1 /* 2 * Copyright (c) 1989, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * This code is derived from software contributed to Berkeley by 6 * Landon Curt Noll. 7 * 8 * Redistribution and use in source and binary forms, with or without 9 * modification, are permitted provided that the following conditions 10 * are met: 11 * 1. Redistributions of source code must retain the above copyright 12 * notice, this list of conditions and the following disclaimer. 13 * 2. Redistributions in binary form must reproduce the above copyright 14 * notice, this list of conditions and the following disclaimer in the 15 * documentation and/or other materials provided with the distribution. 16 * 3. Neither the name of the University nor the names of its contributors 17 * may be used to endorse or promote products derived from this software 18 * without specific prior written permission. 19 * 20 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30 * SUCH DAMAGE. 31 */ 32 33 #ifndef lint 34 #include <sys/cdefs.h> 35 #ifdef __COPYRIGHT 36 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\ 37 The Regents of the University of California. All rights reserved."); 38 #endif 39 #ifdef __SCCSID 40 __SCCSID("@(#)factor.c 8.4 (Berkeley) 5/4/95"); 41 #endif 42 #ifdef __RCSID 43 __RCSID("$NetBSD: factor.c,v 1.19 2009/08/12 05:54:31 dholland Exp $"); 44 #endif 45 #ifdef __FBSDID 46 __FBSDID("$FreeBSD$"); 47 #endif 48 #endif /* not lint */ 49 50 /* 51 * factor - factor a number into primes 52 * 53 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 54 * 55 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 56 * 57 * usage: 58 * factor [-h] [number] ... 59 * 60 * The form of the output is: 61 * 62 * number: factor1 factor1 factor2 factor3 factor3 factor3 ... 63 * 64 * where factor1 <= factor2 <= factor3 <= ... 65 * 66 * If no args are given, the list of numbers are read from stdin. 67 */ 68 69 #include <ctype.h> 70 #include <err.h> 71 #include <errno.h> 72 #include <inttypes.h> 73 #include <limits.h> 74 #include <stdio.h> 75 #include <stdlib.h> 76 #include <unistd.h> 77 78 #include "primes.h" 79 80 #ifdef HAVE_OPENSSL 81 82 #include <openssl/bn.h> 83 84 #define PRIME_CHECKS 5 85 86 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */ 87 88 #else 89 90 typedef ubig BIGNUM; 91 typedef u_long BN_ULONG; 92 93 #define BN_CTX int 94 #define BN_CTX_new() NULL 95 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1)) 96 #define BN_is_zero(v) (*(v) == 0) 97 #define BN_is_one(v) (*(v) == 1) 98 #define BN_mod_word(a, b) (*(a) % (b)) 99 100 static int BN_dec2bn(BIGNUM **a, const char *str); 101 static int BN_hex2bn(BIGNUM **a, const char *str); 102 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG); 103 static void BN_print_fp(FILE *, const BIGNUM *); 104 105 #endif 106 107 static void BN_print_dec_fp(FILE *, const BIGNUM *); 108 109 static void pr_fact(BIGNUM *); /* print factors of a value */ 110 static void pr_print(BIGNUM *); /* print a prime */ 111 static void usage(void); 112 113 static BN_CTX *ctx; /* just use a global context */ 114 static int hflag; 115 116 int 117 main(int argc, char *argv[]) 118 { 119 BIGNUM *val; 120 int ch; 121 char *p, buf[LINE_MAX]; /* > max number of digits. */ 122 123 ctx = BN_CTX_new(); 124 val = BN_new(); 125 if (val == NULL) 126 errx(1, "can't initialise bignum"); 127 128 while ((ch = getopt(argc, argv, "h")) != -1) 129 switch (ch) { 130 case 'h': 131 hflag++; 132 break; 133 case '?': 134 default: 135 usage(); 136 } 137 argc -= optind; 138 argv += optind; 139 140 /* No args supplied, read numbers from stdin. */ 141 if (argc == 0) 142 for (;;) { 143 if (fgets(buf, sizeof(buf), stdin) == NULL) { 144 if (ferror(stdin)) 145 err(1, "stdin"); 146 exit (0); 147 } 148 for (p = buf; isblank(*p); ++p); 149 if (*p == '\n' || *p == '\0') 150 continue; 151 if (*p == '-') 152 errx(1, "negative numbers aren't permitted."); 153 if (BN_dec2bn(&val, buf) == 0 && 154 BN_hex2bn(&val, buf) == 0) 155 errx(1, "%s: illegal numeric format.", buf); 156 pr_fact(val); 157 } 158 /* Factor the arguments. */ 159 else 160 for (; *argv != NULL; ++argv) { 161 if (argv[0][0] == '-') 162 errx(1, "negative numbers aren't permitted."); 163 if (BN_dec2bn(&val, argv[0]) == 0 && 164 BN_hex2bn(&val, argv[0]) == 0) 165 errx(1, "%s: illegal numeric format.", argv[0]); 166 pr_fact(val); 167 } 168 exit(0); 169 } 170 171 /* 172 * pr_fact - print the factors of a number 173 * 174 * Print the factors of the number, from the lowest to the highest. 175 * A factor will be printed multiple times if it divides the value 176 * multiple times. 177 * 178 * Factors are printed with leading tabs. 179 */ 180 static void 181 pr_fact(BIGNUM *val) 182 { 183 const ubig *fact; /* The factor found. */ 184 185 /* Firewall - catch 0 and 1. */ 186 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */ 187 exit(0); 188 if (BN_is_one(val)) { 189 printf("1: 1\n"); 190 return; 191 } 192 193 /* Factor value. */ 194 195 if (hflag) { 196 fputs("0x", stdout); 197 BN_print_fp(stdout, val); 198 } else 199 BN_print_dec_fp(stdout, val); 200 putchar(':'); 201 for (fact = &prime[0]; !BN_is_one(val); ++fact) { 202 /* Look for the smallest factor. */ 203 do { 204 if (BN_mod_word(val, (BN_ULONG)*fact) == 0) 205 break; 206 } while (++fact <= pr_limit); 207 208 /* Watch for primes larger than the table. */ 209 if (fact > pr_limit) { 210 #ifdef HAVE_OPENSSL 211 BIGNUM *bnfact; 212 213 bnfact = BN_new(); 214 BN_set_word(bnfact, *(fact - 1)); 215 if (!BN_sqr(bnfact, bnfact, ctx)) 216 errx(1, "error in BN_sqr()"); 217 if (BN_cmp(bnfact, val) > 0 || 218 BN_is_prime_ex(val, PRIME_CHECKS, NULL, NULL) == 1) 219 pr_print(val); 220 else 221 pollard_pminus1(val); 222 #else 223 pr_print(val); 224 #endif 225 break; 226 } 227 228 /* Divide factor out until none are left. */ 229 do { 230 printf(hflag ? " 0x%" PRIx64 "" : " %" PRIu64 "", *fact); 231 BN_div_word(val, (BN_ULONG)*fact); 232 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0); 233 234 /* Let the user know we're doing something. */ 235 fflush(stdout); 236 } 237 putchar('\n'); 238 } 239 240 static void 241 pr_print(BIGNUM *val) 242 { 243 if (hflag) { 244 fputs(" 0x", stdout); 245 BN_print_fp(stdout, val); 246 } else { 247 putchar(' '); 248 BN_print_dec_fp(stdout, val); 249 } 250 } 251 252 static void 253 usage(void) 254 { 255 fprintf(stderr, "usage: factor [-h] [value ...]\n"); 256 exit(1); 257 } 258 259 #ifdef HAVE_OPENSSL 260 261 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */ 262 static void 263 pollard_pminus1(BIGNUM *val) 264 { 265 BIGNUM *base, *rbase, *num, *i, *x; 266 267 base = BN_new(); 268 rbase = BN_new(); 269 num = BN_new(); 270 i = BN_new(); 271 x = BN_new(); 272 273 BN_set_word(rbase, 1); 274 newbase: 275 if (!BN_add_word(rbase, 1)) 276 errx(1, "error in BN_add_word()"); 277 BN_set_word(i, 2); 278 BN_copy(base, rbase); 279 280 for (;;) { 281 BN_mod_exp(base, base, i, val, ctx); 282 if (BN_is_one(base)) 283 goto newbase; 284 285 BN_copy(x, base); 286 BN_sub_word(x, 1); 287 if (!BN_gcd(x, x, val, ctx)) 288 errx(1, "error in BN_gcd()"); 289 290 if (!BN_is_one(x)) { 291 if (BN_is_prime_ex(x, PRIME_CHECKS, NULL, NULL) == 1) 292 pr_print(x); 293 else 294 pollard_pminus1(x); 295 fflush(stdout); 296 297 BN_div(num, NULL, val, x, ctx); 298 if (BN_is_one(num)) 299 return; 300 if (BN_is_prime_ex(num, PRIME_CHECKS, NULL, 301 NULL) == 1) { 302 pr_print(num); 303 fflush(stdout); 304 return; 305 } 306 BN_copy(val, num); 307 } 308 if (!BN_add_word(i, 1)) 309 errx(1, "error in BN_add_word()"); 310 } 311 } 312 313 /* 314 * Sigh.. No _decimal_ output to file functions in BN. 315 */ 316 static void 317 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 318 { 319 char *buf; 320 321 buf = BN_bn2dec(num); 322 if (buf == NULL) 323 return; /* XXX do anything here? */ 324 fprintf(fp, "%s", buf); 325 free(buf); 326 } 327 328 #else 329 330 static void 331 BN_print_fp(FILE *fp, const BIGNUM *num) 332 { 333 fprintf(fp, "%lx", (unsigned long)*num); 334 } 335 336 static void 337 BN_print_dec_fp(FILE *fp, const BIGNUM *num) 338 { 339 fprintf(fp, "%lu", (unsigned long)*num); 340 } 341 342 static int 343 BN_dec2bn(BIGNUM **a, const char *str) 344 { 345 char *p; 346 347 errno = 0; 348 **a = strtoul(str, &p, 10); 349 return (errno == 0 && (*p == '\n' || *p == '\0')); 350 } 351 352 static int 353 BN_hex2bn(BIGNUM **a, const char *str) 354 { 355 char *p; 356 357 errno = 0; 358 **a = strtoul(str, &p, 16); 359 return (errno == 0 && (*p == '\n' || *p == '\0')); 360 } 361 362 static BN_ULONG 363 BN_div_word(BIGNUM *a, BN_ULONG b) 364 { 365 BN_ULONG mod; 366 367 mod = *a % b; 368 *a /= b; 369 return mod; 370 } 371 372 #endif 373