1 /* $NetBSD: primes.c,v 1.19 2011/08/30 02:58:04 jakllsch 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\ 38 The Regents of the University of California. All rights reserved."); 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 1.19 2011/08/30 02:58:04 jakllsch 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 static 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 static int dflag; 107 108 static void primes(ubig, ubig); 109 static ubig read_num_buf(void); 110 static void usage(void) __dead; 111 112 int 113 main(int argc, char *argv[]) 114 { 115 ubig start; /* where to start generating */ 116 ubig stop; /* don't generate at or above this value */ 117 int ch; 118 char *p; 119 120 while ((ch = getopt(argc, argv, "d")) != -1) 121 switch (ch) { 122 case 'd': 123 dflag++; 124 break; 125 case '?': 126 default: 127 usage(); 128 } 129 argc -= optind; 130 argv += optind; 131 132 start = 0; 133 stop = BIG; 134 135 /* 136 * Convert low and high args. Strtoul(3) sets errno to 137 * ERANGE if the number is too large, but, if there's 138 * a leading minus sign it returns the negation of the 139 * result of the conversion, which we'd rather disallow. 140 */ 141 switch (argc) { 142 case 2: 143 /* Start and stop supplied on the command line. */ 144 if (argv[0][0] == '-' || argv[1][0] == '-') 145 errx(1, "negative numbers aren't permitted."); 146 147 errno = 0; 148 start = strtoul(argv[0], &p, 10); 149 if (errno) 150 err(1, "%s", argv[0]); 151 if (*p != '\0') 152 errx(1, "%s: illegal numeric format.", argv[0]); 153 154 errno = 0; 155 stop = strtoul(argv[1], &p, 10); 156 if (errno) 157 err(1, "%s", argv[1]); 158 if (*p != '\0') 159 errx(1, "%s: illegal numeric format.", argv[1]); 160 break; 161 case 1: 162 /* Start on the command line. */ 163 if (argv[0][0] == '-') 164 errx(1, "negative numbers aren't permitted."); 165 166 errno = 0; 167 start = strtoul(argv[0], &p, 10); 168 if (errno) 169 err(1, "%s", argv[0]); 170 if (*p != '\0') 171 errx(1, "%s: illegal numeric format.", argv[0]); 172 break; 173 case 0: 174 start = read_num_buf(); 175 break; 176 default: 177 usage(); 178 } 179 180 if (start > stop) 181 errx(1, "start value must be less than stop value."); 182 primes(start, stop); 183 exit(0); 184 } 185 186 /* 187 * read_num_buf -- 188 * This routine returns a number n, where 0 <= n && n <= BIG. 189 */ 190 ubig 191 read_num_buf(void) 192 { 193 ubig val; 194 char *p, buf[100]; /* > max number of digits. */ 195 196 for (;;) { 197 if (fgets(buf, sizeof(buf), stdin) == NULL) { 198 if (ferror(stdin)) 199 err(1, "stdin"); 200 exit(0); 201 } 202 for (p = buf; isblank((unsigned char)*p); ++p); 203 if (*p == '\n' || *p == '\0') 204 continue; 205 if (*p == '-') 206 errx(1, "negative numbers aren't permitted."); 207 errno = 0; 208 val = strtoul(buf, &p, 10); 209 if (errno) 210 err(1, "%s", buf); 211 if (*p != '\n') 212 errx(1, "%s: illegal numeric format.", buf); 213 return (val); 214 } 215 } 216 217 /* 218 * primes - sieve and print primes from start up to and but not including stop 219 * 220 * start where to start generating 221 * stop don't generate at or above this value 222 */ 223 void 224 primes(ubig start, ubig stop) 225 { 226 char *q; /* sieve spot */ 227 ubig factor; /* index and factor */ 228 char *tab_lim; /* the limit to sieve on the table */ 229 const ubig *p; /* prime table pointer */ 230 ubig fact_lim; /* highest prime for current block */ 231 ubig mod; /* temp storage for mod */ 232 ubig prev = 0; 233 234 /* 235 * A number of systems can not convert double values into unsigned 236 * longs when the values are larger than the largest signed value. 237 * We don't have this problem, so we can go all the way to BIG. 238 */ 239 if (start < 3) { 240 start = (ubig)2; 241 } 242 if (stop < 3) { 243 stop = (ubig)2; 244 } 245 if (stop <= start) { 246 return; 247 } 248 249 /* 250 * be sure that the values are odd, or 2 251 */ 252 if (start != 2 && (start&0x1) == 0) { 253 ++start; 254 } 255 if (stop != 2 && (stop&0x1) == 0) { 256 ++stop; 257 } 258 259 /* 260 * quick list of primes <= pr_limit 261 */ 262 if (start <= *pr_limit) { 263 /* skip primes up to the start value */ 264 for (p = &prime[0], factor = prime[0]; 265 factor < stop && p <= pr_limit; factor = *(++p)) { 266 if (factor >= start) { 267 printf("%lu", (unsigned long) factor); 268 if (dflag) { 269 printf(" (%lu)", 270 (unsigned long) factor - prev); 271 } 272 putchar('\n'); 273 } 274 prev = factor; 275 } 276 /* return early if we are done */ 277 if (p <= pr_limit) { 278 return; 279 } 280 start = *pr_limit+2; 281 } 282 283 /* 284 * we shall sieve a bytemap window, note primes and move the window 285 * upward until we pass the stop point 286 */ 287 while (start < stop) { 288 /* 289 * factor out 3, 5, 7, 11 and 13 290 */ 291 /* initial pattern copy */ 292 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 293 memcpy(table, &pattern[factor], pattern_size-factor); 294 /* main block pattern copies */ 295 for (fact_lim=pattern_size-factor; 296 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 297 memcpy(&table[fact_lim], pattern, pattern_size); 298 } 299 /* final block pattern copy */ 300 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 301 302 /* 303 * sieve for primes 17 and higher 304 */ 305 /* note highest useful factor and sieve spot */ 306 if (stop-start > TABSIZE+TABSIZE) { 307 tab_lim = &table[TABSIZE]; /* sieve it all */ 308 fact_lim = sqrt((double)(start)+TABSIZE+TABSIZE+1.0); 309 } else { 310 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 311 fact_lim = sqrt((double)(stop)+1.0); 312 } 313 /* sieve for factors >= 17 */ 314 factor = 17; /* 17 is first prime to use */ 315 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 316 do { 317 /* determine the factor's initial sieve point */ 318 mod = start%factor; 319 if (mod & 0x1) { 320 q = &table[(factor-mod)/2]; 321 } else { 322 q = &table[mod ? factor-(mod/2) : 0]; 323 } 324 /* sieve for our current factor */ 325 for ( ; q < tab_lim; q += factor) { 326 *q = '\0'; /* sieve out a spot */ 327 } 328 } while ((factor=(ubig)(*(p++))) <= fact_lim); 329 330 /* 331 * print generated primes 332 */ 333 for (q = table; q < tab_lim; ++q, start+=2) { 334 if (*q) { 335 printf("%lu", (unsigned long) start); 336 if (dflag) { 337 printf(" (%lu)", 338 (unsigned long) start - prev); 339 prev = start; 340 } 341 putchar('\n'); 342 } 343 } 344 } 345 } 346 347 void 348 usage(void) 349 { 350 (void)fprintf(stderr, "usage: primes [-d] [start [stop]]\n"); 351 exit(1); 352 } 353