1 /* $NetBSD: factor.c,v 1.22 2010/04/28 18:04:31 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 1.22 2010/04/28 18:04:31 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_rho(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_rho(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 static void 286 pollard_rho(BIGNUM *val) 287 { 288 BIGNUM *x, *y, *tmp, *num; 289 BN_ULONG a; 290 unsigned int steps_taken, steps_limit; 291 292 x = BN_new(); 293 y = BN_new(); 294 tmp = BN_new(); 295 num = BN_new(); 296 a = 1; 297 restart: 298 steps_taken = 0; 299 steps_limit = 2; 300 BN_set_word(x, 1); 301 BN_copy(y, x); 302 303 for (;;) { 304 BN_sqr(tmp, x, ctx); 305 BN_add_word(tmp, a); 306 BN_mod(x, tmp, val, ctx); 307 BN_sub(tmp, x, y); 308 if (BN_is_zero(tmp)) { 309 #ifdef DEBUG 310 printf(" (loop)"); 311 #endif 312 a++; 313 goto restart; 314 } 315 BN_gcd(tmp, tmp, val, ctx); 316 317 if (!BN_is_one(tmp)) { 318 if (BN_is_prime(tmp, PRIME_CHECKS, NULL, NULL, 319 NULL) == 1) { 320 putchar(' '); 321 BN_print_dec_fp(stdout, tmp); 322 } else { 323 #ifdef DEBUG 324 printf(" (recurse for "); 325 BN_print_dec_fp(stdout, tmp); 326 putchar(')'); 327 #endif 328 pollard_rho(BN_dup(tmp)); 329 #ifdef DEBUG 330 printf(" (back)"); 331 #endif 332 } 333 fflush(stdout); 334 335 BN_div(num, NULL, val, tmp, ctx); 336 if (BN_is_one(num)) 337 return; 338 if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL, 339 NULL) == 1) { 340 putchar(' '); 341 BN_print_dec_fp(stdout, num); 342 fflush(stdout); 343 return; 344 } 345 BN_copy(val, num); 346 goto restart; 347 } 348 steps_taken++; 349 if (steps_taken == steps_limit) { 350 BN_copy(y, x); /* teleport the turtle */ 351 steps_taken = 0; 352 steps_limit *= 2; 353 if (steps_limit == 0) { 354 #ifdef DEBUG 355 printf(" (overflow)"); 356 #endif 357 a++; 358 goto restart; 359 } 360 } 361 } 362 } 363 #else 364 char * 365 BN_bn2dec(const BIGNUM *val) 366 { 367 char *buf; 368 369 buf = malloc(100); 370 if (!buf) 371 return buf; 372 snprintf(buf, 100, "%ld", (long)*val); 373 return buf; 374 } 375 376 static BN_ULONG 377 BN_div_word(BIGNUM *a, BN_ULONG b) 378 { 379 BN_ULONG mod; 380 381 mod = *a % b; 382 *a /= b; 383 return mod; 384 } 385 #endif 386