From: Ben Gras Date: Sun, 30 Jan 2011 23:40:51 +0000 (+0000) Subject: some extra math functions from netbsd for netpbm. X-Git-Tag: v3.2.0~692 X-Git-Url: http://zhaoyanbai.com/repos/icons/debian/static/man.7.txt?a=commitdiff_plain;h=dee29bbd3c1ab7d1fe105bf0098e2b603c9869a2;p=minix.git some extra math functions from netbsd for netpbm. --- diff --git a/lib/libc/math/Makefile.inc b/lib/libc/math/Makefile.inc index 67fa7ad34..67baac740 100644 --- a/lib/libc/math/Makefile.inc +++ b/lib/libc/math/Makefile.inc @@ -21,4 +21,7 @@ SRCS+= \ sinh.c \ sqrt.c \ tan.c \ - tanh.c + n_j1.c \ + tanh.c \ + s_finite.c \ + s_copysign.c diff --git a/lib/libc/math/mathimpl.h b/lib/libc/math/mathimpl.h new file mode 100644 index 000000000..92e578fab --- /dev/null +++ b/lib/libc/math/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/libc/math/n_j1.c b/lib/libc/math/n_j1.c new file mode 100644 index 000000000..9f824ce33 --- /dev/null +++ b/lib/libc/math/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/libc/math/s_copysign.c b/lib/libc/math/s_copysign.c new file mode 100644 index 000000000..5640014c5 --- /dev/null +++ b/lib/libc/math/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 $"); +#endif + +/* + * copysign(double x, double y) + * copysign(x,y) returns a value with the magnitude of x and + * with the sign bit of y. + */ + +#include "math.h" +#include "math_private.h" + +double +copysign(double x, double y) +{ + unsigned long hx,hy; + GET_HIGH_WORD(hx,x); + GET_HIGH_WORD(hy,y); + SET_HIGH_WORD(x,(hx&0x7fffffff)|(hy&0x80000000)); + return x; +} diff --git a/lib/libc/math/s_finite.c b/lib/libc/math/s_finite.c new file mode 100644 index 000000000..9f2756c8f --- /dev/null +++ b/lib/libc/math/s_finite.c @@ -0,0 +1,32 @@ +/* @(#)s_finite.c 5.1 93/09/24 */ +/* + * ==================================================== + * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. + * + * Developed at SunPro, a Sun Microsystems, Inc. business. + * Permission to use, copy, modify, and distribute this + * software is freely granted, provided that this notice + * is preserved. + * ==================================================== + */ + +#include +#if defined(LIBM_SCCS) && !defined(lint) +__RCSID("$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) +{ + int hx; + GET_HIGH_WORD(hx,x); + return (int)((unsigned int)((hx&0x7fffffff)-0x7ff00000)>>31); +}