factor.c revision 1.25.4.1
1 /* $NetBSD: factor.c,v 1.25.4.1 2011/11/10 14:31:35 yamt 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 1.25.4.1 2011/11/10 14:31:35 yamt Exp $"); 46 #endif 47 #endif /* not lint */ 48 49 /* 50 * factor - factor a number into primes 51 * 52 * By: Landon Curt Noll chongo (at) 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 379
Indexes created Tue Oct 21 16:10:11 GMT 2025