1 /* $OpenBSD: factor.c,v 1.30 2016/09/01 10:48:38 tb Exp $ */ 2 /* $NetBSD: factor.c,v 1.5 1995/03/23 08:28:07 cgd Exp $ */ 3 4 /* 5 * Copyright (c) 1989, 1993 6 * The Regents of the University of California. All rights reserved. 7 * 8 * This code is derived from software contributed to Berkeley by 9 * Landon Curt Noll. 10 * 11 * Redistribution and use in source and binary forms, with or without 12 * modification, are permitted provided that the following conditions 13 * are met: 14 * 1. Redistributions of source code must retain the above copyright 15 * notice, this list of conditions and the following disclaimer. 16 * 2. Redistributions in binary form must reproduce the above copyright 17 * notice, this list of conditions and the following disclaimer in the 18 * documentation and/or other materials provided with the distribution. 19 * 3. Neither the name of the University nor the names of its contributors 20 * may be used to endorse or promote products derived from this software 21 * without specific prior written permission. 22 * 23 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 24 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 25 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 26 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 27 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 28 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 29 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 30 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 31 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 32 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 33 * SUCH DAMAGE. 34 */ 35 36 /* 37 * factor - factor a number into primes 38 * 39 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 40 * 41 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 42 * 43 * usage: 44 * factor [number ...] 45 * 46 * The form of the output is: 47 * 48 * number: factor1 factor1 factor2 factor3 factor3 factor3 ... 49 * 50 * where factor1 < factor2 < factor3 < ... 51 * 52 * If no args are given, the list of numbers are read from stdin. 53 */ 54 55 #include <ctype.h> 56 #include <err.h> 57 #include <errno.h> 58 #include <stdio.h> 59 #include <stdlib.h> 60 #include <string.h> 61 #include <unistd.h> 62 63 #include "primes.h" 64 65 /* 66 * prime[i] is the (i+1)th prime. 67 * 68 * We are able to sieve 2^32-1 because this byte table yields all primes 69 * up to 65537 and 65537^2 > 2^32-1. 70 */ 71 extern const ubig prime[]; 72 extern const ubig *pr_limit; /* largest prime in the prime array */ 73 extern const char pattern[]; 74 extern const int pattern_size; 75 76 static void pr_fact(u_int64_t); /* print factors of a value */ 77 static void pr_bigfact(u_int64_t); 78 static u_int64_t usqrt(u_int64_t); 79 static void __dead usage(void); 80 81 int 82 main(int argc, char *argv[]) 83 { 84 u_int64_t val; 85 int ch; 86 char *p, buf[100]; /* > max number of digits. */ 87 88 if (pledge("stdio", NULL) == -1) 89 err(1, "pledge"); 90 91 while ((ch = getopt(argc, argv, "h")) != -1) { 92 switch (ch) { 93 case 'h': 94 default: 95 usage(); 96 } 97 } 98 argc -= optind; 99 argv += optind; 100 101 /* No args supplied, read numbers from stdin. */ 102 if (argc == 0) { 103 for (;;) { 104 if (fgets(buf, sizeof(buf), stdin) == NULL) { 105 if (ferror(stdin)) 106 err(1, "stdin"); 107 return 0; 108 } 109 buf[strcspn(buf, "\n")] = '\0'; 110 for (p = buf; isblank((unsigned char)*p); ++p) 111 ; 112 if (*p == '\0') 113 continue; 114 if (*p == '-') 115 errx(1, "negative numbers aren't permitted."); 116 errno = 0; 117 val = strtoull(buf, &p, 10); 118 if (errno) 119 err(1, "%s", buf); 120 for (; isblank((unsigned char)*p); ++p) 121 ; 122 if (*p != '\0') 123 errx(1, "%s: illegal numeric format.", buf); 124 pr_fact(val); 125 } 126 /* Factor the arguments. */ 127 } else { 128 for (; *argv != NULL; ++argv) { 129 if (argv[0][0] == '-') 130 errx(1, "negative numbers aren't permitted."); 131 errno = 0; 132 val = strtoull(argv[0], &p, 10); 133 if (errno) 134 err(1, "%s", argv[0]); 135 if (*p != '\0') 136 errx(1, "%s: illegal numeric format.", argv[0]); 137 pr_fact(val); 138 } 139 } 140 return 0; 141 } 142 143 /* 144 * pr_fact - print the prime factors of a number 145 * 146 * If the number is 0 or 1, then print the number and return. 147 * If the number is < 0, print -1, negate the number and continue 148 * processing. 149 * 150 * Print the factors of the number, from the lowest to the highest. 151 * A prime factor will be printed as often as it divides the value. 152 * 153 * Prime factors are printed with leading spaces. 154 */ 155 static void 156 pr_fact(u_int64_t val) /* Factor this value. */ 157 { 158 const ubig *fact; /* The factor found. */ 159 160 /* Firewall - catch 0 and 1. */ 161 if (val == 0) /* Historical practice; 0 just exits. */ 162 exit(0); 163 if (val == 1) { 164 (void)printf("1: 1\n"); 165 return; 166 } 167 168 /* Factor value. */ 169 (void)printf("%llu:", val); 170 fflush(stdout); 171 for (fact = &prime[0]; val > 1; ++fact) { 172 /* Look for the smallest factor. */ 173 do { 174 if (val % (long)*fact == 0) 175 break; 176 } while (++fact <= pr_limit); 177 178 /* Watch for primes larger than the table. */ 179 if (fact > pr_limit) { 180 if (val > BIG) 181 pr_bigfact(val); 182 else 183 (void)printf(" %llu", val); 184 break; 185 } 186 187 /* Divide factor out until none are left. */ 188 do { 189 (void)printf(" %lu", (unsigned long) *fact); 190 val /= (long)*fact; 191 } while ((val % (long)*fact) == 0); 192 193 /* Let the user know we're doing something. */ 194 (void)fflush(stdout); 195 } 196 (void)putchar('\n'); 197 } 198 199 /* 200 * At this point, our number may have factors greater than those in primes[]; 201 * however, we can generate primes up to 32 bits (see primes(6)), which is 202 * sufficient to factor a 64-bit quad. 203 */ 204 static void 205 pr_bigfact(u_int64_t val) /* Factor this value. */ 206 { 207 u_int64_t start, stop; 208 ubig factor; 209 char *q; 210 const ubig *p; 211 ubig fact_lim, mod; 212 char *tab_lim; 213 char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 214 215 start = *pr_limit + 2; 216 stop = usqrt(val) + 1; 217 if ((stop & 0x1) == 0) 218 stop++; 219 /* 220 * Following code barely modified from that in primes(6) 221 * 222 * we shall sieve a bytemap window, note primes and move the window 223 * upward until we pass the stop point 224 */ 225 while (start < stop) { 226 /* 227 * factor out 3, 5, 7, 11 and 13 228 */ 229 /* initial pattern copy */ 230 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 231 memcpy(table, &pattern[factor], pattern_size-factor); 232 /* main block pattern copies */ 233 for (fact_lim = pattern_size - factor; 234 fact_lim + pattern_size <= TABSIZE; 235 fact_lim += pattern_size) { 236 memcpy(&table[fact_lim], pattern, pattern_size); 237 } 238 /* final block pattern copy */ 239 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 240 241 if (stop-start > TABSIZE+TABSIZE) { 242 tab_lim = &table[TABSIZE]; /* sieve it all */ 243 fact_lim = usqrt(start + TABSIZE + TABSIZE + 1); 244 } else { 245 tab_lim = &table[(stop - start)/2]; /* partial sieve */ 246 fact_lim = usqrt(stop + 1); 247 } 248 /* sieve for factors >= 17 */ 249 factor = 17; /* 17 is first prime to use */ 250 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 251 do { 252 /* determine the factor's initial sieve point */ 253 mod = start % factor; 254 if (mod & 0x1) 255 q = &table[(factor-mod)/2]; 256 else 257 q = &table[mod ? factor-(mod/2) : 0]; 258 /* sieve for our current factor */ 259 for ( ; q < tab_lim; q += factor) { 260 *q = '\0'; /* sieve out a spot */ 261 } 262 } while ((factor=(ubig)(*(p++))) <= fact_lim); 263 264 /* 265 * use generated primes 266 */ 267 for (q = table; q < tab_lim; ++q, start+=2) { 268 if (*q) { 269 if (val % start == 0) { 270 do { 271 printf(" %llu", start); 272 val /= start; 273 } while ((val % start) == 0); 274 (void)fflush(stdout); 275 stop = usqrt(val) + 1; 276 if ((stop & 0x1) == 0) 277 stop++; 278 } 279 } 280 } 281 } 282 if (val > 1) 283 printf(" %llu", val); 284 } 285 286 /* Code taken from ping.c */ 287 static u_int64_t 288 usqrt(u_int64_t n) 289 { 290 u_int64_t y, x = 1; 291 292 if (n == 0 || n == 1) 293 return n; 294 295 do { /* newton was a stinker */ 296 y = x; 297 x = n / x; 298 x += y; 299 x /= 2; 300 } while (((y < x) && (x - y) > 1) || (y - x) > 1); 301 302 return x; 303 } 304 305 static void __dead 306 usage(void) 307 { 308 (void)fprintf(stderr, "usage: %s [number ...]\n", getprogname()); 309 exit (1); 310 } 311