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
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20 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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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.
81 #include <openssl/bn.h>
83 #define PRIME_CHECKS 5
85 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */
90 typedef u_long BN_ULONG;
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))
99 static int BN_dec2bn(BIGNUM **a, const char *str);
100 static int BN_hex2bn(BIGNUM **a, const char *str);
101 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
102 static void BN_print_fp(FILE *, const BIGNUM *);
106 static void BN_print_dec_fp(FILE *, const BIGNUM *);
108 static void pr_fact(BIGNUM *); /* print factors of a value */
109 static void pr_print(BIGNUM *); /* print a prime */
110 static void usage(void);
112 static BN_CTX *ctx; /* just use a global context */
116 main(int argc, char *argv[])
120 char *p, buf[LINE_MAX]; /* > max number of digits. */
125 errx(1, "can't initialise bignum");
127 while ((ch = getopt(argc, argv, "h")) != -1)
139 /* No args supplied, read numbers from stdin. */
142 if (fgets(buf, sizeof(buf), stdin) == NULL) {
147 for (p = buf; isblank(*p); ++p);
148 if (*p == '\n' || *p == '\0')
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);
157 /* Factor the arguments. */
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]);
171 * pr_fact - print the factors of a number
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
177 * Factors are printed with leading tabs.
182 const ubig *fact; /* The factor found. */
184 /* Firewall - catch 0 and 1. */
185 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
187 if (BN_is_one(val)) {
196 BN_print_fp(stdout, val);
198 BN_print_dec_fp(stdout, val);
200 for (fact = &prime[0]; !BN_is_one(val); ++fact) {
201 /* Look for the smallest factor. */
203 if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
205 } while (++fact <= pr_limit);
207 /* Watch for primes larger than the table. */
208 if (fact > pr_limit) {
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)
221 pollard_pminus1(val);
228 /* Divide factor out until none are left. */
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);
234 /* Let the user know we're doing something. */
241 pr_print(BIGNUM *val)
244 fputs(" 0x", stdout);
245 BN_print_fp(stdout, val);
248 BN_print_dec_fp(stdout, val);
255 fprintf(stderr, "usage: factor [-h] [value ...]\n");
261 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
263 pollard_pminus1(BIGNUM *val)
265 BIGNUM *base, *rbase, *num, *i, *x;
273 BN_set_word(rbase, 1);
275 if (!BN_add_word(rbase, 1))
276 errx(1, "error in BN_add_word()");
278 BN_copy(base, rbase);
281 BN_mod_exp(base, base, i, val, ctx);
287 if (!BN_gcd(x, x, val, ctx))
288 errx(1, "error in BN_gcd()");
291 if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL,
298 BN_div(num, NULL, val, x, ctx);
301 if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
309 if (!BN_add_word(i, 1))
310 errx(1, "error in BN_add_word()");
315 * Sigh.. No _decimal_ output to file functions in BN.
318 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
322 buf = BN_bn2dec(num);
324 return; /* XXX do anything here? */
325 fprintf(fp, "%s", buf);
332 BN_print_fp(FILE *fp, const BIGNUM *num)
334 fprintf(fp, "%lx", (unsigned long)*num);
338 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
340 fprintf(fp, "%lu", (unsigned long)*num);
344 BN_dec2bn(BIGNUM **a, const char *str)
349 **a = strtoul(str, &p, 10);
350 return (errno == 0 && (*p == '\n' || *p == '\0'));
354 BN_hex2bn(BIGNUM **a, const char *str)
359 **a = strtoul(str, &p, 16);
360 return (errno == 0 && (*p == '\n' || *p == '\0'));
364 BN_div_word(BIGNUM *a, BN_ULONG b)