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. Neither the name of the University nor the names of its contributors 17 * may be used to endorse or promote products derived from this software 18 * without specific prior written permission. 19 * 20 * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND 21 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 22 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 23 * ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE 24 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 25 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 26 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 27 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 28 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 29 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 30 * SUCH DAMAGE. 31 */ 32 33 /* 34 * primes - generate a table of primes between two values 35 * 36 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 37 * 38 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 39 * 40 * usage: 41 * primes [-h] [start [stop]] 42 * 43 * Print primes >= start and < stop. If stop is omitted, 44 * the value 18446744073709551615 (2^64-1) is assumed. If 45 * start is omitted, start is read from standard input. 46 * 47 * validation check: there are 664579 primes between 0 and 10^7 48 */ 49 50 #include <capsicum_helpers.h> 51 #include <ctype.h> 52 #include <err.h> 53 #include <errno.h> 54 #include <inttypes.h> 55 #include <limits.h> 56 #include <math.h> 57 #include <stdio.h> 58 #include <stdlib.h> 59 #include <string.h> 60 #include <nl_types.h> 61 #include <unistd.h> 62 63 #include "primes.h" 64 65 /* 66 * Eratosthenes sieve table 67 * 68 * We only sieve the odd numbers. The base of our sieve windows are always 69 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 70 * sieve, table[i] == 1 if and only if 2*i-1 is prime. 71 * 72 * We make TABSIZE large to reduce the overhead of inner loop setup. 73 */ 74 static char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 75 76 static int hflag; 77 78 static void primes(ubig, ubig); 79 static ubig read_num_buf(void); 80 static void usage(void); 81 82 int 83 main(int argc, char *argv[]) 84 { 85 ubig start; /* where to start generating */ 86 ubig stop; /* don't generate at or above this value */ 87 int ch; 88 char *p; 89 90 caph_cache_catpages(); 91 if (caph_enter() < 0) 92 err(1, "cap_enter"); 93 94 while ((ch = getopt(argc, argv, "h")) != -1) 95 switch (ch) { 96 case 'h': 97 hflag++; 98 break; 99 case '?': 100 default: 101 usage(); 102 } 103 argc -= optind; 104 argv += optind; 105 106 start = 0; 107 stop = (uint64_t)(-1); 108 109 /* 110 * Convert low and high args. Strtoumax(3) sets errno to 111 * ERANGE if the number is too large, but, if there's 112 * a leading minus sign it returns the negation of the 113 * result of the conversion, which we'd rather disallow. 114 */ 115 switch (argc) { 116 case 2: 117 /* Start and stop supplied on the command line. */ 118 if (argv[0][0] == '-' || argv[1][0] == '-') 119 errx(1, "negative numbers aren't permitted."); 120 121 errno = 0; 122 start = strtoumax(argv[0], &p, 0); 123 if (errno) 124 err(1, "%s", argv[0]); 125 if (*p != '\0') 126 errx(1, "%s: illegal numeric format.", argv[0]); 127 128 errno = 0; 129 stop = strtoumax(argv[1], &p, 0); 130 if (errno) 131 err(1, "%s", argv[1]); 132 if (*p != '\0') 133 errx(1, "%s: illegal numeric format.", argv[1]); 134 break; 135 case 1: 136 /* Start on the command line. */ 137 if (argv[0][0] == '-') 138 errx(1, "negative numbers aren't permitted."); 139 140 errno = 0; 141 start = strtoumax(argv[0], &p, 0); 142 if (errno) 143 err(1, "%s", argv[0]); 144 if (*p != '\0') 145 errx(1, "%s: illegal numeric format.", argv[0]); 146 break; 147 case 0: 148 start = read_num_buf(); 149 break; 150 default: 151 usage(); 152 } 153 154 if (start > stop) 155 errx(1, "start value must be less than stop value."); 156 primes(start, stop); 157 return (0); 158 } 159 160 /* 161 * read_num_buf -- 162 * This routine returns a number n, where 0 <= n && n <= BIG. 163 */ 164 static ubig 165 read_num_buf(void) 166 { 167 ubig val; 168 char *p, buf[LINE_MAX]; /* > max number of digits. */ 169 170 for (;;) { 171 if (fgets(buf, sizeof(buf), stdin) == NULL) { 172 if (ferror(stdin)) 173 err(1, "stdin"); 174 exit(0); 175 } 176 for (p = buf; isblank(*p); ++p); 177 if (*p == '\n' || *p == '\0') 178 continue; 179 if (*p == '-') 180 errx(1, "negative numbers aren't permitted."); 181 errno = 0; 182 val = strtoumax(buf, &p, 0); 183 if (errno) 184 err(1, "%s", buf); 185 if (*p != '\n') 186 errx(1, "%s: illegal numeric format.", buf); 187 return (val); 188 } 189 } 190 191 /* 192 * primes - sieve and print primes from start up to and but not including stop 193 */ 194 static void 195 primes(ubig start, ubig stop) 196 { 197 char *q; /* sieve spot */ 198 ubig factor; /* index and factor */ 199 char *tab_lim; /* the limit to sieve on the table */ 200 const ubig *p; /* prime table pointer */ 201 ubig fact_lim; /* highest prime for current block */ 202 ubig mod; /* temp storage for mod */ 203 204 /* 205 * A number of systems can not convert double values into unsigned 206 * longs when the values are larger than the largest signed value. 207 * We don't have this problem, so we can go all the way to BIG. 208 */ 209 if (start < 3) { 210 start = (ubig)2; 211 } 212 if (stop < 3) { 213 stop = (ubig)2; 214 } 215 if (stop <= start) { 216 return; 217 } 218 219 /* 220 * be sure that the values are odd, or 2 221 */ 222 if (start != 2 && (start&0x1) == 0) { 223 ++start; 224 } 225 if (stop != 2 && (stop&0x1) == 0) { 226 ++stop; 227 } 228 229 /* 230 * quick list of primes <= pr_limit 231 */ 232 if (start <= *pr_limit) { 233 /* skip primes up to the start value */ 234 for (p = &prime[0], factor = prime[0]; 235 factor < stop && p <= pr_limit; factor = *(++p)) { 236 if (factor >= start) { 237 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", factor); 238 } 239 } 240 /* return early if we are done */ 241 if (p <= pr_limit) { 242 return; 243 } 244 start = *pr_limit+2; 245 } 246 247 /* 248 * we shall sieve a bytemap window, note primes and move the window 249 * upward until we pass the stop point 250 */ 251 while (start < stop) { 252 /* 253 * factor out 3, 5, 7, 11 and 13 254 */ 255 /* initial pattern copy */ 256 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 257 memcpy(table, &pattern[factor], pattern_size-factor); 258 /* main block pattern copies */ 259 for (fact_lim=pattern_size-factor; 260 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 261 memcpy(&table[fact_lim], pattern, pattern_size); 262 } 263 /* final block pattern copy */ 264 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 265 266 /* 267 * sieve for primes 17 and higher 268 */ 269 /* note highest useful factor and sieve spot */ 270 if (stop-start > TABSIZE+TABSIZE) { 271 tab_lim = &table[TABSIZE]; /* sieve it all */ 272 fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE); 273 } else { 274 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 275 fact_lim = sqrt(stop+1.0); 276 } 277 /* sieve for factors >= 17 */ 278 factor = 17; /* 17 is first prime to use */ 279 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 280 do { 281 /* determine the factor's initial sieve point */ 282 mod = start%factor; 283 if (mod & 0x1) { 284 q = &table[(factor-mod)/2]; 285 } else { 286 q = &table[mod ? factor-(mod/2) : 0]; 287 } 288 /* sive for our current factor */ 289 for ( ; q < tab_lim; q += factor) { 290 *q = '\0'; /* sieve out a spot */ 291 } 292 factor = *p++; 293 } while (factor <= fact_lim); 294 295 /* 296 * print generated primes 297 */ 298 for (q = table; q < tab_lim; ++q, start+=2) { 299 if (*q) { 300 if (start > SIEVEMAX) { 301 if (!isprime(start)) 302 continue; 303 } 304 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", start); 305 } 306 } 307 } 308 } 309 310 static void 311 usage(void) 312 { 313 fprintf(stderr, "usage: primes [-h] [start [stop]]\n"); 314 exit(1); 315 } 316