primes/primes.c

   1 /*      $NetBSD: primes.c,v 1.9 1999/09/08 21:17:55 jsm 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. All advertising materials mentioning features or use of this software
  19  *    must display the following acknowledgement:
  20  *      This product includes software developed by the University of
  21  *      California, Berkeley and its contributors.
  22  * 4. Neither the name of the University nor the names of its contributors
  23  *    may be used to endorse or promote products derived from this software
  24  *    without specific prior written permission.
  25  *
  26  * THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
  27  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
  28  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
  29  * ARE DISCLAIMED.  IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
  30  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
  31  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
  32  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
  33  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  34  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
  35  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
  36  * SUCH DAMAGE.
  37  */
  38
  39 #include <sys/cdefs.h>
  40 #ifndef lint
  41 __COPYRIGHT("@(#) Copyright (c) 1989, 1993\n\
  42         The Regents of the University of California.  All rights reserved.\n");
  43 #endif /* not lint */
  44
  45 #ifndef lint
  46 #if 0
  47 static char sccsid[] = "@(#)primes.c    8.5 (Berkeley) 5/10/95";
  48 #else
  49 __RCSID("$NetBSD: primes.c,v 1.9 1999/09/08 21:17:55 jsm Exp $");
  50 #endif
  51 #endif /* not lint */
  52
  53 /*
  54  * primes - generate a table of primes between two values
  55  *
  56  * By: Landon Curt Noll chongo@toad.com, ...!{sun,tolsoft}!hoptoad!chongo
  57  *
  58  * chongo <for a good prime call: 391581 * 2^216193 - 1> /\oo/\
  59  *
  60  * usage:
  61  *      primes [start [stop]]
  62  *
  63  *      Print primes >= start and < stop.  If stop is omitted,
  64  *      the value 4294967295 (2^32-1) is assumed.  If start is
  65  *      omitted, start is read from standard input.
  66  *
  67  * validation check: there are 664579 primes between 0 and 10^7
  68  */
  69
  70 #include <ctype.h>
  71 #include <err.h>
  72 #include <errno.h>
  73 #include <limits.h>
  74 #include <math.h>
  75 #include <memory.h>
  76 #include <stdio.h>
  77 #include <stdlib.h>
  78 #include <unistd.h>
  79
  80 #include "primes.h"
  81
  82 /*
  83  * Eratosthenes sieve table
  84  *
  85  * We only sieve the odd numbers.  The base of our sieve windows are always
  86  * odd.  If the base of table is 1, table[i] represents 2*i-1.  After the
  87  * sieve, table[i] == 1 if and only iff 2*i-1 is prime.
  88  *
  89  * We make TABSIZE large to reduce the overhead of inner loop setup.
  90  */
  91 char table[TABSIZE];     /* Eratosthenes sieve of odd numbers */
  92
  93 /*
  94  * prime[i] is the (i-1)th prime.
  95  *
  96  * We are able to sieve 2^32-1 because this byte table yields all primes
  97  * up to 65537 and 65537^2 > 2^32-1.
  98  */
  99 extern const ubig prime[];
 100 extern const ubig *pr_limit;            /* largest prime in the prime array */
 101
 102 /*
 103  * To avoid excessive sieves for small factors, we use the table below to
 104  * setup our sieve blocks.  Each element represents a odd number starting
 105  * with 1.  All non-zero elements are factors of 3, 5, 7, 11 and 13.
 106  */
 107 extern const char pattern[];
 108 extern const int pattern_size;  /* length of pattern array */
 109
 110 int     main __P((int, char *[]));
 111 void    primes __P((ubig, ubig));
 112 ubig    read_num_buf __P((void));
 113 void    usage __P((void)) __attribute__((__noreturn__));
 114
 115 int
 116 main(argc, argv)
 117         int argc;
 118         char *argv[];
 119 {
 120         ubig start;             /* where to start generating */
 121         ubig stop;              /* don't generate at or above this value */
 122         int ch;
 123         char *p;
 124
 125         while ((ch = getopt(argc, argv, "")) != -1)
 126                 switch (ch) {
 127                 case '?':
 128                 default:
 129                         usage();
 130                 }
 131         argc -= optind;
 132         argv += optind;
 133
 134         start = 0;
 135         stop = BIG;
 136
 137         /*
 138          * Convert low and high args.  Strtoul(3) sets errno to
 139          * ERANGE if the number is too large, but, if there's
 140          * a leading minus sign it returns the negation of the
 141          * result of the conversion, which we'd rather disallow.
 142          */
 143         switch (argc) {
 144         case 2:
 145                 /* Start and stop supplied on the command line. */
 146                 if (argv[0][0] == '-' || argv[1][0] == '-')
 147                         errx(1, "negative numbers aren't permitted.");
 148
 149                 errno = 0;
 150                 start = strtoul(argv[0], &p, 10);
 151                 if (errno)
 152                         err(1, "%s", argv[0]);
 153                 if (*p != '\0')
 154                         errx(1, "%s: illegal numeric format.", argv[0]);
 155
 156                 errno = 0;
 157                 stop = strtoul(argv[1], &p, 10);
 158                 if (errno)
 159                         err(1, "%s", argv[1]);
 160                 if (*p != '\0')
 161                         errx(1, "%s: illegal numeric format.", argv[1]);
 162                 break;
 163         case 1:
 164                 /* Start on the command line. */
 165                 if (argv[0][0] == '-')
 166                         errx(1, "negative numbers aren't permitted.");
 167
 168                 errno = 0;
 169                 start = strtoul(argv[0], &p, 10);
 170                 if (errno)
 171                         err(1, "%s", argv[0]);
 172                 if (*p != '\0')
 173                         errx(1, "%s: illegal numeric format.", argv[0]);
 174                 break;
 175         case 0:
 176                 start = read_num_buf();
 177                 break;
 178         default:
 179                 usage();
 180         }
 181
 182         if (start > stop)
 183                 errx(1, "start value must be less than stop value.");
 184         primes(start, stop);
 185         exit(0);
 186 }
 187
 188 /*
 189  * read_num_buf --
 190  *      This routine returns a number n, where 0 <= n && n <= BIG.
 191  */
 192 ubig
 193 read_num_buf()
 194 {
 195         ubig val;
 196         char *p, buf[100];              /* > max number of digits. */
 197
 198         for (;;) {
 199                 if (fgets(buf, sizeof(buf), stdin) == NULL) {
 200                         if (ferror(stdin))
 201                                 err(1, "stdin");
 202                         exit(0);
 203                 }
 204                 for (p = buf; isblank(*p); ++p);
 205                 if (*p == '\n' || *p == '\0')
 206                         continue;
 207                 if (*p == '-')
 208                         errx(1, "negative numbers aren't permitted.");
 209                 errno = 0;
 210                 val = strtoul(buf, &p, 10);
 211                 if (errno)
 212                         err(1, "%s", buf);
 213                 if (*p != '\n')
 214                         errx(1, "%s: illegal numeric format.", buf);
 215                 return (val);
 216         }
 217 }
 218
 219 /*
 220  * primes - sieve and print primes from start up to and but not including stop
 221  */
 222 void
 223 primes(start, stop)
 224         ubig start;     /* where to start generating */
 225         ubig stop;      /* don't generate at or above this value */
 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
 233         /*
 234          * A number of systems can not convert double values into unsigned
 235          * longs when the values are larger than the largest signed value.
 236          * We don't have this problem, so we can go all the way to BIG.
 237          */
 238         if (start < 3) {
 239                 start = (ubig)2;
 240         }
 241         if (stop < 3) {
 242                 stop = (ubig)2;
 243         }
 244         if (stop <= start) {
 245                 return;
 246         }
 247
 248         /*
 249          * be sure that the values are odd, or 2
 250          */
 251         if (start != 2 && (start&0x1) == 0) {
 252                 ++start;
 253         }
 254         if (stop != 2 && (stop&0x1) == 0) {
 255                 ++stop;
 256         }
 257
 258         /*
 259          * quick list of primes <= pr_limit
 260          */
 261         if (start <= *pr_limit) {
 262                 /* skip primes up to the start value */
 263                 for (p = &prime[0], factor = prime[0];
 264                     factor < stop && p <= pr_limit; factor = *(++p)) {
 265                         if (factor >= start) {
 266                                 printf("%lu\n", (unsigned long) factor);
 267                         }
 268                 }
 269                 /* return early if we are done */
 270                 if (p <= pr_limit) {
 271                         return;
 272                 }
 273                 start = *pr_limit+2;
 274         }
 275
 276         /*
 277          * we shall sieve a bytemap window, note primes and move the window
 278          * upward until we pass the stop point
 279          */
 280         while (start < stop) {
 281                 /*
 282                  * factor out 3, 5, 7, 11 and 13
 283                  */
 284                 /* initial pattern copy */
 285                 factor = (start%(2*3*5*7*11*13))/2; /* starting copy spot */
 286                 memcpy(table, &pattern[factor], pattern_size-factor);
 287                 /* main block pattern copies */
 288                 for (fact_lim=pattern_size-factor;
 289                     fact_lim+pattern_size<=TABSIZE; fact_lim+=pattern_size) {
 290                         memcpy(&table[fact_lim], pattern, pattern_size);
 291                 }
 292                 /* final block pattern copy */
 293                 memcpy(&table[fact_lim], pattern, TABSIZE-fact_lim);
 294
 295                 /*
 296                  * sieve for primes 17 and higher
 297                  */
 298                 /* note highest useful factor and sieve spot */
 299                 if (stop-start > TABSIZE+TABSIZE) {
 300                         tab_lim = &table[TABSIZE]; /* sieve it all */
 301                         fact_lim = (int)sqrt(
 302                                         (double)(start)+TABSIZE+TABSIZE+1.0);
 303                 } else {
 304                         tab_lim = &table[(stop-start)/2]; /* partial sieve */
 305                         fact_lim = (int)sqrt((double)(stop)+1.0);
 306                 }
 307                 /* sieve for factors >= 17 */
 308                 factor = 17;    /* 17 is first prime to use */
 309                 p = &prime[7];  /* 19 is next prime, pi(19)=7 */
 310                 do {
 311                         /* determine the factor's initial sieve point */
 312                         q = (char *)(start%factor); /* temp storage for mod */
 313                         if ((long)q & 0x1) {
 314                                 q = &table[(factor-(long)q)/2];
 315                         } else {
 316                                 q = &table[q ? factor-((long)q/2) : 0];
 317                         }
 318                         /* sive for our current factor */
 319                         for ( ; q < tab_lim; q += factor) {
 320                                 *q = '\0'; /* sieve out a spot */
 321                         }
 322                 } while ((factor=(ubig)(*(p++))) <= fact_lim);
 323
 324                 /*
 325                  * print generated primes
 326                  */
 327                 for (q = table; q < tab_lim; ++q, start+=2) {
 328                         if (*q) {
 329                                 printf("%lu\n", (unsigned long) start);
 330                         }
 331                 }
 332         }
 333 }
 334
 335 void
 336 usage()
 337 {
 338         (void)fprintf(stderr, "usage: primes [start [stop]]\n");
 339         exit(1);
 340 }