+/* $NetBSD: factor.c,v 1.38 2020/10/12 13:54:51 christos Exp $ */
/*
- * Copyright (c) 1989 The Regents of the University of California.
- * All rights reserved.
+ * Copyright (c) 1989, 1993
+ * The Regents of the University of California. All rights reserved.
*
* This code is derived from software contributed to Berkeley by
* Landon Curt Noll.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
- * 3. All advertising materials mentioning features or use of this software
- * must display the following acknowledgement:
- * This product includes software developed by the University of
- * California, Berkeley and its contributors.
- * 4. Neither the name of the University nor the names of its contributors
+ * 3. Neither the name of the University nor the names of its contributors
* may be used to endorse or promote products derived from this software
* without specific prior written permission.
*
*/
#ifndef lint
-char copyright[] =
-"@(#) Copyright (c) 1989 The Regents of the University of California.\n\
- All rights reserved.\n";
-#endif /* not lint */
-
-#ifndef lint
-static char sccsid[] = "@(#)factor.c 4.4 (Berkeley) 6/1/90";
+#include <sys/cdefs.h>
+#ifdef __COPYRIGHT
+__COPYRIGHT("@(#) Copyright (c) 1989, 1993\
+ The Regents of the University of California. All rights reserved.");
+#endif
+#ifdef __SCCSID
+__SCCSID("@(#)factor.c 8.4 (Berkeley) 5/4/95");
+#endif
+#ifdef __RCSID
+__RCSID("$NetBSD: factor.c,v 1.38 2020/10/12 13:54:51 christos Exp $");
+#endif
+#ifdef __FBSDID
+__FBSDID("$FreeBSD: head/usr.bin/factor/factor.c 356666 2020-01-12 20:25:11Z gad $");
+#endif
#endif /* not lint */
/*
* chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
*
* usage:
- * factor [number] ...
+ * factor [-hx] [number] ...
*
* The form of the output is:
*
* number: factor1 factor1 factor2 factor3 factor3 factor3 ...
*
- * where factor1 < factor2 < factor3 < ...
+ * where factor1 <= factor2 <= factor3 <= ...
+ *
+ * If the -h flag is specified, the output is in "human-readable" format.
+ * Duplicate factors are printed in the form of x^n.
+ *
+ * If the -x flag is specified numbers are printed in hex.
*
- * If no args are given, the list of numbers are read from stdin.
+ * If no number args are given, the list of numbers are read from stdin.
*/
-#include <stdio.h>
#include <ctype.h>
+#include <err.h>
+#include <errno.h>
+#include <inttypes.h>
+#include <limits.h>
+#include <stdbool.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <unistd.h>
+
#include "primes.h"
-/*
- * prime[i] is the (i-1)th prime.
- *
- * We are able to sieve 2^32-1 because this byte table yields all primes
- * up to 65537 and 65537^2 > 2^32-1.
- */
-extern ubig prime[];
-extern ubig *pr_limit; /* largest prime in the prime array */
+#ifdef HAVE_OPENSSL
-#define MAX_LINE 255 /* max line allowed on stdin */
+#include <openssl/bn.h>
-void pr_fact(); /* print factors of a value */
-long small_fact(); /* find smallest factor of a value */
-char *read_num_buf(); /* read a number buffer */
-char *program; /* name of this program */
+#define PRIME_CHECKS 5
-main(argc, argv)
- int argc; /* arg count */
- char *argv[]; /* the args */
-{
- int arg; /* which arg to factor */
- long val; /* the value to factor */
- char buf[MAX_LINE+1]; /* input buffer */
+/* print factors for big numbers */
+static void pollard_pminus1(BIGNUM *, int, int);
- /* parse args */
- program = argv[0];
- if (argc >= 2) {
+#else
- /* factor each arg */
- for (arg=1; arg < argc; ++arg) {
+typedef long BIGNUM;
+typedef u_long BN_ULONG;
- /* process the buffer */
- if (read_num_buf(NULL, argv[arg]) == NULL) {
- fprintf(stderr, "%s: ouch\n", program);
- exit(1);
- }
+#define BN_CTX int
+#define BN_CTX_new() NULL
+#define BN_new() calloc(sizeof(BIGNUM), 1)
+#define BN_free(a) free(a)
- /* factor the argument */
- if (sscanf(argv[arg], "%ld", &val) == 1) {
- pr_fact(val);
- } else {
- fprintf(stderr, "%s: ouch\n", program);
- exit(1);
- }
- }
+#define BN_copy(a, b) *(a) = *(b)
+#define BN_cmp(a, b) (*(a) - *(b))
+#define BN_is_zero(v) (*(v) == 0)
+#define BN_is_one(v) (*(v) == 1)
+#define BN_mod_word(a, b) (*(a) % (b))
- /* no args supplied, read numbers from stdin */
- } else {
- /*
- * read asciii numbers from input
- */
- while (read_num_buf(stdin, buf) != NULL) {
-
- /* factor the argument */
- if (sscanf(buf, "%ld", &val) == 1) {
- pr_fact(val);
+static BIGNUM *BN_dup(const BIGNUM *);
+static int BN_dec2bn(BIGNUM **, const char *);
+static int BN_hex2bn(BIGNUM **, const char *);
+static BN_ULONG BN_div_word(BIGNUM *, BN_ULONG);
+static void BN_print_fp(FILE *, const BIGNUM *);
+
+#endif
+
+static void BN_print_dec_fp(FILE *, const BIGNUM *);
+static void convert_str2bn(BIGNUM **, char *);
+static void pr_fact(BIGNUM *, int, int); /* print factors of a value */
+static void pr_print(BIGNUM *, int, int); /* print a prime */
+static void usage(void) __dead;
+
+static BN_CTX *ctx; /* just use a global context */
+
+int
+main(int argc, char *argv[])
+{
+ BIGNUM *val;
+ int ch, hflag, xflag;
+ char *p, buf[LINE_MAX]; /* > max number of digits. */
+
+ hflag = xflag = 0;
+ ctx = BN_CTX_new();
+ val = BN_new();
+ if (val == NULL)
+ errx(1, "can't initialise bignum");
+
+ while ((ch = getopt(argc, argv, "hx")) != -1)
+ switch (ch) {
+ case 'h':
+ hflag++;
+ break;
+ case 'x':
+ xflag++;
+ break;
+ case '?':
+ default:
+ usage();
+ }
+ argc -= optind;
+ argv += optind;
+
+ /* No args supplied, read numbers from stdin. */
+ if (argc == 0)
+ for (;;) {
+ if (fgets(buf, sizeof(buf), stdin) == NULL) {
+ if (ferror(stdin))
+ err(1, "stdin");
+ exit (0);
}
+ for (p = buf; isblank((unsigned char)*p); ++p);
+ if (*p == '\n' || *p == '\0')
+ continue;
+ convert_str2bn(&val, p);
+ pr_fact(val, hflag, xflag);
+ }
+ /* Factor the arguments. */
+ else
+ for (p = *argv; p != NULL; p = *++argv) {
+ convert_str2bn(&val, p);
+ pr_fact(val, hflag, xflag);
}
- }
exit(0);
}
+static void
+pr_exp(int i, int xflag)
+{
+ printf(xflag && i > 9 ? "^0x%x" : "^%d", i);
+}
+
+static void
+pr_uint64(uint64_t i, int xflag)
+{
+ printf(xflag ? " 0x%" PRIx64 : " %" PRIu64, i);
+}
+
/*
- * read_num_buf - read a number buffer from a stream
- *
- * Read a number on a line of the form:
- *
- * ^[ \t]*\([+-]?[0-9][0-9]\)*.*$
- *
- * where ? is a 1-or-0 operator and the number is within \( \).
- *
- * If does not match the above pattern, it is ignored and a new
- * line is read. If the number is too large or small, we will
- * print ouch and read a new line.
+ * pr_fact - print the factors of a number
*
- * We have to be very careful on how we check the magnitude of the
- * input. We can not use numeric checks because of the need to
- * check values against maximum numeric values.
+ * Print the factors of the number, from the lowest to the highest.
+ * A factor will be printed multiple times if it divides the value
+ * multiple times.
*
- * This routine will return a line containing a ascii number between
- * NEG_SEMIBIG and SEMIBIG, or it will return NULL.
+ * If hflag is specified, duplicate factors are printed in "human-
+ * readable" form of x^n.
*
- * If the stream is NULL then buf will be processed as if were
- * a single line stream.
+ * If the xflag is specified, numbers will be printed in hex.
*
- * returns:
- * char * pointer to leading digit, + or -
- * NULL EOF or error
+ * Factors are printed with leading tabs.
*/
-char *
-read_num_buf(input, buf)
- FILE *input; /* input stream or NULL */
- char *buf; /* input buffer */
+static void
+pr_fact(BIGNUM *val, int hflag, int xflag)
{
- static char limit[MAX_LINE+1]; /* ascii value of SEMIBIG */
- static int limit_len; /* digit count of limit */
- static char neg_limit[MAX_LINE+1]; /* value of NEG_SEMIBIG */
- static int neg_limit_len; /* digit count of neg_limit */
- int len; /* digits in input (excluding +/-) */
- char *s; /* line start marker */
- char *d; /* first digit, skip +/- */
- char *p; /* scan pointer */
- char *z; /* zero scan pointer */
-
- /* form the ascii value of SEMIBIG if needed */
- if (!isascii(limit[0]) || !isdigit(limit[0])) {
- sprintf(limit, "%ld", SEMIBIG);
- limit_len = strlen(limit);
- sprintf(neg_limit, "%ld", NEG_SEMIBIG);
- neg_limit_len = strlen(neg_limit)-1; /* exclude - */
- }
-
- /*
- * the search for a good line
- */
- if (input != NULL && fgets(buf, MAX_LINE, input) == NULL) {
- /* error or EOF */
- return NULL;
+ int i;
+ const uint64_t *fact; /* The factor found. */
+
+ /* Firewall - catch 0 and 1. */
+ if (BN_is_zero(val)) /* Historical practice; 0 just exits. */
+ exit(0);
+ if (BN_is_one(val)) {
+ printf("1: 1\n");
+ return;
}
- do {
- /* ignore leading whitespace */
- for (s=buf; *s && s < buf+MAX_LINE; ++s) {
- if (!isascii(*s) || !isspace(*s)) {
+ /* Factor value. */
+
+ if (xflag) {
+ fputs("0x", stdout);
+ BN_print_fp(stdout, val);
+ } else
+ BN_print_dec_fp(stdout, val);
+ putchar(':');
+ fflush(stdout);
+ for (fact = &prime[0]; !BN_is_one(val); ++fact) {
+ /* Look for the smallest factor. */
+ do {
+ if (BN_mod_word(val, (BN_ULONG)*fact) == 0)
break;
- }
- }
+ } while (++fact <= pr_limit);
- /* skip over any leading + or - */
- if (*s == '+' || *s == '-') {
- d = s+1;
- } else {
- d = s;
+ /* Watch for primes larger than the table. */
+ if (fact > pr_limit) {
+#ifdef HAVE_OPENSSL
+ BIGNUM *bnfact;
+
+ bnfact = BN_new();
+ BN_set_word(bnfact, *(fact - 1));
+ if (!BN_sqr(bnfact, bnfact, ctx))
+ errx(1, "error in BN_sqr()");
+ if (BN_cmp(bnfact, val) > 0 ||
+ BN_is_prime_ex(val, PRIME_CHECKS, NULL, NULL) == 1)
+ pr_print(val, hflag, xflag);
+ else
+ pollard_pminus1(val, hflag, xflag);
+#else
+ pr_print(val, hflag, xflag);
+#endif
+ pr_print(NULL, hflag, xflag);
+ break;
}
- /* note leading zeros */
- for (z=d; *z && z < buf+MAX_LINE; ++z) {
- if (*z != '0') {
- break;
- }
+ /* Divide factor out until none are left. */
+ i = 0;
+ do {
+ i++;
+ if (!hflag)
+ pr_uint64(*fact, xflag);
+ BN_div_word(val, (BN_ULONG)*fact);
+ } while (BN_mod_word(val, (BN_ULONG)*fact) == 0);
+
+ if (hflag) {
+ pr_uint64(*fact, xflag);
+ if (i > 1)
+ pr_exp(i, xflag);
}
- /* scan for the first non-digit */
- for (p=d; *p && p < buf+MAX_LINE; ++p) {
- if (!isascii(*p) || !isdigit(*p)) {
- break;
- }
+ /* Let the user know we're doing something. */
+ fflush(stdout);
+ }
+ putchar('\n');
+}
+
+static void
+pr_print(BIGNUM *val, int hflag, int xflag)
+{
+ static BIGNUM *sval;
+ static int ex = 1;
+ BIGNUM *pval;
+
+ if (hflag) {
+ if (sval == NULL) {
+ sval = BN_dup(val);
+ return;
}
- /* ignore empty lines */
- if (p == d) {
- continue;
+ if (val != NULL && BN_cmp(val, sval) == 0) {
+ ex++;
+ return;
}
- *p = '\0';
-
- /* object if too many digits */
- len = strlen(z);
- len = (len<=0) ? 1 : len;
- if (*s == '-') {
- /* accept if digit count is below limit */
- if (len < neg_limit_len) {
- /* we have good input */
- return s;
-
- /* reject very large numbers */
- } else if (len > neg_limit_len) {
- fprintf(stderr, "%s: ouch\n", program);
- exit(1);
-
- /* carefully check against near limit numbers */
- } else if (strcmp(z, neg_limit+1) > 0) {
- fprintf(stderr, "%s: ouch\n", program);
- exit(1);
- }
- /* number is near limit, but is under it */
- return s;
-
+ pval = sval;
+ } else if (val == NULL) {
+ return;
+ } else {
+ pval = val;
+ }
+
+ if (xflag) {
+ fputs(" 0x", stdout);
+ BN_print_fp(stdout, pval);
+ } else {
+ putchar(' ');
+ BN_print_dec_fp(stdout, pval);
+ }
+
+ if (hflag) {
+ if (ex > 1)
+ pr_exp(ex, xflag);
+
+ if (val != NULL) {
+ BN_copy(sval, val);
} else {
- /* accept if digit count is below limit */
- if (len < limit_len) {
- /* we have good input */
- return s;
-
- /* reject very large numbers */
- } else if (len > limit_len) {
- fprintf(stderr, "%s: ouch\n", program);
- exit(1);
-
- /* carefully check against near limit numbers */
- } else if (strcmp(z, limit) > 0) {
- fprintf(stderr, "%s: ouch\n", program);
- exit(1);
- }
- /* number is near limit, but is under it */
- return s;
+ BN_free(sval);
+ sval = NULL;
}
- } while (input != NULL && fgets(buf, MAX_LINE, input) != NULL);
+ ex = 1;
+ }
+}
- /* error or EOF */
- return NULL;
+static void
+usage(void)
+{
+ fprintf(stderr, "Usage: %s [-hx] [value ...]\n", getprogname());
+ exit(1);
}
+#ifdef HAVE_OPENSSL
+
+/* pollard p-1, algorithm from Jim Gillogly, May 2000 */
+static void
+pollard_pminus1(BIGNUM *val, int hflag, int xflag)
+{
+ BIGNUM *base, *rbase, *num, *i, *x;
+
+ base = BN_new();
+ rbase = BN_new();
+ num = BN_new();
+ i = BN_new();
+ x = BN_new();
+
+ BN_set_word(rbase, 1);
+newbase:
+ if (!BN_add_word(rbase, 1))
+ errx(1, "error in BN_add_word()");
+ BN_set_word(i, 2);
+ BN_copy(base, rbase);
+
+ for (;;) {
+ BN_mod_exp(base, base, i, val, ctx);
+ if (BN_is_one(base))
+ goto newbase;
+
+ BN_copy(x, base);
+ BN_sub_word(x, 1);
+ if (!BN_gcd(x, x, val, ctx))
+ errx(1, "error in BN_gcd()");
+
+ if (!BN_is_one(x)) {
+ if (BN_is_prime_ex(x, PRIME_CHECKS, NULL, NULL) == 1)
+ pr_print(x, hflag, xflag);
+ else
+ pollard_pminus1(x, hflag, xflag);
+ fflush(stdout);
+
+ BN_div(num, NULL, val, x, ctx);
+ if (BN_is_one(num))
+ return;
+ if (BN_is_prime_ex(num, PRIME_CHECKS, NULL,
+ NULL) == 1) {
+ pr_print(num, hflag, xflag);
+ fflush(stdout);
+ return;
+ }
+ BN_copy(val, num);
+ }
+ if (!BN_add_word(i, 1))
+ errx(1, "error in BN_add_word()");
+ }
+}
/*
- * pr_fact - print the factors of a number
- *
- * If the number is 0 or 1, then print the number and return.
- * If the number is < 0, print -1, negate the number and continue
- * processing.
- *
- * Print the factors of the number, from the lowest to the highest.
- * A factor will be printed numtiple times if it divides the value
- * multiple times.
- *
- * Factors are printed with leading tabs.
+ * Sigh.. No _decimal_ output to file functions in BN.
*/
-void
-pr_fact(val)
- long val; /* factor this value */
+static void
+BN_print_dec_fp(FILE *fp, const BIGNUM *num)
{
- ubig *fact; /* the factor found */
+ char *buf;
- /* firewall - catch 0 and 1 */
- switch (val) {
- case -2147483648:
- /* avoid negation problems */
- puts("-2147483648: -1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2\n");
- return;
- case -1:
- puts("-1: -1\n");
- return;
- case 0:
- exit(0);
- case 1:
- puts("1: 1\n");
- return;
- default:
- if (val < 0) {
- val = -val;
- printf("%ld: -1", val);
- } else {
- printf("%ld:", val);
- }
- fflush(stdout);
- break;
- }
+ buf = BN_bn2dec(num);
+ if (buf == NULL)
+ return; /* XXX do anything here? */
+ fprintf(fp, "%s", buf);
+ free(buf);
+}
- /*
- * factor value
- */
- fact = &prime[0];
- while (val > 1) {
+#else
- /* look for the smallest factor */
- do {
- if (val%(long)*fact == 0) {
- break;
- }
- } while (++fact <= pr_limit);
+static void
+BN_print_fp(FILE *fp, const BIGNUM *num)
+{
+ fprintf(fp, "%lx", (unsigned long)*num);
+}
- /* watch for primes larger than the table */
- if (fact > pr_limit) {
- printf(" %ld\n", val);
- return;
- }
+static void
+BN_print_dec_fp(FILE *fp, const BIGNUM *num)
+{
+ fprintf(fp, "%lu", (unsigned long)*num);
+}
- /* divide factor out until none are left */
- do {
- printf(" %ld", *fact);
- val /= (long)*fact;
- } while ((val % (long)*fact) == 0);
- fflush(stdout);
- ++fact;
+static int
+BN_dec2bn(BIGNUM **a, const char *str)
+{
+ char *p;
+
+ errno = 0;
+ **a = strtoul(str, &p, 10);
+ return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */
+}
+
+static int
+BN_hex2bn(BIGNUM **a, const char *str)
+{
+ char *p;
+
+ errno = 0;
+ **a = strtoul(str, &p, 16);
+ return (errno == 0 ? 1 : 0); /* OpenSSL returns 0 on error! */
+}
+
+static BN_ULONG
+BN_div_word(BIGNUM *a, BN_ULONG b)
+{
+ BN_ULONG mod;
+
+ mod = *a % b;
+ *a /= b;
+ return mod;
+}
+
+static BIGNUM *
+BN_dup(const BIGNUM *a)
+{
+ BIGNUM *b = BN_new();
+ BN_copy(b, a);
+ return b;
+}
+
+#endif
+
+/* Convert string pointed to by *str to a bignum. */
+static void
+convert_str2bn(BIGNUM **val, char *p)
+{
+ int n = 0;
+
+ if (*p == '+') p++;
+ if (*p == '-')
+ errx(1, "negative numbers aren't permitted.");
+ if (*p == '0' && (p[1] == 'x' || p[1] == 'X')) {
+ n = BN_hex2bn(val, p + 2);
+ } else {
+ n = BN_dec2bn(val, p);
}
- putchar('\n');
- return;
+ if (n == 0)
+ errx(1, "%s: illegal numeric format.", p);
}
git.ckatri.com / bsdgames-darwin.git / blobdiff