1 /* $NetBSD: primes.c,v 1.12 2004/01/27 20:30:30 jsm Exp $ */ 2 3 /* 4 * Copyright (c) 1989, 1993 5 * The Regents of the University of California. All rights reserved. 6 * 7 * This code is derived from software contributed to Berkeley by 8 * Landon Curt Noll. 9 * 10 * Redistribution and use in source and binary forms, with or without 11 * modification, are permitted provided that the following conditions 12 * are met: 13 * 1. Redistributions of source code must retain the above copyright 14 * notice, this list of conditions and the following disclaimer. 15 * 2. Redistributions in binary form must reproduce the above copyright 16 * notice, this list of conditions and the following disclaimer in the 17 * documentation and/or other materials provided with the distribution. 18 * 3. Neither the name of the University nor the names of its contributors 19 * may be used to endorse or promote products derived from this software 20 * without specific prior written permission. 21 * 22 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 23 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 24 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 25 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 26 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 27 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 28 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 29 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 30 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 31 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 32 * SUCH DAMAGE. 33 */ 34 35 #include <sys/cdefs.h> 36 #ifndef lint 37 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\n\ 38 The Regents of the University of California. All rights reserved.\n"); 39 #endif /* not lint */ 40 41 #ifndef lint 42 #if 0 43 static char sccsid[] = "@(#)primes.c 8.5 (Berkeley) 5/10/95"; 44 #else 45 __RCSID("$NetBSD: primes.c,v 1.12 2004/01/27 20:30:30 jsm Exp $"); 46 #endif 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 */ 87 char 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 */ 95 extern const ubig prime[]; 96 extern const 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 */ 103 extern const char pattern[]; 104 extern const int pattern_size; /* length of pattern array */ 105 106 int main(int, char *[]); 107 void primes(ubig, ubig); 108 ubig read_num_buf(void); 109 void usage(void) __attribute__((__noreturn__)); 110 111 int 112 main(argc, argv) 113 int argc; 114 char *argv[]; 115 { 116 ubig start; /* where to start generating */ 117 ubig stop; /* don't generate at or above this value */ 118 int ch; 119 char *p; 120 121 while ((ch = getopt(argc, argv, "")) != -1) 122 switch (ch) { 123 case '?': 124 default: 125 usage(); 126 } 127 argc -= optind; 128 argv += optind; 129 130 start = 0; 131 stop = BIG; 132 133 /* 134 * Convert low and high args. Strtoul(3) sets errno to 135 * ERANGE if the number is too large, but, if there's 136 * a leading minus sign it returns the negation of the 137 * result of the conversion, which we'd rather disallow. 138 */ 139 switch (argc) { 140 case 2: 141 /* Start and stop supplied on the command line. */ 142 if (argv[0][0] == '-' || argv[1][0] == '-') 143 errx(1, "negative numbers aren't permitted."); 144 145 errno = 0; 146 start = strtoul(argv[0], &p, 10); 147 if (errno) 148 err(1, "%s", argv[0]); 149 if (*p != '\0') 150 errx(1, "%s: illegal numeric format.", argv[0]); 151 152 errno = 0; 153 stop = strtoul(argv[1], &p, 10); 154 if (errno) 155 err(1, "%s", argv[1]); 156 if (*p != '\0') 157 errx(1, "%s: illegal numeric format.", argv[1]); 158 break; 159 case 1: 160 /* Start on the command line. */ 161 if (argv[0][0] == '-') 162 errx(1, "negative numbers aren't permitted."); 163 164 errno = 0; 165 start = strtoul(argv[0], &p, 10); 166 if (errno) 167 err(1, "%s", argv[0]); 168 if (*p != '\0') 169 errx(1, "%s: illegal numeric format.", argv[0]); 170 break; 171 case 0: 172 start = read_num_buf(); 173 break; 174 default: 175 usage(); 176 } 177 178 if (start > stop) 179 errx(1, "start value must be less than stop value."); 180 primes(start, stop); 181 exit(0); 182 } 183 184 /* 185 * read_num_buf -- 186 * This routine returns a number n, where 0 <= n && n <= BIG. 187 */ 188 ubig 189 read_num_buf() 190 { 191 ubig val; 192 char *p, buf[100]; /* > max number of digits. */ 193 194 for (;;) { 195 if (fgets(buf, sizeof(buf), stdin) == NULL) { 196 if (ferror(stdin)) 197 err(1, "stdin"); 198 exit(0); 199 } 200 for (p = buf; isblank(*p); ++p); 201 if (*p == '\n' || *p == '\0') 202 continue; 203 if (*p == '-') 204 errx(1, "negative numbers aren't permitted."); 205 errno = 0; 206 val = strtoul(buf, &p, 10); 207 if (errno) 208 err(1, "%s", buf); 209 if (*p != '\n') 210 errx(1, "%s: illegal numeric format.", buf); 211 return (val); 212 } 213 } 214 215 /* 216 * primes - sieve and print primes from start up to and but not including stop 217 */ 218 void 219 primes(start, stop) 220 ubig start; /* where to start generating */ 221 ubig stop; /* don't generate at or above this value */ 222 { 223 char *q; /* sieve spot */ 224 ubig factor; /* index and factor */ 225 char *tab_lim; /* the limit to sieve on the table */ 226 const ubig *p; /* prime table pointer */ 227 ubig fact_lim; /* highest prime for current block */ 228 ubig mod; /* temp storage for mod */ 229 230 /* 231 * A number of systems can not convert double values into unsigned 232 * longs when the values are larger than the largest signed value. 233 * We don't have this problem, so we can go all the way to BIG. 234 */ 235 if (start < 3) { 236 start = (ubig)2; 237 } 238 if (stop < 3) { 239 stop = (ubig)2; 240 } 241 if (stop <= start) { 242 return; 243 } 244 245 /* 246 * be sure that the values are odd, or 2 247 */ 248 if (start != 2 && (start&0x1) == 0) { 249 ++start; 250 } 251 if (stop != 2 && (stop&0x1) == 0) { 252 ++stop; 253 } 254 255 /* 256 * quick list of primes <= pr_limit 257 */ 258 if (start <= *pr_limit) { 259 /* skip primes up to the start value */ 260 for (p = &prime[0], factor = prime[0]; 261 factor < stop && p <= pr_limit; factor = *(++p)) { 262 if (factor >= start) { 263 printf("%lu\n", (unsigned long) factor); 264 } 265 } 266 /* return early if we are done */ 267 if (p <= pr_limit) { 268 return; 269 } 270 start = *pr_limit+2; 271 } 272 273 /* 274 * we shall sieve a bytemap window, note primes and move the window 275 * upward until we pass the stop point 276 */ 277 while (start < stop) { 278 /* 279 * factor out 3, 5, 7, 11 and 13 280 */ 281 /* initial pattern copy */ 282 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 283 memcpy(table, &pattern[factor], pattern_size-factor); 284 /* main block pattern copies */ 285 for (fact_lim=pattern_size-factor; 286 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 287 memcpy(&table[fact_lim], pattern, pattern_size); 288 } 289 /* final block pattern copy */ 290 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 291 292 /* 293 * sieve for primes 17 and higher 294 */ 295 /* note highest useful factor and sieve spot */ 296 if (stop-start > TABSIZE+TABSIZE) { 297 tab_lim = &table[TABSIZE]; /* sieve it all */ 298 fact_lim = (int)sqrt( 299 (double)(start)+TABSIZE+TABSIZE+1.0); 300 } else { 301 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 302 fact_lim = (int)sqrt((double)(stop)+1.0); 303 } 304 /* sieve for factors >= 17 */ 305 factor = 17; /* 17 is first prime to use */ 306 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 307 do { 308 /* determine the factor's initial sieve point */ 309 mod = start%factor; 310 if (mod & 0x1) { 311 q = &table[(factor-mod)/2]; 312 } else { 313 q = &table[mod ? factor-(mod/2) : 0]; 314 } 315 /* sive for our current factor */ 316 for ( ; q < tab_lim; q += factor) { 317 *q = '\0'; /* sieve out a spot */ 318 } 319 } while ((factor=(ubig)(*(p++))) <= fact_lim); 320 321 /* 322 * print generated primes 323 */ 324 for (q = table; q < tab_lim; ++q, start+=2) { 325 if (*q) { 326 printf("%lu\n", (unsigned long) start); 327 } 328 } 329 } 330 } 331 332 void 333 usage() 334 { 335 (void)fprintf(stderr, "usage: primes [start [stop]]\n"); 336 exit(1); 337 } 338