games/factor/factor.c

   1 /*      $NetBSD: factor.c,v 1.18 2008/07/20 01:03:21 lukem 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 1.18 2008/07/20 01:03:21 lukem 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
 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_pminus1(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(*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, "negative numbers 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))    /* Historical practice; 0 just exits. */
 205                 exit(0);
 206         if (BN_is_one(val)) {
 207                 printf("1: 1\n");
 208                 return;
 209         }
 210
 211         /* Factor value. */
 212
 213         BN_print_dec_fp(stdout, val);
 214         putchar(':');
 215         for (fact = &prime[0]; !BN_is_one(val); ++fact) {
 216                 /* Look for the smallest factor. */
 217                 do {
 218                         if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
 219                                 break;
 220                 } while (++fact <= pr_limit);
 221
 222                 /* Watch for primes larger than the table. */
 223                 if (fact > pr_limit) {
 224 #ifdef HAVE_OPENSSL
 225                         BIGNUM *bnfact;
 226
 227                         bnfact = BN_new();
 228                         BN_set_word(bnfact, *(fact - 1));
 229                         BN_sqr(bnfact, bnfact, ctx);
 230                         if (BN_cmp(bnfact, val) > 0
 231                             || BN_is_prime(val, PRIME_CHECKS, NULL, NULL,
 232                                            NULL) == 1) {
 233                                 putchar(' ');
 234                                 BN_print_dec_fp(stdout, val);
 235                         } else
 236                                 pollard_pminus1(val);
 237 #else
 238                         printf(" %s", BN_bn2dec(val));
 239 #endif
 240                         break;
 241                 }
 242
 243                 /* Divide factor out until none are left. */
 244                 do {
 245                         printf(" %lu", *fact);
 246                         BN_div_word(val, (BN_ULONG)*fact);
 247                 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
 248
 249                 /* Let the user know we're doing something. */
 250                 fflush(stdout);
 251         }
 252         putchar('\n');
 253 }
 254
 255 /*
 256  * Sigh..  No _decimal_ output to file functions in BN.
 257  */
 258 static void
 259 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
 260 {
 261         char *buf;
 262
 263         buf = BN_bn2dec(num);
 264         if (buf == NULL)
 265                 return; /* XXX do anything here? */
 266         fprintf(fp, buf);
 267         free(buf);
 268 }
 269
 270 void
 271 usage(void)
 272 {
 273         fprintf(stderr, "usage: factor [value ...]\n");
 274         exit (0);
 275 }
 276
 277
 278
 279
 280 #ifdef HAVE_OPENSSL
 281 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
 282
 283 static void
 284 pollard_pminus1(BIGNUM *val)
 285 {
 286         BIGNUM *base, *rbase, *num, *i, *x;
 287
 288         base = BN_new();
 289         rbase = BN_new();
 290         num = BN_new();
 291         i = BN_new();
 292         x = BN_new();
 293
 294         BN_set_word(rbase, 1);
 295  newbase:
 296         BN_add_word(rbase, 1);
 297         BN_set_word(i, 2);
 298         BN_copy(base, rbase);
 299
 300         for (;;) {
 301                 BN_mod_exp(base, base, i, val, ctx);
 302                 if (BN_is_one(base))
 303                         goto newbase;
 304
 305                 BN_copy(x, base);
 306                 BN_sub_word(x, 1);
 307                 BN_gcd(x, x, val, ctx);
 308
 309                 if (!BN_is_one(x)) {
 310                         if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL,
 311                             NULL) == 1) {
 312                                 putchar(' ');
 313                                 BN_print_dec_fp(stdout, x);
 314                         } else
 315                                 pollard_pminus1(x);
 316                         fflush(stdout);
 317
 318                         BN_div(num, NULL, val, x, ctx);
 319                         if (BN_is_one(num))
 320                                 return;
 321                         if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
 322                             NULL) == 1) {
 323                                 putchar(' ');
 324                                 BN_print_dec_fp(stdout, num);
 325                                 fflush(stdout);
 326                                 return;
 327                         }
 328                         BN_copy(val, num);
 329                 }
 330                 BN_add_word(i, 1);
 331         }
 332 }
 333 #else
 334 char *
 335 BN_bn2dec(const BIGNUM *val)
 336 {
 337         char *buf;
 338
 339         buf = malloc(100);
 340         if (!buf)
 341                 return buf;
 342         snprintf(buf, 100, "%ld", (long)*val);
 343         return buf;
 344 }
 345
 346 static BN_ULONG
 347 BN_div_word(BIGNUM *a, BN_ULONG b)
 348 {
 349         BN_ULONG mod;
 350
 351         mod = *a % b;
 352         *a /= b;
 353         return mod;
 354 }
 355 #endif