1 /* $NetBSD: factor.c,v 1.19 2009/08/12 05:54:31 dholland 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 1.19 2009/08/12 05:54:31 dholland 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 */ 101 102 #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_pminus1(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(*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, "negative numbers 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)) /* Historical practice; 0 just exits. */ 205 exit(0); 206 if (BN_is_one(val)) { 207 printf("1: 1\n"); 208 return; 209 } 210 211 /* Factor value. */ 212 213 BN_print_dec_fp(stdout, val); 214 putchar(':'); 215 for (fact = &prime[0]; !BN_is_one(val); ++fact) { 216 /* Look for the smallest factor. */ 217 do { 218 if (BN_mod_word(val, (BN_ULONG)*fact) == 0) 219 break; 220 } while (++fact <= pr_limit); 221 222 /* Watch for primes larger than the table. */ 223 if (fact > pr_limit) { 224 #ifdef HAVE_OPENSSL 225 BIGNUM *bnfact; 226 227 bnfact = BN_new(); 228 BN_set_word(bnfact, *(fact - 1)); 229 BN_sqr(bnfact, bnfact, ctx); 230 if (BN_cmp(bnfact, val) > 0 231 || BN_is_prime(val, PRIME_CHECKS, NULL, NULL, 232 NULL) == 1) { 233 putchar(' '); 234 BN_print_dec_fp(stdout, val); 235 } else 236 pollard_pminus1(val); 237 #else 238 printf(" %s", BN_bn2dec(val)); 239 #endif 240 break; 241 } 242 243 /* Divide factor out until none are left. */ 244 do { 245 printf(" %lu", *fact); 246 BN_div_word(val, (BN_ULONG)*fact); 247 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); 248 249 /* Let the user know we're doing something. */ 250 fflush(stdout); 251 } 252 putchar('\n'); 253 } 254 255 /* 256 * Sigh.. No _decimal_ output to file functions in BN. 257 */ 258 static void 259 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 260 { 261 char *buf; 262 263 buf = BN_bn2dec(num); 264 if (buf == NULL) 265 return; /* XXX do anything here? */ 266 fprintf(fp, buf); 267 free(buf); 268 } 269 270 void 271 usage(void) 272 { 273 fprintf(stderr, "usage: factor [value ...]\n"); 274 exit (0); 275 } 276 277 278 279 280 #ifdef HAVE_OPENSSL 281 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */ 282 283 static void 284 pollard_pminus1(BIGNUM *val) 285 { 286 BIGNUM *base, *rbase, *num, *i, *x; 287 288 base = BN_new(); 289 rbase = BN_new(); 290 num = BN_new(); 291 i = BN_new(); 292 x = BN_new(); 293 294 BN_set_word(rbase, 1); 295 newbase: 296 BN_add_word(rbase, 1); 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 BN_gcd(x, x, val, ctx); 308 309 if (!BN_is_one(x)) { 310 if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL, 311 NULL) == 1) { 312 putchar(' '); 313 BN_print_dec_fp(stdout, x); 314 } else 315 pollard_pminus1(x); 316 fflush(stdout); 317 318 BN_div(num, NULL, val, x, ctx); 319 if (BN_is_one(num)) 320 return; 321 if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL, 322 NULL) == 1) { 323 putchar(' '); 324 BN_print_dec_fp(stdout, num); 325 fflush(stdout); 326 return; 327 } 328 BN_copy(val, num); 329 } 330 BN_add_word(i, 1); 331 } 332 } 333 #else 334 char * 335 BN_bn2dec(const BIGNUM *val) 336 { 337 char *buf; 338 339 buf = malloc(100); 340 if (!buf) 341 return buf; 342 snprintf(buf, 100, "%ld", (long)*val); 343 return buf; 344 } 345 346 static BN_ULONG 347 BN_div_word(BIGNUM *a, BN_ULONG b) 348 { 349 BN_ULONG mod; 350 351 mod = *a % b; 352 *a /= b; 353 return mod; 354 } 355 #endif 356