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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9 * modification, are permitted provided that the following conditions
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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
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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.
82 #include <openssl/bn.h>
84 #define PRIME_CHECKS 5
86 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */
91 typedef u_long BN_ULONG;
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))
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 *);
107 static void BN_print_dec_fp(FILE *, const BIGNUM *);
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);
113 static BN_CTX *ctx; /* just use a global context */
117 main(int argc, char *argv[])
121 char *p, buf[LINE_MAX]; /* > max number of digits. */
126 errx(1, "can't initialise bignum");
128 while ((ch = getopt(argc, argv, "h")) != -1)
140 /* No args supplied, read numbers from stdin. */
143 if (fgets(buf, sizeof(buf), stdin) == NULL) {
148 for (p = buf; isblank(*p); ++p);
149 if (*p == '\n' || *p == '\0')
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);
158 /* Factor the arguments. */
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]);
172 * pr_fact - print the factors of a number
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
178 * Factors are printed with leading tabs.
183 const ubig *fact; /* The factor found. */
185 /* Firewall - catch 0 and 1. */
186 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
188 if (BN_is_one(val)) {
197 BN_print_fp(stdout, val);
199 BN_print_dec_fp(stdout, val);
201 for (fact = &prime[0]; !BN_is_one(val); ++fact) {
202 /* Look for the smallest factor. */
204 if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
206 } while (++fact <= pr_limit);
208 /* Watch for primes larger than the table. */
209 if (fact > pr_limit) {
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(val, PRIME_CHECKS,
219 NULL, NULL, NULL) == 1)
222 pollard_pminus1(val);
229 /* Divide factor out until none are left. */
231 printf(hflag ? " 0x%" PRIx64 "" : " %" PRIu64 "", *fact);
232 BN_div_word(val, (BN_ULONG)*fact);
233 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
235 /* Let the user know we're doing something. */
242 pr_print(BIGNUM *val)
245 fputs(" 0x", stdout);
246 BN_print_fp(stdout, val);
249 BN_print_dec_fp(stdout, val);
256 fprintf(stderr, "usage: factor [-h] [value ...]\n");
262 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
264 pollard_pminus1(BIGNUM *val)
266 BIGNUM *base, *rbase, *num, *i, *x;
274 BN_set_word(rbase, 1);
276 if (!BN_add_word(rbase, 1))
277 errx(1, "error in BN_add_word()");
279 BN_copy(base, rbase);
282 BN_mod_exp(base, base, i, val, ctx);
288 if (!BN_gcd(x, x, val, ctx))
289 errx(1, "error in BN_gcd()");
292 if (BN_is_prime(x, PRIME_CHECKS, NULL, NULL,
299 BN_div(num, NULL, val, x, ctx);
302 if (BN_is_prime(num, PRIME_CHECKS, NULL, NULL,
310 if (!BN_add_word(i, 1))
311 errx(1, "error in BN_add_word()");
316 * Sigh.. No _decimal_ output to file functions in BN.
319 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
323 buf = BN_bn2dec(num);
325 return; /* XXX do anything here? */
326 fprintf(fp, "%s", buf);
333 BN_print_fp(FILE *fp, const BIGNUM *num)
335 fprintf(fp, "%lx", (unsigned long)*num);
339 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
341 fprintf(fp, "%lu", (unsigned long)*num);
345 BN_dec2bn(BIGNUM **a, const char *str)
350 **a = strtoul(str, &p, 10);
351 return (errno == 0 && (*p == '\n' || *p == '\0'));
355 BN_hex2bn(BIGNUM **a, const char *str)
360 **a = strtoul(str, &p, 16);
361 return (errno == 0 && (*p == '\n' || *p == '\0'));
365 BN_div_word(BIGNUM *a, BN_ULONG b)