1 /* $NetBSD: primes.c,v 1.15 2008/02/02 18:15:14 matt 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 1.15 2008/02/02 18:15:14 matt 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 dflag; 107 108 int main(int, char *[]); 109 void primes(ubig, ubig); 110 ubig read_num_buf(void); 111 void usage(void) __dead; 112 113 int 114 main(int argc, 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, "d")) != -1) 122 switch (ch) { 123 case 'd': 124 dflag++; 125 break; 126 case '?': 127 default: 128 usage(); 129 } 130 argc -= optind; 131 argv += optind; 132 133 start = 0; 134 stop = BIG; 135 136 /* 137 * Convert low and high args. Strtoul(3) sets errno to 138 * ERANGE if the number is too large, but, if there's 139 * a leading minus sign it returns the negation of the 140 * result of the conversion, which we'd rather disallow. 141 */ 142 switch (argc) { 143 case 2: 144 /* Start and stop supplied on the command line. */ 145 if (argv[0][0] == '-' || argv[1][0] == '-') 146 errx(1, "negative numbers aren't permitted."); 147 148 errno = 0; 149 start = strtoul(argv[0], &p, 10); 150 if (errno) 151 err(1, "%s", argv[0]); 152 if (*p != '\0') 153 errx(1, "%s: illegal numeric format.", argv[0]); 154 155 errno = 0; 156 stop = strtoul(argv[1], &p, 10); 157 if (errno) 158 err(1, "%s", argv[1]); 159 if (*p != '\0') 160 errx(1, "%s: illegal numeric format.", argv[1]); 161 break; 162 case 1: 163 /* Start on the command line. */ 164 if (argv[0][0] == '-') 165 errx(1, "negative numbers aren't permitted."); 166 167 errno = 0; 168 start = strtoul(argv[0], &p, 10); 169 if (errno) 170 err(1, "%s", argv[0]); 171 if (*p != '\0') 172 errx(1, "%s: illegal numeric format.", argv[0]); 173 break; 174 case 0: 175 start = read_num_buf(); 176 break; 177 default: 178 usage(); 179 } 180 181 if (start > stop) 182 errx(1, "start value must be less than stop value."); 183 primes(start, stop); 184 exit(0); 185 } 186 187 /* 188 * read_num_buf -- 189 * This routine returns a number n, where 0 <= n && n <= BIG. 190 */ 191 ubig 192 read_num_buf(void) 193 { 194 ubig val; 195 char *p, buf[100]; /* > max number of digits. */ 196 197 for (;;) { 198 if (fgets(buf, sizeof(buf), stdin) == NULL) { 199 if (ferror(stdin)) 200 err(1, "stdin"); 201 exit(0); 202 } 203 for (p = buf; isblank(*p); ++p); 204 if (*p == '\n' || *p == '\0') 205 continue; 206 if (*p == '-') 207 errx(1, "negative numbers aren't permitted."); 208 errno = 0; 209 val = strtoul(buf, &p, 10); 210 if (errno) 211 err(1, "%s", buf); 212 if (*p != '\n') 213 errx(1, "%s: illegal numeric format.", buf); 214 return (val); 215 } 216 } 217 218 /* 219 * primes - sieve and print primes from start up to and but not including stop 220 * 221 * start where to start generating 222 * stop don't generate at or above this value 223 */ 224 void 225 primes(ubig start, ubig stop) 226 { 227 char *q; /* sieve spot */ 228 ubig factor; /* index and factor */ 229 char *tab_lim; /* the limit to sieve on the table */ 230 const ubig *p; /* prime table pointer */ 231 ubig fact_lim; /* highest prime for current block */ 232 ubig mod; /* temp storage for mod */ 233 ubig prev = 0; 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("%lu", (unsigned long) factor); 269 if (dflag) { 270 printf(" (%lu)", 271 (unsigned long) factor - prev); 272 } 273 putchar('\n'); 274 } 275 prev = factor; 276 } 277 /* return early if we are done */ 278 if (p <= pr_limit) { 279 return; 280 } 281 start = *pr_limit+2; 282 } 283 284 /* 285 * we shall sieve a bytemap window, note primes and move the window 286 * upward until we pass the stop point 287 */ 288 while (start < stop) { 289 /* 290 * factor out 3, 5, 7, 11 and 13 291 */ 292 /* initial pattern copy */ 293 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 294 memcpy(table, &pattern[factor], pattern_size-factor); 295 /* main block pattern copies */ 296 for (fact_lim=pattern_size-factor; 297 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 298 memcpy(&table[fact_lim], pattern, pattern_size); 299 } 300 /* final block pattern copy */ 301 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 302 303 /* 304 * sieve for primes 17 and higher 305 */ 306 /* note highest useful factor and sieve spot */ 307 if (stop-start > TABSIZE+TABSIZE) { 308 tab_lim = &table[TABSIZE]; /* sieve it all */ 309 fact_lim = (int)sqrt( 310 (double)(start)+TABSIZE+TABSIZE+1.0); 311 } else { 312 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 313 fact_lim = (int)sqrt((double)(stop)+1.0); 314 } 315 /* sieve for factors >= 17 */ 316 factor = 17; /* 17 is first prime to use */ 317 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 318 do { 319 /* determine the factor's initial sieve point */ 320 mod = start%factor; 321 if (mod & 0x1) { 322 q = &table[(factor-mod)/2]; 323 } else { 324 q = &table[mod ? factor-(mod/2) : 0]; 325 } 326 /* sieve for our current factor */ 327 for ( ; q < tab_lim; q += factor) { 328 *q = '\0'; /* sieve out a spot */ 329 } 330 } while ((factor=(ubig)(*(p++))) <= fact_lim); 331 332 /* 333 * print generated primes 334 */ 335 for (q = table; q < tab_lim; ++q, start+=2) { 336 if (*q) { 337 printf("%lu", (unsigned long) start); 338 if (dflag) { 339 printf(" (%lu)", 340 (unsigned long) start - prev); 341 prev = start; 342 } 343 putchar('\n'); 344 } 345 } 346 } 347 } 348 349 void 350 usage(void) 351 { 352 (void)fprintf(stderr, "usage: primes [-d] [start [stop]]\n"); 353 exit(1); 354 } 355