factor.c revision 1.15
1 /* $NetBSD: factor.c,v 1.15 2004/02/08 11:47:36 jsm 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\n\ 38 The Regents of the University of California. All rights reserved.\n"); 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 1.15 2004/02/08 11:47:36 jsm 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 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 BN_CTX *ctx; /* just use a global context */ 106 #endif 107 108 int main(int, char *[]); 109 void pr_fact(BIGNUM *); /* print factors of a value */ 110 void BN_print_dec_fp(FILE *, const BIGNUM *); 111 void usage(void) __attribute__((__noreturn__)); 112 #ifdef HAVE_OPENSSL 113 void pollard_pminus1(BIGNUM *); /* print factors for big numbers */ 114 #else 115 char *BN_bn2dec(const BIGNUM *); 116 BN_ULONG BN_div_word(BIGNUM *, BN_ULONG); 117 #endif 118 119 120 #ifndef HAVE_OPENSSL 121 int 122 BN_dec2bn(BIGNUM **a, const char *str) 123 { 124 char *p; 125 126 errno = 0; 127 **a = strtoul(str, &p, 10); 128 if (errno) 129 err(1, "%s", str); 130 return (*p == '\n' || *p == '\0'); 131 } 132 #endif 133 134 int 135 main(int argc, char *argv[]) 136 { 137 BIGNUM *val; 138 int ch; 139 char *p, buf[LINE_MAX]; /* > max number of digits. */ 140 141 #ifdef HAVE_OPENSSL 142 ctx = BN_CTX_new(); 143 #endif 144 val = BN_new(); 145 if (val == NULL) 146 errx(1, "can't initialise bignum"); 147 148 while ((ch = getopt(argc, argv, "")) != -1) 149 switch (ch) { 150 case '?': 151 default: 152 usage(); 153 } 154 argc -= optind; 155 argv += optind; 156 157 /* No args supplied, read numbers from stdin. */ 158 if (argc == 0) 159 for (;;) { 160 if (fgets(buf, sizeof(buf), stdin) == NULL) { 161 if (ferror(stdin)) 162 err(1, "stdin"); 163 exit (0); 164 } 165 for (p = buf; isblank(*p); ++p); 166 if (*p == '\n' || *p == '\0') 167 continue; 168 if (*p == '-') 169 errx(1, "negative numbers aren't permitted."); 170 if (BN_dec2bn(&val, buf) == 0) 171 errx(1, "%s: illegal numeric format.", argv[0]); 172 pr_fact(val); 173 } 174 /* Factor the arguments. */ 175 else 176 for (; *argv != NULL; ++argv) { 177 if (argv[0][0] == '-') 178 errx(1, "negative numbers aren't permitted."); 179 if (BN_dec2bn(&val, argv[0]) == 0) 180 errx(1, "%s: illegal numeric format.", argv[0]); 181 pr_fact(val); 182 } 183 exit(0); 184 } 185 186 /* 187 * pr_fact - print the factors of a number 188 * 189 * If the number is 0 or 1, then print the number and return. 190 * If the number is < 0, print -1, negate the number and continue 191 * processing. 192 * 193 * Print the factors of the number, from the lowest to the highest. 194 * A factor will be printed numtiple times if it divides the value 195 * multiple times. 196 * 197 * Factors are printed with leading tabs. 198 */ 199 void 200 pr_fact(BIGNUM *val) 201 { 202 const ubig *fact; /* The factor found. */ 203 204 /* Firewall - catch 0 and 1. */ 205 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */ 206 exit(0); 207 if (BN_is_one(val)) { 208 printf("1: 1\n"); 209 return; 210 } 211 212 /* Factor value. */ 213 214 BN_print_dec_fp(stdout, val); 215 putchar(':'); 216 for (fact = &prime[0]; !BN_is_one(val); ++fact) { 217 /* Look for the smallest factor. */ 218 do { 219 if (BN_mod_word(val, (BN_ULONG)*fact) == 0) 220 break; 221 } while (++fact <= pr_limit); 222 223 /* Watch for primes larger than the table. */ 224 if (fact > pr_limit) { 225 #ifdef HAVE_OPENSSL 226 BIGNUM *bnfact; 227 228 bnfact = BN_new(); 229 BN_set_word(bnfact, *(fact - 1)); 230 BN_sqr(bnfact, bnfact, ctx); 231 if (BN_cmp(bnfact, val) > 0 232 || BN_is_prime(val, PRIME_CHECKS, NULL, NULL, 233 NULL) == 1) { 234 putchar(' '); 235 BN_print_dec_fp(stdout, val); 236 } else 237 pollard_pminus1(val); 238 #else 239 printf(" %s", BN_bn2dec(val)); 240 #endif 241 break; 242 } 243 244 /* Divide factor out until none are left. */ 245 do { 246 printf(" %lu", *fact); 247 BN_div_word(val, (BN_ULONG)*fact); 248 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); 249 250 /* Let the user know we're doing something. */ 251 fflush(stdout); 252 } 253 putchar('\n'); 254 } 255 256 /* 257 * Sigh.. No _decimal_ output to file functions in BN. 258 */ 259 void 260 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 261 { 262 char *buf; 263 264 buf = BN_bn2dec(num); 265 if (buf == NULL) 266 return; /* XXX do anything here? */ 267 fprintf(fp, buf); 268 free(buf); 269 } 270 271 void 272 usage(void) 273 { 274 fprintf(stderr, "usage: factor [value ...]\n"); 275 exit (0); 276 } 277 278 279 280 281 #ifdef HAVE_OPENSSL 282 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */ 283 284 void 285 pollard_pminus1(BIGNUM *val) 286 { 287 BIGNUM *base, *rbase, *num, *i, *x; 288 289 base = BN_new(); 290 rbase = BN_new(); 291 num = BN_new(); 292 i = BN_new(); 293 x = BN_new(); 294 295 BN_set_word(rbase, 1); 296 newbase: 297 BN_add_word(rbase, 1); 298 BN_set_word(i, 2); 299 BN_copy(base, rbase); 300 301 for (;;) { 302 BN_mod_exp(base, base, i, val, ctx); 303 if (BN_is_one(base)) 304 goto newbase; 305 306 BN_copy(x, base); 307 BN_sub_word(x, 1); 308 BN_gcd(x, x, val, ctx); 309 310 if (!BN_is_one(x)) { 311 if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL, 312 NULL) == 1) { 313 putchar(' '); 314 BN_print_dec_fp(stdout, x); 315 } else 316 pollard_pminus1(x); 317 fflush(stdout); 318 319 BN_div(num, NULL, val, x, ctx); 320 if (BN_is_one(num)) 321 return; 322 if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL, 323 NULL) == 1) { 324 putchar(' '); 325 BN_print_dec_fp(stdout, num); 326 fflush(stdout); 327 return; 328 } 329 BN_copy(val, num); 330 } 331 BN_add_word(i, 1); 332 } 333 } 334 #else 335 char * 336 BN_bn2dec(const BIGNUM *val) 337 { 338 char *buf; 339 340 buf = malloc(100); 341 if (!buf) 342 return buf; 343 snprintf(buf, 100, "%ld", (long)*val); 344 return buf; 345 } 346 347 BN_ULONG 348 BN_div_word(BIGNUM *a, BN_ULONG b) 349 { 350 BN_ULONG mod; 351 352 mod = *a % b; 353 *a /= b; 354 return mod; 355 } 356 #endif 357
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