1 /* $OpenBSD: primes.c,v 1.15 2009/10/27 23:59:26 deraadt Exp $ */ 2 /* $NetBSD: primes.c,v 1.5 1995/04/24 12:24:47 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 * primes - generate a table of primes between two values 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 * primes [start [stop]] 45 * 46 * Print primes >= start and < stop. If stop is omitted, 47 * the value 4294967295 (2^32-1) is assumed. If start is 48 * omitted, start is read from standard input. 49 * 50 * validation check: there are 664579 primes between 0 and 10^7 51 */ 52 53 #include <sys/types.h> 54 #include <ctype.h> 55 #include <err.h> 56 #include <errno.h> 57 #include <limits.h> 58 #include <math.h> 59 #include <stdio.h> 60 #include <stdlib.h> 61 #include <string.h> 62 #include <unistd.h> 63 64 #include "primes.h" 65 66 /* 67 * Eratosthenes sieve table 68 * 69 * We only sieve the odd numbers. The base of our sieve windows are always 70 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 71 * sieve, table[i] == 1 if and only iff 2*i-1 is prime. 72 * 73 * We make TABSIZE large to reduce the overhead of inner loop setup. 74 */ 75 char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 76 77 /* 78 * prime[i] is the (i+1)th prime. 79 * 80 * We are able to sieve 2^32-1 because this byte table yields all primes 81 * up to 65537 and 65537^2 > 2^32-1. 82 */ 83 extern const ubig prime[]; 84 extern const ubig *pr_limit; /* largest prime in the prime array */ 85 86 /* 87 * To avoid excessive sieves for small factors, we use the table below to 88 * setup our sieve blocks. Each element represents a odd number starting 89 * with 1. All non-zero elements are factors of 3, 5, 7, 11 and 13. 90 */ 91 extern const char pattern[]; 92 extern const int pattern_size; /* length of pattern array */ 93 94 void primes(ubig, ubig); 95 ubig read_num_buf(void); 96 void usage(void); 97 98 int 99 main(int argc, char *argv[]) 100 { 101 ubig start; /* where to start generating */ 102 ubig stop; /* don't generate at or above this value */ 103 int ch; 104 char *p; 105 106 while ((ch = getopt(argc, argv, "")) != -1) 107 switch (ch) { 108 case '?': 109 default: 110 usage(); 111 } 112 argc -= optind; 113 argv += optind; 114 115 start = 0; 116 stop = BIG; 117 118 /* 119 * Convert low and high args. Strtoul(3) sets errno to 120 * ERANGE if the number is too large, but, if there's 121 * a leading minus sign it returns the negation of the 122 * result of the conversion, which we'd rather disallow. 123 */ 124 switch (argc) { 125 case 2: 126 /* Start and stop supplied on the command line. */ 127 if (argv[0][0] == '-' || argv[1][0] == '-') 128 errx(1, "negative numbers aren't permitted."); 129 130 errno = 0; 131 start = strtoul(argv[0], &p, 10); 132 if (errno) 133 err(1, "%s", argv[0]); 134 if (*p != '\0') 135 errx(1, "%s: illegal numeric format.", argv[0]); 136 137 errno = 0; 138 stop = strtoul(argv[1], &p, 10); 139 if (errno) 140 err(1, "%s", argv[1]); 141 if (*p != '\0') 142 errx(1, "%s: illegal numeric format.", argv[1]); 143 break; 144 case 1: 145 /* Start on the command line. */ 146 if (argv[0][0] == '-') 147 errx(1, "negative numbers aren't permitted."); 148 149 errno = 0; 150 start = strtoul(argv[0], &p, 10); 151 if (errno) 152 err(1, "%s", argv[0]); 153 if (*p != '\0') 154 errx(1, "%s: illegal numeric format.", argv[0]); 155 break; 156 case 0: 157 start = read_num_buf(); 158 break; 159 default: 160 usage(); 161 } 162 163 if (start > stop) 164 errx(1, "start value must be less than stop value."); 165 primes(start, stop); 166 exit(0); 167 } 168 169 /* 170 * read_num_buf -- 171 * This routine returns a number n, where 0 <= n && n <= BIG. 172 */ 173 ubig 174 read_num_buf(void) 175 { 176 ubig val; 177 char *p, buf[100]; /* > max number of digits. */ 178 179 for (;;) { 180 if (fgets(buf, sizeof(buf), stdin) == NULL) { 181 if (ferror(stdin)) 182 err(1, "stdin"); 183 exit(0); 184 } 185 buf[strcspn(buf, "\n")] = '\0'; 186 for (p = buf; isblank(*p); ++p); 187 if (*p == '\0') 188 continue; 189 if (*p == '-') 190 errx(1, "negative numbers aren't permitted."); 191 errno = 0; 192 val = strtoul(buf, &p, 10); 193 if (errno) 194 err(1, "%s", buf); 195 for (; isblank(*p); ++p); 196 if (*p != '\0') 197 errx(1, "%s: illegal numeric format.", buf); 198 return (val); 199 } 200 } 201 202 /* 203 * primes - sieve and print primes from start up to and but not including stop 204 * start: where to start generating 205 * stop : don't generate at or above this value 206 */ 207 void 208 primes(ubig start, ubig stop) 209 { 210 char *q; /* sieve spot */ 211 ubig factor; /* index and factor */ 212 char *tab_lim; /* the limit to sieve on the table */ 213 const ubig *p; /* prime table pointer */ 214 ubig fact_lim; /* highest prime for current block */ 215 ubig mod; 216 217 /* 218 * A number of systems can not convert double values into unsigned 219 * longs when the values are larger than the largest signed value. 220 * We don't have this problem, so we can go all the way to BIG. 221 */ 222 if (start < 3) { 223 start = (ubig)2; 224 } 225 if (stop < 3) { 226 stop = (ubig)2; 227 } 228 if (stop <= start) { 229 return; 230 } 231 232 /* 233 * be sure that the values are odd, or 2 234 */ 235 if (start != 2 && (start&0x1) == 0) { 236 ++start; 237 } 238 if (stop != 2 && (stop&0x1) == 0) { 239 ++stop; 240 } 241 242 /* 243 * quick list of primes <= pr_limit 244 */ 245 if (start <= *pr_limit) { 246 /* skip primes up to the start value */ 247 for (p = &prime[0], factor = prime[0]; 248 factor < stop && p <= pr_limit; factor = *(++p)) { 249 if (factor >= start) { 250 printf("%lu\n", (unsigned long) factor); 251 } 252 } 253 /* return early if we are done */ 254 if (p <= pr_limit) { 255 return; 256 } 257 start = *pr_limit+2; 258 } 259 260 /* 261 * we shall sieve a bytemap window, note primes and move the window 262 * upward until we pass the stop point 263 */ 264 while (start < stop) { 265 /* 266 * factor out 3, 5, 7, 11 and 13 267 */ 268 /* initial pattern copy */ 269 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 270 memcpy(table, &pattern[factor], pattern_size-factor); 271 /* main block pattern copies */ 272 for (fact_lim=pattern_size-factor; 273 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 274 memcpy(&table[fact_lim], pattern, pattern_size); 275 } 276 /* final block pattern copy */ 277 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 278 279 /* 280 * sieve for primes 17 and higher 281 */ 282 /* note highest useful factor and sieve spot */ 283 if (stop-start > TABSIZE+TABSIZE) { 284 tab_lim = &table[TABSIZE]; /* sieve it all */ 285 fact_lim = (int)sqrt( 286 (double)(start)+TABSIZE+TABSIZE+1.0); 287 } else { 288 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 289 fact_lim = (int)sqrt((double)(stop)+1.0); 290 } 291 /* sieve for factors >= 17 */ 292 factor = 17; /* 17 is first prime to use */ 293 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 294 do { 295 /* determine the factor's initial sieve point */ 296 mod = start % factor; 297 if (mod & 0x1) 298 q = &table[(factor - mod)/2]; 299 else 300 q = &table[mod ? factor-(mod/2) : 0]; 301 /* sieve for our current factor */ 302 for ( ; q < tab_lim; q += factor) { 303 *q = '\0'; /* sieve out a spot */ 304 } 305 } while ((factor=(ubig)(*(p++))) <= fact_lim); 306 307 /* 308 * print generated primes 309 */ 310 for (q = table; q < tab_lim; ++q, start+=2) { 311 if (*q) { 312 printf("%lu\n", (unsigned long) start); 313 } 314 } 315 } 316 } 317 318 void 319 usage(void) 320 { 321 (void)fprintf(stderr, "usage: primes [start [stop]]\n"); 322 exit(1); 323 } 324