primes.c revision 38153
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 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 44static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95"; 45#endif /* not lint */ 46 47/* 48 * primes - generate a table of primes between two values 49 * 50 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 51 * 52 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 53 * 54 * usage: 55 * primes [start [stop]] 56 * 57 * Print primes >= start and < stop. If stop is omitted, 58 * the value 4294967295 (2^32-1) is assumed. If start is 59 * omitted, start is read from standard input. 60 * 61 * validation check: there are 664579 primes between 0 and 10^7 62 */ 63 64#include <ctype.h> 65#include <err.h> 66#include <errno.h> 67#include <limits.h> 68#include <math.h> 69#include <memory.h> 70#include <stdio.h> 71#include <stdlib.h> 72#include <unistd.h> 73 74#include "primes.h" 75 76/* 77 * Eratosthenes sieve table 78 * 79 * We only sieve the odd numbers. The base of our sieve windows are always 80 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 81 * sieve, table[i] == 1 if and only iff 2*i-1 is prime. 82 * 83 * We make TABSIZE large to reduce the overhead of inner loop setup. 84 */ 85char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 86 87/* 88 * prime[i] is the (i-1)th prime. 89 * 90 * We are able to sieve 2^32-1 because this byte table yields all primes 91 * up to 65537 and 65537^2 > 2^32-1. 92 */ 93extern ubig prime[]; 94extern ubig *pr_limit; /* largest prime in the prime array */ 95 96/* 97 * To avoid excessive sieves for small factors, we use the table below to 98 * setup our sieve blocks. Each element represents a odd number starting 99 * with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13. 100 */ 101extern char pattern[]; 102extern int pattern_size; /* length of pattern array */ 103 104void primes __P((ubig, ubig, int)); 105ubig read_num_buf __P((int)); 106void usage __P((void)); 107 108int 109main(argc, argv) 110 int argc; 111 char *argv[]; 112{ 113 ubig start; /* where to start generating */ 114 ubig stop; /* don't generate at or above this value */ 115 int ch; 116 char *p; 117 int hexa = 0; 118 119 while ((ch = getopt(argc, argv, "h")) != EOF) 120 switch (ch) { 121 case 'h': 122 hexa = 1; 123 break; 124 case '?': 125 default: 126 usage(); 127 } 128 argc -= optind; 129 argv += optind; 130 131 start = 0; 132 stop = BIG; 133 134 /* 135 * Convert low and high args. Strtoul(3) sets errno to 136 * ERANGE if the number is too large, but, if there's 137 * a leading minus sign it returns the negation of the 138 * result of the conversion, which we'd rather disallow. 139 */ 140 switch (argc) { 141 case 2: 142 /* Start and stop supplied on the command line. */ 143 if (argv[0][0] == '-' || argv[1][0] == '-') 144 errx(1, "negative numbers aren't permitted."); 145 146 errno = 0; 147 start = strtoul(argv[0], &p, 0); 148 if (errno) 149 err(1, "%s", argv[0]); 150 if (*p != '\0') 151 errx(1, "%s: illegal numeric format.", argv[0]); 152 153 errno = 0; 154 stop = strtoul(argv[1], &p, 0); 155 if (errno) 156 err(1, "%s", argv[1]); 157 if (*p != '\0') 158 errx(1, "%s: illegal numeric format.", argv[1]); 159 break; 160 case 1: 161 /* Start on the command line. */ 162 if (argv[0][0] == '-') 163 errx(1, "negative numbers aren't permitted."); 164 165 errno = 0; 166 start = strtoul(argv[0], &p, 0); 167 if (errno) 168 err(1, "%s", argv[0]); 169 if (*p != '\0') 170 errx(1, "%s: illegal numeric format.", argv[0]); 171 break; 172 case 0: 173 start = read_num_buf(hexa); 174 break; 175 default: 176 usage(); 177 } 178 179 if (start > stop) 180 errx(1, "start value must be less than stop value."); 181 primes(start, stop, hexa); 182 exit(0); 183} 184 185/* 186 * read_num_buf -- 187 * This routine returns a number n, where 0 <= n && n <= BIG. 188 */ 189ubig 190read_num_buf(int hexa) 191{ 192 ubig val; 193 char *p, buf[100]; /* > max number of digits. */ 194 195 for (;;) { 196 if (fgets(buf, sizeof(buf), stdin) == NULL) { 197 if (ferror(stdin)) 198 err(1, "stdin"); 199 exit(0); 200 } 201 for (p = buf; isblank(*p); ++p); 202 if (*p == '\n' || *p == '\0') 203 continue; 204 if (*p == '-') 205 errx(1, "negative numbers aren't permitted."); 206 errno = 0; 207 val = strtoul(buf, &p, 0); 208 if (errno) 209 err(1, "%s", buf); 210 if (*p != '\n') 211 errx(1, "%s: illegal numeric format.", buf); 212 return (val); 213 } 214} 215 216/* 217 * primes - sieve and print primes from start up to and but not including stop 218 */ 219void 220primes(start, stop, hexa) 221 ubig start; /* where to start generating */ 222 ubig stop; /* don't generate at or above this value */ 223 int hexa; 224{ 225 register char *q; /* sieve spot */ 226 register ubig factor; /* index and factor */ 227 register char *tab_lim; /* the limit to sieve on the table */ 228 register ubig *p; /* prime table pointer */ 229 register ubig fact_lim; /* highest prime for current block */ 230 231 /* 232 * A number of systems can not convert double values into unsigned 233 * longs when the values are larger than the largest signed value. 234 * We don't have this problem, so we can go all the way to BIG. 235 */ 236 if (start < 3) { 237 start = (ubig)2; 238 } 239 if (stop < 3) { 240 stop = (ubig)2; 241 } 242 if (stop <= start) { 243 return; 244 } 245 246 /* 247 * be sure that the values are odd, or 2 248 */ 249 if (start != 2 && (start&0x1) == 0) { 250 ++start; 251 } 252 if (stop != 2 && (stop&0x1) == 0) { 253 ++stop; 254 } 255 256 /* 257 * quick list of primes <= pr_limit 258 */ 259 if (start <= *pr_limit) { 260 /* skip primes up to the start value */ 261 for (p = &prime[0], factor = prime[0]; 262 factor < stop && p <= pr_limit; factor = *(++p)) { 263 if (factor >= start) { 264 printf(hexa ? "0x%x\n" : "%u\n", factor); 265 } 266 } 267 /* return early if we are done */ 268 if (p <= pr_limit) { 269 return; 270 } 271 start = *pr_limit+2; 272 } 273 274 /* 275 * we shall sieve a bytemap window, note primes and move the window 276 * upward until we pass the stop point 277 */ 278 while (start < stop) { 279 /* 280 * factor out 3, 5, 7, 11 and 13 281 */ 282 /* initial pattern copy */ 283 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 284 memcpy(table, &pattern[factor], pattern_size-factor); 285 /* main block pattern copies */ 286 for (fact_lim=pattern_size-factor; 287 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 288 memcpy(&table[fact_lim], pattern, pattern_size); 289 } 290 /* final block pattern copy */ 291 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 292 293 /* 294 * sieve for primes 17 and higher 295 */ 296 /* note highest useful factor and sieve spot */ 297 if (stop-start > TABSIZE+TABSIZE) { 298 tab_lim = &table[TABSIZE]; /* sieve it all */ 299 fact_lim = (int)sqrt( 300 (double)(start)+TABSIZE+TABSIZE+1.0); 301 } else { 302 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 303 fact_lim = (int)sqrt((double)(stop)+1.0); 304 } 305 /* sieve for factors >= 17 */ 306 factor = 17; /* 17 is first prime to use */ 307 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 308 do { 309 /* determine the factor's initial sieve point */ 310 q = (char *)(start%factor); /* temp storage for mod */ 311 if ((long)q & 0x1) { 312 q = &table[(factor-(long)q)/2]; 313 } else { 314 q = &table[q ? factor-((long)q/2) : 0]; 315 } 316 /* sive for our current factor */ 317 for ( ; q < tab_lim; q += factor) { 318 *q = '\0'; /* sieve out a spot */ 319 } 320 } while ((factor=(ubig)(*(p++))) <= fact_lim); 321 322 /* 323 * print generated primes 324 */ 325 for (q = table; q < tab_lim; ++q, start+=2) { 326 if (*q) { 327 printf(hexa ? "0x%x\n" : "%u\n", start); 328 } 329 } 330 } 331} 332 333void 334usage() 335{ 336 (void)fprintf(stderr, "usage: primes [start [stop]]\n"); 337 exit(1); 338} 339