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 #ifndef lint 34 static const char copyright[] = 35 "@(#) Copyright (c) 1989, 1993\n\ 36 The Regents of the University of California. All rights reserved.\n"; 37 #endif /* not lint */ 38 39 #ifndef lint 40 #endif /* not lint */ 41 42 /* 43 * primes - generate a table of primes between two values 44 * 45 * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo 46 * 47 * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\ 48 * 49 * usage: 50 * primes [-h] [start [stop]] 51 * 52 * Print primes >= start and < stop. If stop is omitted, 53 * the value 18446744073709551615 (2^64-1) is assumed. If 54 * start is omitted, start is read from standard input. 55 * 56 * validation check: there are 664579 primes between 0 and 10^7 57 */ 58 59 #include <capsicum_helpers.h> 60 #include <ctype.h> 61 #include <err.h> 62 #include <errno.h> 63 #include <inttypes.h> 64 #include <limits.h> 65 #include <math.h> 66 #include <stdio.h> 67 #include <stdlib.h> 68 #include <string.h> 69 #include <nl_types.h> 70 #include <unistd.h> 71 72 #include "primes.h" 73 74 /* 75 * Eratosthenes sieve table 76 * 77 * We only sieve the odd numbers. The base of our sieve windows are always 78 * odd. If the base of table is 1, table[i] represents 2*i-1. After the 79 * sieve, table[i] == 1 if and only if 2*i-1 is prime. 80 * 81 * We make TABSIZE large to reduce the overhead of inner loop setup. 82 */ 83 static char table[TABSIZE]; /* Eratosthenes sieve of odd numbers */ 84 85 static int hflag; 86 87 static void primes(ubig, ubig); 88 static ubig read_num_buf(void); 89 static void usage(void); 90 91 int 92 main(int argc, char *argv[]) 93 { 94 ubig start; /* where to start generating */ 95 ubig stop; /* don't generate at or above this value */ 96 int ch; 97 char *p; 98 99 caph_cache_catpages(); 100 if (caph_enter() < 0) 101 err(1, "cap_enter"); 102 103 while ((ch = getopt(argc, argv, "h")) != -1) 104 switch (ch) { 105 case 'h': 106 hflag++; 107 break; 108 case '?': 109 default: 110 usage(); 111 } 112 argc -= optind; 113 argv += optind; 114 115 start = 0; 116 stop = (uint64_t)(-1); 117 118 /* 119 * Convert low and high args. Strtoumax(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 = strtoumax(argv[0], &p, 0); 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 = strtoumax(argv[1], &p, 0); 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 = strtoumax(argv[0], &p, 0); 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 return (0); 167 } 168 169 /* 170 * read_num_buf -- 171 * This routine returns a number n, where 0 <= n && n <= BIG. 172 */ 173 static ubig 174 read_num_buf(void) 175 { 176 ubig val; 177 char *p, buf[LINE_MAX]; /* > 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 for (p = buf; isblank(*p); ++p); 186 if (*p == '\n' || *p == '\0') 187 continue; 188 if (*p == '-') 189 errx(1, "negative numbers aren't permitted."); 190 errno = 0; 191 val = strtoumax(buf, &p, 0); 192 if (errno) 193 err(1, "%s", buf); 194 if (*p != '\n') 195 errx(1, "%s: illegal numeric format.", buf); 196 return (val); 197 } 198 } 199 200 /* 201 * primes - sieve and print primes from start up to and but not including stop 202 */ 203 static void 204 primes(ubig start, ubig stop) 205 { 206 char *q; /* sieve spot */ 207 ubig factor; /* index and factor */ 208 char *tab_lim; /* the limit to sieve on the table */ 209 const ubig *p; /* prime table pointer */ 210 ubig fact_lim; /* highest prime for current block */ 211 ubig mod; /* temp storage for mod */ 212 213 /* 214 * A number of systems can not convert double values into unsigned 215 * longs when the values are larger than the largest signed value. 216 * We don't have this problem, so we can go all the way to BIG. 217 */ 218 if (start < 3) { 219 start = (ubig)2; 220 } 221 if (stop < 3) { 222 stop = (ubig)2; 223 } 224 if (stop <= start) { 225 return; 226 } 227 228 /* 229 * be sure that the values are odd, or 2 230 */ 231 if (start != 2 && (start&0x1) == 0) { 232 ++start; 233 } 234 if (stop != 2 && (stop&0x1) == 0) { 235 ++stop; 236 } 237 238 /* 239 * quick list of primes <= pr_limit 240 */ 241 if (start <= *pr_limit) { 242 /* skip primes up to the start value */ 243 for (p = &prime[0], factor = prime[0]; 244 factor < stop && p <= pr_limit; factor = *(++p)) { 245 if (factor >= start) { 246 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", factor); 247 } 248 } 249 /* return early if we are done */ 250 if (p <= pr_limit) { 251 return; 252 } 253 start = *pr_limit+2; 254 } 255 256 /* 257 * we shall sieve a bytemap window, note primes and move the window 258 * upward until we pass the stop point 259 */ 260 while (start < stop) { 261 /* 262 * factor out 3, 5, 7, 11 and 13 263 */ 264 /* initial pattern copy */ 265 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */ 266 memcpy(table, &pattern[factor], pattern_size-factor); 267 /* main block pattern copies */ 268 for (fact_lim=pattern_size-factor; 269 fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) { 270 memcpy(&table[fact_lim], pattern, pattern_size); 271 } 272 /* final block pattern copy */ 273 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim); 274 275 /* 276 * sieve for primes 17 and higher 277 */ 278 /* note highest useful factor and sieve spot */ 279 if (stop-start > TABSIZE+TABSIZE) { 280 tab_lim = &table[TABSIZE]; /* sieve it all */ 281 fact_lim = sqrt(start+1.0+TABSIZE+TABSIZE); 282 } else { 283 tab_lim = &table[(stop-start)/2]; /* partial sieve */ 284 fact_lim = sqrt(stop+1.0); 285 } 286 /* sieve for factors >= 17 */ 287 factor = 17; /* 17 is first prime to use */ 288 p = &prime[7]; /* 19 is next prime, pi(19)=7 */ 289 do { 290 /* determine the factor's initial sieve point */ 291 mod = start%factor; 292 if (mod & 0x1) { 293 q = &table[(factor-mod)/2]; 294 } else { 295 q = &table[mod ? factor-(mod/2) : 0]; 296 } 297 /* sive for our current factor */ 298 for ( ; q < tab_lim; q += factor) { 299 *q = '\0'; /* sieve out a spot */ 300 } 301 factor = *p++; 302 } while (factor <= fact_lim); 303 304 /* 305 * print generated primes 306 */ 307 for (q = table; q < tab_lim; ++q, start+=2) { 308 if (*q) { 309 if (start > SIEVEMAX) { 310 if (!isprime(start)) 311 continue; 312 } 313 printf(hflag ? "%" PRIx64 "\n" : "%" PRIu64 "\n", start); 314 } 315 } 316 } 317 } 318 319 static void 320 usage(void) 321 { 322 fprintf(stderr, "usage: primes [-h] [start [stop]]\n"); 323 exit(1); 324 } 325