/* $OpenBSD: factor.c,v 1.30 2016/09/01 10:48:38 tb Exp $ */ /* $NetBSD: factor.c,v 1.5 1995/03/23 08:28:07 cgd Exp $ */ /* * 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. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * 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. 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. * * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. */ /* * factor - factor a number into primes * * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo * * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ * * usage: * factor [number ...] * * The form of the output is: * * number: factor1 factor1 factor2 factor3 factor3 factor3 ... * * where factor1 < factor2 < factor3 < ... * * If no args are given, the list of numbers are read from stdin. */ #include <ctype.h> #include <err.h> #include <errno.h> #include <stdio.h> #include <stdlib.h> #include <string.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 const ubig prime[]; extern const ubig *pr_limit; /* largest prime in the prime array */ extern const char pattern[]; extern const int pattern_size; static void pr_fact(u_int64_t); /* print factors of a value */ static void pr_bigfact(u_int64_t); static u_int64_t usqrt(u_int64_t); static void __dead usage(void); int main(int argc, char *argv[]) { u_int64_t val; int ch; char *p, buf[100]; /* > max number of digits. */ if (pledge("stdio", NULL) == -1) err(1, "pledge"); while ((ch = getopt(argc, argv, "h")) != -1) { switch (ch) { case 'h': 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"); return 0; } buf[strcspn(buf, "\n")] = '\0'; for (p = buf; isblank((unsigned char)*p); ++p) ; if (*p == '\0') continue; if (*p == '-') errx(1, "negative numbers aren't permitted."); errno = 0; val = strtoull(buf, &p, 10); if (errno) err(1, "%s", buf); for (; isblank((unsigned char)*p); ++p) ; if (*p != '\0') errx(1, "%s: illegal numeric format.", buf); pr_fact(val); } /* Factor the arguments. */ } else { for (; *argv != NULL; ++argv) { if (argv[0][0] == '-') errx(1, "negative numbers aren't permitted."); errno = 0; val = strtoull(argv[0], &p, 10); if (errno) err(1, "%s", argv[0]); if (*p != '\0') errx(1, "%s: illegal numeric format.", argv[0]); pr_fact(val); } } return 0; } /* * pr_fact - print the prime 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 prime factor will be printed as often as it divides the value. * * Prime factors are printed with leading spaces. */ static void pr_fact(u_int64_t val) /* Factor this value. */ { const ubig *fact; /* The factor found. */ /* Firewall - catch 0 and 1. */ if (val == 0) /* Historical practice; 0 just exits. */ exit(0); if (val == 1) { (void)printf("1: 1\n"); return; } /* Factor value. */ (void)printf("%llu:", val); fflush(stdout); for (fact = &prime[0]; val > 1; ++fact) { /* Look for the smallest factor. */ do { if (val % (long)*fact == 0) break; } while (++fact <= pr_limit); /* Watch for primes larger than the table. */ if (fact > pr_limit) { if (val > BIG) pr_bigfact(val); else (void)printf(" %llu", val); break; } /* Divide factor out until none are left. */ do { (void)printf(" %lu", (unsigned long) *fact); val /= (long)*fact; } while ((val % (long)*fact) == 0); /* Let the user know we're doing something. */ (void)fflush(stdout); } (void)putchar('\n'); } /* * At this point, our number may have factors greater than those in primes[]; * however, we can generate primes up to 32 bits (see primes(6)), which is * sufficient to factor a 64-bit quad. */ static void pr_bigfact(u_int64_t val) /* Factor this value. */ { u_int64_t start, stop; ubig factor; char *q; const ubig *p; ubig fact_lim, mod; char *tab_lim; char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ start = *pr_limit + 2; stop = usqrt(val) + 1; if ((stop & 0x1) == 0) stop++; /* * Following code barely modified from that in primes(6) * * we shall sieve a bytemap window, note primes and move the window * upward until we pass the stop point */ while (start < stop) { /* * factor out 3, 5, 7, 11 and 13 */ /* initial pattern copy */ factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ memcpy(table, &pattern[factor], pattern_size-factor); /* main block pattern copies */ for (fact_lim = pattern_size - factor; fact_lim + pattern_size <= TABSIZE; fact_lim += pattern_size) { memcpy(&table[fact_lim], pattern, pattern_size); } /* final block pattern copy */ memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); if (stop-start > TABSIZE+TABSIZE) { tab_lim = &table[TABSIZE]; /* sieve it all */ fact_lim = usqrt(start + TABSIZE + TABSIZE + 1); } else { tab_lim = &table[(stop - start)/2]; /* partial sieve */ fact_lim = usqrt(stop + 1); } /* sieve for factors >= 17 */ factor = 17; /* 17 is first prime to use */ p = &prime[7]; /* 19 is next prime, pi(19)=7 */ do { /* determine the factor's initial sieve point */ mod = start % factor; if (mod & 0x1) q = &table[(factor-mod)/2]; else q = &table[mod ? factor-(mod/2) : 0]; /* sieve for our current factor */ for ( ; q < tab_lim; q += factor) { *q = '\0'; /* sieve out a spot */ } } while ((factor=(ubig)(*(p++))) <= fact_lim); /* * use generated primes */ for (q = table; q < tab_lim; ++q, start+=2) { if (*q) { if (val % start == 0) { do { printf(" %llu", start); val /= start; } while ((val % start) == 0); (void)fflush(stdout); stop = usqrt(val) + 1; if ((stop & 0x1) == 0) stop++; } } } } if (val > 1) printf(" %llu", val); } /* Code taken from ping.c */ static u_int64_t usqrt(u_int64_t n) { u_int64_t y, x = 1; if (n == 0 || n == 1) return n; do { /* newton was a stinker */ y = x; x = n / x; x += y; x /= 2; } while (((y < x) && (x - y) > 1) || (y - x) > 1); return x; } static void __dead usage(void) { (void)fprintf(stderr, "usage: %s [number ...]\n", getprogname()); exit (1); }
