--- /dev/null
+.\" $NetBSD: factor.6,v 1.12 2010/05/15 21:22:39 joerg Exp $
+.\"
+.\" Copyright (c) 1989, 1993
+.\" The Regents of the University of California. All rights reserved.
+.\"
+.\" This code is derived from software contributed to Berkeley by
+.\" Landon Curt Noll.
+.\"
+.\" 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.
+.\"
+.\" @(#)factor.6 8.1 (Berkeley) 5/31/93
+.\"
+.\"
+.\" By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
+.\"
+.\" chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
+.\"
+.Dd May 15, 2010
+.Dt FACTOR 6
+.Os
+.Sh NAME
+.Nm factor
+.Nd factor a number
+.Sh SYNOPSIS
+.Nm
+.Op Ar number ...
+.Sh DESCRIPTION
+The
+.Nm
+utility factors integers larger than 1.
+When a number is factored, it is printed, followed by a
+.Dq \&: ,
+and the list of
+.Pq prime
+factors on a single line.
+Factors are listed in ascending order, and are preceded by a space.
+If a factor divides a value more than once, it will be printed more than once.
+.Pp
+When
+.Nm
+is invoked with one or more arguments, each argument will be factored.
+.Pp
+When
+.Nm
+is invoked with no arguments,
+.Nm
+reads numbers, one per line, from standard input, until end of file or error.
+Leading white-space and empty lines are ignored.
+Numbers may be preceded by a single +.
+Integer less than 2 are rejected.
+Numbers are terminated by a non-digit character (such as a newline).
+After a number is read, it is factored.
+Input lines must not be longer than
+.Dv LINE_MAX \- 1
+(currently 2047) characters.
+.Pp
+By default,
+.Nm
+is compiled against the OpenSSL bignum implementation
+.Xr openssl_bn 3 ,
+which lets it handle arbitrarily large values.
+.Pq Note however that very large values can take a very long time to factor.
+If
+.Nm
+is compiled without OpenSSL it is limited to the maximum value of
+.Vt unsigned long .
+.Sh DIAGNOSTICS
+Out of range or invalid input results in
+an appropriate error message
+being written to standard error.
+.\".Sh BUGS
+.\".Nm
+.\"cannot handle the
+.\".Dq 10 most wanted
+.\"factor list.
--- /dev/null
+/* $NetBSD: factor.c,v 1.26 2011/11/09 20:17:44 drochner Exp $ */
+
+/*
+ * Copyright (c) 1989, 1993
+ * The Regents of the University of California. All rights reserved.
+ *
+ * This code is derived from software contributed to Berkeley by
+ * Landon Curt Noll.
+ *
+ * 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.
+ */
+
+#include <sys/cdefs.h>
+#ifndef lint
+__COPYRIGHT("@(#) Copyright (c) 1989, 1993\
+ The Regents of the University of California. All rights reserved.");
+#endif /* not lint */
+
+#ifndef lint
+#if 0
+static char sccsid[] = "@(#)factor.c 8.4 (Berkeley) 5/4/95";
+#else
+__RCSID("$NetBSD: factor.c,v 1.26 2011/11/09 20:17:44 drochner Exp $");
+#endif
+#endif /* not lint */
+
+/*
+ * factor - factor a number into primes
+ *
+ * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
+ *
+ * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
+ *
+ * usage:
+ * factor [number] ...
+ *
+ * The form of the output is:
+ *
+ * number: factor1 factor1 factor2 factor3 factor3 factor3 ...
+ *
+ * where factor1 <= factor2 <= factor3 <= ...
+ *
+ * If no args are given, the list of numbers are read from stdin.
+ */
+
+#include <ctype.h>
+#include <err.h>
+#include <errno.h>
+#include <limits.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <unistd.h>
+
+#ifdef HAVE_OPENSSL
+#include <openssl/bn.h>
+#else
+typedef long BIGNUM;
+typedef u_long BN_ULONG;
+static int BN_dec2bn(BIGNUM **a, const char *str);
+#define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1))
+#define BN_is_zero(v) (*(v) == 0)
+#define BN_is_one(v) (*(v) == 1)
+#define BN_mod_word(a, b) (*(a) % (b))
+#endif
+
+#include "primes.h"
+
+/*
+ * prime[i] is the (i-1)th prime.
+ *
+ * We are able to sieve 2^32-1 because this byte table yields all primes
+ * up to 65537 and 65537^2 > 2^32-1.
+ */
+extern const ubig prime[];
+extern const ubig *pr_limit; /* largest prime in the prime array */
+#if 0 /* debugging: limit table use to stress the "pollard" code */
+#define pr_limit &prime[0]
+#endif
+
+#define PRIME_CHECKS 5
+
+#ifdef HAVE_OPENSSL
+static BN_CTX *ctx; /* just use a global context */
+#endif
+
+static void pr_fact(BIGNUM *); /* print factors of a value */
+static void BN_print_dec_fp(FILE *, const BIGNUM *);
+static void usage(void) __dead;
+#ifdef HAVE_OPENSSL
+static void pollard_rho(BIGNUM *); /* print factors for big numbers */
+#else
+static char *BN_bn2dec(const BIGNUM *);
+static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
+#endif
+
+
+#ifndef HAVE_OPENSSL
+static int
+BN_dec2bn(BIGNUM **a, const char *str)
+{
+ char *p;
+
+ errno = 0;
+ **a = strtoul(str, &p, 10);
+ if (errno)
+ err(1, "%s", str);
+ return (*p == '\n' || *p == '\0');
+}
+#endif
+
+int
+main(int argc, char *argv[])
+{
+ BIGNUM *val;
+ int ch;
+ char *p, buf[LINE_MAX]; /* > max number of digits. */
+
+#ifdef HAVE_OPENSSL
+ ctx = BN_CTX_new();
+#endif
+ val = BN_new();
+ if (val == NULL)
+ errx(1, "can't initialise bignum");
+
+ while ((ch = getopt(argc, argv, "")) != -1)
+ switch (ch) {
+ case '?':
+ default:
+ usage();
+ }
+ argc -= optind;
+ argv += optind;
+
+ /* No args supplied, read numbers from stdin. */
+ if (argc == 0)
+ for (;;) {
+ if (fgets(buf, sizeof(buf), stdin) == NULL) {
+ if (ferror(stdin))
+ err(1, "stdin");
+ exit (0);
+ }
+ for (p = buf; isblank((unsigned char)*p); ++p);
+ if (*p == '\n' || *p == '\0')
+ continue;
+ if (*p == '-')
+ errx(1, "negative numbers aren't permitted.");
+ if (BN_dec2bn(&val, buf) == 0)
+ errx(1, "%s: illegal numeric format.", argv[0]);
+ pr_fact(val);
+ }
+ /* Factor the arguments. */
+ else
+ for (; *argv != NULL; ++argv) {
+ if (argv[0][0] == '-')
+ errx(1, "numbers <= 1 aren't permitted.");
+ if (BN_dec2bn(&val, argv[0]) == 0)
+ errx(1, "%s: illegal numeric format.", argv[0]);
+ pr_fact(val);
+ }
+ exit(0);
+}
+
+/*
+ * pr_fact - print the factors of a number
+ *
+ * If the number is 0 or 1, then print the number and return.
+ * If the number is < 0, print -1, negate the number and continue
+ * processing.
+ *
+ * Print the factors of the number, from the lowest to the highest.
+ * A factor will be printed numtiple times if it divides the value
+ * multiple times.
+ *
+ * Factors are printed with leading tabs.
+ */
+static void
+pr_fact(BIGNUM *val)
+{
+ const ubig *fact; /* The factor found. */
+
+ /* Firewall - catch 0 and 1. */
+ if (BN_is_zero(val) || BN_is_one(val))
+ errx(1, "numbers <= 1 aren't permitted.");
+
+ /* Factor value. */
+
+ BN_print_dec_fp(stdout, val);
+ putchar(':');
+ for (fact = &prime[0]; !BN_is_one(val); ++fact) {
+ /* Look for the smallest factor. */
+ while (fact <= pr_limit) {
+ if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
+ break;
+ fact++;
+ }
+
+ /* Watch for primes larger than the table. */
+ if (fact > pr_limit) {
+#ifdef HAVE_OPENSSL
+ BIGNUM *bnfact;
+
+ bnfact = BN_new();
+ BN_set_word(bnfact, (BN_ULONG)*(fact - 1));
+ BN_sqr(bnfact, bnfact, ctx);
+ if (BN_cmp(bnfact, val) > 0
+ || BN_is_prime(val, PRIME_CHECKS, NULL, NULL,
+ NULL) == 1) {
+ putchar(' ');
+ BN_print_dec_fp(stdout, val);
+ } else
+ pollard_rho(val);
+#else
+ printf(" %s", BN_bn2dec(val));
+#endif
+ break;
+ }
+
+ /* Divide factor out until none are left. */
+ do {
+ printf(" %lu", *fact);
+ BN_div_word(val, (BN_ULONG)*fact);
+ } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
+
+ /* Let the user know we're doing something. */
+ fflush(stdout);
+ }
+ putchar('\n');
+}
+
+/*
+ * Sigh.. No _decimal_ output to file functions in BN.
+ */
+static void
+BN_print_dec_fp(FILE *fp, const BIGNUM *num)
+{
+ char *buf;
+
+ buf = BN_bn2dec(num);
+ if (buf == NULL)
+ return; /* XXX do anything here? */
+ fprintf(fp, "%s", buf);
+ free(buf);
+}
+
+void
+usage(void)
+{
+ fprintf(stderr, "usage: factor [value ...]\n");
+ exit (0);
+}
+
+
+
+
+#ifdef HAVE_OPENSSL
+static void
+pollard_rho(BIGNUM *val)
+{
+ BIGNUM *x, *y, *tmp, *num;
+ BN_ULONG a;
+ unsigned int steps_taken, steps_limit;
+
+ x = BN_new();
+ y = BN_new();
+ tmp = BN_new();
+ num = BN_new();
+ a = 1;
+restart:
+ steps_taken = 0;
+ steps_limit = 2;
+ BN_set_word(x, 1);
+ BN_copy(y, x);
+
+ for (;;) {
+ BN_sqr(tmp, x, ctx);
+ BN_add_word(tmp, a);
+ BN_mod(x, tmp, val, ctx);
+ BN_sub(tmp, x, y);
+ if (BN_is_zero(tmp)) {
+#ifdef DEBUG
+ printf(" (loop)");
+#endif
+ a++;
+ goto restart;
+ }
+ BN_gcd(tmp, tmp, val, ctx);
+
+ if (!BN_is_one(tmp)) {
+ if (BN_is_prime(tmp, PRIME_CHECKS, NULL, NULL,
+ NULL) == 1) {
+ putchar(' ');
+ BN_print_dec_fp(stdout, tmp);
+ } else {
+#ifdef DEBUG
+ printf(" (recurse for ");
+ BN_print_dec_fp(stdout, tmp);
+ putchar(')');
+#endif
+ pollard_rho(BN_dup(tmp));
+#ifdef DEBUG
+ printf(" (back)");
+#endif
+ }
+ fflush(stdout);
+
+ BN_div(num, NULL, val, tmp, ctx);
+ if (BN_is_one(num))
+ return;
+ if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
+ NULL) == 1) {
+ putchar(' ');
+ BN_print_dec_fp(stdout, num);
+ fflush(stdout);
+ return;
+ }
+ BN_copy(val, num);
+ goto restart;
+ }
+ steps_taken++;
+ if (steps_taken == steps_limit) {
+ BN_copy(y, x); /* teleport the turtle */
+ steps_taken = 0;
+ steps_limit *= 2;
+ if (steps_limit == 0) {
+#ifdef DEBUG
+ printf(" (overflow)");
+#endif
+ a++;
+ goto restart;
+ }
+ }
+ }
+}
+#else
+char *
+BN_bn2dec(const BIGNUM *val)
+{
+ char *buf;
+
+ buf = malloc(100);
+ if (!buf)
+ return buf;
+ snprintf(buf, 100, "%ld", (long)*val);
+ return buf;
+}
+
+static BN_ULONG
+BN_div_word(BIGNUM *a, BN_ULONG b)
+{
+ BN_ULONG mod;
+
+ mod = *a % b;
+ *a /= b;
+ return mod;
+}
+#endif