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 <limits.h> 73#include <stdio.h> 74#include <stdlib.h> 75#include <unistd.h> 76 77#include "primes.h" 78 79#ifdef HAVE_OPENSSL 80 81#include <openssl/bn.h> 82 83#define PRIME_CHECKS 5 84 85static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */ 86 87#else 88 89typedef ubig BIGNUM; 90typedef u_long BN_ULONG; 91 92#define BN_CTX int 93#define BN_CTX_new() NULL 94#define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1)) 95#define BN_is_zero(v) (*(v) == 0) 96#define BN_is_one(v) (*(v) == 1) 97#define BN_mod_word(a, b) (*(a) % (b)) 98 99static int BN_dec2bn(BIGNUM **a, const char *str); 100static int BN_hex2bn(BIGNUM **a, const char *str); 101static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG); 102static void BN_print_fp(FILE *, const BIGNUM *); 103 104#endif 105 106static void BN_print_dec_fp(FILE *, const BIGNUM *); 107 108static void pr_fact(BIGNUM *); /* print factors of a value */ 109static void pr_print(BIGNUM *); /* print a prime */ 110static void usage(void); 111 112static BN_CTX *ctx; /* just use a global context */ 113static int hflag; 114 115int 116main(int argc, char *argv[]) 117{ 118 BIGNUM *val; 119 int ch; 120 char *p, buf[LINE_MAX]; /* > max number of digits. */ 121 122 ctx = BN_CTX_new(); 123 val = BN_new(); 124 if (val == NULL) 125 errx(1, "can't initialise bignum"); 126 127 while ((ch = getopt(argc, argv, "h")) != -1) 128 switch (ch) { 129 case 'h': 130 hflag++; 131 break; 132 case '?': 133 default: 134 usage(); 135 } 136 argc -= optind; 137 argv += optind; 138 139 /* No args supplied, read numbers from stdin. */ 140 if (argc == 0) 141 for (;;) { 142 if (fgets(buf, sizeof(buf), stdin) == NULL) { 143 if (ferror(stdin)) 144 err(1, "stdin"); 145 exit (0); 146 } 147 for (p = buf; isblank(*p); ++p); 148 if (*p == '\n' || *p == '\0') 149 continue; 150 if (*p == '-') 151 errx(1, "negative numbers aren't permitted."); 152 if (BN_dec2bn(&val, buf) == 0 && 153 BN_hex2bn(&val, buf) == 0) 154 errx(1, "%s: illegal numeric format.", buf); 155 pr_fact(val); 156 } 157 /* Factor the arguments. */ 158 else 159 for (; *argv != NULL; ++argv) { 160 if (argv[0][0] == '-') 161 errx(1, "negative numbers aren't permitted."); 162 if (BN_dec2bn(&val, argv[0]) == 0 && 163 BN_hex2bn(&val, argv[0]) == 0) 164 errx(1, "%s: illegal numeric format.", argv[0]); 165 pr_fact(val); 166 } 167 exit(0); 168} 169 170/* 171 * pr_fact - print the factors of a number 172 * 173 * Print the factors of the number, from the lowest to the highest. 174 * A factor will be printed multiple times if it divides the value 175 * multiple times. 176 * 177 * Factors are printed with leading tabs. 178 */ 179static void 180pr_fact(BIGNUM *val) 181{ 182 const ubig *fact; /* The factor found. */ 183 184 /* Firewall - catch 0 and 1. */ 185 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */ 186 exit(0); 187 if (BN_is_one(val)) { 188 printf("1: 1\n"); 189 return; 190 } 191 192 /* Factor value. */ 193 194 if (hflag) { 195 fputs("0x", stdout); 196 BN_print_fp(stdout, val); 197 } else 198 BN_print_dec_fp(stdout, val); 199 putchar(':'); 200 for (fact = &prime[0]; !BN_is_one(val); ++fact) { 201 /* Look for the smallest factor. */ 202 do { 203 if (BN_mod_word(val, (BN_ULONG)*fact) == 0) 204 break; 205 } while (++fact <= pr_limit); 206 207 /* Watch for primes larger than the table. */ 208 if (fact > pr_limit) { 209#ifdef HAVE_OPENSSL 210 BIGNUM *bnfact; 211 212 bnfact = BN_new(); 213 BN_set_word(bnfact, *(fact - 1)); 214 if (!BN_sqr(bnfact, bnfact, ctx)) 215 errx(1, "error in BN_sqr()"); 216 if (BN_cmp(bnfact, val) > 0 || 217 BN_is_prime(val, PRIME_CHECKS, 218 NULL, 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%lx" : " %lu", *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 240static void 241pr_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 252static void 253usage(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 */ 262static void 263pollard_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); 274newbase: 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(x, PRIME_CHECKS, NULL, NULL, 292 NULL) == 1) 293 pr_print(x); 294 else 295 pollard_pminus1(x); 296 fflush(stdout); 297 298 BN_div(num, NULL, val, x, ctx); 299 if (BN_is_one(num)) 300 return; 301 if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL, 302 NULL) == 1) { 303 pr_print(num); 304 fflush(stdout); 305 return; 306 } 307 BN_copy(val, num); 308 } 309 if (!BN_add_word(i, 1)) 310 errx(1, "error in BN_add_word()"); 311 } 312} 313 314/* 315 * Sigh.. No _decimal_ output to file functions in BN. 316 */ 317static void 318BN_print_dec_fp(FILE *fp, const BIGNUM *num) 319{ 320 char *buf; 321 322 buf = BN_bn2dec(num); 323 if (buf == NULL) 324 return; /* XXX do anything here? */ 325 fprintf(fp, "%s", buf); 326 free(buf); 327} 328 329#else 330 331static void 332BN_print_fp(FILE *fp, const BIGNUM *num) 333{ 334 fprintf(fp, "%lx", (unsigned long)*num); 335} 336 337static void 338BN_print_dec_fp(FILE *fp, const BIGNUM *num) 339{ 340 fprintf(fp, "%lu", (unsigned long)*num); 341} 342 343static int 344BN_dec2bn(BIGNUM **a, const char *str) 345{ 346 char *p; 347 348 errno = 0; 349 **a = strtoul(str, &p, 10); 350 return (errno == 0 && (*p == '\n' || *p == '\0')); 351} 352 353static int 354BN_hex2bn(BIGNUM **a, const char *str) 355{ 356 char *p; 357 358 errno = 0; 359 **a = strtoul(str, &p, 16); 360 return (errno == 0 && (*p == '\n' || *p == '\0')); 361} 362 363static BN_ULONG 364BN_div_word(BIGNUM *a, BN_ULONG b) 365{ 366 BN_ULONG mod; 367 368 mod = *a % b; 369 *a /= b; 370 return mod; 371} 372 373#endif 374