factor/factor.c

   1 /*      $NetBSD: factor.c,v 1.26 2011/11/09 20:17:44 drochner Exp $     */
   2
   3 /*
   4  * Copyright (c) 1989, 1993
   5  *      The Regents of the University of California.  All rights reserved.
   6  *
   7  * This code is derived from software contributed to Berkeley by
   8  * Landon Curt Noll.
   9  *
  10  * Redistribution and use in source and binary forms, with or without
  11  * modification, are permitted provided that the following conditions
  12  * are met:
  13  * 1. Redistributions of source code must retain the above copyright
  14  *    notice, this list of conditions and the following disclaimer.
  15  * 2. Redistributions in binary form must reproduce the above copyright
  16  *    notice, this list of conditions and the following disclaimer in the
  17  *    documentation and/or other materials provided with the distribution.
  18  * 3. Neither the name of the University nor the names of its contributors
  19  *    may be used to endorse or promote products derived from this software
  20  *    without specific prior written permission.
  21  *
  22  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  23  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  24  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  25  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  26  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  27  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  28  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  29  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  30  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  31  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  32  * SUCH DAMAGE.
  33  */
  34
  35 #include <sys/cdefs.h>
  36 #ifndef lint
  37 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\
  38  The Regents of the University of California.  All rights reserved.");
  39 #endif /* not lint */
  40
  41 #ifndef lint
  42 #if 0
  43 static char sccsid[] = "@(#)factor.c    8.4 (Berkeley) 5/4/95";
  44 #else
  45 __RCSID("$NetBSD: factor.c,v 1.26 2011/11/09 20:17:44 drochner Exp $");
  46 #endif
  47 #endif /* not lint */
  48
  49 /*
  50  * factor - factor a number into primes
  51  *
  52  * By: Landon Curt Noll   chongo@toad.com,   ...!{sun,tolsoft}!hoptoad!chongo
  53  *
  54  *   chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
  55  *
  56  * usage:
  57  *      factor [number] ...
  58  *
  59  * The form of the output is:
  60  *
  61  *      number: factor1 factor1 factor2 factor3 factor3 factor3 ...
  62  *
  63  * where factor1 <= factor2 <= factor3 <= ...
  64  *
  65  * If no args are given, the list of numbers are read from stdin.
  66  */
  67
  68 #include <ctype.h>
  69 #include <err.h>
  70 #include <errno.h>
  71 #include <limits.h>
  72 #include <stdio.h>
  73 #include <stdlib.h>
  74 #include <unistd.h>
  75
  76 #ifdef HAVE_OPENSSL
  77 #include <openssl/bn.h>
  78 #else
  79 typedef long    BIGNUM;
  80 typedef u_long  BN_ULONG;
  81 static int BN_dec2bn(BIGNUM **a, const char *str);
  82 #define BN_new()                ((BIGNUM *)calloc(sizeof(BIGNUM), 1))
  83 #define BN_is_zero(v)           (*(v) == 0)
  84 #define BN_is_one(v)            (*(v) == 1)
  85 #define BN_mod_word(a, b)       (*(a) % (b))
  86 #endif
  87
  88 #include "primes.h"
  89
  90 /*
  91  * prime[i] is the (i-1)th prime.
  92  *
  93  * We are able to sieve 2^32-1 because this byte table yields all primes
  94  * up to 65537 and 65537^2 > 2^32-1.
  95  */
  96 extern const ubig prime[];
  97 extern const ubig *pr_limit;            /* largest prime in the prime array */
  98 #if 0 /* debugging: limit table use to stress the "pollard" code */
  99 #define pr_limit &prime[0]
 100 #endif
 101
 102 #define PRIME_CHECKS    5
 103
 104 #ifdef HAVE_OPENSSL
 105 static BN_CTX *ctx;                     /* just use a global context */
 106 #endif
 107
 108 static void pr_fact(BIGNUM *);          /* print factors of a value */
 109 static void BN_print_dec_fp(FILE *, const BIGNUM *);
 110 static void usage(void) __dead;
 111 #ifdef HAVE_OPENSSL
 112 static void pollard_rho(BIGNUM *);      /* print factors for big numbers */
 113 #else
 114 static char *BN_bn2dec(const BIGNUM *);
 115 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
 116 #endif
 117
 118
 119 #ifndef HAVE_OPENSSL
 120 static int
 121 BN_dec2bn(BIGNUM **a, const char *str)
 122 {
 123         char *p;
 124
 125         errno = 0;
 126         **a = strtoul(str, &p, 10);
 127         if (errno)
 128                 err(1, "%s", str);
 129         return (*p == '\n' || *p == '\0');
 130 }
 131 #endif
 132
 133 int
 134 main(int argc, char *argv[])
 135 {
 136         BIGNUM *val;
 137         int ch;
 138         char *p, buf[LINE_MAX];         /* > max number of digits. */
 139
 140 #ifdef HAVE_OPENSSL
 141         ctx = BN_CTX_new();
 142 #endif
 143         val = BN_new();
 144         if (val == NULL)
 145                 errx(1, "can't initialise bignum");
 146
 147         while ((ch = getopt(argc, argv, "")) != -1)
 148                 switch (ch) {
 149                 case '?':
 150                 default:
 151                         usage();
 152                 }
 153         argc -= optind;
 154         argv += optind;
 155
 156         /* No args supplied, read numbers from stdin. */
 157         if (argc == 0)
 158                 for (;;) {
 159                         if (fgets(buf, sizeof(buf), stdin) == NULL) {
 160                                 if (ferror(stdin))
 161                                         err(1, "stdin");
 162                                 exit (0);
 163                         }
 164                         for (p = buf; isblank((unsigned char)*p); ++p);
 165                         if (*p == '\n' || *p == '\0')
 166                                 continue;
 167                         if (*p == '-')
 168                                 errx(1, "negative numbers aren't permitted.");
 169                         if (BN_dec2bn(&val, buf) == 0)
 170                                 errx(1, "%s: illegal numeric format.", argv[0]);
 171                         pr_fact(val);
 172                 }
 173         /* Factor the arguments. */
 174         else
 175                 for (; *argv != NULL; ++argv) {
 176                         if (argv[0][0] == '-')
 177                                 errx(1, "numbers <= 1 aren't permitted.");
 178                         if (BN_dec2bn(&val, argv[0]) == 0)
 179                                 errx(1, "%s: illegal numeric format.", argv[0]);
 180                         pr_fact(val);
 181                 }
 182         exit(0);
 183 }
 184
 185 /*
 186  * pr_fact - print the factors of a number
 187  *
 188  * If the number is 0 or 1, then print the number and return.
 189  * If the number is < 0, print -1, negate the number and continue
 190  * processing.
 191  *
 192  * Print the factors of the number, from the lowest to the highest.
 193  * A factor will be printed numtiple times if it divides the value
 194  * multiple times.
 195  *
 196  * Factors are printed with leading tabs.
 197  */
 198 static void
 199 pr_fact(BIGNUM *val)
 200 {
 201         const ubig *fact;               /* The factor found. */
 202
 203         /* Firewall - catch 0 and 1. */
 204         if (BN_is_zero(val) || BN_is_one(val))
 205                 errx(1, "numbers <= 1 aren't permitted.");
 206
 207         /* Factor value. */
 208
 209         BN_print_dec_fp(stdout, val);
 210         putchar(':');
 211         for (fact = &prime[0]; !BN_is_one(val); ++fact) {
 212                 /* Look for the smallest factor. */
 213                 while (fact <= pr_limit) {
 214                         if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
 215                                 break;
 216                         fact++;
 217                 }
 218
 219                 /* Watch for primes larger than the table. */
 220                 if (fact > pr_limit) {
 221 #ifdef HAVE_OPENSSL
 222                         BIGNUM *bnfact;
 223
 224                         bnfact = BN_new();
 225                         BN_set_word(bnfact, (BN_ULONG)*(fact - 1));
 226                         BN_sqr(bnfact, bnfact, ctx);
 227                         if (BN_cmp(bnfact, val) > 0
 228                             || BN_is_prime(val, PRIME_CHECKS, NULL, NULL,
 229                                            NULL) == 1) {
 230                                 putchar(' ');
 231                                 BN_print_dec_fp(stdout, val);
 232                         } else
 233                                 pollard_rho(val);
 234 #else
 235                         printf(" %s", BN_bn2dec(val));
 236 #endif
 237                         break;
 238                 }
 239
 240                 /* Divide factor out until none are left. */
 241                 do {
 242                         printf(" %lu", *fact);
 243                         BN_div_word(val, (BN_ULONG)*fact);
 244                 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
 245
 246                 /* Let the user know we're doing something. */
 247                 fflush(stdout);
 248         }
 249         putchar('\n');
 250 }
 251
 252 /*
 253  * Sigh..  No _decimal_ output to file functions in BN.
 254  */
 255 static void
 256 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
 257 {
 258         char *buf;
 259
 260         buf = BN_bn2dec(num);
 261         if (buf == NULL)
 262                 return; /* XXX do anything here? */
 263         fprintf(fp, "%s", buf);
 264         free(buf);
 265 }
 266
 267 void
 268 usage(void)
 269 {
 270         fprintf(stderr, "usage: factor [value ...]\n");
 271         exit (0);
 272 }
 273
 274
 275
 276
 277 #ifdef HAVE_OPENSSL
 278 static void
 279 pollard_rho(BIGNUM *val)
 280 {
 281         BIGNUM *x, *y, *tmp, *num;
 282         BN_ULONG a;
 283         unsigned int steps_taken, steps_limit;
 284
 285         x = BN_new();
 286         y = BN_new();
 287         tmp = BN_new();
 288         num = BN_new();
 289         a = 1;
 290 restart:
 291         steps_taken = 0;
 292         steps_limit = 2;
 293         BN_set_word(x, 1);
 294         BN_copy(y, x);
 295
 296         for (;;) {
 297                 BN_sqr(tmp, x, ctx);
 298                 BN_add_word(tmp, a);
 299                 BN_mod(x, tmp, val, ctx);
 300                 BN_sub(tmp, x, y);
 301                 if (BN_is_zero(tmp)) {
 302 #ifdef DEBUG
 303                         printf(" (loop)");
 304 #endif
 305                         a++;
 306                         goto restart;
 307                 }
 308                 BN_gcd(tmp, tmp, val, ctx);
 309
 310                 if (!BN_is_one(tmp)) {
 311                         if (BN_is_prime(tmp, PRIME_CHECKS, NULL, NULL,
 312                             NULL) == 1) {
 313                                 putchar(' ');
 314                                 BN_print_dec_fp(stdout, tmp);
 315                         } else {
 316 #ifdef DEBUG
 317                                 printf(" (recurse for ");
 318                                 BN_print_dec_fp(stdout, tmp);
 319                                 putchar(')');
 320 #endif
 321                                 pollard_rho(BN_dup(tmp));
 322 #ifdef DEBUG
 323                                 printf(" (back)");
 324 #endif
 325                         }
 326                         fflush(stdout);
 327
 328                         BN_div(num, NULL, val, tmp, ctx);
 329                         if (BN_is_one(num))
 330                                 return;
 331                         if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
 332                             NULL) == 1) {
 333                                 putchar(' ');
 334                                 BN_print_dec_fp(stdout, num);
 335                                 fflush(stdout);
 336                                 return;
 337                         }
 338                         BN_copy(val, num);
 339                         goto restart;
 340                 }
 341                 steps_taken++;
 342                 if (steps_taken == steps_limit) {
 343                         BN_copy(y, x); /* teleport the turtle */
 344                         steps_taken = 0;
 345                         steps_limit *= 2;
 346                         if (steps_limit == 0) {
 347 #ifdef DEBUG
 348                                 printf(" (overflow)");
 349 #endif
 350                                 a++;
 351                                 goto restart;
 352                         }
 353                 }
 354         }
 355 }
 356 #else
 357 char *
 358 BN_bn2dec(const BIGNUM *val)
 359 {
 360         char *buf;
 361
 362         buf = malloc(100);
 363         if (!buf)
 364                 return buf;
 365         snprintf(buf, 100, "%ld", (long)*val);
 366         return buf;
 367 }
 368
 369 static BN_ULONG
 370 BN_div_word(BIGNUM *a, BN_ULONG b)
 371 {
 372         BN_ULONG mod;
 373
 374         mod = *a % b;
 375         *a /= b;
 376         return mod;
 377 }
 378 #endif