primes.c revision 53210
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 * $FreeBSD: head/games/primes/primes.c 53210 1999-11-16 02:58:06Z billf $ 37 */ 38 39#ifndef lint 40static char copyright[] = 41"@(#) Copyright (c) 1989, 1993\n\ 42 The Regents of the University of California. All rights reserved.\n"; 43#endif /* not lint */ 44 45#ifndef lint 46static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95"; 47#endif /* not lint */ 48 49/* 50 * primes - generate a table of primes between two values 51 * 52 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 53 * 54 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 55 * 56 * usage: 57 * primes [start [stop]] 58 * 59 * Print primes >= start and < stop. If stop is omitted, 60 * the value 4294967295 (2^32-1) is assumed. If start is 61 * omitted, start is read from standard input. 62 * 63 * validation check: there are 664579 primes between 0 and 10^7 64 */ 65 66#include <ctype.h> 67#include <err.h> 68#include <errno.h> 69#include <limits.h> 70#include <math.h> 71#include <memory.h> 72#include <stdio.h> 73#include <stdlib.h> 74#include <unistd.h> 75 76#include "primes.h" 77 78/* 79 * Eratosthenes sieve table 80 * 81 * We only sieve the odd numbers. The base of our sieve windows are always 82 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 83 * sieve, table[i] == 1 if and only iff 2*i-1 is prime. 84 * 85 * We make TABSIZE large to reduce the overhead of inner loop setup. 86 */ 87char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 88 89/* 90 * prime[i] is the (i-1)th prime. 91 * 92 * We are able to sieve 2^32-1 because this byte table yields all primes 93 * up to 65537 and 65537^2 > 2^32-1. 94 */ 95extern ubig prime[]; 96extern ubig *pr_limit; /* largest prime in the prime array */ 97 98/* 99 * To avoid excessive sieves for small factors, we use the table below to 100 * setup our sieve blocks. Each element represents a odd number starting 101 * with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13. 102 */ 103extern char pattern[]; 104extern int pattern_size; /* length of pattern array */ 105 106int hflag; 107 108void primes __P((ubig, ubig)); 109ubig read_num_buf __P((void)); 110void usage __P((void)); 111 112int 113main(argc, argv) 114 int argc; 115 char *argv[]; 116{ 117 ubig start; /* where to start generating */ 118 ubig stop; /* don't generate at or above this value */ 119 int ch; 120 char *p; 121 122 while ((ch = getopt(argc, argv, "h")) != -1) 123 switch (ch) { 124 case 'h': 125 hflag++; 126 break; 127 case '?': 128 default: 129 usage(); 130 } 131 argc -= optind; 132 argv += optind; 133 134 start = 0; 135 stop = BIG; 136 137 /* 138 * Convert low and high args. Strtoul(3) sets errno to 139 * ERANGE if the number is too large, but, if there's 140 * a leading minus sign it returns the negation of the 141 * result of the conversion, which we'd rather disallow. 142 */ 143 switch (argc) { 144 case 2: 145 /* Start and stop supplied on the command line. */ 146 if (argv[0][0] == '-' || argv[1][0] == '-') 147 errx(1, "negative numbers aren't permitted."); 148 149 errno = 0; 150 start = strtoul(argv[0], &p, 0); 151 if (errno) 152 err(1, "%s", argv[0]); 153 if (*p != '\0') 154 errx(1, "%s: illegal numeric format.", argv[0]); 155 156 errno = 0; 157 stop = strtoul(argv[1], &p, 0); 158 if (errno) 159 err(1, "%s", argv[1]); 160 if (*p != '\0') 161 errx(1, "%s: illegal numeric format.", argv[1]); 162 break; 163 case 1: 164 /* Start on the command line. */ 165 if (argv[0][0] == '-') 166 errx(1, "negative numbers aren't permitted."); 167 168 errno = 0; 169 start = strtoul(argv[0], &p, 0); 170 if (errno) 171 err(1, "%s", argv[0]); 172 if (*p != '\0') 173 errx(1, "%s: illegal numeric format.", argv[0]); 174 break; 175 case 0: 176 start = read_num_buf(); 177 break; 178 default: 179 usage(); 180 } 181 182 if (start > stop) 183 errx(1, "start value must be less than stop value."); 184 primes(start, stop); 185 exit(0); 186} 187 188/* 189 * read_num_buf -- 190 * This routine returns a number n, where 0 <= n && n <= BIG. 191 */ 192ubig 193read_num_buf() 194{ 195 ubig val; 196 char *p, buf[100]; /* > max number of digits. */ 197 198 for (;;) { 199 if (fgets(buf, sizeof(buf), stdin) == NULL) { 200 if (ferror(stdin)) 201 err(1, "stdin"); 202 exit(0); 203 } 204 for (p = buf; isblank(*p); ++p); 205 if (*p == '\n' || *p == '\0') 206 continue; 207 if (*p == '-') 208 errx(1, "negative numbers aren't permitted."); 209 errno = 0; 210 val = strtoul(buf, &p, 0); 211 if (errno) 212 err(1, "%s", buf); 213 if (*p != '\n') 214 errx(1, "%s: illegal numeric format.", buf); 215 return (val); 216 } 217} 218 219/* 220 * primes - sieve and print primes from start up to and but not including stop 221 */ 222void 223primes(start, stop) 224 ubig start; /* where to start generating */ 225 ubig stop; /* don't generate at or above this value */ 226{ 227 char *q; /* sieve spot */ 228 ubig factor; /* index and factor */ 229 char *tab_lim; /* the limit to sieve on the table */ 230 ubig *p; /* prime table pointer */ 231 ubig fact_lim; /* highest prime for current block */ 232 233 /* 234 * A number of systems can not convert double values into unsigned 235 * longs when the values are larger than the largest signed value. 236 * We don't have this problem, so we can go all the way to BIG. 237 */ 238 if (start < 3) { 239 start = (ubig)2; 240 } 241 if (stop < 3) { 242 stop = (ubig)2; 243 } 244 if (stop <= start) { 245 return; 246 } 247 248 /* 249 * be sure that the values are odd, or 2 250 */ 251 if (start != 2 && (start&0x1) == 0) { 252 ++start; 253 } 254 if (stop != 2 && (stop&0x1) == 0) { 255 ++stop; 256 } 257 258 /* 259 * quick list of primes <= pr_limit 260 */ 261 if (start <= *pr_limit) { 262 /* skip primes up to the start value */ 263 for (p = &prime[0], factor = prime[0]; 264 factor < stop && p <= pr_limit; factor = *(++p)) { 265 if (factor >= start) { 266 printf(hflag ? "0x%lx\n" : "%lu\n", factor); 267 } 268 } 269 /* return early if we are done */ 270 if (p <= pr_limit) { 271 return; 272 } 273 start = *pr_limit+2; 274 } 275 276 /* 277 * we shall sieve a bytemap window, note primes and move the window 278 * upward until we pass the stop point 279 */ 280 while (start < stop) { 281 /* 282 * factor out 3, 5, 7, 11 and 13 283 */ 284 /* initial pattern copy */ 285 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 286 memcpy(table, &pattern[factor], pattern_size-factor); 287 /* main block pattern copies */ 288 for (fact_lim=pattern_size-factor; 289 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 290 memcpy(&table[fact_lim], pattern, pattern_size); 291 } 292 /* final block pattern copy */ 293 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 294 295 /* 296 * sieve for primes 17 and higher 297 */ 298 /* note highest useful factor and sieve spot */ 299 if (stop-start > TABSIZE+TABSIZE) { 300 tab_lim = &table[TABSIZE]; /* sieve it all */ 301 fact_lim = (int)sqrt( 302 (double)(start)+TABSIZE+TABSIZE+1.0); 303 } else { 304 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 305 fact_lim = (int)sqrt((double)(stop)+1.0); 306 } 307 /* sieve for factors >= 17 */ 308 factor = 17; /* 17 is first prime to use */ 309 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 310 do { 311 /* determine the factor's initial sieve point */ 312 q = (char *)(start%factor); /* temp storage for mod */ 313 if ((long)q & 0x1) { 314 q = &table[(factor-(long)q)/2]; 315 } else { 316 q = &table[q ? factor-((long)q/2) : 0]; 317 } 318 /* sive for our current factor */ 319 for ( ; q < tab_lim; q += factor) { 320 *q = '\0'; /* sieve out a spot */ 321 } 322 } while ((factor=(ubig)(*(p++))) <= fact_lim); 323 324 /* 325 * print generated primes 326 */ 327 for (q = table; q < tab_lim; ++q, start+=2) { 328 if (*q) { 329 printf(hflag ? "0x%lx\n" : "%lu\n", start); 330 } 331 } 332 } 333} 334 335void 336usage() 337{ 338 (void)fprintf(stderr, "usage: primes [-h] [start [stop]]\n"); 339 exit(1); 340} 341