factor/factor.c

   1 /*      $NetBSD: factor.c,v 1.21 2010/04/27 18:11:19 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 1.21 2010/04/27 18:11:19 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_new()                ((BIGNUM *)calloc(sizeof(BIGNUM), 1))
  86 #define BN_is_zero(v)           (*(v) == 0)
  87 #define BN_is_one(v)            (*(v) == 1)
  88 #define BN_mod_word(a, b)       (*(a) % (b))
  89 #endif
  90
  91 #include "primes.h"
  92
  93 /*
  94  * prime[i] is the (i-1)th prime.
  95  *
  96  * We are able to sieve 2^32-1 because this byte table yields all primes
  97  * up to 65537 and 65537^2 > 2^32-1.
  98  */
  99 extern const ubig prime[];
 100 extern const ubig *pr_limit;            /* largest prime in the prime array */
 101 #if 0 /* debugging: limit table use to stress the "pollard" code */
 102 #define pr_limit &prime[0]
 103 #endif
 104
 105 #define PRIME_CHECKS    5
 106
 107 #ifdef HAVE_OPENSSL
 108 static BN_CTX *ctx;                     /* just use a global context */
 109 #endif
 110
 111 static void pr_fact(BIGNUM *);          /* print factors of a value */
 112 static void BN_print_dec_fp(FILE *, const BIGNUM *);
 113 static void usage(void) __dead;
 114 #ifdef HAVE_OPENSSL
 115 static void pollard_pminus1(BIGNUM *);  /* print factors for big numbers */
 116 #else
 117 static char *BN_bn2dec(const BIGNUM *);
 118 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
 119 #endif
 120
 121
 122 #ifndef HAVE_OPENSSL
 123 static int
 124 BN_dec2bn(BIGNUM **a, const char *str)
 125 {
 126         char *p;
 127
 128         errno = 0;
 129         **a = strtoul(str, &p, 10);
 130         if (errno)
 131                 err(1, "%s", str);
 132         return (*p == '\n' || *p == '\0');
 133 }
 134 #endif
 135
 136 int
 137 main(int argc, char *argv[])
 138 {
 139         BIGNUM *val;
 140         int ch;
 141         char *p, buf[LINE_MAX];         /* > max number of digits. */
 142
 143 #ifdef HAVE_OPENSSL
 144         ctx = BN_CTX_new();
 145 #endif
 146         val = BN_new();
 147         if (val == NULL)
 148                 errx(1, "can't initialise bignum");
 149
 150         while ((ch = getopt(argc, argv, "")) != -1)
 151                 switch (ch) {
 152                 case '?':
 153                 default:
 154                         usage();
 155                 }
 156         argc -= optind;
 157         argv += optind;
 158
 159         /* No args supplied, read numbers from stdin. */
 160         if (argc == 0)
 161                 for (;;) {
 162                         if (fgets(buf, sizeof(buf), stdin) == NULL) {
 163                                 if (ferror(stdin))
 164                                         err(1, "stdin");
 165                                 exit (0);
 166                         }
 167                         for (p = buf; isblank(*p); ++p);
 168                         if (*p == '\n' || *p == '\0')
 169                                 continue;
 170                         if (*p == '-')
 171                                 errx(1, "negative numbers aren't permitted.");
 172                         if (BN_dec2bn(&val, buf) == 0)
 173                                 errx(1, "%s: illegal numeric format.", argv[0]);
 174                         pr_fact(val);
 175                 }
 176         /* Factor the arguments. */
 177         else
 178                 for (; *argv != NULL; ++argv) {
 179                         if (argv[0][0] == '-')
 180                                 errx(1, "negative numbers aren't permitted.");
 181                         if (BN_dec2bn(&val, argv[0]) == 0)
 182                                 errx(1, "%s: illegal numeric format.", argv[0]);
 183                         pr_fact(val);
 184                 }
 185         exit(0);
 186 }
 187
 188 /*
 189  * pr_fact - print the factors of a number
 190  *
 191  * If the number is 0 or 1, then print the number and return.
 192  * If the number is < 0, print -1, negate the number and continue
 193  * processing.
 194  *
 195  * Print the factors of the number, from the lowest to the highest.
 196  * A factor will be printed numtiple times if it divides the value
 197  * multiple times.
 198  *
 199  * Factors are printed with leading tabs.
 200  */
 201 static void
 202 pr_fact(BIGNUM *val)
 203 {
 204         const ubig *fact;               /* The factor found. */
 205
 206         /* Firewall - catch 0 and 1. */
 207         if (BN_is_zero(val))    /* Historical practice; 0 just exits. */
 208                 exit(0);
 209         if (BN_is_one(val)) {
 210                 printf("1: 1\n");
 211                 return;
 212         }
 213
 214         /* Factor value. */
 215
 216         BN_print_dec_fp(stdout, val);
 217         putchar(':');
 218         for (fact = &prime[0]; !BN_is_one(val); ++fact) {
 219                 /* Look for the smallest factor. */
 220                 while (fact <= pr_limit) {
 221                         if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
 222                                 break;
 223                         fact++;
 224                 }
 225
 226                 /* Watch for primes larger than the table. */
 227                 if (fact > pr_limit) {
 228 #ifdef HAVE_OPENSSL
 229                         BIGNUM *bnfact;
 230
 231                         bnfact = BN_new();
 232                         BN_set_word(bnfact, (BN_ULONG)*(fact - 1));
 233                         BN_sqr(bnfact, bnfact, ctx);
 234                         if (BN_cmp(bnfact, val) > 0
 235                             || BN_is_prime(val, PRIME_CHECKS, NULL, NULL,
 236                                            NULL) == 1) {
 237                                 putchar(' ');
 238                                 BN_print_dec_fp(stdout, val);
 239                         } else
 240                                 pollard_pminus1(val);
 241 #else
 242                         printf(" %s", BN_bn2dec(val));
 243 #endif
 244                         break;
 245                 }
 246
 247                 /* Divide factor out until none are left. */
 248                 do {
 249                         printf(" %lu", *fact);
 250                         BN_div_word(val, (BN_ULONG)*fact);
 251                 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
 252
 253                 /* Let the user know we're doing something. */
 254                 fflush(stdout);
 255         }
 256         putchar('\n');
 257 }
 258
 259 /*
 260  * Sigh..  No _decimal_ output to file functions in BN.
 261  */
 262 static void
 263 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
 264 {
 265         char *buf;
 266
 267         buf = BN_bn2dec(num);
 268         if (buf == NULL)
 269                 return; /* XXX do anything here? */
 270         fprintf(fp, buf);
 271         free(buf);
 272 }
 273
 274 void
 275 usage(void)
 276 {
 277         fprintf(stderr, "usage: factor [value ...]\n");
 278         exit (0);
 279 }
 280
 281
 282
 283
 284 #ifdef HAVE_OPENSSL
 285 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
 286
 287 static void
 288 pollard_pminus1(BIGNUM *val)
 289 {
 290         BIGNUM *x, *y, *tmp, *num;
 291         BN_ULONG a;
 292         unsigned int steps_taken, steps_limit;
 293
 294         x = BN_new();
 295         y = BN_new();
 296         tmp = BN_new();
 297         num = BN_new();
 298         a = 1;
 299 restart:
 300         steps_taken = 0;
 301         steps_limit = 2;
 302         BN_set_word(x, 1);
 303         BN_copy(y, x);
 304
 305         for (;;) {
 306                 BN_sqr(tmp, x, ctx);
 307                 BN_add_word(tmp, a);
 308                 BN_mod(x, tmp, val, ctx);
 309                 BN_sub(tmp, x, y);
 310                 if (BN_is_zero(tmp)) {
 311 #ifdef DEBUG
 312                         printf(" (loop)");
 313 #endif
 314                         a++;
 315                         goto restart;
 316                 }
 317                 BN_gcd(tmp, tmp, val, ctx);
 318
 319                 if (!BN_is_one(tmp)) {
 320                         if (BN_is_prime(tmp, PRIME_CHECKS, NULL, NULL,
 321                             NULL) == 1) {
 322                                 putchar(' ');
 323                                 BN_print_dec_fp(stdout, tmp);
 324                         } else {
 325 #ifdef DEBUG
 326                                 printf(" (recurse for ");
 327                                 BN_print_dec_fp(stdout, tmp);
 328                                 putchar(')');
 329 #endif
 330                                 pollard_pminus1(BN_dup(tmp));
 331 #ifdef DEBUG
 332                                 printf(" (back)");
 333 #endif
 334                         }
 335                         fflush(stdout);
 336
 337                         BN_div(num, NULL, val, tmp, ctx);
 338                         if (BN_is_one(num))
 339                                 return;
 340                         if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
 341                             NULL) == 1) {
 342                                 putchar(' ');
 343                                 BN_print_dec_fp(stdout, num);
 344                                 fflush(stdout);
 345                                 return;
 346                         }
 347                         BN_copy(val, num);
 348                         goto restart;
 349                 }
 350                 steps_taken++;
 351                 if (steps_taken == steps_limit) {
 352                         BN_copy(y, x); /* teleport the turtle */
 353                         steps_taken = 0;
 354                         steps_limit *= 2;
 355                         if (steps_limit == 0) {
 356 #ifdef DEBUG
 357                                 printf(" (overflow)");
 358 #endif
 359                                 a++;
 360                                 goto restart;
 361                         }
 362                 }
 363         }
 364 }
 365 #else
 366 char *
 367 BN_bn2dec(const BIGNUM *val)
 368 {
 369         char *buf;
 370
 371         buf = malloc(100);
 372         if (!buf)
 373                 return buf;
 374         snprintf(buf, 100, "%ld", (long)*val);
 375         return buf;
 376 }
 377
 378 static BN_ULONG
 379 BN_div_word(BIGNUM *a, BN_ULONG b)
 380 {
 381         BN_ULONG mod;
 382
 383         mod = *a % b;
 384         *a /= b;
 385         return mod;
 386 }
 387 #endif