primes.c revision 90828
1/* 2 * Copyright (c) 1989, 1993 3 * The Regents of the University of California. All rights reserved. 4 * 5 * This code is derived from software contributed to Berkeley by 6 * Landon Curt Noll. 7 * 8 * Redistribution and use in source and binary forms, with or without 9 * modification, are permitted provided that the following conditions 10 * are met: 11 * 1. Redistributions of source code must retain the above copyright 12 * notice, this list of conditions and the following disclaimer. 13 * 2. Redistributions in binary form must reproduce the above copyright 14 * notice, this list of conditions and the following disclaimer in the 15 * documentation and/or other materials provided with the distribution. 16 * 3. All advertising materials mentioning features or use of this software 17 * must display the following acknowledgement: 18 * This product includes software developed by the University of 19 * California, Berkeley and its contributors. 20 * 4. Neither the name of the University nor the names of its contributors 21 * may be used to endorse or promote products derived from this software 22 * without specific prior written permission. 23 * 24 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 25 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 26 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 27 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 28 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 29 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 30 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 31 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 32 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 33 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 34 * SUCH DAMAGE. 35 */ 36 37#ifndef lint 38static const char copyright[] = 39"@(#) Copyright (c) 1989, 1993\n\ 40 The Regents of the University of California. All rights reserved.\n"; 41#endif /* not lint */ 42 43#ifndef lint 44#if 0 45static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95"; 46#endif 47static const char rcsid[] = 48 "$FreeBSD: head/games/primes/primes.c 90828 2002-02-18 05:15:19Z imp $"; 49#endif /* not lint */ 50 51/* 52 * primes - generate a table of primes between two values 53 * 54 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 55 * 56 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 57 * 58 * usage: 59 * primes [start [stop]] 60 * 61 * Print primes >= start and < stop. If stop is omitted, 62 * the value 4294967295 (2^32-1) is assumed. If start is 63 * omitted, start is read from standard input. 64 * 65 * validation check: there are 664579 primes between 0 and 10^7 66 */ 67 68#include <ctype.h> 69#include <err.h> 70#include <errno.h> 71#include <limits.h> 72#include <math.h> 73#include <memory.h> 74#include <stdio.h> 75#include <stdlib.h> 76#include <unistd.h> 77 78#include "primes.h" 79 80/* 81 * Eratosthenes sieve table 82 * 83 * We only sieve the odd numbers. The base of our sieve windows are always 84 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 85 * sieve, table[i] == 1 if and only if 2*i-1 is prime. 86 * 87 * We make TABSIZE large to reduce the overhead of inner loop setup. 88 */ 89char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 90 91/* 92 * prime[i] is the (i-1)th prime. 93 * 94 * We are able to sieve 2^32-1 because this byte table yields all primes 95 * up to 65537 and 65537^2 > 2^32-1. 96 */ 97extern ubig prime[]; 98extern ubig *pr_limit; /* largest prime in the prime array */ 99 100/* 101 * To avoid excessive sieves for small factors, we use the table below to 102 * setup our sieve blocks. Each element represents a odd number starting 103 * with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13. 104 */ 105extern char pattern[]; 106extern int pattern_size; /* length of pattern array */ 107 108int hflag; 109 110void primes(ubig, ubig); 111ubig read_num_buf(void); 112void usage(void); 113 114int 115main(argc, argv) 116 int argc; 117 char *argv[]; 118{ 119 ubig start; /* where to start generating */ 120 ubig stop; /* don't generate at or above this value */ 121 int ch; 122 char *p; 123 124 while ((ch = getopt(argc, argv, "h")) != -1) 125 switch (ch) { 126 case 'h': 127 hflag++; 128 break; 129 case '?': 130 default: 131 usage(); 132 } 133 argc -= optind; 134 argv += optind; 135 136 start = 0; 137 stop = BIG; 138 139 /* 140 * Convert low and high args. Strtoul(3) sets errno to 141 * ERANGE if the number is too large, but, if there's 142 * a leading minus sign it returns the negation of the 143 * result of the conversion, which we'd rather disallow. 144 */ 145 switch (argc) { 146 case 2: 147 /* Start and stop supplied on the command line. */ 148 if (argv[0][0] == '-' || argv[1][0] == '-') 149 errx(1, "negative numbers aren't permitted."); 150 151 errno = 0; 152 start = strtoul(argv[0], &p, 0); 153 if (errno) 154 err(1, "%s", argv[0]); 155 if (*p != '\0') 156 errx(1, "%s: illegal numeric format.", argv[0]); 157 158 errno = 0; 159 stop = strtoul(argv[1], &p, 0); 160 if (errno) 161 err(1, "%s", argv[1]); 162 if (*p != '\0') 163 errx(1, "%s: illegal numeric format.", argv[1]); 164 break; 165 case 1: 166 /* Start on the command line. */ 167 if (argv[0][0] == '-') 168 errx(1, "negative numbers aren't permitted."); 169 170 errno = 0; 171 start = strtoul(argv[0], &p, 0); 172 if (errno) 173 err(1, "%s", argv[0]); 174 if (*p != '\0') 175 errx(1, "%s: illegal numeric format.", argv[0]); 176 break; 177 case 0: 178 start = read_num_buf(); 179 break; 180 default: 181 usage(); 182 } 183 184 if (start > stop) 185 errx(1, "start value must be less than stop value."); 186 primes(start, stop); 187 exit(0); 188} 189 190/* 191 * read_num_buf -- 192 * This routine returns a number n, where 0 <= n && n <= BIG. 193 */ 194ubig 195read_num_buf() 196{ 197 ubig val; 198 char *p, buf[100]; /* > max number of digits. */ 199 200 for (;;) { 201 if (fgets(buf, sizeof(buf), stdin) == NULL) { 202 if (ferror(stdin)) 203 err(1, "stdin"); 204 exit(0); 205 } 206 for (p = buf; isblank(*p); ++p); 207 if (*p == '\n' || *p == '\0') 208 continue; 209 if (*p == '-') 210 errx(1, "negative numbers aren't permitted."); 211 errno = 0; 212 val = strtoul(buf, &p, 0); 213 if (errno) 214 err(1, "%s", buf); 215 if (*p != '\n') 216 errx(1, "%s: illegal numeric format.", buf); 217 return (val); 218 } 219} 220 221/* 222 * primes - sieve and print primes from start up to and but not including stop 223 */ 224void 225primes(start, stop) 226 ubig start; /* where to start generating */ 227 ubig stop; /* don't generate at or above this value */ 228{ 229 char *q; /* sieve spot */ 230 ubig factor; /* index and factor */ 231 char *tab_lim; /* the limit to sieve on the table */ 232 ubig *p; /* prime table pointer */ 233 ubig fact_lim; /* highest prime for current block */ 234 235 /* 236 * A number of systems can not convert double values into unsigned 237 * longs when the values are larger than the largest signed value. 238 * We don't have this problem, so we can go all the way to BIG. 239 */ 240 if (start < 3) { 241 start = (ubig)2; 242 } 243 if (stop < 3) { 244 stop = (ubig)2; 245 } 246 if (stop <= start) { 247 return; 248 } 249 250 /* 251 * be sure that the values are odd, or 2 252 */ 253 if (start != 2 && (start&0x1) == 0) { 254 ++start; 255 } 256 if (stop != 2 && (stop&0x1) == 0) { 257 ++stop; 258 } 259 260 /* 261 * quick list of primes <= pr_limit 262 */ 263 if (start <= *pr_limit) { 264 /* skip primes up to the start value */ 265 for (p = &prime[0], factor = prime[0]; 266 factor < stop && p <= pr_limit; factor = *(++p)) { 267 if (factor >= start) { 268 printf(hflag ? "0x%lx\n" : "%lu\n", factor); 269 } 270 } 271 /* return early if we are done */ 272 if (p <= pr_limit) { 273 return; 274 } 275 start = *pr_limit+2; 276 } 277 278 /* 279 * we shall sieve a bytemap window, note primes and move the window 280 * upward until we pass the stop point 281 */ 282 while (start < stop) { 283 /* 284 * factor out 3, 5, 7, 11 and 13 285 */ 286 /* initial pattern copy */ 287 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 288 memcpy(table, &pattern[factor], pattern_size-factor); 289 /* main block pattern copies */ 290 for (fact_lim=pattern_size-factor; 291 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 292 memcpy(&table[fact_lim], pattern, pattern_size); 293 } 294 /* final block pattern copy */ 295 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 296 297 /* 298 * sieve for primes 17 and higher 299 */ 300 /* note highest useful factor and sieve spot */ 301 if (stop-start > TABSIZE+TABSIZE) { 302 tab_lim = &table[TABSIZE]; /* sieve it all */ 303 fact_lim = (int)sqrt( 304 (double)(start)+TABSIZE+TABSIZE+1.0); 305 } else { 306 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 307 fact_lim = (int)sqrt((double)(stop)+1.0); 308 } 309 /* sieve for factors >= 17 */ 310 factor = 17; /* 17 is first prime to use */ 311 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 312 do { 313 /* determine the factor's initial sieve point */ 314 q = (char *)(start%factor); /* temp storage for mod */ 315 if ((long)q & 0x1) { 316 q = &table[(factor-(long)q)/2]; 317 } else { 318 q = &table[q ? factor-((long)q/2) : 0]; 319 } 320 /* sive for our current factor */ 321 for ( ; q < tab_lim; q += factor) { 322 *q = '\0'; /* sieve out a spot */ 323 } 324 } while ((factor=(ubig)(*(p++))) <= fact_lim); 325 326 /* 327 * print generated primes 328 */ 329 for (q = table; q < tab_lim; ++q, start+=2) { 330 if (*q) { 331 printf(hflag ? "0x%lx\n" : "%lu\n", start); 332 } 333 } 334 } 335} 336 337void 338usage() 339{ 340 (void)fprintf(stderr, "usage: primes [-h] [start [stop]]\n"); 341 exit(1); 342} 343