 0x1.4c00p-48, + 0x1.da9e603db32aep-1, 0x1.f900p-48, + 0x1.dbe7cd63a8325p-1, 0x1.9800p-49, + 0x1.dd321f301b445p-1, -0x1.5200p-48, + 0x1.de7d5641c05bfp-1, -0x1.d700p-46, + 0x1.dfc97337b9aecp-1, -0x1.6140p-46, + 0x1.e11676b197d5ep-1, 0x1.b480p-47, + 0x1.e264614f5a3e7p-1, 0x1.0ce0p-43, + 0x1.e3b333b16ee5cp-1, 0x1.c680p-47, + 0x1.e502ee78b3fb4p-1, -0x1.9300p-47, + 0x1.e653924676d68p-1, -0x1.5000p-49, + 0x1.e7a51fbc74c44p-1, -0x1.7f80p-47, + 0x1.e8f7977cdb726p-1, -0x1.3700p-48, + 0x1.ea4afa2a490e8p-1, 0x1.5d00p-49, + 0x1.eb9f4867ccae4p-1, 0x1.61a0p-46, + 0x1.ecf482d8e680dp-1, 0x1.5500p-48, + 0x1.ee4aaa2188514p-1, 0x1.6400p-51, + 0x1.efa1bee615a13p-1, -0x1.e800p-49, + 0x1.f0f9c1cb64106p-1, -0x1.a880p-48, + 0x1.f252b376bb963p-1, -0x1.c900p-45, + 0x1.f3ac948dd7275p-1, 0x1.a000p-53, + 0x1.f50765b6e4524p-1, -0x1.4f00p-48, + 0x1.f6632798844fdp-1, 0x1.a800p-51, + 0x1.f7bfdad9cbe38p-1, 0x1.abc0p-48, + 0x1.f91d802243c82p-1, -0x1.4600p-50, + 0x1.fa7c1819e908ep-1, -0x1.b0c0p-47, + 0x1.fbdba3692d511p-1, -0x1.0e00p-51, + 0x1.fd3c22b8f7194p-1, -0x1.0de8p-46, + 0x1.fe9d96b2a23eep-1, 0x1.e430p-49, + 0x1.0000000000000p+0, 0x0.0000p+0, + 0x1.00b1afa5abcbep+0, -0x1.3400p-52, + 0x1.0163da9fb3303p+0, -0x1.2170p-46, + 0x1.02168143b0282p+0, 0x1.a400p-52, + 0x1.02c9a3e77806cp+0, 0x1.f980p-49, + 0x1.037d42e11bbcap+0, -0x1.7400p-51, + 0x1.04315e86e7f89p+0, 0x1.8300p-50, + 0x1.04e5f72f65467p+0, -0x1.a3f0p-46, + 0x1.059b0d315855ap+0, -0x1.2840p-47, + 0x1.0650a0e3c1f95p+0, 0x1.1600p-48, + 0x1.0706b29ddf71ap+0, 0x1.5240p-46, + 0x1.07bd42b72a82dp+0, -0x1.9a00p-49, + 0x1.0874518759bd0p+0, 0x1.6400p-49, + 0x1.092bdf66607c8p+0, -0x1.0780p-47, + 0x1.09e3ecac6f383p+0, -0x1.8000p-54, + 0x1.0a9c79b1f3930p+0, 0x1.fa00p-48, + 0x1.0b5586cf988fcp+0, -0x1.ac80p-48, + 0x1.0c0f145e46c8ap+0, 0x1.9c00p-50, + 0x1.0cc922b724816p+0, 0x1.5200p-47, + 0x1.0d83b23395dd8p+0, -0x1.ad00p-48, + 0x1.0e3ec32d3d1f3p+0, 0x1.bac0p-46, + 0x1.0efa55fdfa9a6p+0, -0x1.4e80p-47, + 0x1.0fb66affed2f0p+0, -0x1.d300p-47, + 0x1.1073028d7234bp+0, 0x1.1500p-48, + 0x1.11301d0125b5bp+0, 0x1.c000p-49, + 0x1.11edbab5e2af9p+0, 0x1.6bc0p-46, + 0x1.12abdc06c31d5p+0, 0x1.8400p-49, + 0x1.136a814f2047dp+0, -0x1.ed00p-47, + 0x1.1429aaea92de9p+0, 0x1.8e00p-49, + 0x1.14e95934f3138p+0, 0x1.b400p-49, + 0x1.15a98c8a58e71p+0, 0x1.5300p-47, + 0x1.166a45471c3dfp+0, 0x1.3380p-47, + 0x1.172b83c7d5211p+0, 0x1.8d40p-45, + 0x1.17ed48695bb9fp+0, -0x1.5d00p-47, + 0x1.18af9388c8d93p+0, -0x1.c880p-46, + 0x1.1972658375d66p+0, 0x1.1f00p-46, + 0x1.1a35beb6fcba7p+0, 0x1.0480p-46, + 0x1.1af99f81387e3p+0, -0x1.7390p-43, + 0x1.1bbe084045d54p+0, 0x1.4e40p-45, + 0x1.1c82f95281c43p+0, -0x1.a200p-47, + 0x1.1d4873168b9b2p+0, 0x1.3800p-49, + 0x1.1e0e75eb44031p+0, 0x1.ac00p-49, + 0x1.1ed5022fcd938p+0, 0x1.1900p-47, + 0x1.1f9c18438cdf7p+0, -0x1.b780p-46, + 0x1.2063b88628d8fp+0, 0x1.d940p-45, + 0x1.212be3578a81ep+0, 0x1.8000p-50, + 0x1.21f49917ddd41p+0, 0x1.b340p-45, + 0x1.22bdda2791323p+0, 0x1.9f80p-46, + 0x1.2387a6e7561e7p+0, -0x1.9c80p-46, + 0x1.2451ffb821427p+0, 0x1.2300p-47, + 0x1.251ce4fb2a602p+0, -0x1.3480p-46, + 0x1.25e85711eceb0p+0, 0x1.2700p-46, + 0x1.26b4565e27d16p+0, 0x1.1d00p-46, + 0x1.2780e341de00fp+0, 0x1.1ee0p-44, + 0x1.284dfe1f5633ep+0, -0x1.4c00p-46, + 0x1.291ba7591bb30p+0, -0x1.3d80p-46, + 0x1.29e9df51fdf09p+0, 0x1.8b00p-47, + 0x1.2ab8a66d10e9bp+0, -0x1.27c0p-45, + 0x1.2b87fd0dada3ap+0, 0x1.a340p-45, + 0x1.2c57e39771af9p+0, -0x1.0800p-46, + 0x1.2d285a6e402d9p+0, -0x1.ed00p-47, + 0x1.2df961f641579p+0, -0x1.4200p-48, + 0x1.2ecafa93e2ecfp+0, -0x1.4980p-45, + 0x1.2f9d24abd8822p+0, -0x1.6300p-46, + 0x1.306fe0a31b625p+0, -0x1.2360p-44, + 0x1.31432edeea50bp+0, -0x1.0df8p-40, + 0x1.32170fc4cd7b8p+0, -0x1.2480p-45, + 0x1.32eb83ba8e9a2p+0, -0x1.5980p-45, + 0x1.33c08b2641766p+0, 0x1.ed00p-46, + 0x1.3496266e3fa27p+0, -0x1.c000p-50, + 0x1.356c55f929f0fp+0, -0x1.0d80p-44, + 0x1.36431a2de88b9p+0, 0x1.2c80p-45, + 0x1.371a7373aaa39p+0, 0x1.0600p-45, + 0x1.37f26231e74fep+0, -0x1.6600p-46, + 0x1.38cae6d05d838p+0, -0x1.ae00p-47, + 0x1.39a401b713ec3p+0, -0x1.4720p-43, + 0x1.3a7db34e5a020p+0, 0x1.8200p-47, + 0x1.3b57fbfec6e95p+0, 0x1.e800p-44, + 0x1.3c32dc313a8f2p+0, 0x1.f800p-49, + 0x1.3d0e544ede122p+0, -0x1.7a00p-46, + 0x1.3dea64c1234bbp+0, 0x1.6300p-45, + 0x1.3ec70df1c4eccp+0, -0x1.8a60p-43, + 0x1.3fa4504ac7e8cp+0, -0x1.cdc0p-44, + 0x1.40822c367a0bbp+0, 0x1.5b80p-45, + 0x1.4160a21f72e95p+0, 0x1.ec00p-46, + 0x1.423fb27094646p+0, -0x1.3600p-46, + 0x1.431f5d950a920p+0, 0x1.3980p-45, + 0x1.43ffa3f84b9ebp+0, 0x1.a000p-48, + 0x1.44e0860618919p+0, -0x1.6c00p-48, + 0x1.45c2042a7d201p+0, -0x1.bc00p-47, + 0x1.46a41ed1d0016p+0, -0x1.2800p-46, + 0x1.4786d668b3326p+0, 0x1.0e00p-44, + 0x1.486a2b5c13c00p+0, -0x1.d400p-45, + 0x1.494e1e192af04p+0, 0x1.c200p-47, + 0x1.4a32af0d7d372p+0, -0x1.e500p-46, + 0x1.4b17dea6db801p+0, 0x1.7800p-47, + 0x1.4bfdad53629e1p+0, -0x1.3800p-46, + 0x1.4ce41b817c132p+0, 0x1.0800p-47, + 0x1.4dcb299fddddbp+0, 0x1.c700p-45, + 0x1.4eb2d81d8ab96p+0, -0x1.ce00p-46, + 0x1.4f9b2769d2d02p+0, 0x1.9200p-46, + 0x1.508417f4531c1p+0, -0x1.8c00p-47, + 0x1.516daa2cf662ap+0, -0x1.a000p-48, + 0x1.5257de83f51eap+0, 0x1.a080p-43, + 0x1.5342b569d4edap+0, -0x1.6d80p-45, + 0x1.542e2f4f6ac1ap+0, -0x1.2440p-44, + 0x1.551a4ca5d94dbp+0, 0x1.83c0p-43, + 0x1.56070dde9116bp+0, 0x1.4b00p-45, + 0x1.56f4736b529dep+0, 0x1.15a0p-43, + 0x1.57e27dbe2c40ep+0, -0x1.9e00p-45, + 0x1.58d12d497c76fp+0, -0x1.3080p-45, + 0x1.59c0827ff0b4cp+0, 0x1.dec0p-43, + 0x1.5ab07dd485427p+0, -0x1.4000p-51, + 0x1.5ba11fba87af4p+0, 0x1.0080p-44, + 0x1.5c9268a59460bp+0, -0x1.6c80p-45, + 0x1.5d84590998e3fp+0, 0x1.69a0p-43, + 0x1.5e76f15ad20e1p+0, -0x1.b400p-46, + 0x1.5f6a320dcebcap+0, 0x1.7700p-46, + 0x1.605e1b976dcb8p+0, 0x1.6f80p-45, + 0x1.6152ae6cdf715p+0, 0x1.1000p-47, + 0x1.6247eb03a5531p+0, -0x1.5d00p-46, + 0x1.633dd1d1929b5p+0, -0x1.2d00p-46, + 0x1.6434634ccc313p+0, -0x1.a800p-49, + 0x1.652b9febc8efap+0, -0x1.8600p-45, + 0x1.6623882553397p+0, 0x1.1fe0p-40, + 0x1.671c1c708328ep+0, -0x1.7200p-44, + 0x1.68155d44ca97ep+0, 0x1.6800p-49, + 0x1.690f4b19e9471p+0, -0x1.9780p-45, +}; + +/* + * exp2(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.503 ulp for normalized results. + * + * Method: (accurate tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z - eps[i] for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z - eps[i]), + * with |z - eps[i]| <= 2**-9 + 2**-39 for the table used. + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z - eps[i]) via + * a degree-5 minimax polynomial with maximum error under 1.3 * 2**-61. + * The values in exp2t[] and eps[] are chosen such that + * exp2t[i] = exp2(i/TBLSIZE + eps[i]), and eps[i] is a small offset such + * that exp2t[i] is accurate to 2**-64. + * + * Note that the range of i is +-TBLSIZE/2, so we actually index the tables + * by i0 = i + TBLSIZE/2. For cache efficiency, exp2t[] and eps[] are + * virtual tables, interleaved in the real table tbl[]. + * + * This method is due to Gal, with many details due to Gal and Bachelis: + * + * Gal, S. and Bachelis, B. An Accurate Elementary Mathematical Library + * for the IEEE Floating Point Standard. TOMS 17(1), 26-46 (1991). + */ +double +exp2(double x) +{ + double r, t, twopk, twopkp1000, z; + uint32_t hx, ix, lx, i0; + int k; + + /* Filter out exceptional cases. */ + GET_HIGH_WORD(hx,x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if(ix >= 0x40900000) { /* |x| >= 1024 */ + if(ix >= 0x7ff00000) { + GET_LOW_WORD(lx,x); + if(((ix & 0xfffff) | lx) != 0 || (hx & 0x80000000) == 0) + return (x + x); /* x is NaN or +Inf */ + else + return (0.0); /* x is -Inf */ + } + if(x >= 0x1.0p10) + return (huge * huge); /* overflow */ + if(x <= -0x1.0ccp10) + return (twom1000 * twom1000); /* underflow */ + } else if (ix < 0x3c900000) { /* |x| < 0x1p-54 */ + return (1.0 + x); + } + + /* Reduce x, computing z, i0, and k. */ + STRICT_ASSIGN(double, t, x + redux); + GET_LOW_WORD(i0, t); + i0 += TBLSIZE / 2; + k = (i0 >> TBLBITS) << 20; + i0 = (i0 & (TBLSIZE - 1)) << 1; + t -= redux; + z = x - t; + + /* Compute r = exp2(y) = exp2t[i0] * p(z - eps[i]). */ + t = tbl[i0]; /* exp2t[i0] */ + z -= tbl[i0 + 1]; /* eps[i0] */ + if (k >= -1021 << 20) + INSERT_WORDS(twopk, 0x3ff00000 + k, 0); + else + INSERT_WORDS(twopkp1000, 0x3ff00000 + k + (1000 << 20), 0); + r = t + t * z * (P1 + z * (P2 + z * (P3 + z * (P4 + z * P5)))); + + /* Scale by 2**(k>>20). */ + if(k >= -1021 << 20) { + if (k == 1024 << 20) + return (r * 2.0 * 0x1p1023); + return (r * twopk); + } else { + return (r * twopkp1000 * twom1000); + } +} + +#ifdef notyet +#if (LDBL_MANT_DIG == 53) +__weak_reference(exp2, exp2l); +#endif +#endif diff --git a/lib/nbsd_libm/src/s_exp2f.c b/lib/nbsd_libm/src/s_exp2f.c new file mode 100644 index 000000000..d08123f40 --- /dev/null +++ b/lib/nbsd_libm/src/s_exp2f.c @@ -0,0 +1,139 @@ +/*- + * Copyright (c) 2005 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_exp2f.c,v 1.1 2010/01/11 16:28:39 christos Exp $"); +#ifdef __FBSDID +__FBSDID("$FreeBSD: src/lib/msun/src/s_exp2f.c,v 1.9 2008/02/22 02:27:34 das Exp $"); +#endif + +#include + +#include "math.h" +#include "math_private.h" + +#define TBLBITS 4 +#define TBLSIZE (1 << TBLBITS) + +static const float + huge = 0x1p100f, + redux = 0x1.8p23f / TBLSIZE, + P1 = 0x1.62e430p-1f, + P2 = 0x1.ebfbe0p-3f, + P3 = 0x1.c6b348p-5f, + P4 = 0x1.3b2c9cp-7f; + +static volatile float twom100 = 0x1p-100f; + +static const double exp2ft[TBLSIZE] = { + 0x1.6a09e667f3bcdp-1, + 0x1.7a11473eb0187p-1, + 0x1.8ace5422aa0dbp-1, + 0x1.9c49182a3f090p-1, + 0x1.ae89f995ad3adp-1, + 0x1.c199bdd85529cp-1, + 0x1.d5818dcfba487p-1, + 0x1.ea4afa2a490dap-1, + 0x1.0000000000000p+0, + 0x1.0b5586cf9890fp+0, + 0x1.172b83c7d517bp+0, + 0x1.2387a6e756238p+0, + 0x1.306fe0a31b715p+0, + 0x1.3dea64c123422p+0, + 0x1.4bfdad5362a27p+0, + 0x1.5ab07dd485429p+0, +}; + +/* + * exp2f(x): compute the base 2 exponential of x + * + * Accuracy: Peak error < 0.501 ulp; location of peak: -0.030110927. + * + * Method: (equally-spaced tables) + * + * Reduce x: + * x = 2**k + y, for integer k and |y| <= 1/2. + * Thus we have exp2f(x) = 2**k * exp2(y). + * + * Reduce y: + * y = i/TBLSIZE + z for integer i near y * TBLSIZE. + * Thus we have exp2(y) = exp2(i/TBLSIZE) * exp2(z), + * with |z| <= 2**-(TBLSIZE+1). + * + * We compute exp2(i/TBLSIZE) via table lookup and exp2(z) via a + * degree-4 minimax polynomial with maximum error under 1.4 * 2**-33. + * Using double precision for everything except the reduction makes + * roundoff error insignificant and simplifies the scaling step. + * + * This method is due to Tang, but I do not use his suggested parameters: + * + * Tang, P. Table-driven Implementation of the Exponential Function + * in IEEE Floating-Point Arithmetic. TOMS 15(2), 144-157 (1989). + */ +float +exp2f(float x) +{ + double tv, twopk, u, z; + float t; + uint32_t hx, ix, i0; + int32_t k; + + /* Filter out exceptional cases. */ + GET_FLOAT_WORD(hx, x); + ix = hx & 0x7fffffff; /* high word of |x| */ + if(ix >= 0x43000000) { /* |x| >= 128 */ + if(ix >= 0x7f800000) { + if ((ix & 0x7fffff) != 0 || (hx & 0x80000000) == 0) + return (x + x); /* x is NaN or +Inf */ + else + return (0.0); /* x is -Inf */ + } + if(x >= 0x1.0p7f) + return (huge * huge); /* overflow */ + if(x <= -0x1.2cp7f) + return (twom100 * twom100); /* underflow */ + } else if (ix <= 0x33000000) { /* |x| <= 0x1p-25 */ + return (1.0f + x); + } + + /* Reduce x, computing z, i0, and k. */ + STRICT_ASSIGN(float, t, x + redux); + GET_FLOAT_WORD(i0, t); + i0 += TBLSIZE / 2; + k = (i0 >> TBLBITS) << 20; + i0 &= TBLSIZE - 1; + t -= redux; + z = x - t; + INSERT_WORDS(twopk, 0x3ff00000 + k, 0); + + /* Compute r = exp2(y) = exp2ft[i0] * p(z). */ + tv = exp2ft[i0]; + u = tv * z; + tv = tv + u * (P1 + z * P2) + u * (z * z) * (P3 + z * P4); + + /* Scale by 2**(k>>20). */ + return (tv * twopk); +} diff --git a/lib/nbsd_libm/src/s_expm1.c b/lib/nbsd_libm/src/s_expm1.c new file mode 100644 index 000000000..7ac6fc90a --- /dev/null +++ b/lib/nbsd_libm/src/s_expm1.c @@ -0,0 +1,223 @@ +/* @(#)s_expm1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_expm1.c,v 1.12 2002/05/26 22:01:55 wiz Exp $"); +#endif + +/* expm1(x) + * Returns exp(x)-1, the exponential of x minus 1. + * + * Method + * 1. Argument reduction: + * Given x, find r and integer k such that + * + * x = k*ln2 + r, |r| <= 0.5*ln2 ~ 0.34658 + * + * Here a correction term c will be computed to compensate + * the error in r when rounded to a floating-point number. + * + * 2. Approximating expm1(r) by a special rational function on + * the interval [0,0.34658]: + * Since + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 - r^4/360 + ... + * we define R1(r*r) by + * r*(exp(r)+1)/(exp(r)-1) = 2+ r^2/6 * R1(r*r) + * That is, + * R1(r**2) = 6/r *((exp(r)+1)/(exp(r)-1) - 2/r) + * = 6/r * ( 1 + 2.0*(1/(exp(r)-1) - 1/r)) + * = 1 - r^2/60 + r^4/2520 - r^6/100800 + ... + * We use a special Reme algorithm on [0,0.347] to generate + * a polynomial of degree 5 in r*r to approximate R1. The + * maximum error of this polynomial approximation is bounded + * by 2**-61. In other words, + * R1(z) ~ 1.0 + Q1*z + Q2*z**2 + Q3*z**3 + Q4*z**4 + Q5*z**5 + * where Q1 = -1.6666666666666567384E-2, + * Q2 = 3.9682539681370365873E-4, + * Q3 = -9.9206344733435987357E-6, + * Q4 = 2.5051361420808517002E-7, + * Q5 = -6.2843505682382617102E-9; + * (where z=r*r, and the values of Q1 to Q5 are listed below) + * with error bounded by + * | 5 | -61 + * | 1.0+Q1*z+...+Q5*z - R1(z) | <= 2 + * | | + * + * expm1(r) = exp(r)-1 is then computed by the following + * specific way which minimize the accumulation rounding error: + * 2 3 + * r r [ 3 - (R1 + R1*r/2) ] + * expm1(r) = r + --- + --- * [--------------------] + * 2 2 [ 6 - r*(3 - R1*r/2) ] + * + * To compensate the error in the argument reduction, we use + * expm1(r+c) = expm1(r) + c + expm1(r)*c + * ~ expm1(r) + c + r*c + * Thus c+r*c will be added in as the correction terms for + * expm1(r+c). Now rearrange the term to avoid optimization + * screw up: + * ( 2 2 ) + * ({ ( r [ R1 - (3 - R1*r/2) ] ) } r ) + * expm1(r+c)~r - ({r*(--- * [--------------------]-c)-c} - --- ) + * ({ ( 2 [ 6 - r*(3 - R1*r/2) ] ) } 2 ) + * ( ) + * + * = r - E + * 3. Scale back to obtain expm1(x): + * From step 1, we have + * expm1(x) = either 2^k*[expm1(r)+1] - 1 + * = or 2^k*[expm1(r) + (1-2^-k)] + * 4. Implementation notes: + * (A). To save one multiplication, we scale the coefficient Qi + * to Qi*2^i, and replace z by (x^2)/2. + * (B). To achieve maximum accuracy, we compute expm1(x) by + * (i) if x < -56*ln2, return -1.0, (raise inexact if x!=inf) + * (ii) if k=0, return r-E + * (iii) if k=-1, return 0.5*(r-E)-0.5 + * (iv) if k=1 if r < -0.25, return 2*((r+0.5)- E) + * else return 1.0+2.0*(r-E); + * (v) if (k<-2||k>56) return 2^k(1-(E-r)) - 1 (or exp(x)-1) + * (vi) if k <= 20, return 2^k((1-2^-k)-(E-r)), else + * (vii) return 2^k(1-((E+2^-k)-r)) + * + * Special cases: + * expm1(INF) is INF, expm1(NaN) is NaN; + * expm1(-INF) is -1, and + * for finite argument, only expm1(0)=0 is exact. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Misc. info. + * For IEEE double + * if x > 7.09782712893383973096e+02 then expm1(x) overflow + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + */ + +#include "math.h" +#include "math_private.h" + +static const double +one = 1.0, +huge = 1.0e+300, +tiny = 1.0e-300, +o_threshold = 7.09782712893383973096e+02,/* 0x40862E42, 0xFEFA39EF */ +ln2_hi = 6.93147180369123816490e-01,/* 0x3fe62e42, 0xfee00000 */ +ln2_lo = 1.90821492927058770002e-10,/* 0x3dea39ef, 0x35793c76 */ +invln2 = 1.44269504088896338700e+00,/* 0x3ff71547, 0x652b82fe */ + /* scaled coefficients related to expm1 */ +Q1 = -3.33333333333331316428e-02, /* BFA11111 111110F4 */ +Q2 = 1.58730158725481460165e-03, /* 3F5A01A0 19FE5585 */ +Q3 = -7.93650757867487942473e-05, /* BF14CE19 9EAADBB7 */ +Q4 = 4.00821782732936239552e-06, /* 3ED0CFCA 86E65239 */ +Q5 = -2.01099218183624371326e-07; /* BE8AFDB7 6E09C32D */ + +double +expm1(double x) +{ + double y,hi,lo,c,t,e,hxs,hfx,r1; + int32_t k,xsb; + u_int32_t hx; + + c = 0; + GET_HIGH_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4043687A) { /* if |x|>=56*ln2 */ + if(hx >= 0x40862E42) { /* if |x|>=709.78... */ + if(hx>=0x7ff00000) { + u_int32_t low; + GET_LOW_WORD(low,x); + if(((hx&0xfffff)|low)!=0) + return x+x; /* NaN */ + else return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + } + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -56*ln2, return -1.0 with inexact */ + if(x+tiny<0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3fd62e42) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3FF0A2B2) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?0.5:-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x3c900000) { /* when |x|<2**-54, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = 0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = 3.0-r1*hfx; + e = hxs*((r1-t)/(6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return 0.5*(x-e)-0.5; + if(k==1) { + if(x < -0.25) return -2.0*(e-(x+0.5)); + else return one+2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + u_int32_t high; + y = one-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<20) { + u_int32_t high; + SET_HIGH_WORD(t,0x3ff00000 - (0x200000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } else { + u_int32_t high; + SET_HIGH_WORD(t,((0x3ff-k)<<20)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_HIGH_WORD(high,y); + SET_HIGH_WORD(y,high+(k<<20)); /* add k to y's exponent */ + } + } + return y; +} diff --git a/lib/nbsd_libm/src/s_expm1f.c b/lib/nbsd_libm/src/s_expm1f.c new file mode 100644 index 000000000..30ee5ae4f --- /dev/null +++ b/lib/nbsd_libm/src/s_expm1f.c @@ -0,0 +1,128 @@ +/* s_expm1f.c -- float version of s_expm1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_expm1f.c,v 1.10 2002/05/26 22:01:55 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e+30, tiny = 1.0e-30; + +static const float +one = 1.0, +o_threshold = 8.8721679688e+01,/* 0x42b17180 */ +ln2_hi = 6.9313812256e-01,/* 0x3f317180 */ +ln2_lo = 9.0580006145e-06,/* 0x3717f7d1 */ +invln2 = 1.4426950216e+00,/* 0x3fb8aa3b */ + /* scaled coefficients related to expm1 */ +Q1 = -3.3333335072e-02, /* 0xbd088889 */ +Q2 = 1.5873016091e-03, /* 0x3ad00d01 */ +Q3 = -7.9365076090e-05, /* 0xb8a670cd */ +Q4 = 4.0082177293e-06, /* 0x36867e54 */ +Q5 = -2.0109921195e-07; /* 0xb457edbb */ + +float +expm1f(float x) +{ + float y,hi,lo,c,t,e,hxs,hfx,r1; + int32_t k,xsb; + u_int32_t hx; + + c = 0; + GET_FLOAT_WORD(hx,x); + xsb = hx&0x80000000; /* sign bit of x */ + if(xsb==0) y=x; else y= -x; /* y = |x| */ + hx &= 0x7fffffff; /* high word of |x| */ + + /* filter out huge and non-finite argument */ + if(hx >= 0x4195b844) { /* if |x|>=27*ln2 */ + if(hx >= 0x42b17218) { /* if |x|>=88.721... */ + if(hx>0x7f800000) + return x+x; /* NaN */ + if(hx==0x7f800000) + return (xsb==0)? x:-1.0;/* exp(+-inf)={inf,-1} */ + if(x > o_threshold) return huge*huge; /* overflow */ + } + if(xsb!=0) { /* x < -27*ln2, return -1.0 with inexact */ + if(x+tiny<(float)0.0) /* raise inexact */ + return tiny-one; /* return -1 */ + } + } + + /* argument reduction */ + if(hx > 0x3eb17218) { /* if |x| > 0.5 ln2 */ + if(hx < 0x3F851592) { /* and |x| < 1.5 ln2 */ + if(xsb==0) + {hi = x - ln2_hi; lo = ln2_lo; k = 1;} + else + {hi = x + ln2_hi; lo = -ln2_lo; k = -1;} + } else { + k = invln2*x+((xsb==0)?(float)0.5:(float)-0.5); + t = k; + hi = x - t*ln2_hi; /* t*ln2_hi is exact here */ + lo = t*ln2_lo; + } + x = hi - lo; + c = (hi-x)-lo; + } + else if(hx < 0x33000000) { /* when |x|<2**-25, return x */ + t = huge+x; /* return x with inexact flags when x!=0 */ + return x - (t-(huge+x)); + } + else k = 0; + + /* x is now in primary range */ + hfx = (float)0.5*x; + hxs = x*hfx; + r1 = one+hxs*(Q1+hxs*(Q2+hxs*(Q3+hxs*(Q4+hxs*Q5)))); + t = (float)3.0-r1*hfx; + e = hxs*((r1-t)/((float)6.0 - x*t)); + if(k==0) return x - (x*e-hxs); /* c is 0 */ + else { + e = (x*(e-c)-c); + e -= hxs; + if(k== -1) return (float)0.5*(x-e)-(float)0.5; + if(k==1) { + if(x < (float)-0.25) return -(float)2.0*(e-(x+(float)0.5)); + else return one+(float)2.0*(x-e); + } + if (k <= -2 || k>56) { /* suffice to return exp(x)-1 */ + int32_t i; + y = one-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + return y-one; + } + t = one; + if(k<23) { + int32_t i; + SET_FLOAT_WORD(t,0x3f800000 - (0x1000000>>k)); /* t=1-2^-k */ + y = t-(e-x); + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } else { + int32_t i; + SET_FLOAT_WORD(t,((0x7f-k)<<23)); /* 2^-k */ + y = x-(e+t); + y += one; + GET_FLOAT_WORD(i,y); + SET_FLOAT_WORD(y,i+(k<<23)); /* add k to y's exponent */ + } + } + return y; +} diff --git a/lib/nbsd_libm/src/s_fabs.c b/lib/nbsd_libm/src/s_fabs.c new file mode 100644 index 000000000..93227cfc1 --- /dev/null +++ b/lib/nbsd_libm/src/s_fabs.c @@ -0,0 +1,32 @@ +/* @(#)s_fabs.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_fabs.c,v 1.10 2002/05/26 22:01:55 wiz Exp $"); +#endif + +/* + * fabs(x) returns the absolute value of x. + */ + +#include "math.h" +#include "math_private.h" + +double +fabs(double x) +{ + u_int32_t high; + GET_HIGH_WORD(high,x); + SET_HIGH_WORD(x,high&0x7fffffff); + return x; +} diff --git a/lib/nbsd_libm/src/s_fabsf.c b/lib/nbsd_libm/src/s_fabsf.c new file mode 100644 index 000000000..66f8191c7 --- /dev/null +++ b/lib/nbsd_libm/src/s_fabsf.c @@ -0,0 +1,35 @@ +/* s_fabsf.c -- float version of s_fabs.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_fabsf.c,v 1.7 2002/05/26 22:01:55 wiz Exp $"); +#endif + +/* + * fabsf(x) returns the absolute value of x. + */ + +#include "math.h" +#include "math_private.h" + +float +fabsf(float x) +{ + u_int32_t ix; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x7fffffff); + return x; +} diff --git a/lib/nbsd_libm/src/s_fabsl.c b/lib/nbsd_libm/src/s_fabsl.c new file mode 100644 index 000000000..b2c8cfc01 --- /dev/null +++ b/lib/nbsd_libm/src/s_fabsl.c @@ -0,0 +1,49 @@ +/* $NetBSD: s_fabsl.c,v 1.2 2010/09/17 20:39:39 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS + * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED + * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR + * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS + * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR + * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF + * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS + * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN + * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) + * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE + * POSSIBILITY OF SUCH DAMAGE. + */ +#include +__RCSID("$NetBSD: s_fabsl.c,v 1.2 2010/09/17 20:39:39 christos Exp $"); + +#include +#include + +/* + * fabsl(long double x) + * This function returns the absolute value of its argumetn x, |x|. + */ +#ifdef EXT_EXP_INFNAN +long double +fabsl(long double x) +{ + union ieee_ext_u ux; + + ux.extu_ld = x; + ux.extu_ext.ext_sign = 0; + + return (ux.extu_ld); +} +#endif diff --git a/lib/nbsd_libm/src/s_fdim.c b/lib/nbsd_libm/src/s_fdim.c new file mode 100644 index 000000000..5a7bfc250 --- /dev/null +++ b/lib/nbsd_libm/src/s_fdim.c @@ -0,0 +1,49 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD$"); +#ifdef notdef +__FBSDID("$FreeBSD: src/lib/msun/src/s_fdim.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#endif + +#include + +#define DECL(type, fn) \ +type \ +fn(type x, type y) \ +{ \ + \ + if (isnan(x)) \ + return (x); \ + if (isnan(y)) \ + return (y); \ + return (x > y ? x - y : 0.0); \ +} + +DECL(double, fdim) +DECL(float, fdimf) +DECL(long double, fdiml) diff --git a/lib/nbsd_libm/src/s_finite.c b/lib/nbsd_libm/src/s_finite.c new file mode 100644 index 000000000..4b3f1f1ef --- /dev/null +++ b/lib/nbsd_libm/src/s_finite.c @@ -0,0 +1,32 @@ +/* @(#)s_finite.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_finite.c,v 1.11 2002/05/26 22:01:55 wiz Exp $"); +#endif + +/* + * finite(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +finite(double x) +{ + int32_t hx; + GET_HIGH_WORD(hx,x); + return (int)((u_int32_t)((hx&0x7fffffff)-0x7ff00000)>>31); +} diff --git a/lib/nbsd_libm/src/s_finitef.c b/lib/nbsd_libm/src/s_finitef.c new file mode 100644 index 000000000..59f6c1034 --- /dev/null +++ b/lib/nbsd_libm/src/s_finitef.c @@ -0,0 +1,35 @@ +/* s_finitef.c -- float version of s_finite.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_finitef.c,v 1.7 2002/05/26 22:01:55 wiz Exp $"); +#endif + +/* + * finitef(x) returns 1 is x is finite, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +finitef(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + return (int)((u_int32_t)((ix&0x7fffffff)-0x7f800000)>>31); +} diff --git a/lib/nbsd_libm/src/s_floor.c b/lib/nbsd_libm/src/s_floor.c new file mode 100644 index 000000000..b977c9bca --- /dev/null +++ b/lib/nbsd_libm/src/s_floor.c @@ -0,0 +1,74 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_floor.c,v 1.13 2009/02/16 01:27:36 lukem Exp $"); +#endif + +/* + * floor(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floor(x). + */ + +#include "math.h" +#include "math_private.h" + +static const double huge = 1.0e300; + +double +floor(double x) +{ + int32_t i0,i1,jj0; + u_int32_t i,j; + EXTRACT_WORDS(i0,i1,x); + jj0 = ((i0>>20)&0x7ff)-0x3ff; + if(jj0<20) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=i1=0;} + else if(((i0&0x7fffffff)|i1)!=0) + { i0=0xbff00000;i1=0;} + } + } else { + i = (0x000fffff)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00100000)>>jj0; + i0 &= (~i); i1=0; + } + } + } else if (jj0>51) { + if(jj0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(jj0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + if(i0<0) { + if(jj0==20) i0+=1; + else { + j = i1+(1<<(52-jj0)); + if(j<(u_int32_t)i1) i0 +=1 ; /* got a carry */ + i1=j; + } + } + i1 &= (~i); + } + } + INSERT_WORDS(x,i0,i1); + return x; +} diff --git a/lib/nbsd_libm/src/s_floorf.c b/lib/nbsd_libm/src/s_floorf.c new file mode 100644 index 000000000..4971e8995 --- /dev/null +++ b/lib/nbsd_libm/src/s_floorf.c @@ -0,0 +1,63 @@ +/* s_floorf.c -- float version of s_floor.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_floorf.c,v 1.8 2008/04/25 22:21:53 christos Exp $"); +#endif + +/* + * floorf(x) + * Return x rounded toward -inf to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to floorf(x). + */ + +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e30; + +float +floorf(float x) +{ + int32_t i0,jj0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + jj0 = ((i0>>23)&0xff)-0x7f; + if(jj0<23) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>(float)0.0) {/* return 0*sign(x) if |x|<1 */ + if(i0>=0) {i0=0;} + else if((i0&0x7fffffff)!=0) + { i0=0xbf800000;} + } + } else { + i = (0x007fffff)>>jj0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>(float)0.0) { /* raise inexact flag */ + if(i0<0) i0 += (0x00800000)>>jj0; + i0 &= (~i); + } + } + } else { + if(jj0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/lib/nbsd_libm/src/s_fmax.c b/lib/nbsd_libm/src/s_fmax.c new file mode 100644 index 000000000..728a4dfc0 --- /dev/null +++ b/lib/nbsd_libm/src/s_fmax.c @@ -0,0 +1,58 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_fmax.c,v 1.2 2010/03/08 01:05:20 snj Exp $"); +#ifdef notdef +__FBSDID("$FreeBSD: src/lib/msun/src/s_fmax.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#endif + +#include + +#include + +double +fmax(double x, double y) +{ + union ieee_double_u u[2]; + + u[0].dblu_d = x; + u[1].dblu_d = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].dblu_dbl.dbl_exp == DBL_EXP_INFNAN && + (u[0].dblu_dbl.dbl_frach | u[0].dblu_dbl.dbl_fracl) != 0) + return (y); + if (u[1].dblu_dbl.dbl_exp == DBL_EXP_INFNAN && + (u[1].dblu_dbl.dbl_frach | u[1].dblu_dbl.dbl_fracl) != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].dblu_dbl.dbl_sign != u[1].dblu_dbl.dbl_sign) + return (u[u[0].dblu_dbl.dbl_sign].dblu_d); + + return (x > y ? x : y); +} diff --git a/lib/nbsd_libm/src/s_fmaxf.c b/lib/nbsd_libm/src/s_fmaxf.c new file mode 100644 index 000000000..a96655a97 --- /dev/null +++ b/lib/nbsd_libm/src/s_fmaxf.c @@ -0,0 +1,58 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_fmaxf.c,v 1.2 2010/03/08 01:05:20 snj Exp $"); +#ifdef notdef +__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaxf.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#endif + +#include + +#include + +float +fmaxf(float x, float y) +{ + union ieee_single_u u[2]; + + u[0].sngu_f = x; + u[1].sngu_f = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].sngu_sng.sng_exp == SNG_EXP_INFNAN && + u[0].sngu_sng.sng_frac != 0) + return (y); + if (u[1].sngu_sng.sng_exp == SNG_EXP_INFNAN && + u[1].sngu_sng.sng_frac != 0) + return (x); + + /* Handle comparisons of sng_signed zeroes. */ + if (u[0].sngu_sng.sng_sign != u[1].sngu_sng.sng_sign) + return (u[u[0].sngu_sng.sng_sign].sngu_f); + + return (x > y ? x : y); +} diff --git a/lib/nbsd_libm/src/s_fmaxl.c b/lib/nbsd_libm/src/s_fmaxl.c new file mode 100644 index 000000000..9c1ffc635 --- /dev/null +++ b/lib/nbsd_libm/src/s_fmaxl.c @@ -0,0 +1,61 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_fmaxl.c,v 1.2 2010/03/08 01:05:20 snj Exp $"); +#ifdef notdef +__FBSDID("$FreeBSD: src/lib/msun/src/s_fmaxl.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#endif + +#include + +#include +#ifdef EXT_EXP_INFNAN +long double +fmaxl(long double x, long double y) +{ + union ieee_ext_u u[2]; + + u[0].extu_ld = x; + u[0].extu_ext.ext_frach &= ~0x80000000; + u[1].extu_ld = y; + u[1].extu_ext.ext_frach &= ~0x80000000; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].extu_ext.ext_exp == EXT_EXP_INFNAN && + (u[0].extu_ext.ext_frach | u[0].extu_ext.ext_fracl) != 0) + return (y); + if (u[1].extu_ext.ext_exp == EXT_EXP_INFNAN && + (u[1].extu_ext.ext_frach | u[1].extu_ext.ext_fracl) != 0) + return (x); + + /* Handle comparisons of ext_signed zeroes. */ + if (u[0].extu_ext.ext_sign != u[1].extu_ext.ext_sign) + return (u[0].extu_ext.ext_sign ? y : x); + + return (x > y ? x : y); +} +#endif diff --git a/lib/nbsd_libm/src/s_fmin.c b/lib/nbsd_libm/src/s_fmin.c new file mode 100644 index 000000000..dcf2e388b --- /dev/null +++ b/lib/nbsd_libm/src/s_fmin.c @@ -0,0 +1,58 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_fmin.c,v 1.1 2009/10/04 22:04:30 christos Exp $"); +#ifdef notdef +__FBSDID("$FreeBSD: src/lib/msun/src/s_fmin.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#endif + +#include + +#include + +double +fmin(double x, double y) +{ + union ieee_double_u u[2]; + + u[0].dblu_d = x; + u[1].dblu_d = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].dblu_dbl.dbl_exp == DBL_EXP_INFNAN && + (u[0].dblu_dbl.dbl_frach | u[0].dblu_dbl.dbl_fracl) != 0) + return (y); + if (u[1].dblu_dbl.dbl_exp == DBL_EXP_INFNAN && + (u[1].dblu_dbl.dbl_frach | u[1].dblu_dbl.dbl_fracl) != 0) + return (x); + + /* Handle comparisons of signed zeroes. */ + if (u[0].dblu_dbl.dbl_sign != u[1].dblu_dbl.dbl_sign) + return (u[u[1].dblu_dbl.dbl_sign].dblu_d); + + return (x < y ? x : y); +} diff --git a/lib/nbsd_libm/src/s_fminf.c b/lib/nbsd_libm/src/s_fminf.c new file mode 100644 index 000000000..59f6ce3c3 --- /dev/null +++ b/lib/nbsd_libm/src/s_fminf.c @@ -0,0 +1,58 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_fminf.c,v 1.2 2010/03/08 01:05:20 snj Exp $"); +#ifdef notdef +__FBSDID("$FreeBSD: src/lib/msun/src/s_fminf.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#endif + +#include + +#include + +float +fminf(float x, float y) +{ + union ieee_single_u u[2]; + + u[0].sngu_f = x; + u[1].sngu_f = y; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].sngu_sng.sng_exp == SNG_EXP_INFNAN && + u[0].sngu_sng.sng_frac != 0) + return (y); + if (u[1].sngu_sng.sng_exp == SNG_EXP_INFNAN && + u[1].sngu_sng.sng_frac != 0) + return (x); + + /* Handle comparisons of sng_singed zeroes. */ + if (u[0].sngu_sng.sng_sign != u[1].sngu_sng.sng_sign) + return (u[u[1].sngu_sng.sng_sign].sngu_f); + + return (x < y ? x : y); +} diff --git a/lib/nbsd_libm/src/s_fminl.c b/lib/nbsd_libm/src/s_fminl.c new file mode 100644 index 000000000..55a5e43bd --- /dev/null +++ b/lib/nbsd_libm/src/s_fminl.c @@ -0,0 +1,61 @@ +/*- + * Copyright (c) 2004 David Schultz + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND + * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE + * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE + * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE + * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL + * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS + * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) + * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT + * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY + * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF + * SUCH DAMAGE. + */ + +#include +__RCSID("$NetBSD: s_fminl.c,v 1.2 2010/03/08 01:05:20 snj Exp $"); +#ifdef notdef +__FBSDID("$FreeBSD: src/lib/msun/src/s_fminl.c,v 1.1 2004/06/30 07:04:01 das Exp $"); +#endif + +#include + +#include +#ifdef EXT_EXP_INFNAN +long double +fminl(long double x, long double y) +{ + union ieee_ext_u u[2]; + + u[0].extu_ld = x; + u[0].extu_ext.ext_frach &= ~0x80000000; + u[1].extu_ld = y; + u[1].extu_ext.ext_frach &= ~0x80000000; + + /* Check for NaNs to avoid raising spurious exceptions. */ + if (u[0].extu_ext.ext_exp == EXT_EXP_INFNAN && + (u[0].extu_ext.ext_frach | u[0].extu_ext.ext_fracl) != 0) + return (y); + if (u[1].extu_ext.ext_exp == EXT_EXP_INFNAN && + (u[1].extu_ext.ext_frach | u[1].extu_ext.ext_fracl) != 0) + return (x); + + /* Handle comparisons of ext_signed zeroes. */ + if (u[0].extu_ext.ext_sign != u[1].extu_ext.ext_sign) + return (u[1].extu_ext.ext_sign ? y : x); + + return (x < y ? x : y); +} +#endif diff --git a/lib/nbsd_libm/src/s_frexp.c b/lib/nbsd_libm/src/s_frexp.c new file mode 100644 index 000000000..12d07cb8f --- /dev/null +++ b/lib/nbsd_libm/src/s_frexp.c @@ -0,0 +1,52 @@ +/* @(#)s_frexp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_frexp.c,v 1.13 2008/09/28 18:54:55 christos Exp $"); +#endif + +/* + * for non-zero x + * x = frexp(arg,&exp); + * return a double fp quantity x such that 0.5 <= |x| <1.0 + * and the corresponding binary exponent "exp". That is + * arg = x*2^exp. + * If arg is inf, 0.0, or NaN, then frexp(arg,&exp) returns arg + * with *exp=0. + */ + +#include "math.h" +#include "math_private.h" + +static const double +two54 = 1.80143985094819840000e+16; /* 0x43500000, 0x00000000 */ + +double +frexp(double x, int *eptr) +{ + int32_t hx, ix, lx; + EXTRACT_WORDS(hx,lx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7ff00000||((ix|lx)==0)) return x; /* 0,inf,nan */ + if (ix<0x00100000) { /* subnormal */ + x *= two54; + GET_HIGH_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -54; + } + *eptr += ((uint32_t)ix>>20)-1022; + hx = (hx&0x800fffff)|0x3fe00000; + SET_HIGH_WORD(x,hx); + return x; +} diff --git a/lib/nbsd_libm/src/s_frexpf.c b/lib/nbsd_libm/src/s_frexpf.c new file mode 100644 index 000000000..a6ee5818c --- /dev/null +++ b/lib/nbsd_libm/src/s_frexpf.c @@ -0,0 +1,45 @@ +/* s_frexpf.c -- float version of s_frexp.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_frexpf.c,v 1.10 2007/08/21 20:12:27 drochner Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +two25 = 3.3554432000e+07; /* 0x4c000000 */ + +float +frexpf(float x, int *eptr) +{ + int32_t hx,ix; + GET_FLOAT_WORD(hx,x); + ix = 0x7fffffff&hx; + *eptr = 0; + if(ix>=0x7f800000||(ix==0)) return x; /* 0,inf,nan */ + if (ix<0x00800000) { /* subnormal */ + x *= two25; + GET_FLOAT_WORD(hx,x); + ix = hx&0x7fffffff; + *eptr = -25; + } + *eptr += (ix>>23)-126; + hx = (hx&0x807fffff)|0x3f000000; + SET_FLOAT_WORD(x,hx); + return x; +} diff --git a/lib/nbsd_libm/src/s_ilogb.c b/lib/nbsd_libm/src/s_ilogb.c new file mode 100644 index 000000000..29befbb3b --- /dev/null +++ b/lib/nbsd_libm/src/s_ilogb.c @@ -0,0 +1,48 @@ +/* @(#)s_ilogb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_ilogb.c,v 1.12 2002/05/26 22:01:56 wiz Exp $"); +#endif + +/* ilogb(double x) + * return the binary exponent of non-zero x + * ilogb(0) = 0x80000001 + * ilogb(inf/NaN) = 0x7fffffff (no signal is raised) + */ + +#include "math.h" +#include "math_private.h" + +int +ilogb(double x) +{ + int32_t hx,lx,ix; + + GET_HIGH_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00100000) { + GET_LOW_WORD(lx,x); + if((hx|lx)==0) + return 0x80000001; /* ilogb(0) = 0x80000001 */ + else /* subnormal x */ + if(hx==0) { + for (ix = -1043; lx>0; lx<<=1) ix -=1; + } else { + for (ix = -1022,hx<<=11; hx>0; hx<<=1) ix -=1; + } + return ix; + } + else if (hx<0x7ff00000) return (hx>>20)-1023; + else return 0x7fffffff; +} diff --git a/lib/nbsd_libm/src/s_ilogbf.c b/lib/nbsd_libm/src/s_ilogbf.c new file mode 100644 index 000000000..a35398c5e --- /dev/null +++ b/lib/nbsd_libm/src/s_ilogbf.c @@ -0,0 +1,40 @@ +/* s_ilogbf.c -- float version of s_ilogb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_ilogbf.c,v 1.7 2002/05/26 22:01:56 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +int +ilogbf(float x) +{ + int32_t hx,ix; + + GET_FLOAT_WORD(hx,x); + hx &= 0x7fffffff; + if(hx<0x00800000) { + if(hx==0) + return 0x80000001; /* ilogb(0) = 0x80000001 */ + else /* subnormal x */ + for (ix = -126,hx<<=8; hx>0; hx<<=1) ix -=1; + return ix; + } + else if (hx<0x7f800000) return (hx>>23)-127; + else return 0x7fffffff; +} diff --git a/lib/nbsd_libm/src/s_infinity.c b/lib/nbsd_libm/src/s_infinity.c new file mode 100644 index 000000000..af2b64471 --- /dev/null +++ b/lib/nbsd_libm/src/s_infinity.c @@ -0,0 +1,14 @@ +/* $NetBSD: s_infinity.c,v 1.5 2003/07/26 19:25:05 salo Exp $ */ + +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include + +#if BYTE_ORDER == LITTLE_ENDIAN +char __infinity[] = { 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xf0, 0x7f }; +#else +char __infinity[] = { 0x7f, 0xf0, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00 }; +#endif diff --git a/lib/nbsd_libm/src/s_isinf.c b/lib/nbsd_libm/src/s_isinf.c new file mode 100644 index 000000000..bb44036c9 --- /dev/null +++ b/lib/nbsd_libm/src/s_isinf.c @@ -0,0 +1,28 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_isinf.c,v 1.6 2003/07/26 19:25:05 salo Exp $"); +#endif + +/* + * isinf(x) returns 1 is x is inf, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +isinf(double x) +{ + int32_t hx,lx; + EXTRACT_WORDS(hx,lx,x); + hx &= 0x7fffffff; + hx ^= 0x7ff00000; + hx |= lx; + return (hx == 0); +} diff --git a/lib/nbsd_libm/src/s_isinff.c b/lib/nbsd_libm/src/s_isinff.c new file mode 100644 index 000000000..f289abf70 --- /dev/null +++ b/lib/nbsd_libm/src/s_isinff.c @@ -0,0 +1,27 @@ +/* + * Written by J.T. Conklin . + * Public domain. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_isinff.c,v 1.6 2003/07/26 19:25:06 salo Exp $"); +#endif + +/* + * isinff(x) returns 1 is x is inf, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +isinff(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + ix ^= 0x7f800000; + return (ix == 0); +} diff --git a/lib/nbsd_libm/src/s_isnan.c b/lib/nbsd_libm/src/s_isnan.c new file mode 100644 index 000000000..9a319530e --- /dev/null +++ b/lib/nbsd_libm/src/s_isnan.c @@ -0,0 +1,35 @@ +/* @(#)s_isnan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_isnan.c,v 1.11 2002/05/26 22:01:56 wiz Exp $"); +#endif + +/* + * isnan(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +isnan(double x) +{ + int32_t hx,lx; + EXTRACT_WORDS(hx,lx,x); + hx &= 0x7fffffff; + hx |= (u_int32_t)(lx|(-lx))>>31; + hx = 0x7ff00000 - hx; + return (int)((u_int32_t)(hx))>>31; +} diff --git a/lib/nbsd_libm/src/s_isnanf.c b/lib/nbsd_libm/src/s_isnanf.c new file mode 100644 index 000000000..457a414ae --- /dev/null +++ b/lib/nbsd_libm/src/s_isnanf.c @@ -0,0 +1,37 @@ +/* s_isnanf.c -- float version of s_isnan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_isnanf.c,v 1.7 2002/05/26 22:01:56 wiz Exp $"); +#endif + +/* + * isnanf(x) returns 1 is x is nan, else 0; + * no branching! + */ + +#include "math.h" +#include "math_private.h" + +int +isnanf(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; + ix = 0x7f800000 - ix; + return (int)(((u_int32_t)(ix))>>31); +} diff --git a/lib/nbsd_libm/src/s_ldexp.c b/lib/nbsd_libm/src/s_ldexp.c new file mode 100644 index 000000000..2f97ac5b7 --- /dev/null +++ b/lib/nbsd_libm/src/s_ldexp.c @@ -0,0 +1,30 @@ +/* @(#)s_ldexp0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_ldexp.c,v 1.11 2010/04/23 19:17:07 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" +#include + +double +ldexp(double value, int exp0) +{ + if(!finite(value)||value==0.0) return value; + value = scalbn(value,exp0); + if(!finite(value)||value==0.0) errno = ERANGE; + return value; +} diff --git a/lib/nbsd_libm/src/s_ldexpf.c b/lib/nbsd_libm/src/s_ldexpf.c new file mode 100644 index 000000000..e0c7141f8 --- /dev/null +++ b/lib/nbsd_libm/src/s_ldexpf.c @@ -0,0 +1,33 @@ +/* s_ldexp0f.c -- float version of s_ldexp0.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_ldexpf.c,v 1.8 2010/04/23 19:17:07 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" +#include + +float +ldexpf(float value, int exp0) +{ + if(!finitef(value)||value==(float)0.0) return value; + value = scalbnf(value,exp0); + if(!finitef(value)||value==(float)0.0) errno = ERANGE; + return value; +} diff --git a/lib/nbsd_libm/src/s_lib_version.c b/lib/nbsd_libm/src/s_lib_version.c new file mode 100644 index 000000000..147a2ef32 --- /dev/null +++ b/lib/nbsd_libm/src/s_lib_version.c @@ -0,0 +1,40 @@ +/* @(#)s_lib_ver.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_lib_version.c,v 1.8 1999/07/02 15:37:43 simonb Exp $"); +#endif + +/* + * MACRO for standards + */ + +#include "math.h" +#include "math_private.h" + +/* + * define and initialize _LIB_VERSION + */ +#ifdef _POSIX_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _POSIX_; +#else +#ifdef _XOPEN_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _XOPEN_; +#else +#ifdef _SVID3_MODE +_LIB_VERSION_TYPE _LIB_VERSION = _SVID_; +#else /* default _IEEE_MODE */ +_LIB_VERSION_TYPE _LIB_VERSION = _IEEE_; +#endif +#endif +#endif diff --git a/lib/nbsd_libm/src/s_log1p.c b/lib/nbsd_libm/src/s_log1p.c new file mode 100644 index 000000000..9d2faf0e4 --- /dev/null +++ b/lib/nbsd_libm/src/s_log1p.c @@ -0,0 +1,165 @@ +/* @(#)s_log1p.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_log1p.c,v 1.12 2002/05/26 22:01:57 wiz Exp $"); +#endif + +/* double log1p(double x) + * + * Method : + * 1. Argument Reduction: find k and f such that + * 1+x = 2^k * (1+f), + * where sqrt(2)/2 < 1+f < sqrt(2) . + * + * Note. If k=0, then f=x is exact. However, if k!=0, then f + * may not be representable exactly. In that case, a correction + * term is need. Let u=1+x rounded. Let c = (1+x)-u, then + * log(1+x) - log(u) ~ c/u. Thus, we proceed to compute log(u), + * and add back the correction term c/u. + * (Note: when x > 2**53, one can simply return log(x)) + * + * 2. Approximation of log1p(f). + * Let s = f/(2+f) ; based on log(1+f) = log(1+s) - log(1-s) + * = 2s + 2/3 s**3 + 2/5 s**5 + ....., + * = 2s + s*R + * We use a special Reme algorithm on [0,0.1716] to generate + * a polynomial of degree 14 to approximate R The maximum error + * of this polynomial approximation is bounded by 2**-58.45. In + * other words, + * 2 4 6 8 10 12 14 + * R(z) ~ Lp1*s +Lp2*s +Lp3*s +Lp4*s +Lp5*s +Lp6*s +Lp7*s + * (the values of Lp1 to Lp7 are listed in the program) + * and + * | 2 14 | -58.45 + * | Lp1*s +...+Lp7*s - R(z) | <= 2 + * | | + * Note that 2s = f - s*f = f - hfsq + s*hfsq, where hfsq = f*f/2. + * In order to guarantee error in log below 1ulp, we compute log + * by + * log1p(f) = f - (hfsq - s*(hfsq+R)). + * + * 3. Finally, log1p(x) = k*ln2 + log1p(f). + * = k*ln2_hi+(f-(hfsq-(s*(hfsq+R)+k*ln2_lo))) + * Here ln2 is split into two floating point number: + * ln2_hi + ln2_lo, + * where n*ln2_hi is always exact for |n| < 2000. + * + * Special cases: + * log1p(x) is NaN with signal if x < -1 (including -INF) ; + * log1p(+INF) is +INF; log1p(-1) is -INF with signal; + * log1p(NaN) is that NaN with no signal. + * + * Accuracy: + * according to an error analysis, the error is always less than + * 1 ulp (unit in the last place). + * + * Constants: + * The hexadecimal values are the intended ones for the following + * constants. The decimal values may be used, provided that the + * compiler will convert from decimal to binary accurately enough + * to produce the hexadecimal values shown. + * + * Note: Assuming log() return accurate answer, the following + * algorithm can be used to compute log1p(x) to within a few ULP: + * + * u = 1+x; + * if(u==1.0) return x ; else + * return log(u)*(x/(u-1.0)); + * + * See HP-15C Advanced Functions Handbook, p.193. + */ + +#include "math.h" +#include "math_private.h" + +static const double +ln2_hi = 6.93147180369123816490e-01, /* 3fe62e42 fee00000 */ +ln2_lo = 1.90821492927058770002e-10, /* 3dea39ef 35793c76 */ +two54 = 1.80143985094819840000e+16, /* 43500000 00000000 */ +Lp1 = 6.666666666666735130e-01, /* 3FE55555 55555593 */ +Lp2 = 3.999999999940941908e-01, /* 3FD99999 9997FA04 */ +Lp3 = 2.857142874366239149e-01, /* 3FD24924 94229359 */ +Lp4 = 2.222219843214978396e-01, /* 3FCC71C5 1D8E78AF */ +Lp5 = 1.818357216161805012e-01, /* 3FC74664 96CB03DE */ +Lp6 = 1.531383769920937332e-01, /* 3FC39A09 D078C69F */ +Lp7 = 1.479819860511658591e-01; /* 3FC2F112 DF3E5244 */ + +static const double zero = 0.0; + +double +log1p(double x) +{ + double hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + f = c = 0; + hu = 0; + GET_HIGH_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3FDA827A) { /* x < 0.41422 */ + if(ax>=0x3ff00000) { /* x <= -1.0 */ + if(x==-1.0) return -two54/zero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x3e200000) { /* |x| < 2**-29 */ + if(two54+x>zero /* raise inexact */ + &&ax<0x3c900000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*0.5; + } + if(hx>0||hx<=((int32_t)0xbfd2bec3)) { + k=0;f=x;hu=1;} /* -0.2929= 0x7ff00000) return x+x; + if(k!=0) { + if(hx<0x43400000) { + u = 1.0+x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = (k>0)? 1.0-(u-x):x-(u-1.0);/* correction term */ + c /= u; + } else { + u = x; + GET_HIGH_WORD(hu,u); + k = (hu>>20)-1023; + c = 0; + } + hu &= 0x000fffff; + if(hu<0x6a09e) { + SET_HIGH_WORD(u,hu|0x3ff00000); /* normalize u */ + } else { + k += 1; + SET_HIGH_WORD(u,hu|0x3fe00000); /* normalize u/2 */ + hu = (0x00100000-hu)>>2; + } + f = u-1.0; + } + hfsq=0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*(1.0-0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/(2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff --git a/lib/nbsd_libm/src/s_log1pf.c b/lib/nbsd_libm/src/s_log1pf.c new file mode 100644 index 000000000..b7afa8434 --- /dev/null +++ b/lib/nbsd_libm/src/s_log1pf.c @@ -0,0 +1,104 @@ +/* s_log1pf.c -- float version of s_log1p.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_log1pf.c,v 1.8 2002/05/26 22:01:57 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +ln2_hi = 6.9313812256e-01, /* 0x3f317180 */ +ln2_lo = 9.0580006145e-06, /* 0x3717f7d1 */ +two25 = 3.355443200e+07, /* 0x4c000000 */ +Lp1 = 6.6666668653e-01, /* 3F2AAAAB */ +Lp2 = 4.0000000596e-01, /* 3ECCCCCD */ +Lp3 = 2.8571429849e-01, /* 3E924925 */ +Lp4 = 2.2222198546e-01, /* 3E638E29 */ +Lp5 = 1.8183572590e-01, /* 3E3A3325 */ +Lp6 = 1.5313838422e-01, /* 3E1CD04F */ +Lp7 = 1.4798198640e-01; /* 3E178897 */ + +static const float zero = 0.0; + +float +log1pf(float x) +{ + float hfsq,f,c,s,z,R,u; + int32_t k,hx,hu,ax; + + f = c = 0; + hu = 0; + GET_FLOAT_WORD(hx,x); + ax = hx&0x7fffffff; + + k = 1; + if (hx < 0x3ed413d7) { /* x < 0.41422 */ + if(ax>=0x3f800000) { /* x <= -1.0 */ + if(x==(float)-1.0) return -two25/zero; /* log1p(-1)=+inf */ + else return (x-x)/(x-x); /* log1p(x<-1)=NaN */ + } + if(ax<0x31000000) { /* |x| < 2**-29 */ + if(two25+x>zero /* raise inexact */ + &&ax<0x24800000) /* |x| < 2**-54 */ + return x; + else + return x - x*x*(float)0.5; + } + if(hx>0||hx<=((int32_t)0xbe95f61f)) { + k=0;f=x;hu=1;} /* -0.2929= 0x7f800000) return x+x; + if(k!=0) { + if(hx<0x5a000000) { + u = (float)1.0+x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + /* correction term */ + c = (k>0)? (float)1.0-(u-x):x-(u-(float)1.0); + c /= u; + } else { + u = x; + GET_FLOAT_WORD(hu,u); + k = (hu>>23)-127; + c = 0; + } + hu &= 0x007fffff; + if(hu<0x3504f7) { + SET_FLOAT_WORD(u,hu|0x3f800000);/* normalize u */ + } else { + k += 1; + SET_FLOAT_WORD(u,hu|0x3f000000); /* normalize u/2 */ + hu = (0x00800000-hu)>>2; + } + f = u-(float)1.0; + } + hfsq=(float)0.5*f*f; + if(hu==0) { /* |f| < 2**-20 */ + if(f==zero) { if(k==0) return zero; + else {c += k*ln2_lo; return k*ln2_hi+c;} + } + R = hfsq*((float)1.0-(float)0.66666666666666666*f); + if(k==0) return f-R; else + return k*ln2_hi-((R-(k*ln2_lo+c))-f); + } + s = f/((float)2.0+f); + z = s*s; + R = z*(Lp1+z*(Lp2+z*(Lp3+z*(Lp4+z*(Lp5+z*(Lp6+z*Lp7)))))); + if(k==0) return f-(hfsq-s*(hfsq+R)); else + return k*ln2_hi-((hfsq-(s*(hfsq+R)+(k*ln2_lo+c)))-f); +} diff --git a/lib/nbsd_libm/src/s_logb.c b/lib/nbsd_libm/src/s_logb.c new file mode 100644 index 000000000..9a77e49e6 --- /dev/null +++ b/lib/nbsd_libm/src/s_logb.c @@ -0,0 +1,39 @@ +/* @(#)s_logb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_logb.c,v 1.11 2002/05/26 22:01:57 wiz Exp $"); +#endif + +/* + * double logb(x) + * IEEE 754 logb. Included to pass IEEE test suite. Not recommend. + * Use ilogb instead. + */ + +#include "math.h" +#include "math_private.h" + +double +logb(double x) +{ + int32_t lx,ix; + EXTRACT_WORDS(ix,lx,x); + ix &= 0x7fffffff; /* high |x| */ + if((ix|lx)==0) return -1.0/fabs(x); + if(ix>=0x7ff00000) return x*x; + if((ix>>=20)==0) /* IEEE 754 logb */ + return -1022.0; + else + return (double) (ix-1023); +} diff --git a/lib/nbsd_libm/src/s_logbf.c b/lib/nbsd_libm/src/s_logbf.c new file mode 100644 index 000000000..73fdff2e1 --- /dev/null +++ b/lib/nbsd_libm/src/s_logbf.c @@ -0,0 +1,36 @@ +/* s_logbf.c -- float version of s_logb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_logbf.c,v 1.7 2002/05/26 22:01:57 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +logbf(float x) +{ + int32_t ix; + GET_FLOAT_WORD(ix,x); + ix &= 0x7fffffff; /* high |x| */ + if(ix==0) return (float)-1.0/fabsf(x); + if(ix>=0x7f800000) return x*x; + if((ix>>=23)==0) /* IEEE 754 logb */ + return -126.0; + else + return (float) (ix-127); +} diff --git a/lib/nbsd_libm/src/s_matherr.c b/lib/nbsd_libm/src/s_matherr.c new file mode 100644 index 000000000..f330a1755 --- /dev/null +++ b/lib/nbsd_libm/src/s_matherr.c @@ -0,0 +1,27 @@ +/* @(#)s_matherr.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_matherr.c,v 1.9 2002/05/26 22:01:57 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +int +matherr(struct exception *x) +{ + int n=0; + if(x->arg1!=x->arg1) return 0; + return n; +} diff --git a/lib/nbsd_libm/src/s_modf.c b/lib/nbsd_libm/src/s_modf.c new file mode 100644 index 000000000..63f3f40c4 --- /dev/null +++ b/lib/nbsd_libm/src/s_modf.c @@ -0,0 +1,78 @@ +/* @(#)s_modf.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_modf.c,v 1.14 2010/01/27 14:07:41 drochner Exp $"); +#endif + +/* + * modf(double x, double *iptr) + * return fraction part of x, and return x's integral part in *iptr. + * Method: + * Bit twiddling. + * + * Exception: + * No exception. + */ + +#include "math.h" +#include "math_private.h" + +static const double one = 1.0; + +double +modf(double x, double *iptr) +{ + int32_t i0,i1,jj0; + u_int32_t i; + EXTRACT_WORDS(i0,i1,x); + jj0 = (((uint32_t)i0>>20)&0x7ff)-0x3ff; /* exponent of x */ + if(jj0<20) { /* integer part in high x */ + if(jj0<0) { /* |x|<1 */ + INSERT_WORDS(*iptr,i0&0x80000000,0); /* *iptr = +-0 */ + return x; + } else { + i = (0x000fffff)>>jj0; + if(((i0&i)|i1)==0) { /* x is integral */ + u_int32_t high; + *iptr = x; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0&(~i),0); + return x - *iptr; + } + } + } else if (jj0>51) { /* no fraction part */ + u_int32_t high; + *iptr = x*one; + if (jj0 == 0x400) /* +-inf or NaN */ + return 0.0 / x; /* +-0 or NaN */ + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { /* fraction part in low x */ + i = ((u_int32_t)(0xffffffff))>>(jj0-20); + if((i1&i)==0) { /* x is integral */ + u_int32_t high; + *iptr = x; + GET_HIGH_WORD(high,x); + INSERT_WORDS(x,high&0x80000000,0); /* return +-0 */ + return x; + } else { + INSERT_WORDS(*iptr,i0,i1&(~i)); + return x - *iptr; + } + } +} diff --git a/lib/nbsd_libm/src/s_modff.c b/lib/nbsd_libm/src/s_modff.c new file mode 100644 index 000000000..46ddc3877 --- /dev/null +++ b/lib/nbsd_libm/src/s_modff.c @@ -0,0 +1,59 @@ +/* s_modff.c -- float version of s_modf.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_modff.c,v 1.9 2010/01/27 14:07:41 drochner Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float one = 1.0; + +float +modff(float x, float *iptr) +{ + int32_t i0,jj0; + u_int32_t i; + GET_FLOAT_WORD(i0,x); + jj0 = ((i0>>23)&0xff)-0x7f; /* exponent of x */ + if(jj0<23) { /* integer part in x */ + if(jj0<0) { /* |x|<1 */ + SET_FLOAT_WORD(*iptr,i0&0x80000000); /* *iptr = +-0 */ + return x; + } else { + i = (0x007fffff)>>jj0; + if((i0&i)==0) { /* x is integral */ + u_int32_t ix; + *iptr = x; + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } else { + SET_FLOAT_WORD(*iptr,i0&(~i)); + return x - *iptr; + } + } + } else { /* no fraction part */ + u_int32_t ix; + *iptr = x*one; + if (jj0 == 0x80) /* +-inf or NaN */ + return 0.0 / x; /* +-0 or NaN */ + GET_FLOAT_WORD(ix,x); + SET_FLOAT_WORD(x,ix&0x80000000); /* return +-0 */ + return x; + } +} diff --git a/lib/nbsd_libm/src/s_nextafter.c b/lib/nbsd_libm/src/s_nextafter.c new file mode 100644 index 000000000..f6fafca85 --- /dev/null +++ b/lib/nbsd_libm/src/s_nextafter.c @@ -0,0 +1,76 @@ +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_nextafter.c,v 1.11 2002/05/26 22:01:57 wiz Exp $"); +#endif + +/* IEEE functions + * nextafter(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + */ + +#include "math.h" +#include "math_private.h" + +double +nextafter(double x, double y) +{ + int32_t hx,hy,ix,iy; + u_int32_t lx,ly; + + EXTRACT_WORDS(hx,lx,x); + EXTRACT_WORDS(hy,ly,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if(((ix>=0x7ff00000)&&((ix-0x7ff00000)|lx)!=0) || /* x is nan */ + ((iy>=0x7ff00000)&&((iy-0x7ff00000)|ly)!=0)) /* y is nan */ + return x+y; + if(x==y) return x; /* x=y, return x */ + if((ix|lx)==0) { /* x == 0 */ + INSERT_WORDS(x,hy&0x80000000,1); /* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy||((hx==hy)&&(lx>ly))) { /* x > y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x < y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy||((hx==hy)&&(lx>ly))){/* x < y, x -= ulp */ + if(lx==0) hx -= 1; + lx -= 1; + } else { /* x > y, x += ulp */ + lx += 1; + if(lx==0) hx += 1; + } + } + hy = hx&0x7ff00000; + if(hy>=0x7ff00000) return x+x; /* overflow */ + if(hy<0x00100000) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + INSERT_WORDS(y,hx,lx); + return y; + } + } + INSERT_WORDS(x,hx,lx); + return x; +} diff --git a/lib/nbsd_libm/src/s_nextafterf.c b/lib/nbsd_libm/src/s_nextafterf.c new file mode 100644 index 000000000..c5dc958e4 --- /dev/null +++ b/lib/nbsd_libm/src/s_nextafterf.c @@ -0,0 +1,67 @@ +/* s_nextafterf.c -- float version of s_nextafter.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_nextafterf.c,v 1.7 2002/05/26 22:01:58 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +nextafterf(float x, float y) +{ + int32_t hx,hy,ix,iy; + + GET_FLOAT_WORD(hx,x); + GET_FLOAT_WORD(hy,y); + ix = hx&0x7fffffff; /* |x| */ + iy = hy&0x7fffffff; /* |y| */ + + if((ix>0x7f800000) || /* x is nan */ + (iy>0x7f800000)) /* y is nan */ + return x+y; + if(x==y) return x; /* x=y, return x */ + if(ix==0) { /* x == 0 */ + SET_FLOAT_WORD(x,(hy&0x80000000)|1);/* return +-minsubnormal */ + y = x*x; + if(y==x) return y; else return x; /* raise underflow flag */ + } + if(hx>=0) { /* x > 0 */ + if(hx>hy) { /* x > y, x -= ulp */ + hx -= 1; + } else { /* x < y, x += ulp */ + hx += 1; + } + } else { /* x < 0 */ + if(hy>=0||hx>hy){ /* x < y, x -= ulp */ + hx -= 1; + } else { /* x > y, x += ulp */ + hx += 1; + } + } + hy = hx&0x7f800000; + if(hy>=0x7f800000) return x+x; /* overflow */ + if(hy<0x00800000) { /* underflow */ + y = x*x; + if(y!=x) { /* raise underflow flag */ + SET_FLOAT_WORD(y,hx); + return y; + } + } + SET_FLOAT_WORD(x,hx); + return x; +} diff --git a/lib/nbsd_libm/src/s_nextafterl.c b/lib/nbsd_libm/src/s_nextafterl.c new file mode 100644 index 000000000..87488e2f5 --- /dev/null +++ b/lib/nbsd_libm/src/s_nextafterl.c @@ -0,0 +1,94 @@ +/* $NetBSD: s_nextafterl.c,v 1.2 2010/09/17 20:39:39 christos Exp $ */ + +/* @(#)s_nextafter.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +__RCSID("$NetBSD: s_nextafterl.c,v 1.2 2010/09/17 20:39:39 christos Exp $"); + +#include +#include +#include + +#ifdef EXT_EXP_INFNAN +#if LDBL_MAX_EXP != 0x4000 +#error "Unsupported long double format" +#endif + +/* + * IEEE functions + * nextafterl(x,y) + * return the next machine floating-point number of x in the + * direction toward y. + * Special cases: + * If x == y, y shall be returned + * If x or y is NaN, a NaN shall be returned + */ +long double +nextafterl(long double x, long double y) +{ + volatile long double t; + union ieee_ext_u ux, uy; + + ux.extu_ld = x; + uy.extu_ld = y; + + if ((ux.extu_exp == EXT_EXP_NAN && + ((ux.extu_frach &~ LDBL_NBIT)|ux.extu_fracl) != 0) || + (uy.extu_exp == EXT_EXP_NAN && + ((uy.extu_frach &~ LDBL_NBIT)|uy.extu_fracl) != 0)) + return x+y; /* x or y is nan */ + + if (x == y) return y; /* x=y, return y */ + + if (x == 0.0) { + ux.extu_frach = 0; /* return +-minsubnormal */ + ux.extu_fracl = 1; + ux.extu_sign = uy.extu_sign; + t = ux.extu_ld * ux.extu_ld; + if (t == ux.extu_ld) + return t; + else + return ux.extu_ld; /* raise underflow flag */ + } + + if ((x>0.0) ^ (x +__RCSID("$NetBSD: s_nexttoward.c,v 1.1 2010/09/15 16:12:05 christos Exp $"); + +/* + * We assume that a long double has a 15-bit exponent. On systems + * where long double is the same as double, nexttoward() is an alias + * for nextafter(), so we don't use this routine. + */ +#include + +#include +#include "math.h" +#include "math_private.h" + +#if LDBL_MAX_EXP != 0x4000 +#error "Unsupported long double format" +#endif + +/* + * The nexttoward() function is equivalent to nextafter() function, + * except that the second parameter shall have type long double and + * the functions shall return y converted to the type of the function + * if x equals y. + * + * Special cases: XXX + */ +double +nexttoward(double x, long double y) +{ + union ieee_ext_u uy; + volatile double t; + int32_t hx, ix; + uint32_t lx; + + EXTRACT_WORDS(hx, lx, x); + ix = hx & 0x7fffffff; /* |x| */ + uy.extu_ld = y; + + if (((ix >= 0x7ff00000) && ((ix - 0x7ff00000) | lx) != 0) || + (uy.extu_exp == 0x7fff && + ((uy.extu_frach & ~LDBL_NBIT) | uy.extu_fracl) != 0)) + return x+y; /* x or y is nan */ + + if (x == y) + return (double)y; /* x=y, return y */ + + if (x == 0.0) { + INSERT_WORDS(x, uy.extu_sign<<31, 1); /* return +-minsubnormal */ + t = x*x; + if (t == x) + return t; + else + return x; /* raise underflow flag */ + } + + if ((hx > 0.0) ^ (x < y)) { /* x -= ulp */ + if (lx == 0) hx -= 1; + lx -= 1; + } else { /* x += ulp */ + lx += 1; + if (lx == 0) hx += 1; + } + ix = hx & 0x7ff00000; + if (ix >= 0x7ff00000) return x+x; /* overflow */ + if (ix < 0x00100000) { /* underflow */ + t = x*x; + if (t != x) { /* raise underflow flag */ + INSERT_WORDS(y, hx, lx); + return y; + } + } + INSERT_WORDS(x, hx, lx); + + return x; +} diff --git a/lib/nbsd_libm/src/s_rint.c b/lib/nbsd_libm/src/s_rint.c new file mode 100644 index 000000000..276e33c8c --- /dev/null +++ b/lib/nbsd_libm/src/s_rint.c @@ -0,0 +1,79 @@ +/* @(#)s_rint.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_rint.c,v 1.12 2008/04/25 22:21:53 christos Exp $"); +#endif + +/* + * rint(x) + * Return x rounded to integral value according to the prevailing + * rounding mode. + * Method: + * Using floating addition. + * Exception: + * Inexact flag raised if x not equal to rint(x). + */ + +#include "math.h" +#include "math_private.h" + +static const double +TWO52[2]={ + 4.50359962737049600000e+15, /* 0x43300000, 0x00000000 */ + -4.50359962737049600000e+15, /* 0xC3300000, 0x00000000 */ +}; + +double +rint(double x) +{ + int32_t i0,jj0,sx; + u_int32_t i,i1; + double w,t; + EXTRACT_WORDS(i0,i1,x); + sx = (i0>>31)&1; + jj0 = ((i0>>20)&0x7ff)-0x3ff; + if(jj0<20) { + if(jj0<0) { + if(((i0&0x7fffffff)|i1)==0) return x; + i1 |= (i0&0x0fffff); + i0 &= 0xfffe0000; + i0 |= ((i1|-i1)>>12)&0x80000; + SET_HIGH_WORD(x,i0); + w = TWO52[sx]+x; + t = w-TWO52[sx]; + GET_HIGH_WORD(i0,t); + SET_HIGH_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x000fffff)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + i>>=1; + if(((i0&i)|i1)!=0) { + if(jj0==19) i1 = 0x40000000; else + i0 = (i0&(~i))|((0x20000)>>jj0); + } + } + } else if (jj0>51) { + if(jj0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(jj0-20); + if((i1&i)==0) return x; /* x is integral */ + i>>=1; + if((i1&i)!=0) i1 = (i1&(~i))|((0x40000000)>>(jj0-20)); + } + INSERT_WORDS(x,i0,i1); + w = TWO52[sx]+x; + return w-TWO52[sx]; +} diff --git a/lib/nbsd_libm/src/s_rintf.c b/lib/nbsd_libm/src/s_rintf.c new file mode 100644 index 000000000..07573c52d --- /dev/null +++ b/lib/nbsd_libm/src/s_rintf.c @@ -0,0 +1,68 @@ +/* s_rintf.c -- float version of s_rint.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_rintf.c,v 1.9 2008/04/25 22:21:53 christos Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float +TWO23[2]={ + 8.3886080000e+06, /* 0x4b000000 */ + -8.3886080000e+06, /* 0xcb000000 */ +}; + +float +rintf(float x) +{ + int32_t i0,jj0,sx; + u_int32_t i,i1; +#ifdef __i386__ /* XXX gcc4 will omit the rounding otherwise */ + volatile +#endif + float w; + float t; + GET_FLOAT_WORD(i0,x); + sx = (i0>>31)&1; + jj0 = ((i0>>23)&0xff)-0x7f; + if(jj0<23) { + if(jj0<0) { + if((i0&0x7fffffff)==0) return x; + i1 = (i0&0x07fffff); + i0 &= 0xfff00000; + i0 |= ((i1|-i1)>>9)&0x400000; + SET_FLOAT_WORD(x,i0); + w = TWO23[sx]+x; + t = w-TWO23[sx]; + GET_FLOAT_WORD(i0,t); + SET_FLOAT_WORD(t,(i0&0x7fffffff)|(sx<<31)); + return t; + } else { + i = (0x007fffff)>>jj0; + if((i0&i)==0) return x; /* x is integral */ + i>>=1; + if((i0&i)!=0) i0 = (i0&(~i))|((0x100000)>>jj0); + } + } else { + if(jj0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + w = TWO23[sx]+x; + return w-TWO23[sx]; +} diff --git a/lib/nbsd_libm/src/s_round.c b/lib/nbsd_libm/src/s_round.c new file mode 100644 index 000000000..7c06bbbac --- /dev/null +++ b/lib/nbsd_libm/src/s_round.c @@ -0,0 +1,59 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_round.c,v 1.2 2007/08/21 20:10:27 drochner Exp $"); +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_round.c,v 1.1 2004/06/07 08:05:36 das Exp $"); +#endif +#endif + +#include + +double +round(double x) +{ + double t; + int i; + + i = fpclassify(x); + if (i == FP_INFINITE || i == FP_NAN) + return (x); + + if (x >= 0.0) { + t = floor(x); + if (x - t >= 0.5) + t += 1.0; + return (t); + } else { + x = -x; + t = floor(x); + if (x - t >= 0.5) + t += 1.0; + return (-t); + } +} diff --git a/lib/nbsd_libm/src/s_roundf.c b/lib/nbsd_libm/src/s_roundf.c new file mode 100644 index 000000000..a1bbc9f18 --- /dev/null +++ b/lib/nbsd_libm/src/s_roundf.c @@ -0,0 +1,59 @@ +/*- + * Copyright (c) 2003, Steven G. Kargl + * All rights reserved. + * + * Redistribution and use in source and binary forms, with or without + * modification, are permitted provided that the following conditions + * are met: + * 1. Redistributions of source code must retain the above copyright + * notice unmodified, this list of conditions, and the following + * disclaimer. + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the distribution. + * + * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR + * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES + * OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. + * IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, + * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT + * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, + * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY + * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT + * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF + * THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_roundf.c,v 1.2 2007/08/21 20:10:27 drochner Exp $"); +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_roundf.c,v 1.1 2004/06/07 08:05:36 das Exp $"); +#endif +#endif + +#include + +float +roundf(float x) +{ + float t; + int i; + + i = fpclassify(x); + if (i == FP_INFINITE || i == FP_NAN) + return (x); + + if (x >= 0.0) { + t = floorf(x); + if (x - t >= 0.5) + t += 1.0; + return (t); + } else { + x = -x; + t = floorf(x); + if (x - t >= 0.5) + t += 1.0; + return (-t); + } +} diff --git a/lib/nbsd_libm/src/s_scalbn.c b/lib/nbsd_libm/src/s_scalbn.c new file mode 100644 index 000000000..f8b2f8c3a --- /dev/null +++ b/lib/nbsd_libm/src/s_scalbn.c @@ -0,0 +1,65 @@ +/* @(#)s_scalbn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_scalbn.c,v 1.14 2010/04/23 19:17:07 drochner Exp $"); +#endif + +/* + * scalbn (double x, int n) + * scalbn(x,n) returns x* 2**n computed by exponent + * manipulation rather than by actually performing an + * exponentiation or a multiplication. + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(scalbn, _scalbn) +#endif + +static const double +two54 = 1.80143985094819840000e+16, /* 0x43500000, 0x00000000 */ +twom54 = 5.55111512312578270212e-17, /* 0x3C900000, 0x00000000 */ +huge = 1.0e+300, +tiny = 1.0e-300; + +double +scalbn(double x, int n) +{ + int32_t k,hx,lx; + EXTRACT_WORDS(hx,lx,x); + k = ((uint32_t)hx&0x7ff00000)>>20; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((lx|(hx&0x7fffffff))==0) return x; /* +-0 */ + x *= two54; + GET_HIGH_WORD(hx,x); + k = (((uint32_t)hx&0x7ff00000)>>20) - 54; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0x7ff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0x7fe) return huge*copysign(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); return x;} + if (k <= -54) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysign(huge,x); /*overflow*/ + else return tiny*copysign(tiny,x); /*underflow*/ + } + k += 54; /* subnormal result */ + SET_HIGH_WORD(x,(hx&0x800fffff)|(k<<20)); + return x*twom54; +} diff --git a/lib/nbsd_libm/src/s_scalbnf.c b/lib/nbsd_libm/src/s_scalbnf.c new file mode 100644 index 000000000..35d2faac3 --- /dev/null +++ b/lib/nbsd_libm/src/s_scalbnf.c @@ -0,0 +1,61 @@ +/* s_scalbnf.c -- float version of s_scalbn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_scalbnf.c,v 1.9 2010/04/23 19:17:07 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(scalbnf, _scalbnf) +#endif + +static const float +two25 = 3.355443200e+07, /* 0x4c000000 */ +twom25 = 2.9802322388e-08, /* 0x33000000 */ +huge = 1.0e+30, +tiny = 1.0e-30; + +float +scalbnf(float x, int n) +{ + int32_t k,ix; + GET_FLOAT_WORD(ix,x); + k = (ix&0x7f800000)>>23; /* extract exponent */ + if (k==0) { /* 0 or subnormal x */ + if ((ix&0x7fffffff)==0) return x; /* +-0 */ + x *= two25; + GET_FLOAT_WORD(ix,x); + k = ((ix&0x7f800000)>>23) - 25; + if (n< -50000) return tiny*x; /*underflow*/ + } + if (k==0xff) return x+x; /* NaN or Inf */ + k = k+n; + if (k > 0xfe) return huge*copysignf(huge,x); /* overflow */ + if (k > 0) /* normal result */ + {SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); return x;} + if (k <= -25) { + if (n > 50000) /* in case integer overflow in n+k */ + return huge*copysignf(huge,x); /*overflow*/ + else return tiny*copysignf(tiny,x); /*underflow*/ + } + k += 25; /* subnormal result */ + SET_FLOAT_WORD(x,(ix&0x807fffff)|(k<<23)); + return x*twom25; +} diff --git a/lib/nbsd_libm/src/s_signgam.c b/lib/nbsd_libm/src/s_signgam.c new file mode 100644 index 000000000..ad20c577c --- /dev/null +++ b/lib/nbsd_libm/src/s_signgam.c @@ -0,0 +1,5 @@ +/* $NetBSD: s_signgam.c,v 1.4 1998/01/09 03:15:46 perry Exp $ */ + +#include "math.h" +#include "math_private.h" +int signgam = 0; diff --git a/lib/nbsd_libm/src/s_significand.c b/lib/nbsd_libm/src/s_significand.c new file mode 100644 index 000000000..467611c6c --- /dev/null +++ b/lib/nbsd_libm/src/s_significand.c @@ -0,0 +1,31 @@ +/* @(#)s_signif.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_significand.c,v 1.9 2002/05/26 22:01:58 wiz Exp $"); +#endif + +/* + * significand(x) computes just + * scalb(x, (double) -ilogb(x)), + * for exercising the fraction-part(F) IEEE 754-1985 test vector. + */ + +#include "math.h" +#include "math_private.h" + +double +significand(double x) +{ + return __ieee754_scalb(x,(double) -ilogb(x)); +} diff --git a/lib/nbsd_libm/src/s_significandf.c b/lib/nbsd_libm/src/s_significandf.c new file mode 100644 index 000000000..27c9bf7bd --- /dev/null +++ b/lib/nbsd_libm/src/s_significandf.c @@ -0,0 +1,28 @@ +/* s_significandf.c -- float version of s_significand.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_significandf.c,v 1.6 2002/05/26 22:01:58 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +significandf(float x) +{ + return __ieee754_scalbf(x,(float) -ilogbf(x)); +} diff --git a/lib/nbsd_libm/src/s_sin.c b/lib/nbsd_libm/src/s_sin.c new file mode 100644 index 000000000..9bddce280 --- /dev/null +++ b/lib/nbsd_libm/src/s_sin.c @@ -0,0 +1,86 @@ +/* @(#)s_sin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_sin.c,v 1.11 2007/08/20 16:01:39 drochner Exp $"); +#endif + +/* sin(x) + * Return sine function of x. + * + * kernel function: + * __kernel_sin ... sine function on [-pi/4,pi/4] + * __kernel_cos ... cose function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#if 0 /* notyet */ +#ifdef __weak_alias +__weak_alias(sin, _sin) +#endif +#endif + +double +sin(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_sin(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + switch(n&3) { + case 0: return __kernel_sin(y[0],y[1],1); + case 1: return __kernel_cos(y[0],y[1]); + case 2: return -__kernel_sin(y[0],y[1],1); + default: + return -__kernel_cos(y[0],y[1]); + } + } +} diff --git a/lib/nbsd_libm/src/s_sinf.c b/lib/nbsd_libm/src/s_sinf.c new file mode 100644 index 000000000..9d525be4a --- /dev/null +++ b/lib/nbsd_libm/src/s_sinf.c @@ -0,0 +1,57 @@ +/* s_sinf.c -- float version of s_sin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_sinf.c,v 1.8 2007/08/20 16:01:39 drochner Exp $"); +#endif + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#if 0 /* notyet */ +#ifdef __weak_alias +__weak_alias(sinf, _sinf) +#endif +#endif + +float +sinf(float x) +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fd8) return __kernel_sinf(x,z,0); + + /* sin(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + switch(n&3) { + case 0: return __kernel_sinf(y[0],y[1],1); + case 1: return __kernel_cosf(y[0],y[1]); + case 2: return -__kernel_sinf(y[0],y[1],1); + default: + return -__kernel_cosf(y[0],y[1]); + } + } +} diff --git a/lib/nbsd_libm/src/s_tan.c b/lib/nbsd_libm/src/s_tan.c new file mode 100644 index 000000000..51b83330f --- /dev/null +++ b/lib/nbsd_libm/src/s_tan.c @@ -0,0 +1,73 @@ +/* @(#)s_tan.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_tan.c,v 1.10 2002/05/26 22:01:58 wiz Exp $"); +#endif + +/* tan(x) + * Return tangent function of x. + * + * kernel function: + * __kernel_tan ... tangent function on [-pi/4,pi/4] + * __ieee754_rem_pio2 ... argument reduction routine + * + * Method. + * Let S,C and T denote the sin, cos and tan respectively on + * [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 + * in [-pi/4 , +pi/4], and let n = k mod 4. + * We have + * + * n sin(x) cos(x) tan(x) + * ---------------------------------------------------------- + * 0 S C T + * 1 C -S -1/T + * 2 -S -C T + * 3 -C S -1/T + * ---------------------------------------------------------- + * + * Special cases: + * Let trig be any of sin, cos, or tan. + * trig(+-INF) is NaN, with signals; + * trig(NaN) is that NaN; + * + * Accuracy: + * TRIG(x) returns trig(x) nearly rounded + */ + +#include "math.h" +#include "math_private.h" + +double +tan(double x) +{ + double y[2],z=0.0; + int32_t n, ix; + + /* High word of x. */ + GET_HIGH_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3fe921fb) return __kernel_tan(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7ff00000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2(x,y); + return __kernel_tan(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} diff --git a/lib/nbsd_libm/src/s_tanf.c b/lib/nbsd_libm/src/s_tanf.c new file mode 100644 index 000000000..ecfdc066d --- /dev/null +++ b/lib/nbsd_libm/src/s_tanf.c @@ -0,0 +1,45 @@ +/* s_tanf.c -- float version of s_tan.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_tanf.c,v 1.7 2002/05/26 22:01:58 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +tanf(float x) +{ + float y[2],z=0.0; + int32_t n, ix; + + GET_FLOAT_WORD(ix,x); + + /* |x| ~< pi/4 */ + ix &= 0x7fffffff; + if(ix <= 0x3f490fda) return __kernel_tanf(x,z,1); + + /* tan(Inf or NaN) is NaN */ + else if (ix>=0x7f800000) return x-x; /* NaN */ + + /* argument reduction needed */ + else { + n = __ieee754_rem_pio2f(x,y); + return __kernel_tanf(y[0],y[1],1-((n&1)<<1)); /* 1 -- n even + -1 -- n odd */ + } +} diff --git a/lib/nbsd_libm/src/s_tanh.c b/lib/nbsd_libm/src/s_tanh.c new file mode 100644 index 000000000..ec1fe2725 --- /dev/null +++ b/lib/nbsd_libm/src/s_tanh.c @@ -0,0 +1,79 @@ +/* @(#)s_tanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_tanh.c,v 1.10 2002/05/26 22:01:59 wiz Exp $"); +#endif + +/* Tanh(x) + * Return the Hyperbolic Tangent of x + * + * Method : + * x -x + * e - e + * 0. tanh(x) is defined to be ----------- + * x -x + * e + e + * 1. reduce x to non-negative by tanh(-x) = -tanh(x). + * 2. 0 <= x <= 2**-55 : tanh(x) := x*(one+x) + * -t + * 2**-55 < x <= 1 : tanh(x) := -----; t = expm1(-2x) + * t + 2 + * 2 + * 1 <= x <= 22.0 : tanh(x) := 1- ----- ; t=expm1(2x) + * t + 2 + * 22.0 < x <= INF : tanh(x) := 1. + * + * Special cases: + * tanh(NaN) is NaN; + * only tanh(0)=0 is exact for finite argument. + */ + +#include "math.h" +#include "math_private.h" + +static const double one=1.0, two=2.0, tiny = 1.0e-300; + +double +tanh(double x) +{ + double t,z; + int32_t jx,ix; + + /* High word of |x|. */ + GET_HIGH_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7ff00000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x40360000) { /* |x|<22 */ + if (ix<0x3c800000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3ff00000) { /* |x|>=1 */ + t = expm1(two*fabs(x)); + z = one - two/(t+two); + } else { + t = expm1(-two*fabs(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} diff --git a/lib/nbsd_libm/src/s_tanhf.c b/lib/nbsd_libm/src/s_tanhf.c new file mode 100644 index 000000000..4c42533ed --- /dev/null +++ b/lib/nbsd_libm/src/s_tanhf.c @@ -0,0 +1,57 @@ +/* s_tanhf.c -- float version of s_tanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_tanhf.c,v 1.7 2002/05/26 22:01:59 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +static const float one=1.0, two=2.0, tiny = 1.0e-30; + +float +tanhf(float x) +{ + float t,z; + int32_t jx,ix; + + GET_FLOAT_WORD(jx,x); + ix = jx&0x7fffffff; + + /* x is INF or NaN */ + if(ix>=0x7f800000) { + if (jx>=0) return one/x+one; /* tanh(+-inf)=+-1 */ + else return one/x-one; /* tanh(NaN) = NaN */ + } + + /* |x| < 22 */ + if (ix < 0x41b00000) { /* |x|<22 */ + if (ix<0x24000000) /* |x|<2**-55 */ + return x*(one+x); /* tanh(small) = small */ + if (ix>=0x3f800000) { /* |x|>=1 */ + t = expm1f(two*fabsf(x)); + z = one - two/(t+two); + } else { + t = expm1f(-two*fabsf(x)); + z= -t/(t+two); + } + /* |x| > 22, return +-1 */ + } else { + z = one - tiny; /* raised inexact flag */ + } + return (jx>=0)? z: -z; +} diff --git a/lib/nbsd_libm/src/s_trunc.c b/lib/nbsd_libm/src/s_trunc.c new file mode 100644 index 000000000..61169b2e4 --- /dev/null +++ b/lib/nbsd_libm/src/s_trunc.c @@ -0,0 +1,66 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_trunc.c,v 1.1 2004/06/20 09:25:43 das Exp $"); +#endif +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_trunc.c,v 1.3 2008/04/25 22:21:53 christos Exp $"); +#endif + +/* + * trunc(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to trunc(x). + */ + +#include "math.h" +#include "math_private.h" + +static const double huge = 1.0e300; + +double +trunc(double x) +{ + int32_t i0,i1,jj0; + uint32_t i; + EXTRACT_WORDS(i0,i1,x); + jj0 = ((i0>>20)&0x7ff)-0x3ff; + if(jj0<20) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0) {/* |x|<1, so return 0*sign(x) */ + i0 &= 0x80000000U; + i1 = 0; + } + } else { + i = (0x000fffff)>>jj0; + if(((i0&i)|i1)==0) return x; /* x is integral */ + if(huge+x>0.0) { /* raise inexact flag */ + i0 &= (~i); i1=0; + } + } + } else if (jj0>51) { + if(jj0==0x400) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } else { + i = ((u_int32_t)(0xffffffff))>>(jj0-20); + if((i1&i)==0) return x; /* x is integral */ + if(huge+x>0.0) /* raise inexact flag */ + i1 &= (~i); + } + INSERT_WORDS(x,i0,i1); + return x; +} diff --git a/lib/nbsd_libm/src/s_truncf.c b/lib/nbsd_libm/src/s_truncf.c new file mode 100644 index 000000000..6ec960932 --- /dev/null +++ b/lib/nbsd_libm/src/s_truncf.c @@ -0,0 +1,58 @@ +/* @(#)s_floor.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if 0 +__FBSDID("$FreeBSD: src/lib/msun/src/s_truncf.c,v 1.1 2004/06/20 09:25:43 das Exp $"); +#endif +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: s_truncf.c,v 1.4 2008/04/25 22:21:53 christos Exp $"); +#endif + +/* + * truncf(x) + * Return x rounded toward 0 to integral value + * Method: + * Bit twiddling. + * Exception: + * Inexact flag raised if x not equal to truncf(x). + */ + +#include "math.h" +#include "math_private.h" + +static const float huge = 1.0e30F; + +float +truncf(float x) +{ + int32_t i0,jj0; + uint32_t i; + GET_FLOAT_WORD(i0,x); + jj0 = ((i0>>23)&0xff)-0x7f; + if(jj0<23) { + if(jj0<0) { /* raise inexact if x != 0 */ + if(huge+x>0.0F) /* |x|<1, so return 0*sign(x) */ + i0 &= 0x80000000; + } else { + i = (0x007fffff)>>jj0; + if((i0&i)==0) return x; /* x is integral */ + if(huge+x>0.0F) /* raise inexact flag */ + i0 &= (~i); + } + } else { + if(jj0==0x80) return x+x; /* inf or NaN */ + else return x; /* x is integral */ + } + SET_FLOAT_WORD(x,i0); + return x; +} diff --git a/lib/nbsd_libm/src/w_acos.c b/lib/nbsd_libm/src/w_acos.c new file mode 100644 index 000000000..475c9a4f4 --- /dev/null +++ b/lib/nbsd_libm/src/w_acos.c @@ -0,0 +1,40 @@ +/* @(#)w_acos.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_acos.c,v 1.9 2002/05/26 22:01:59 wiz Exp $"); +#endif + +/* + * wrap_acos(x) + */ + +#include "math.h" +#include "math_private.h" + + +double +acos(double x) /* wrapper acos */ +{ +#ifdef _IEEE_LIBM + return __ieee754_acos(x); +#else + double z; + z = __ieee754_acos(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + return __kernel_standard(x,x,1); /* acos(|x|>1) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_acosf.c b/lib/nbsd_libm/src/w_acosf.c new file mode 100644 index 000000000..61a1555ab --- /dev/null +++ b/lib/nbsd_libm/src/w_acosf.c @@ -0,0 +1,44 @@ +/* w_acosf.c -- float version of w_acos.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_acosf.c,v 1.6 2002/05/26 22:01:59 wiz Exp $"); +#endif + +/* + * wrap_acosf(x) + */ + +#include "math.h" +#include "math_private.h" + + +float +acosf(float x) /* wrapper acosf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_acosf(x); +#else + float z; + z = __ieee754_acosf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)1.0) { + /* acosf(|x|>1) */ + return (float)__kernel_standard((double)x,(double)x,101); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_acosh.c b/lib/nbsd_libm/src/w_acosh.c new file mode 100644 index 000000000..7049a88c9 --- /dev/null +++ b/lib/nbsd_libm/src/w_acosh.c @@ -0,0 +1,39 @@ +/* @(#)w_acosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_acosh.c,v 1.9 2002/05/26 22:01:59 wiz Exp $"); +#endif + +/* + * wrapper acosh(x) + */ + +#include "math.h" +#include "math_private.h" + +double +acosh(double x) /* wrapper acosh */ +{ +#ifdef _IEEE_LIBM + return __ieee754_acosh(x); +#else + double z; + z = __ieee754_acosh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<1.0) { + return __kernel_standard(x,x,29); /* acosh(x<1) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_acoshf.c b/lib/nbsd_libm/src/w_acoshf.c new file mode 100644 index 000000000..4ed0b41ef --- /dev/null +++ b/lib/nbsd_libm/src/w_acoshf.c @@ -0,0 +1,44 @@ +/* w_acoshf.c -- float version of w_acosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + * + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_acoshf.c,v 1.6 2002/05/26 22:01:59 wiz Exp $"); +#endif + +/* + * wrapper acoshf(x) + */ + +#include "math.h" +#include "math_private.h" + +float +acoshf(float x) /* wrapper acoshf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_acoshf(x); +#else + float z; + z = __ieee754_acoshf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(x<(float)1.0) { + /* acosh(x<1) */ + return (float)__kernel_standard((double)x,(double)x,129); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_asin.c b/lib/nbsd_libm/src/w_asin.c new file mode 100644 index 000000000..98fe35c86 --- /dev/null +++ b/lib/nbsd_libm/src/w_asin.c @@ -0,0 +1,44 @@ +/* @(#)w_asin.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_asin.c,v 1.10 2007/08/20 16:01:39 drochner Exp $"); +#endif + +/* + * wrapper asin(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(asin, _asin) +#endif + +double +asin(double x) /* wrapper asin */ +{ +#ifdef _IEEE_LIBM + return __ieee754_asin(x); +#else + double z; + z = __ieee754_asin(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>1.0) { + return __kernel_standard(x,x,2); /* asin(|x|>1) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_asinf.c b/lib/nbsd_libm/src/w_asinf.c new file mode 100644 index 000000000..e94df621f --- /dev/null +++ b/lib/nbsd_libm/src/w_asinf.c @@ -0,0 +1,48 @@ +/* w_asinf.c -- float version of w_asin.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_asinf.c,v 1.7 2007/08/20 16:01:39 drochner Exp $"); +#endif + +/* + * wrapper asinf(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(asinf, _asinf) +#endif + +float +asinf(float x) /* wrapper asinf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_asinf(x); +#else + float z; + z = __ieee754_asinf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)1.0) { + /* asinf(|x|>1) */ + return (float)__kernel_standard((double)x,(double)x,102); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_atan2.c b/lib/nbsd_libm/src/w_atan2.c new file mode 100644 index 000000000..ae46ef3b1 --- /dev/null +++ b/lib/nbsd_libm/src/w_atan2.c @@ -0,0 +1,44 @@ +/* @(#)w_atan2.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_atan2.c,v 1.10 2007/08/10 21:20:36 drochner Exp $"); +#endif + +/* + * wrapper atan2(y,x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(atan2, _atan2) +#endif + +double +atan2(double y, double x) /* wrapper atan2 */ +{ +#ifdef _IEEE_LIBM + return __ieee754_atan2(y,x); +#else + double z; + z = __ieee754_atan2(y,x); + if(_LIB_VERSION == _IEEE_||isnan(x)||isnan(y)) return z; + if(x==0.0&&y==0.0) { + return __kernel_standard(y,x,3); /* atan2(+-0,+-0) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_atan2f.c b/lib/nbsd_libm/src/w_atan2f.c new file mode 100644 index 000000000..8461e1e82 --- /dev/null +++ b/lib/nbsd_libm/src/w_atan2f.c @@ -0,0 +1,48 @@ +/* w_atan2f.c -- float version of w_atan2.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_atan2f.c,v 1.7 2007/08/10 21:20:36 drochner Exp $"); +#endif + +/* + * wrapper atan2f(y,x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(atan2f, _atan2f) +#endif + +float +atan2f(float y, float x) /* wrapper atan2f */ +{ +#ifdef _IEEE_LIBM + return __ieee754_atan2f(y,x); +#else + float z; + z = __ieee754_atan2f(y,x); + if(_LIB_VERSION == _IEEE_||isnanf(x)||isnanf(y)) return z; + if(x==(float)0.0&&y==(float)0.0) { + /* atan2f(+-0,+-0) */ + return (float)__kernel_standard((double)y,(double)x,103); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_atanh.c b/lib/nbsd_libm/src/w_atanh.c new file mode 100644 index 000000000..0abd7ae97 --- /dev/null +++ b/lib/nbsd_libm/src/w_atanh.c @@ -0,0 +1,44 @@ +/* @(#)w_atanh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_atanh.c,v 1.9 2002/05/26 22:02:00 wiz Exp $"); +#endif + +/* + * wrapper atanh(x) + */ + +#include "math.h" +#include "math_private.h" + + +double +atanh(double x) /* wrapper atanh */ +{ +#ifdef _IEEE_LIBM + return __ieee754_atanh(x); +#else + double z,y; + z = __ieee754_atanh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + y = fabs(x); + if(y>=1.0) { + if(y>1.0) + return __kernel_standard(x,x,30); /* atanh(|x|>1) */ + else + return __kernel_standard(x,x,31); /* atanh(|x|==1) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_atanhf.c b/lib/nbsd_libm/src/w_atanhf.c new file mode 100644 index 000000000..0bd1c591f --- /dev/null +++ b/lib/nbsd_libm/src/w_atanhf.c @@ -0,0 +1,49 @@ +/* w_atanhf.c -- float version of w_atanh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_atanhf.c,v 1.6 2002/05/26 22:02:00 wiz Exp $"); +#endif + +/* + * wrapper atanhf(x) + */ + +#include "math.h" +#include "math_private.h" + + +float +atanhf(float x) /* wrapper atanhf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_atanhf(x); +#else + float z,y; + z = __ieee754_atanhf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + y = fabsf(x); + if(y>=(float)1.0) { + if(y>(float)1.0) + /* atanhf(|x|>1) */ + return (float)__kernel_standard((double)x,(double)x,130); + else + /* atanhf(|x|==1) */ + return (float)__kernel_standard((double)x,(double)x,131); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_cosh.c b/lib/nbsd_libm/src/w_cosh.c new file mode 100644 index 000000000..887a4b118 --- /dev/null +++ b/lib/nbsd_libm/src/w_cosh.c @@ -0,0 +1,44 @@ +/* @(#)w_cosh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_cosh.c,v 1.10 2007/08/20 16:01:39 drochner Exp $"); +#endif + +/* + * wrapper cosh(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(cosh, _cosh) +#endif + +double +cosh(double x) /* wrapper cosh */ +{ +#ifdef _IEEE_LIBM + return __ieee754_cosh(x); +#else + double z; + z = __ieee754_cosh(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>7.10475860073943863426e+02) { + return __kernel_standard(x,x,5); /* cosh overflow */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_coshf.c b/lib/nbsd_libm/src/w_coshf.c new file mode 100644 index 000000000..ea5a2e29d --- /dev/null +++ b/lib/nbsd_libm/src/w_coshf.c @@ -0,0 +1,48 @@ +/* w_coshf.c -- float version of w_cosh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_coshf.c,v 1.7 2007/08/20 16:01:40 drochner Exp $"); +#endif + +/* + * wrapper coshf(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(coshf, _coshf) +#endif + +float +coshf(float x) /* wrapper coshf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_coshf(x); +#else + float z; + z = __ieee754_coshf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)8.9415985107e+01) { + /* cosh overflow */ + return (float)__kernel_standard((double)x,(double)x,105); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_drem.c b/lib/nbsd_libm/src/w_drem.c new file mode 100644 index 000000000..12de57af2 --- /dev/null +++ b/lib/nbsd_libm/src/w_drem.c @@ -0,0 +1,19 @@ +/* + * drem() wrapper for remainder(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_drem.c,v 1.4 2004/06/25 15:57:38 drochner Exp $"); +#endif + +#include + +double +drem(double x, double y) +{ + return remainder(x, y); +} diff --git a/lib/nbsd_libm/src/w_dremf.c b/lib/nbsd_libm/src/w_dremf.c new file mode 100644 index 000000000..9e2303153 --- /dev/null +++ b/lib/nbsd_libm/src/w_dremf.c @@ -0,0 +1,20 @@ +/* + * dremf() wrapper for remainderf(). + * + * Written by J.T. Conklin, + * Placed into the Public Domain, 1994. + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_dremf.c,v 1.4 2004/06/25 15:57:38 drochner Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +dremf(float x, float y) +{ + return remainderf(x, y); +} diff --git a/lib/nbsd_libm/src/w_exp.c b/lib/nbsd_libm/src/w_exp.c new file mode 100644 index 000000000..a6f79fc92 --- /dev/null +++ b/lib/nbsd_libm/src/w_exp.c @@ -0,0 +1,51 @@ +/* @(#)w_exp.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_exp.c,v 1.10 2007/08/20 16:01:40 drochner Exp $"); +#endif + +/* + * wrapper exp(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(exp, _exp) +#endif + +static const double +o_threshold= 7.09782712893383973096e+02, /* 0x40862E42, 0xFEFA39EF */ +u_threshold= -7.45133219101941108420e+02; /* 0xc0874910, 0xD52D3051 */ + +double +exp(double x) /* wrapper exp */ +{ +#ifdef _IEEE_LIBM + return __ieee754_exp(x); +#else + double z; + z = __ieee754_exp(x); + if(_LIB_VERSION == _IEEE_) return z; + if(finite(x)) { + if(x>o_threshold) + return __kernel_standard(x,x,6); /* exp overflow */ + else if(x +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_expf.c,v 1.7 2007/08/20 16:01:40 drochner Exp $"); +#endif + +/* + * wrapper expf(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(expf, _expf) +#endif + +static const float +o_threshold= 8.8721679688e+01, /* 0x42b17180 */ +u_threshold= -1.0397208405e+02; /* 0xc2cff1b5 */ + +float +expf(float x) /* wrapper expf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_expf(x); +#else + float z; + z = __ieee754_expf(x); + if(_LIB_VERSION == _IEEE_) return z; + if(finitef(x)) { + if(x>o_threshold) + /* exp overflow */ + return (float)__kernel_standard((double)x,(double)x,106); + else if(x +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_fmod.c,v 1.9 2002/05/26 22:02:00 wiz Exp $"); +#endif + +/* + * wrapper fmod(x,y) + */ + +#include "math.h" +#include "math_private.h" + + +double +fmod(double x, double y) /* wrapper fmod */ +{ +#ifdef _IEEE_LIBM + return __ieee754_fmod(x,y); +#else + double z; + z = __ieee754_fmod(x,y); + if(_LIB_VERSION == _IEEE_ ||isnan(y)||isnan(x)) return z; + if(y==0.0) { + return __kernel_standard(x,y,27); /* fmod(x,0) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_fmodf.c b/lib/nbsd_libm/src/w_fmodf.c new file mode 100644 index 000000000..eb8c4c47d --- /dev/null +++ b/lib/nbsd_libm/src/w_fmodf.c @@ -0,0 +1,44 @@ +/* w_fmodf.c -- float version of w_fmod.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_fmodf.c,v 1.6 2002/05/26 22:02:00 wiz Exp $"); +#endif + +/* + * wrapper fmodf(x,y) + */ + +#include "math.h" +#include "math_private.h" + + +float +fmodf(float x, float y) /* wrapper fmodf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_fmodf(x,y); +#else + float z; + z = __ieee754_fmodf(x,y); + if(_LIB_VERSION == _IEEE_ ||isnanf(y)||isnanf(x)) return z; + if(y==(float)0.0) { + /* fmodf(x,0) */ + return (float)__kernel_standard((double)x,(double)y,127); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_gamma.c b/lib/nbsd_libm/src/w_gamma.c new file mode 100644 index 000000000..4d1993945 --- /dev/null +++ b/lib/nbsd_libm/src/w_gamma.c @@ -0,0 +1,44 @@ +/* @(#)w_gamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_gamma.c,v 1.11 2002/05/26 22:02:00 wiz Exp $"); +#endif + +/* double gamma(double x) + * Return the logarithm of the Gamma function of x. + * + * Method: call gamma_r + */ + +#include "math.h" +#include "math_private.h" + +double +gamma(double x) +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,&signgam); +#else + double y; + y = __ieee754_lgamma_r(x,&signgam); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { + if(floor(x)==x&&x<=0.0) + return __kernel_standard(x,x,41); /* gamma pole */ + else + return __kernel_standard(x,x,40); /* gamma overflow */ + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_gamma_r.c b/lib/nbsd_libm/src/w_gamma_r.c new file mode 100644 index 000000000..2ab5f5332 --- /dev/null +++ b/lib/nbsd_libm/src/w_gamma_r.c @@ -0,0 +1,42 @@ +/* @(#)wr_gamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_gamma_r.c,v 1.11 2002/05/26 22:02:00 wiz Exp $"); +#endif + +/* + * wrapper double gamma_r(double x, int *signgamp) + */ + +#include "math.h" +#include "math_private.h" + +double +gamma_r(double x, int *signgamp) /* wrapper lgamma_r */ +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,signgamp); +#else + double y; + y = __ieee754_lgamma_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { + if(floor(x)==x&&x<=0.0) + return __kernel_standard(x,x,41); /* gamma pole */ + else + return __kernel_standard(x,x,40); /* gamma overflow */ + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_gammaf.c b/lib/nbsd_libm/src/w_gammaf.c new file mode 100644 index 000000000..73235fafe --- /dev/null +++ b/lib/nbsd_libm/src/w_gammaf.c @@ -0,0 +1,43 @@ +/* w_gammaf.c -- float version of w_gamma.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_gammaf.c,v 1.8 2002/05/26 22:02:01 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +gammaf(float x) +{ +#ifdef _IEEE_LIBM + return __ieee754_lgammaf_r(x,&signgam); +#else + float y; + y = __ieee754_lgammaf_r(x,&signgam); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { + if(floorf(x)==x&&x<=(float)0.0) + /* gammaf pole */ + return (float)__kernel_standard((double)x,(double)x,141); + else + /* gammaf overflow */ + return (float)__kernel_standard((double)x,(double)x,140); + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_gammaf_r.c b/lib/nbsd_libm/src/w_gammaf_r.c new file mode 100644 index 000000000..1b01d741e --- /dev/null +++ b/lib/nbsd_libm/src/w_gammaf_r.c @@ -0,0 +1,47 @@ +/* w_gammaf_r.c -- float version of w_gamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_gammaf_r.c,v 1.8 2002/05/26 22:02:01 wiz Exp $"); +#endif + +/* + * wrapper float gammaf_r(float x, int *signgamp) + */ + +#include "math.h" +#include "math_private.h" + +float +gammaf_r(float x, int *signgamp) /* wrapper lgammaf_r */ +{ +#ifdef _IEEE_LIBM + return __ieee754_lgammaf_r(x,signgamp); +#else + float y; + y = __ieee754_lgammaf_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { + if(floorf(x)==x&&x<=(float)0.0) + /* gammaf pole */ + return (float)__kernel_standard((double)x,(double)x,141); + else + /* gamma overflow */ + return (float)__kernel_standard((double)x,(double)x,140); + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_hypot.c b/lib/nbsd_libm/src/w_hypot.c new file mode 100644 index 000000000..4e25a1f1a --- /dev/null +++ b/lib/nbsd_libm/src/w_hypot.c @@ -0,0 +1,44 @@ +/* @(#)w_hypot.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_hypot.c,v 1.10 2007/08/10 21:20:36 drochner Exp $"); +#endif + +/* + * wrapper hypot(x,y) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(hypot, _hypot) +#endif + +double +hypot(double x, double y)/* wrapper hypot */ +{ +#ifdef _IEEE_LIBM + return __ieee754_hypot(x,y); +#else + double z; + z = __ieee754_hypot(x,y); + if(_LIB_VERSION == _IEEE_) return z; + if((!finite(z))&&finite(x)&&finite(y)) + return __kernel_standard(x,y,4); /* hypot overflow */ + else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_hypotf.c b/lib/nbsd_libm/src/w_hypotf.c new file mode 100644 index 000000000..0c88c238c --- /dev/null +++ b/lib/nbsd_libm/src/w_hypotf.c @@ -0,0 +1,48 @@ +/* w_hypotf.c -- float version of w_hypot.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_hypotf.c,v 1.7 2007/08/10 21:20:36 drochner Exp $"); +#endif + +/* + * wrapper hypotf(x,y) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(hypotf, _hypotf) +#endif + +float +hypotf(float x, float y) /* wrapper hypotf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_hypotf(x,y); +#else + float z; + z = __ieee754_hypotf(x,y); + if(_LIB_VERSION == _IEEE_) return z; + if((!finitef(z))&&finitef(x)&&finitef(y)) + /* hypot overflow */ + return (float)__kernel_standard((double)x,(double)y,104); + else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_j0.c b/lib/nbsd_libm/src/w_j0.c new file mode 100644 index 000000000..94679b207 --- /dev/null +++ b/lib/nbsd_libm/src/w_j0.c @@ -0,0 +1,62 @@ +/* @(#)w_j0.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_j0.c,v 1.9 2002/05/26 22:02:01 wiz Exp $"); +#endif + +/* + * wrapper j0(double x), y0(double x) + */ + +#include "math.h" +#include "math_private.h" + +double +j0(double x) /* wrapper j0 */ +{ +#ifdef _IEEE_LIBM + return __ieee754_j0(x); +#else + double z = __ieee754_j0(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(fabs(x)>X_TLOSS) { + return __kernel_standard(x,x,34); /* j0(|x|>X_TLOSS) */ + } else + return z; +#endif +} + +double +y0(double x) /* wrapper y0 */ +{ +#ifdef _IEEE_LIBM + return __ieee754_y0(x); +#else + double z; + z = __ieee754_y0(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ + if(x==0.0) + /* d= -one/(x-x); */ + return __kernel_standard(x,x,8); + else + /* d = zero/(x-x); */ + return __kernel_standard(x,x,9); + } + if(x>X_TLOSS) { + return __kernel_standard(x,x,35); /* y0(x>X_TLOSS) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_j0f.c b/lib/nbsd_libm/src/w_j0f.c new file mode 100644 index 000000000..d7798d299 --- /dev/null +++ b/lib/nbsd_libm/src/w_j0f.c @@ -0,0 +1,67 @@ +/* w_j0f.c -- float version of w_j0.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_j0f.c,v 1.6 2002/05/26 22:02:01 wiz Exp $"); +#endif + +/* + * wrapper j0f(float x), y0f(float x) + */ + +#include "math.h" +#include "math_private.h" + +float +j0f(float x) /* wrapper j0f */ +{ +#ifdef _IEEE_LIBM + return __ieee754_j0f(x); +#else + float z = __ieee754_j0f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(fabsf(x)>(float)X_TLOSS) { + /* j0f(|x|>X_TLOSS) */ + return (float)__kernel_standard((double)x,(double)x,134); + } else + return z; +#endif +} + +float +y0f(float x) /* wrapper y0f */ +{ +#ifdef _IEEE_LIBM + return __ieee754_y0f(x); +#else + float z; + z = __ieee754_y0f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(x <= (float)0.0){ + if(x==(float)0.0) + /* d= -one/(x-x); */ + return (float)__kernel_standard((double)x,(double)x,108); + else + /* d = zero/(x-x); */ + return (float)__kernel_standard((double)x,(double)x,109); + } + if(x>(float)X_TLOSS) { + /* y0(x>X_TLOSS) */ + return (float)__kernel_standard((double)x,(double)x,135); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_j1.c b/lib/nbsd_libm/src/w_j1.c new file mode 100644 index 000000000..5185313e7 --- /dev/null +++ b/lib/nbsd_libm/src/w_j1.c @@ -0,0 +1,63 @@ +/* @(#)w_j1.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_j1.c,v 1.9 2002/05/26 22:02:01 wiz Exp $"); +#endif + +/* + * wrapper of j1,y1 + */ + +#include "math.h" +#include "math_private.h" + +double +j1(double x) /* wrapper j1 */ +{ +#ifdef _IEEE_LIBM + return __ieee754_j1(x); +#else + double z; + z = __ieee754_j1(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(fabs(x)>X_TLOSS) { + return __kernel_standard(x,x,36); /* j1(|x|>X_TLOSS) */ + } else + return z; +#endif +} + +double +y1(double x) /* wrapper y1 */ +{ +#ifdef _IEEE_LIBM + return __ieee754_y1(x); +#else + double z; + z = __ieee754_y1(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ + if(x==0.0) + /* d= -one/(x-x); */ + return __kernel_standard(x,x,10); + else + /* d = zero/(x-x); */ + return __kernel_standard(x,x,11); + } + if(x>X_TLOSS) { + return __kernel_standard(x,x,37); /* y1(x>X_TLOSS) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_j1f.c b/lib/nbsd_libm/src/w_j1f.c new file mode 100644 index 000000000..bd7da996c --- /dev/null +++ b/lib/nbsd_libm/src/w_j1f.c @@ -0,0 +1,68 @@ +/* w_j1f.c -- float version of w_j1.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_j1f.c,v 1.6 2002/05/26 22:02:01 wiz Exp $"); +#endif + +/* + * wrapper of j1f,y1f + */ + +#include "math.h" +#include "math_private.h" + +float +j1f(float x) /* wrapper j1f */ +{ +#ifdef _IEEE_LIBM + return __ieee754_j1f(x); +#else + float z; + z = __ieee754_j1f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(fabsf(x)>(float)X_TLOSS) { + /* j1(|x|>X_TLOSS) */ + return (float)__kernel_standard((double)x,(double)x,136); + } else + return z; +#endif +} + +float +y1f(float x) /* wrapper y1f */ +{ +#ifdef _IEEE_LIBM + return __ieee754_y1f(x); +#else + float z; + z = __ieee754_y1f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(x <= (float)0.0){ + if(x==(float)0.0) + /* d= -one/(x-x); */ + return (float)__kernel_standard((double)x,(double)x,110); + else + /* d = zero/(x-x); */ + return (float)__kernel_standard((double)x,(double)x,111); + } + if(x>(float)X_TLOSS) { + /* y1(x>X_TLOSS) */ + return (float)__kernel_standard((double)x,(double)x,137); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_jn.c b/lib/nbsd_libm/src/w_jn.c new file mode 100644 index 000000000..b23ef995e --- /dev/null +++ b/lib/nbsd_libm/src/w_jn.c @@ -0,0 +1,85 @@ +/* @(#)w_jn.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_jn.c,v 1.9 2002/05/26 22:02:01 wiz Exp $"); +#endif + +/* + * wrapper jn(int n, double x), yn(int n, double x) + * floating point Bessel's function of the 1st and 2nd kind + * of order n + * + * Special cases: + * y0(0)=y1(0)=yn(n,0) = -inf with division by zero signal; + * y0(-ve)=y1(-ve)=yn(n,-ve) are NaN with invalid signal. + * Note 2. About jn(n,x), yn(n,x) + * For n=0, j0(x) is called, + * for n=1, j1(x) is called, + * for nx, a continued fraction approximation to + * j(n,x)/j(n-1,x) is evaluated and then backward + * recursion is used starting from a supposed value + * for j(n,x). The resulting value of j(0,x) is + * compared with the actual value to correct the + * supposed value of j(n,x). + * + * yn(n,x) is similar in all respects, except + * that forward recursion is used for all + * values of n>1. + * + */ + +#include "math.h" +#include "math_private.h" + +double +jn(int n, double x) /* wrapper jn */ +{ +#ifdef _IEEE_LIBM + return __ieee754_jn(n,x); +#else + double z; + z = __ieee754_jn(n,x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(fabs(x)>X_TLOSS) { + return __kernel_standard((double)n,x,38); /* jn(|x|>X_TLOSS,n) */ + } else + return z; +#endif +} + +double +yn(int n, double x) /* wrapper yn */ +{ +#ifdef _IEEE_LIBM + return __ieee754_yn(n,x); +#else + double z; + z = __ieee754_yn(n,x); + if(_LIB_VERSION == _IEEE_ || isnan(x) ) return z; + if(x <= 0.0){ + if(x==0.0) + /* d= -one/(x-x); */ + return __kernel_standard((double)n,x,12); + else + /* d = zero/(x-x); */ + return __kernel_standard((double)n,x,13); + } + if(x>X_TLOSS) { + return __kernel_standard((double)n,x,39); /* yn(x>X_TLOSS,n) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_jnf.c b/lib/nbsd_libm/src/w_jnf.c new file mode 100644 index 000000000..52a43e142 --- /dev/null +++ b/lib/nbsd_libm/src/w_jnf.c @@ -0,0 +1,64 @@ +/* w_jnf.c -- float version of w_jn.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_jnf.c,v 1.6 2002/05/26 22:02:02 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +jnf(int n, float x) /* wrapper jnf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_jnf(n,x); +#else + float z; + z = __ieee754_jnf(n,x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(fabsf(x)>(float)X_TLOSS) { + /* jn(|x|>X_TLOSS,n) */ + return (float)__kernel_standard((double)n,(double)x,138); + } else + return z; +#endif +} + +float +ynf(int n, float x) /* wrapper ynf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_ynf(n,x); +#else + float z; + z = __ieee754_ynf(n,x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) ) return z; + if(x <= (float)0.0){ + if(x==(float)0.0) + /* d= -one/(x-x); */ + return (float)__kernel_standard((double)n,(double)x,112); + else + /* d = zero/(x-x); */ + return (float)__kernel_standard((double)n,(double)x,113); + } + if(x>(float)X_TLOSS) { + /* yn(x>X_TLOSS,n) */ + return (float)__kernel_standard((double)n,(double)x,139); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_lgamma.c b/lib/nbsd_libm/src/w_lgamma.c new file mode 100644 index 000000000..f6ab3891e --- /dev/null +++ b/lib/nbsd_libm/src/w_lgamma.c @@ -0,0 +1,44 @@ +/* @(#)w_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_lgamma.c,v 1.10 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* double lgamma(double x) + * Return the logarithm of the Gamma function of x. + * + * Method: call __ieee754_lgamma_r + */ + +#include "math.h" +#include "math_private.h" + +double +lgamma(double x) +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,&signgam); +#else + double y; + y = __ieee754_lgamma_r(x,&signgam); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { + if(floor(x)==x&&x<=0.0) + return __kernel_standard(x,x,15); /* lgamma pole */ + else + return __kernel_standard(x,x,14); /* lgamma overflow */ + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_lgamma_r.c b/lib/nbsd_libm/src/w_lgamma_r.c new file mode 100644 index 000000000..01860b497 --- /dev/null +++ b/lib/nbsd_libm/src/w_lgamma_r.c @@ -0,0 +1,42 @@ +/* @(#)wr_lgamma.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_lgamma_r.c,v 1.10 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper double lgamma_r(double x, int *signgamp) + */ + +#include "math.h" +#include "math_private.h" + +double +lgamma_r(double x, int *signgamp) /* wrapper lgamma_r */ +{ +#ifdef _IEEE_LIBM + return __ieee754_lgamma_r(x,signgamp); +#else + double y; + y = __ieee754_lgamma_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finite(y)&&finite(x)) { + if(floor(x)==x&&x<=0.0) + return __kernel_standard(x,x,15); /* lgamma pole */ + else + return __kernel_standard(x,x,14); /* lgamma overflow */ + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_lgammaf.c b/lib/nbsd_libm/src/w_lgammaf.c new file mode 100644 index 000000000..bb2bb282b --- /dev/null +++ b/lib/nbsd_libm/src/w_lgammaf.c @@ -0,0 +1,43 @@ +/* w_lgammaf.c -- float version of w_lgamma.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_lgammaf.c,v 1.7 2002/05/26 22:02:02 wiz Exp $"); +#endif + +#include "math.h" +#include "math_private.h" + +float +lgammaf(float x) +{ +#ifdef _IEEE_LIBM + return __ieee754_lgammaf_r(x,&signgam); +#else + float y; + y = __ieee754_lgammaf_r(x,&signgam); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { + if(floorf(x)==x&&x<=(float)0.0) + /* lgamma pole */ + return (float)__kernel_standard((double)x,(double)x,115); + else + /* lgamma overflow */ + return (float)__kernel_standard((double)x,(double)x,114); + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_lgammaf_r.c b/lib/nbsd_libm/src/w_lgammaf_r.c new file mode 100644 index 000000000..853504a1c --- /dev/null +++ b/lib/nbsd_libm/src/w_lgammaf_r.c @@ -0,0 +1,47 @@ +/* w_lgammaf_r.c -- float version of w_lgamma_r.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_lgammaf_r.c,v 1.7 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper float lgammaf_r(float x, int *signgamp) + */ + +#include "math.h" +#include "math_private.h" + +float +lgammaf_r(float x, int *signgamp) /* wrapper lgammaf_r */ +{ +#ifdef _IEEE_LIBM + return __ieee754_lgammaf_r(x,signgamp); +#else + float y; + y = __ieee754_lgammaf_r(x,signgamp); + if(_LIB_VERSION == _IEEE_) return y; + if(!finitef(y)&&finitef(x)) { + if(floorf(x)==x&&x<=(float)0.0) + /* lgamma pole */ + return (float)__kernel_standard((double)x,(double)x,115); + else + /* lgamma overflow */ + return (float)__kernel_standard((double)x,(double)x,114); + } else + return y; +#endif +} diff --git a/lib/nbsd_libm/src/w_log.c b/lib/nbsd_libm/src/w_log.c new file mode 100644 index 000000000..9ab1880e0 --- /dev/null +++ b/lib/nbsd_libm/src/w_log.c @@ -0,0 +1,44 @@ +/* @(#)w_log.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_log.c,v 1.10 2007/08/20 16:01:40 drochner Exp $"); +#endif + +/* + * wrapper log(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(log, _log) +#endif + +double +log(double x) /* wrapper log */ +{ +#ifdef _IEEE_LIBM + return __ieee754_log(x); +#else + double z; + z = __ieee754_log(x); + if(_LIB_VERSION == _IEEE_ || isnan(x) || x > 0.0) return z; + if(x==0.0) + return __kernel_standard(x,x,16); /* log(0) */ + else + return __kernel_standard(x,x,17); /* log(x<0) */ +#endif +} diff --git a/lib/nbsd_libm/src/w_log10.c b/lib/nbsd_libm/src/w_log10.c new file mode 100644 index 000000000..a89e1a98f --- /dev/null +++ b/lib/nbsd_libm/src/w_log10.c @@ -0,0 +1,43 @@ +/* @(#)w_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_log10.c,v 1.9 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper log10(X) + */ + +#include "math.h" +#include "math_private.h" + + +double +log10(double x) /* wrapper log10 */ +{ +#ifdef _IEEE_LIBM + return __ieee754_log10(x); +#else + double z; + z = __ieee754_log10(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<=0.0) { + if(x==0.0) + return __kernel_standard(x,x,18); /* log10(0) */ + else + return __kernel_standard(x,x,19); /* log10(x<0) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_log10f.c b/lib/nbsd_libm/src/w_log10f.c new file mode 100644 index 000000000..d6af2a714 --- /dev/null +++ b/lib/nbsd_libm/src/w_log10f.c @@ -0,0 +1,48 @@ +/* w_log10f.c -- float version of w_log10.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_log10f.c,v 1.6 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper log10f(X) + */ + +#include "math.h" +#include "math_private.h" + + +float +log10f(float x) /* wrapper log10f */ +{ +#ifdef _IEEE_LIBM + return __ieee754_log10f(x); +#else + float z; + z = __ieee754_log10f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(x<=(float)0.0) { + if(x==(float)0.0) + /* log10(0) */ + return (float)__kernel_standard((double)x,(double)x,118); + else + /* log10(x<0) */ + return (float)__kernel_standard((double)x,(double)x,119); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_log2.c b/lib/nbsd_libm/src/w_log2.c new file mode 100644 index 000000000..d828b6180 --- /dev/null +++ b/lib/nbsd_libm/src/w_log2.c @@ -0,0 +1,43 @@ +/* @(#)w_log10.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_log2.c,v 1.1 2005/07/21 16:58:39 christos Exp $"); +#endif + +/* + * wrapper log2(X) + */ + +#include "math.h" +#include "math_private.h" + + +double +log2(double x) /* wrapper log10 */ +{ +#ifdef _IEEE_LIBM + return __ieee754_log2(x); +#else + double z; + z = __ieee754_log2(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<=0.0) { + if(x==0.0) + return __kernel_standard(x,x,48); /* log2(0) */ + else + return __kernel_standard(x,x,49); /* log2(x<0) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_log2f.c b/lib/nbsd_libm/src/w_log2f.c new file mode 100644 index 000000000..229c6aa99 --- /dev/null +++ b/lib/nbsd_libm/src/w_log2f.c @@ -0,0 +1,48 @@ +/* w_log10f.c -- float version of w_log10.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_log2f.c,v 1.1 2005/07/21 16:58:39 christos Exp $"); +#endif + +/* + * wrapper log2f(X) + */ + +#include "math.h" +#include "math_private.h" + + +float +log2f(float x) /* wrapper log2f */ +{ +#ifdef _IEEE_LIBM + return __ieee754_log2f(x); +#else + float z; + z = __ieee754_log2f(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(x<=(float)0.0) { + if(x==(float)0.0) + /* log2(0) */ + return (float)__kernel_standard((double)x,(double)x,148); + else + /* log2(x<0) */ + return (float)__kernel_standard((double)x,(double)x,149); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_logf.c b/lib/nbsd_libm/src/w_logf.c new file mode 100644 index 000000000..e145b1ba5 --- /dev/null +++ b/lib/nbsd_libm/src/w_logf.c @@ -0,0 +1,49 @@ +/* w_logf.c -- float version of w_log.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_logf.c,v 1.7 2007/08/20 16:01:40 drochner Exp $"); +#endif + +/* + * wrapper logf(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(logf, _logf) +#endif + +float +logf(float x) /* wrapper logf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_logf(x); +#else + float z; + z = __ieee754_logf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x) || x > (float)0.0) return z; + if(x==(float)0.0) + /* logf(0) */ + return (float)__kernel_standard((double)x,(double)x,116); + else + /* logf(x<0) */ + return (float)__kernel_standard((double)x,(double)x,117); +#endif +} diff --git a/lib/nbsd_libm/src/w_pow.c b/lib/nbsd_libm/src/w_pow.c new file mode 100644 index 000000000..fa54b2909 --- /dev/null +++ b/lib/nbsd_libm/src/w_pow.c @@ -0,0 +1,62 @@ + + +/* @(#)w_pow.c 5.2 93/10/01 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_pow.c,v 1.7 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper pow(x,y) return x**y + */ + +#include "math.h" +#include "math_private.h" + + +double +pow(double x, double y) /* wrapper pow */ +{ +#ifdef _IEEE_LIBM + return __ieee754_pow(x,y); +#else + double z; + z=__ieee754_pow(x,y); + if(_LIB_VERSION == _IEEE_|| isnan(y)) return z; + if(isnan(x)) { + if(y==0.0) + return __kernel_standard(x,y,42); /* pow(NaN,0.0) */ + else + return z; + } + if(x==0.0){ + if(y==0.0) + return __kernel_standard(x,y,20); /* pow(0.0,0.0) */ + if(finite(y)&&y<0.0) + return __kernel_standard(x,y,23); /* pow(0.0,negative) */ + return z; + } + if(!finite(z)) { + if(finite(x)&&finite(y)) { + if(isnan(z)) + return __kernel_standard(x,y,24); /* pow neg**non-int */ + else + return __kernel_standard(x,y,21); /* pow overflow */ + } + } + if(z==0.0&&finite(x)&&finite(y)) + return __kernel_standard(x,y,22); /* pow underflow */ + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_powf.c b/lib/nbsd_libm/src/w_powf.c new file mode 100644 index 000000000..3ec65801a --- /dev/null +++ b/lib/nbsd_libm/src/w_powf.c @@ -0,0 +1,69 @@ +/* w_powf.c -- float version of w_pow.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_powf.c,v 1.6 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper powf(x,y) return x**y + */ + +#include "math.h" +#include "math_private.h" + + +float +powf(float x, float y) /* wrapper powf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_powf(x,y); +#else + float z; + z=__ieee754_powf(x,y); + if(_LIB_VERSION == _IEEE_|| isnanf(y)) return z; + if(isnanf(x)) { + if(y==(float)0.0) + /* powf(NaN,0.0) */ + return (float)__kernel_standard((double)x,(double)y,142); + else + return z; + } + if(x==(float)0.0){ + if(y==(float)0.0) + /* powf(0.0,0.0) */ + return (float)__kernel_standard((double)x,(double)y,120); + if(finitef(y)&&y<(float)0.0) + /* powf(0.0,negative) */ + return (float)__kernel_standard((double)x,(double)y,123); + return z; + } + if(!finitef(z)) { + if(finitef(x)&&finitef(y)) { + if(isnanf(z)) + /* powf neg**non-int */ + return (float)__kernel_standard((double)x,(double)y,124); + else + /* powf overflow */ + return (float)__kernel_standard((double)x,(double)y,121); + } + } + if(z==(float)0.0&&finitef(x)&&finitef(y)) + /* powf underflow */ + return (float)__kernel_standard((double)x,(double)y,122); + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_remainder.c b/lib/nbsd_libm/src/w_remainder.c new file mode 100644 index 000000000..5438af8c9 --- /dev/null +++ b/lib/nbsd_libm/src/w_remainder.c @@ -0,0 +1,39 @@ +/* @(#)w_remainder.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_remainder.c,v 1.9 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper remainder(x,p) + */ + +#include "math.h" +#include "math_private.h" + +double +remainder(double x, double y) /* wrapper remainder */ +{ +#ifdef _IEEE_LIBM + return __ieee754_remainder(x,y); +#else + double z; + z = __ieee754_remainder(x,y); + if(_LIB_VERSION == _IEEE_ || isnan(y)) return z; + if(y==0.0) + return __kernel_standard(x,y,28); /* remainder(x,0) */ + else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_remainderf.c b/lib/nbsd_libm/src/w_remainderf.c new file mode 100644 index 000000000..761d8edbf --- /dev/null +++ b/lib/nbsd_libm/src/w_remainderf.c @@ -0,0 +1,43 @@ +/* w_remainderf.c -- float version of w_remainder.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_remainderf.c,v 1.6 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper remainderf(x,p) + */ + +#include "math.h" +#include "math_private.h" + +float +remainderf(float x, float y) /* wrapper remainder */ +{ +#ifdef _IEEE_LIBM + return __ieee754_remainderf(x,y); +#else + float z; + z = __ieee754_remainderf(x,y); + if(_LIB_VERSION == _IEEE_ || isnanf(y)) return z; + if(y==(float)0.0) + /* remainder(x,0) */ + return (float)__kernel_standard((double)x,(double)y,128); + else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_scalb.c b/lib/nbsd_libm/src/w_scalb.c new file mode 100644 index 000000000..ad8d84d3a --- /dev/null +++ b/lib/nbsd_libm/src/w_scalb.c @@ -0,0 +1,54 @@ +/* @(#)w_scalb.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_scalb.c,v 1.9 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper scalb(double x, double fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "math.h" +#include "math_private.h" + +#include + +#ifdef _SCALB_INT +double +scalb(double x, int fn) /* wrapper scalb */ +#else +double +scalb(double x, double fn) /* wrapper scalb */ +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_scalb(x,fn); +#else + double z; + z = __ieee754_scalb(x,fn); + if(_LIB_VERSION == _IEEE_) return z; + if(!(finite(z)||isnan(z))&&finite(x)) { + return __kernel_standard(x,(double)fn,32); /* scalb overflow */ + } + if(z==0.0&&z!=x) { + return __kernel_standard(x,(double)fn,33); /* scalb underflow */ + } +#ifndef _SCALB_INT + if(!finite(fn)) errno = ERANGE; +#endif + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_scalbf.c b/lib/nbsd_libm/src/w_scalbf.c new file mode 100644 index 000000000..1fa7db49a --- /dev/null +++ b/lib/nbsd_libm/src/w_scalbf.c @@ -0,0 +1,59 @@ +/* w_scalbf.c -- float version of w_scalb.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_scalbf.c,v 1.6 2002/05/26 22:02:02 wiz Exp $"); +#endif + +/* + * wrapper scalbf(float x, float fn) is provide for + * passing various standard test suite. One + * should use scalbn() instead. + */ + +#include "math.h" +#include "math_private.h" + +#include + +#ifdef _SCALB_INT +float +scalbf(float x, int fn) /* wrapper scalbf */ +#else +float +scalbf(float x, float fn) /* wrapper scalbf */ +#endif +{ +#ifdef _IEEE_LIBM + return __ieee754_scalbf(x,fn); +#else + float z; + z = __ieee754_scalbf(x,fn); + if(_LIB_VERSION == _IEEE_) return z; + if(!(finitef(z)||isnanf(z))&&finitef(x)) { + /* scalbf overflow */ + return (float)__kernel_standard((double)x,(double)fn,132); + } + if(z==(float)0.0&&z!=x) { + /* scalbf underflow */ + return (float)__kernel_standard((double)x,(double)fn,133); + } +#ifndef _SCALB_INT + if(!finitef(fn)) errno = ERANGE; +#endif + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_sinh.c b/lib/nbsd_libm/src/w_sinh.c new file mode 100644 index 000000000..f2f720ff7 --- /dev/null +++ b/lib/nbsd_libm/src/w_sinh.c @@ -0,0 +1,44 @@ +/* @(#)w_sinh.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_sinh.c,v 1.10 2007/08/20 16:01:40 drochner Exp $"); +#endif + +/* + * wrapper sinh(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(sinh, _sinh) +#endif + +double +sinh(double x) /* wrapper sinh */ +{ +#ifdef _IEEE_LIBM + return __ieee754_sinh(x); +#else + double z; + z = __ieee754_sinh(x); + if(_LIB_VERSION == _IEEE_) return z; + if(!finite(z)&&finite(x)) { + return __kernel_standard(x,x,25); /* sinh overflow */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_sinhf.c b/lib/nbsd_libm/src/w_sinhf.c new file mode 100644 index 000000000..42dc1218d --- /dev/null +++ b/lib/nbsd_libm/src/w_sinhf.c @@ -0,0 +1,48 @@ +/* w_sinhf.c -- float version of w_sinh.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_sinhf.c,v 1.7 2007/08/20 16:01:40 drochner Exp $"); +#endif + +/* + * wrapper sinhf(x) + */ + +#include "namespace.h" +#include "math.h" +#include "math_private.h" + +#ifdef __weak_alias +__weak_alias(sinhf, _sinhf) +#endif + +float +sinhf(float x) /* wrapper sinhf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_sinhf(x); +#else + float z; + z = __ieee754_sinhf(x); + if(_LIB_VERSION == _IEEE_) return z; + if(!finitef(z)&&finitef(x)) { + /* sinhf overflow */ + return (float)__kernel_standard((double)x,(double)x,125); + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_sqrt.c b/lib/nbsd_libm/src/w_sqrt.c new file mode 100644 index 000000000..a719ef6e5 --- /dev/null +++ b/lib/nbsd_libm/src/w_sqrt.c @@ -0,0 +1,39 @@ +/* @(#)w_sqrt.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_sqrt.c,v 1.9 2002/05/26 22:02:03 wiz Exp $"); +#endif + +/* + * wrapper sqrt(x) + */ + +#include "math.h" +#include "math_private.h" + +double +sqrt(double x) /* wrapper sqrt */ +{ +#ifdef _IEEE_LIBM + return __ieee754_sqrt(x); +#else + double z; + z = __ieee754_sqrt(x); + if(_LIB_VERSION == _IEEE_ || isnan(x)) return z; + if(x<0.0) { + return __kernel_standard(x,x,26); /* sqrt(negative) */ + } else + return z; +#endif +} diff --git a/lib/nbsd_libm/src/w_sqrtf.c b/lib/nbsd_libm/src/w_sqrtf.c new file mode 100644 index 000000000..edebe73a8 --- /dev/null +++ b/lib/nbsd_libm/src/w_sqrtf.c @@ -0,0 +1,43 @@ +/* w_sqrtf.c -- float version of w_sqrt.c. + * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. + */ + +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$NetBSD: w_sqrtf.c,v 1.6 2002/05/26 22:02:03 wiz Exp $"); +#endif + +/* + * wrapper sqrtf(x) + */ + +#include "math.h" +#include "math_private.h" + +float +sqrtf(float x) /* wrapper sqrtf */ +{ +#ifdef _IEEE_LIBM + return __ieee754_sqrtf(x); +#else + float z; + z = __ieee754_sqrtf(x); + if(_LIB_VERSION == _IEEE_ || isnanf(x)) return z; + if(x<(float)0.0) { + /* sqrtf(negative) */ + return (float)__kernel_standard((double)x,(double)x,126); + } else + return z; +#endif +} -- 2.44.0