2 * Copyright (c) 1989, 1993
3 * The Regents of the University of California. All rights reserved.
5 * This code is derived from software contributed to Berkeley by
8 * Redistribution and use in source and binary forms, with or without
9 * modification, are permitted provided that the following conditions
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.
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
34 #include <sys/cdefs.h>
36 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\
37 The Regents of the University of California. All rights reserved.");
40 __SCCSID("@(#)factor.c 8.4 (Berkeley) 5/4/95");
43 __RCSID("$NetBSD: factor.c,v 1.19 2009/08/12 05:54:31 dholland Exp $");
46 __FBSDID("$FreeBSD$");
51 * factor - factor a number into primes
53 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
55 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
58 * factor [-h] [number] ...
60 * The form of the output is:
62 * number: factor1 factor1 factor2 factor3 factor3 factor3 ...
64 * where factor1 <= factor2 <= factor3 <= ...
66 * If no args are given, the list of numbers are read from stdin.
83 #include <openssl/bn.h>
85 #define PRIME_CHECKS 5
87 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */
92 typedef u_long BN_ULONG;
95 #define BN_CTX_new() NULL
96 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1))
97 #define BN_is_zero(v) (*(v) == 0)
98 #define BN_is_one(v) (*(v) == 1)
99 #define BN_mod_word(a, b) (*(a) % (b))
101 static int BN_dec2bn(BIGNUM **, const char *);
102 static int BN_hex2bn(BIGNUM **, const char *);
103 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
104 static void BN_print_fp(FILE *, const BIGNUM *);
108 static void BN_print_dec_fp(FILE *, const BIGNUM *);
109 static void convert_str2bn(BIGNUM **, char *);
110 static bool is_hex_str(char *);
111 static void pr_fact(BIGNUM *); /* print factors of a value */
112 static void pr_print(BIGNUM *); /* print a prime */
113 static void usage(void);
115 static BN_CTX *ctx; /* just use a global context */
119 main(int argc, char *argv[])
123 char *p, buf[LINE_MAX]; /* > max number of digits. */
128 errx(1, "can't initialise bignum");
130 while ((ch = getopt(argc, argv, "h")) != -1)
142 /* No args supplied, read numbers from stdin. */
145 if (fgets(buf, sizeof(buf), stdin) == NULL) {
150 for (p = buf; isblank(*p); ++p);
151 if (*p == '\n' || *p == '\0')
153 convert_str2bn(&val, p);
156 /* Factor the arguments. */
158 for (p = *argv; p != NULL; p = *++argv) {
159 convert_str2bn(&val, p);
166 * pr_fact - print the factors of a number
168 * Print the factors of the number, from the lowest to the highest.
169 * A factor will be printed multiple times if it divides the value
172 * Factors are printed with leading tabs.
177 const ubig *fact; /* The factor found. */
179 /* Firewall - catch 0 and 1. */
180 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
182 if (BN_is_one(val)) {
191 BN_print_fp(stdout, val);
193 BN_print_dec_fp(stdout, val);
195 for (fact = &prime[0]; !BN_is_one(val); ++fact) {
196 /* Look for the smallest factor. */
198 if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
200 } while (++fact <= pr_limit);
202 /* Watch for primes larger than the table. */
203 if (fact > pr_limit) {
208 BN_set_word(bnfact, *(fact - 1));
209 if (!BN_sqr(bnfact, bnfact, ctx))
210 errx(1, "error in BN_sqr()");
211 if (BN_cmp(bnfact, val) > 0 ||
212 BN_is_prime_ex(val, PRIME_CHECKS, NULL, NULL) == 1)
215 pollard_pminus1(val);
222 /* Divide factor out until none are left. */
224 printf(hflag ? " 0x%" PRIx64 "" : " %" PRIu64 "", *fact);
225 BN_div_word(val, (BN_ULONG)*fact);
226 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
228 /* Let the user know we're doing something. */
235 pr_print(BIGNUM *val)
238 fputs(" 0x", stdout);
239 BN_print_fp(stdout, val);
242 BN_print_dec_fp(stdout, val);
249 fprintf(stderr, "usage: factor [-h] [value ...]\n");
255 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
257 pollard_pminus1(BIGNUM *val)
259 BIGNUM *base, *rbase, *num, *i, *x;
267 BN_set_word(rbase, 1);
269 if (!BN_add_word(rbase, 1))
270 errx(1, "error in BN_add_word()");
272 BN_copy(base, rbase);
275 BN_mod_exp(base, base, i, val, ctx);
281 if (!BN_gcd(x, x, val, ctx))
282 errx(1, "error in BN_gcd()");
285 if (BN_is_prime_ex(x, PRIME_CHECKS, NULL, NULL) == 1)
291 BN_div(num, NULL, val, x, ctx);
294 if (BN_is_prime_ex(num, PRIME_CHECKS, NULL,
302 if (!BN_add_word(i, 1))
303 errx(1, "error in BN_add_word()");
308 * Sigh.. No _decimal_ output to file functions in BN.
311 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
315 buf = BN_bn2dec(num);
317 return; /* XXX do anything here? */
318 fprintf(fp, "%s", buf);
325 BN_print_fp(FILE *fp, const BIGNUM *num)
327 fprintf(fp, "%lx", (unsigned long)*num);
331 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
333 fprintf(fp, "%lu", (unsigned long)*num);
337 BN_dec2bn(BIGNUM **a, const char *str)
342 **a = strtoul(str, &p, 10);
343 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */
347 BN_hex2bn(BIGNUM **a, const char *str)
352 **a = strtoul(str, &p, 16);
353 return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */
357 BN_div_word(BIGNUM *a, BN_ULONG b)
369 * Scan the string from left-to-right to see if the longest substring
370 * is a valid hexadecimal number.
373 is_hex_str(char *str)
376 bool saw_hex = false;
378 for (p = str; *p; p++) {
382 if (c >= 'a' && c <= 'f') {
386 break; /* Not a hexadecimal digit. */
391 /* Convert string pointed to by *str to a bignum. */
393 convert_str2bn(BIGNUM **val, char *p)
399 errx(1, "negative numbers aren't permitted.");
402 if (*p == 'x' || *p == 'X')
403 n = BN_hex2bn(val, ++p);
405 n = is_hex_str(p) ? BN_hex2bn(val, p) : BN_dec2bn(val, p);
408 errx(1, "%s: illegal numeric format.", p);