factor.c revision 1.13
1 /* $NetBSD: factor.c,v 1.13 2002/06/18 23:07:36 simonb 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. All advertising materials mentioning features or use of this software 19 * must display the following acknowledgement: 20 * This product includes software developed by the University of 21 * California, Berkeley and its contributors. 22 * 4. Neither the name of the University nor the names of its contributors 23 * may be used to endorse or promote products derived from this software 24 * without specific prior written permission. 25 * 26 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 27 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 28 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 29 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 30 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 31 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 32 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 33 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 34 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 35 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 36 * SUCH DAMAGE. 37 */ 38 39 #include <sys/cdefs.h> 40 #ifndef lint 41 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\n\ 42 The Regents of the University of California. All rights reserved.\n"); 43 #endif /* not lint */ 44 45 #ifndef lint 46 #if 0 47 static char sccsid[] = "@(#)factor.c 8.4 (Berkeley) 5/4/95"; 48 #else 49 __RCSID("$NetBSD: factor.c,v 1.13 2002/06/18 23:07:36 simonb Exp $"); 50 #endif 51 #endif /* not lint */ 52 53 /* 54 * factor - factor a number into primes 55 * 56 * By: Landon Curt Noll chongo (at) toad.com, ...!{sun,tolsoft}!hoptoad!chongo 57 * 58 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 59 * 60 * usage: 61 * factor [number] ... 62 * 63 * The form of the output is: 64 * 65 * number: factor1 factor1 factor2 factor3 factor3 factor3 ... 66 * 67 * where factor1 < factor2 < factor3 < ... 68 * 69 * If no args are given, the list of numbers are read from stdin. 70 */ 71 72 #include <ctype.h> 73 #include <err.h> 74 #include <errno.h> 75 #include <limits.h> 76 #include <stdio.h> 77 #include <stdlib.h> 78 #include <unistd.h> 79 80 #ifdef HAVE_OPENSSL 81 #include <openssl/bn.h> 82 #else 83 typedef long BIGNUM; 84 typedef u_long BN_ULONG; 85 int BN_dec2bn(BIGNUM **a, const char *str); 86 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1)) 87 #define BN_is_zero(v) (*(v) == 0) 88 #define BN_is_one(v) (*(v) == 1) 89 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1)) 90 #define BN_is_zero(v) (*(v) == 0) 91 #define BN_is_one(v) (*(v) == 1) 92 #define BN_mod_word(a, b) (*(a) % (b)) 93 #endif 94 95 #include "primes.h" 96 97 /* 98 * prime[i] is the (i-1)th prime. 99 * 100 * We are able to sieve 2^32-1 because this byte table yields all primes 101 * up to 65537 and 65537^2 > 2^32-1. 102 */ 103 extern const ubig prime[]; 104 extern const ubig *pr_limit; /* largest prime in the prime array */ 105 106 #define PRIME_CHECKS 5 107 108 #ifdef HAVE_OPENSSL 109 BN_CTX *ctx; /* just use a global context */ 110 #endif 111 112 int main(int, char *[]); 113 void pr_fact(BIGNUM *); /* print factors of a value */ 114 void BN_print_dec_fp(FILE *, const BIGNUM *); 115 void usage(void) __attribute__((__noreturn__)); 116 #ifdef HAVE_OPENSSL 117 void pollard_pminus1(BIGNUM *); /* print factors for big numbers */ 118 #else 119 char *BN_bn2dec(const BIGNUM *); 120 BN_ULONG BN_div_word(BIGNUM *, BN_ULONG); 121 #endif 122 123 124 #ifndef HAVE_OPENSSL 125 int 126 BN_dec2bn(BIGNUM **a, const char *str) 127 { 128 char *p; 129 130 errno = 0; 131 **a = strtoul(str, &p, 10); 132 if (errno) 133 err(1, "%s", str); 134 return (*p == '\n' || *p == '\0'); 135 } 136 #endif 137 138 int 139 main(int argc, char *argv[]) 140 { 141 BIGNUM *val; 142 int ch; 143 char *p, buf[LINE_MAX]; /* > max number of digits. */ 144 145 #ifdef HAVE_OPENSSL 146 ctx = BN_CTX_new(); 147 #endif 148 val = BN_new(); 149 if (val == NULL) 150 errx(1, "can't initialise bignum"); 151 152 while ((ch = getopt(argc, argv, "")) != -1) 153 switch (ch) { 154 case '?': 155 default: 156 usage(); 157 } 158 argc -= optind; 159 argv += optind; 160 161 /* No args supplied, read numbers from stdin. */ 162 if (argc == 0) 163 for (;;) { 164 if (fgets(buf, sizeof(buf), stdin) == NULL) { 165 if (ferror(stdin)) 166 err(1, "stdin"); 167 exit (0); 168 } 169 for (p = buf; isblank(*p); ++p); 170 if (*p == '\n' || *p == '\0') 171 continue; 172 if (*p == '-') 173 errx(1, "negative numbers aren't permitted."); 174 if (BN_dec2bn(&val, buf) == 0) 175 errx(1, "%s: illegal numeric format.", argv[0]); 176 pr_fact(val); 177 } 178 /* Factor the arguments. */ 179 else 180 for (; *argv != NULL; ++argv) { 181 if (argv[0][0] == '-') 182 errx(1, "negative numbers aren't permitted."); 183 if (BN_dec2bn(&val, argv[0]) == 0) 184 errx(1, "%s: illegal numeric format.", argv[0]); 185 pr_fact(val); 186 } 187 exit(0); 188 } 189 190 /* 191 * pr_fact - print the factors of a number 192 * 193 * If the number is 0 or 1, then print the number and return. 194 * If the number is < 0, print -1, negate the number and continue 195 * processing. 196 * 197 * Print the factors of the number, from the lowest to the highest. 198 * A factor will be printed numtiple times if it divides the value 199 * multiple times. 200 * 201 * Factors are printed with leading tabs. 202 */ 203 void 204 pr_fact(BIGNUM *val) 205 { 206 const ubig *fact; /* The factor found. */ 207 208 /* Firewall - catch 0 and 1. */ 209 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */ 210 exit(0); 211 if (BN_is_one(val)) { 212 printf("1: 1\n"); 213 return; 214 } 215 216 /* Factor value. */ 217 218 BN_print_dec_fp(stdout, val); 219 putchar(':'); 220 for (fact = &prime[0]; !BN_is_one(val); ++fact) { 221 /* Look for the smallest factor. */ 222 do { 223 if (BN_mod_word(val, (BN_ULONG)*fact) == 0) 224 break; 225 } while (++fact <= pr_limit); 226 227 /* Watch for primes larger than the table. */ 228 if (fact > pr_limit) { 229 #ifdef HAVE_OPENSSL 230 BIGNUM *bnfact; 231 232 bnfact = BN_new(); 233 BN_set_word(bnfact, *(fact - 1)); 234 BN_sqr(bnfact, bnfact, ctx); 235 if (BN_cmp(bnfact, val) > 0) { 236 putchar(' '); 237 BN_print_dec_fp(stdout, val); 238 } else 239 pollard_pminus1(val); 240 #else 241 printf(" %s", BN_bn2dec(val)); 242 #endif 243 break; 244 } 245 246 /* Divide factor out until none are left. */ 247 do { 248 printf(" %lu", *fact); 249 BN_div_word(val, (BN_ULONG)*fact); 250 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); 251 252 /* Let the user know we're doing something. */ 253 fflush(stdout); 254 } 255 putchar('\n'); 256 } 257 258 /* 259 * Sigh.. No _decimal_ output to file functions in BN. 260 */ 261 void 262 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 263 { 264 char *buf; 265 266 buf = BN_bn2dec(num); 267 if (buf == NULL) 268 return; /* XXX do anything here? */ 269 fprintf(fp, buf); 270 free(buf); 271 } 272 273 void 274 usage(void) 275 { 276 fprintf(stderr, "usage: factor [value ...]\n"); 277 exit (0); 278 } 279 280 281 282 283 #ifdef HAVE_OPENSSL 284 /* pollard rho, algorithm from Jim Gillogly, May 2000 */ 285 286 void 287 pollard_pminus1(BIGNUM *val) 288 { 289 BIGNUM *base, *num, *i, *x; 290 291 base = BN_new(); 292 num = BN_new(); 293 i = BN_new(); 294 x = BN_new(); 295 296 BN_set_word(i, 2); 297 BN_set_word(base, 2); 298 299 for (;;) { 300 BN_mod_exp(base, base, i, val, ctx); 301 302 BN_copy(x, base); 303 BN_sub_word(x, 1); 304 BN_gcd(x, x, val, ctx); 305 306 if (!BN_is_one(x)) { 307 if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL, 308 NULL) == 1) { 309 putchar(' '); 310 BN_print_dec_fp(stdout, x); 311 } else 312 pollard_pminus1(x); 313 fflush(stdout); 314 315 BN_div(num, NULL, val, x, ctx); 316 if (BN_is_one(num)) 317 return; 318 if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL, 319 NULL) == 1) { 320 putchar(' '); 321 BN_print_dec_fp(stdout, num); 322 fflush(stdout); 323 return; 324 } 325 BN_copy(val, num); 326 } 327 BN_add_word(i, 1); 328 } 329 } 330 #else 331 char * 332 BN_bn2dec(const BIGNUM *val) 333 { 334 char *buf; 335 336 buf = malloc(100); 337 if (!buf) 338 return buf; 339 snprintf(buf, 100, "%ld", (long)*val); 340 return buf; 341 } 342 343 BN_ULONG 344 BN_div_word(BIGNUM *a, BN_ULONG b) 345 { 346 BN_ULONG mod; 347 348 mod = *a % b; 349 *a /= b; 350 return mod; 351 } 352 #endif 353
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