primes/primes.c

   1 /*      $NetBSD: primes.c,v 1.14 2008/02/02 17:45:05 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 1.14 2008/02/02 17:45:05 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     main(int, char *[]);
 107 void    primes(ubig, ubig);
 108 ubig    read_num_buf(void);
 109 void    usage(void) __dead;
 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                         /* sieve 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 }