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32 * @(#) Copyright (c) 1989, 1993 The Regents of the University of California. All rights reserved.
33 * @(#)factor.c 8.4 (Berkeley) 5/4/95
34 * $NetBSD: factor.c,v 1.13 2002/06/18 23:07:36 simonb Exp $
35 * $FreeBSD: src/games/factor/factor.c,v 1.9.2.2 2002/10/23 14:59:14 fanf Exp $
39 * factor - factor a number into primes
41 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
43 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
46 * factor [-h] [number] ...
48 * The form of the output is:
50 * number: factor1 factor1 factor2 factor3 factor3 factor3 ...
52 * where factor1 < factor2 < factor3 < ...
54 * If no args are given, the list of numbers are read from stdin.
68 #include <openssl/bn.h>
69 #define PRIME_CHECKS 5
70 static void pollard_pminus1(BIGNUM *); /* print factors for big numbers */
73 typedef u_long BN_ULONG;
76 #define BN_CTX_new() NULL
77 #define BN_new() ((BIGNUM *)calloc(sizeof(BIGNUM), 1))
78 #define BN_is_zero(v) (*(v) == 0)
79 #define BN_is_one(v) (*(v) == 1)
80 #define BN_mod_word(a, b) (*(a) % (b))
82 static int BN_dec2bn(BIGNUM **a, const char *str);
83 static int BN_hex2bn(BIGNUM **a, const char *str);
84 static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
85 static void BN_print_fp(FILE *, const BIGNUM *);
88 static void BN_print_dec_fp(FILE *, const BIGNUM *);
90 static void pr_fact(BIGNUM *); /* print factors of a value */
91 static void pr_print(BIGNUM *); /* print a prime */
92 static void usage(void);
94 static BN_CTX *ctx; /* just use a global context */
98 main(int argc, char *argv[])
102 char *p, buf[LINE_MAX]; /* > max number of digits. */
107 errx(1, "can't initialise bignum");
109 while ((ch = getopt(argc, argv, "h")) != -1)
121 /* No args supplied, read numbers from stdin. */
124 if (fgets(buf, sizeof(buf), stdin) == NULL) {
129 for (p = buf; isblank(*p); ++p);
130 if (*p == '\n' || *p == '\0')
133 errx(1, "negative numbers aren't permitted.");
134 if (BN_dec2bn(&val, buf) == 0 &&
135 BN_hex2bn(&val, buf) == 0)
136 errx(1, "%s: illegal numeric format.", buf);
139 /* Factor the arguments. */
141 for (; *argv != NULL; ++argv) {
142 if (argv[0][0] == '-')
143 errx(1, "negative numbers aren't permitted.");
144 if (BN_dec2bn(&val, argv[0]) == 0 &&
145 BN_hex2bn(&val, argv[0]) == 0)
146 errx(1, "%s: illegal numeric format.", argv[0]);
153 * pr_fact - print the factors of a number
155 * Print the factors of the number, from the lowest to the highest.
156 * A factor will be printed multiple times if it divides the value
159 * Factors are printed with leading tabs.
164 const ubig *fact; /* The factor found. */
166 /* Firewall - catch 0 and 1. */
167 if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
169 if (BN_is_one(val)) {
178 BN_print_fp(stdout, val);
180 BN_print_dec_fp(stdout, val);
182 for (fact = &prime[0]; !BN_is_one(val); ++fact) {
183 /* Look for the smallest factor. */
185 if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
187 } while (++fact <= pr_limit);
189 /* Watch for primes larger than the table. */
190 if (fact > pr_limit) {
195 BN_set_word(bnfact, *(fact - 1));
196 BN_sqr(bnfact, bnfact, ctx);
197 if (BN_cmp(bnfact, val) > 0)
200 pollard_pminus1(val);
207 /* Divide factor out until none are left. */
209 printf(hflag ? " 0x%lx" : " %lu", *fact);
210 BN_div_word(val, (BN_ULONG)*fact);
211 } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
213 /* Let the user know we're doing something. */
220 pr_print(BIGNUM *val)
223 fputs(" 0x", stdout);
224 BN_print_fp(stdout, val);
227 BN_print_dec_fp(stdout, val);
234 fprintf(stderr, "usage: factor [-h] [value ...]\n");
240 /* pollard p-1, algorithm from Jim Gillogly, May 2000 */
242 pollard_pminus1(BIGNUM *val)
244 BIGNUM *base, *num, *i, *x;
252 BN_set_word(base, 2);
255 BN_mod_exp(base, base, i, val, ctx);
259 BN_gcd(x, x, val, ctx);
262 if (BN_is_prime_ex(x, PRIME_CHECKS, NULL, NULL) == 1)
268 BN_div(num, NULL, val, x, ctx);
271 if (BN_is_prime_ex(num, PRIME_CHECKS, NULL, NULL) == 1)
284 * Sigh.. No _decimal_ output to file functions in BN.
287 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
291 buf = BN_bn2dec(num);
293 return; /* XXX do anything here? */
294 fprintf(fp, "%s", buf);
301 BN_print_fp(FILE *fp, const BIGNUM *num)
303 fprintf(fp, "%lx", (unsigned long)*num);
307 BN_print_dec_fp(FILE *fp, const BIGNUM *num)
309 fprintf(fp, "%lu", (unsigned long)*num);
313 BN_dec2bn(BIGNUM **a, const char *str)
318 **a = strtoul(str, &p, 10);
319 return (errno == 0 && (*p == '\n' || *p == '\0'));
323 BN_hex2bn(BIGNUM **a, const char *str)
328 **a = strtoul(str, &p, 16);
329 return (errno == 0 && (*p == '\n' || *p == '\0'));
333 BN_div_word(BIGNUM *a, BN_ULONG b)