factor/factor.c

   1 /*      $NetBSD: factor.c,v 1.30 2020/10/03 22:27:00 christos Exp $     */
   2 /*
   3  * Copyright (c) 1989, 1993
   4  *      The Regents of the University of California.  All rights reserved.
   5  *
   6  * This code is derived from software contributed to Berkeley by
   7  * Landon Curt Noll.
   8  *
   9  * Redistribution and use in source and binary forms, with or without
  10  * modification, are permitted provided that the following conditions
  11  * are met:
  12  * 1. Redistributions of source code must retain the above copyright
  13  *    notice, this list of conditions and the following disclaimer.
  14  * 2. Redistributions in binary form must reproduce the above copyright
  15  *    notice, this list of conditions and the following disclaimer in the
  16  *    documentation and/or other materials provided with the distribution.
  17  * 3. Neither the name of the University nor the names of its contributors
  18  *    may be used to endorse or promote products derived from this software
  19  *    without specific prior written permission.
  20  *
  21  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  22  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  23  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  24  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  25  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  26  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  27  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  28  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  29  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  30  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  31  * SUCH DAMAGE.
  32  */
  33
  34 #ifndef lint
  35 #include <sys/cdefs.h>
  36 #ifdef __COPYRIGHT
  37 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\
  38         The Regents of the University of California.  All rights reserved.");
  39 #endif
  40 #ifdef __SCCSID
  41 __SCCSID("@(#)factor.c  8.4 (Berkeley) 5/4/95");
  42 #endif
  43 #ifdef __RCSID
  44 __RCSID("$NetBSD: factor.c,v 1.30 2020/10/03 22:27:00 christos Exp $");
  45 #endif
  46 #ifdef __FBSDID
  47 __FBSDID("$FreeBSD: head/usr.bin/factor/factor.c 356666 2020-01-12 20:25:11Z gad $");
  48 #endif
  49 #endif /* not lint */
  50
  51 /*
  52  * factor - factor a number into primes
  53  *
  54  * By: Landon Curt Noll   chongo@toad.com,   ...!{sun,tolsoft}!hoptoad!chongo
  55  *
  56  *   chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
  57  *
  58  * usage:
  59  *      factor [-hx] [number] ...
  60  *
  61  * The form of the output is:
  62  *
  63  *      number: factor1 factor1 factor2 factor3 factor3 factor3 ...
  64  *
  65  * where factor1 <= factor2 <= factor3 <= ...
  66  *
  67  * If the -h flag is specified, the output is in "human-readable" format.
  68  * Duplicate factors are printed in the form of x^n.
  69  *
  70  * If the -x flag is specified numbers are printed in hex.
  71  *
  72  * If no number args are given, the list of numbers are read from stdin.
  73  * If no args are given, the list of numbers are read from stdin.
  74  */
  75
  76 #include <ctype.h>
  77 #include <err.h>
  78 #include <errno.h>
  79 #include <inttypes.h>
  80 #include <limits.h>
  81 #include <stdbool.h>
  82 #include <stdio.h>
  83 #include <stdlib.h>
  84 #include <unistd.h>
  85
  86 #include "primes.h"
  87
  88 #ifdef HAVE_OPENSSL
  89
  90 #include <openssl/bn.h>
  91
  92 #define PRIME_CHECKS    5
  93
  94 static void     pollard_pminus1(BIGNUM *, int); /* print factors for big numbers */
  95
  96 #else
  97
  98 typedef long    BIGNUM;
  99 typedef u_long  BN_ULONG;
 100
 101 #define BN_CTX                  int
 102 #define BN_CTX_new()            NULL
 103 #define BN_new()                ((BIGNUM *)calloc(sizeof(BIGNUM), 1))
 104 #define BN_is_zero(v)           (*(v) == 0)
 105 #define BN_is_one(v)            (*(v) == 1)
 106 #define BN_mod_word(a, b)       (*(a) % (b))
 107
 108 static int      BN_dec2bn(BIGNUM **, const char *);
 109 static int      BN_hex2bn(BIGNUM **, const char *);
 110 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
 111 static void     BN_print_fp(FILE *, const BIGNUM *);
 112
 113 #endif
 114
 115 static void     BN_print_dec_fp(FILE *, const BIGNUM *);
 116 static void     convert_str2bn(BIGNUM **, char *);
 117 static bool     is_hex_str(char *);
 118 static void     pr_fact(BIGNUM *, int, int);    /* print factors of a value */
 119 static void     pr_print(BIGNUM *, int);        /* print a prime */
 120 static void     usage(void);
 121
 122 static BN_CTX   *ctx;                   /* just use a global context */
 123
 124 int
 125 main(int argc, char *argv[])
 126 {
 127         BIGNUM *val;
 128         int ch, hflag, xflag;
 129         char *p, buf[LINE_MAX];         /* > max number of digits. */
 130
 131         hflag = xflag = 0;
 132         ctx = BN_CTX_new();
 133         val = BN_new();
 134         if (val == NULL)
 135                 errx(1, "can't initialise bignum");
 136
 137         while ((ch = getopt(argc, argv, "hx")) != -1)
 138                 switch (ch) {
 139                 case 'h':
 140                         hflag++;
 141                         break;
 142                 case 'x':
 143                         xflag++;
 144                         break;
 145                 case '?':
 146                 default:
 147                         usage();
 148                 }
 149         argc -= optind;
 150         argv += optind;
 151
 152         /* No args supplied, read numbers from stdin. */
 153         if (argc == 0)
 154                 for (;;) {
 155                         if (fgets(buf, sizeof(buf), stdin) == NULL) {
 156                                 if (ferror(stdin))
 157                                         err(1, "stdin");
 158                                 exit (0);
 159                         }
 160                         for (p = buf; isblank((unsigned char)*p); ++p);
 161                         if (*p == '\n' || *p == '\0')
 162                                 continue;
 163                         convert_str2bn(&val, p);
 164                         pr_fact(val, hflag, xflag);
 165                 }
 166         /* Factor the arguments. */
 167         else
 168                 for (p = *argv; p != NULL; p = *++argv) {
 169                         convert_str2bn(&val, p);
 170                         pr_fact(val, hflag, xflag);
 171                 }
 172         exit(0);
 173 }
 174
 175 /*
 176  * pr_fact - print the factors of a number
 177  *
 178  * Print the factors of the number, from the lowest to the highest.
 179  * A factor will be printed multiple times if it divides the value
 180  * multiple times.
 181  *
 182  * If hflag is specified, duplicate factors are printed in "human-
 183  * readable" form of x^n.
 184  *
 185  * If the xflag is specified, numbers will be printed in hex.
 186  *
 187  * Factors are printed with leading tabs.
 188  */
 189 static void
 190 pr_fact(BIGNUM *val, int hflag, int xflag)
 191 {
 192         int i;
 193         const uint64_t *fact;   /* The factor found. */
 194
 195         /* Firewall - catch 0 and 1. */
 196         if (BN_is_zero(val))    /* Historical practice; 0 just exits. */
 197                 exit(0);
 198         if (BN_is_one(val)) {
 199                 printf("1: 1\n");
 200                 return;
 201         }
 202
 203         /* Factor value. */
 204
 205         if (xflag) {
 206                 fputs("0x", stdout);
 207                 BN_print_fp(stdout, val);
 208         } else
 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                 do {
 214                         if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
 215                                 break;
 216                 } while (++fact <= pr_limit);
 217
 218                 /* Watch for primes larger than the table. */
 219                 if (fact > pr_limit) {
 220 #ifdef HAVE_OPENSSL
 221                         BIGNUM *bnfact;
 222
 223                         bnfact = BN_new();
 224                         BN_set_word(bnfact, *(fact - 1));
 225                         if (!BN_sqr(bnfact, bnfact, ctx))
 226                                 errx(1, "error in BN_sqr()");
 227                         if (BN_cmp(bnfact, val) > 0 ||
 228                             BN_is_prime_ex(val, PRIME_CHECKS, NULL, NULL) == 1)
 229                                 pr_print(val, xflag);
 230                         else
 231                                 pollard_pminus1(val, xflag);
 232 #else
 233                         pr_print(val, xflag);
 234 #endif
 235                         break;
 236                 }
 237
 238                 /* Divide factor out until none are left. */
 239                 i = 0;
 240                 do {
 241                         i++;
 242                         if (!hflag)
 243                                 printf(xflag ? " 0x%" PRIx64 : " %" PRIu64,
 244                                     *fact);
 245                         BN_div_word(val, (BN_ULONG)*fact);
 246                 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
 247
 248                 if (hflag) {
 249                         printf(xflag ? " 0x%" PRIx64 : " %" PRIu64, *fact);
 250                         if (i > 1)
 251                                 printf(xflag ? "^0x%x" : "^%d", i);
 252                 }
 253
 254                 /* Let the user know we're doing something. */
 255                 fflush(stdout);
 256         }
 257         putchar('\n');
 258 }
 259
 260 static void
 261 pr_print(BIGNUM *val, int xflag)
 262 {
 263         if (xflag) {
 264                 fputs(" 0x", stdout);
 265                 BN_print_fp(stdout, val);
 266         } else {
 267                 putchar(' ');
 268                 BN_print_dec_fp(stdout, val);
 269         }
 270 }
 271
 272 static void
 273 usage(void)
 274 {
 275         fprintf(stderr, "usage: factor [-h] [value ...]\n");
 276         exit(1);
 277 }
 278
 279 #ifdef HAVE_OPENSSL
 280
 281 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
 282 static void
 283 pollard_pminus1(BIGNUM *val, int xflag)
 284 {
 285         BIGNUM *base, *rbase, *num, *i, *x;
 286
 287         base = BN_new();
 288         rbase = BN_new();
 289         num = BN_new();
 290         i = BN_new();
 291         x = BN_new();
 292
 293         BN_set_word(rbase, 1);
 294 newbase:
 295         if (!BN_add_word(rbase, 1))
 296                 errx(1, "error in BN_add_word()");
 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                 if (!BN_gcd(x, x, val, ctx))
 308                         errx(1, "error in BN_gcd()");
 309
 310                 if (!BN_is_one(x)) {
 311                         if (BN_is_prime_ex(x, PRIME_CHECKS, NULL, NULL) == 1)
 312                                 pr_print(x, xflag);
 313                         else
 314                                 pollard_pminus1(x, xflag);
 315                         fflush(stdout);
 316
 317                         BN_div(num, NULL, val, x, ctx);
 318                         if (BN_is_one(num))
 319                                 return;
 320                         if (BN_is_prime_ex(num, PRIME_CHECKS, NULL,
 321                             NULL) == 1) {
 322                                 pr_print(num, xflag);
 323                                 fflush(stdout);
 324                                 return;
 325                         }
 326                         BN_copy(val, num);
 327                 }
 328                 if (!BN_add_word(i, 1))
 329                         errx(1, "error in BN_add_word()");
 330         }
 331 }
 332
 333 /*
 334  * Sigh..  No _decimal_ output to file functions in BN.
 335  */
 336 static void
 337 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
 338 {
 339         char *buf;
 340
 341         buf = BN_bn2dec(num);
 342         if (buf == NULL)
 343                 return; /* XXX do anything here? */
 344         fprintf(fp, "%s", buf);
 345         free(buf);
 346 }
 347
 348 #else
 349
 350 static void
 351 BN_print_fp(FILE *fp, const BIGNUM *num)
 352 {
 353         fprintf(fp, "%lx", (unsigned long)*num);
 354 }
 355
 356 static void
 357 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
 358 {
 359         fprintf(fp, "%lu", (unsigned long)*num);
 360 }
 361
 362 static int
 363 BN_dec2bn(BIGNUM **a, const char *str)
 364 {
 365         char *p;
 366
 367         errno = 0;
 368         **a = strtoul(str, &p, 10);
 369         return (errno == 0 ? 1 : 0);    /* OpenSSL returns 0 on error! */
 370 }
 371
 372 static int
 373 BN_hex2bn(BIGNUM **a, const char *str)
 374 {
 375         char *p;
 376
 377         errno = 0;
 378         **a = strtoul(str, &p, 16);
 379         return (errno == 0 ? 1 : 0);    /* OpenSSL returns 0 on error! */
 380 }
 381
 382 static BN_ULONG
 383 BN_div_word(BIGNUM *a, BN_ULONG b)
 384 {
 385         BN_ULONG mod;
 386
 387         mod = *a % b;
 388         *a /= b;
 389         return mod;
 390 }
 391
 392 #endif
 393
 394 /*
 395  * Scan the string from left-to-right to see if the longest substring
 396  * is a valid hexadecimal number.
 397  */
 398 static bool
 399 is_hex_str(char *str)
 400 {
 401         char c, *p;
 402         bool saw_hex = false;
 403
 404         for (p = str; *p; p++) {
 405                 if (isdigit((unsigned char)*p))
 406                         continue;
 407                 c = tolower((unsigned char)*p);
 408                 if (c >= 'a' && c <= 'f') {
 409                         saw_hex = true;
 410                         continue;
 411                 }
 412                 break;  /* Not a hexadecimal digit. */
 413         }
 414         return saw_hex;
 415 }
 416
 417 /* Convert string pointed to by *str to a bignum.  */
 418 static void
 419 convert_str2bn(BIGNUM **val, char *p)
 420 {
 421         int n = 0;
 422
 423         if (*p == '+') p++;
 424         if (*p == '-')
 425                 errx(1, "negative numbers aren't permitted.");
 426         if (*p == '0') {
 427                 p++;
 428                 if (*p == 'x' || *p == 'X')
 429                         n = BN_hex2bn(val, ++p);
 430         } else {
 431                 n = is_hex_str(p) ? BN_hex2bn(val, p) : BN_dec2bn(val, p);
 432         }
 433         if (n == 0)
 434                 errx(1, "%s: illegal numeric format.", p);
 435 }