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Diff for /OpenXM_contrib/gmp/demos/Attic/primes.c between version 1.1.1.1 and 1.1.1.2

version 1.1.1.1, 2000/09/09 14:13:19 version 1.1.1.2, 2003/08/25 16:06:03
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 /* List and count primes.  /* List and count primes.
      Written by tege while on holiday in Rodupp, August 2001.
      Between 10 and 500 times faster than previous program.
   
 Copyright (C) 2000 Free Software Foundation, Inc.  Copyright 2001 Free Software Foundation, Inc.
   
 This program is free software; you can redistribute it and/or modify it under  This program is free software; you can redistribute it and/or modify it under
 the terms of the GNU General Public License as published by the Free Software  the terms of the GNU General Public License as published by the Free Software
Line 17  Place - Suite 330, Boston, MA 02111-1307, USA.  */
Line 19  Place - Suite 330, Boston, MA 02111-1307, USA.  */
   
 #include <stdlib.h>  #include <stdlib.h>
 #include <stdio.h>  #include <stdio.h>
   #include <string.h>
   #include <math.h>
   #include <assert.h>
   
   /* IDEAS:
    * Do not fill primes[] with real primes when the range [fr,to] is small,
      when fr,to are relatively large.  Fill primes[] with odd numbers instead.
      [Probably a bad idea, since the primes[] array would become very large.]
    * Separate small primes and large primes when sieving.  Either the Montgomery
      way (i.e., having a large array a multiple of L1 cache size), or just
      separate loops for primes <= S and primes > S.  The latter primes do not
      require an inner loop, since they will touch the sieving array at most once.
    * Pre-fill sieving array with an appropriately aligned ...00100100... pattern,
      then omit 3 from primes array.  (May require similar special handling of 3
      as we now have for 2.)
    * A large SIEVE_LIMIT currently implies very large memory usage, mainly due
      to the sieving array in make_primelist, but also because of the primes[]
      array.  We might want to stage the program, using sieve_region/find_primes
      to build primes[].  Make report() a function pointer, as part of achieving
      this.
    * Store primes[] as two arrays, one array with primes represented as delta
      values using just 8 bits (if gaps are too big, store bogus primes!)
      and one array with "rem" values.  The latter needs 32-bit values.
    * A new entry point, mpz_probab_prime_likely_p, would be useful.
    * Improve command line syntax and versatility.  "primes -f FROM -t TO",
      allow either to be omitted for open interval.  (But disallow
      "primes -c -f FROM" since that would be infinity.)  Allow printing a
      limited *number* of primes using syntax like "primes -f FROM -n NUMBER".
    * When looking for maxgaps, we should not perform any primality testing until
      we find possible record gaps.  Should speed up the searches tremendously.
    */
   
 #include "gmp.h"  #include "gmp.h"
   
 /* Sieve table size */  struct primes
 #define ST_SIZE 30000  {
 /* Largest prime to sieve with */    unsigned int prime;
 #define MAX_S_PRIME 1000    signed int rem;
   };
   
 main (int argc, char **argv)  struct primes *primes;
   unsigned long n_primes;
   
   void find_primes (unsigned char *, mpz_t, unsigned long, mpz_t);
   void sieve_region (unsigned char *, mpz_t, unsigned long);
   void make_primelist (unsigned long);
   
   int flag_print = 1;
   int flag_count = 0;
   int flag_maxgap = 0;
   unsigned long maxgap = 0;
   unsigned long total_primes = 0;
   
   void
   report (mpz_t prime)
 {  {
     total_primes += 1;
     if (flag_print)
       {
         mpz_out_str (stdout, 10, prime);
         printf ("\n");
       }
     if (flag_maxgap)
       {
         static unsigned long prev_prime_low = 0;
         unsigned long gap;
         if (prev_prime_low != 0)
           {
             gap = mpz_get_ui (prime) - prev_prime_low;
             if (maxgap < gap)
               maxgap = gap;
           }
         prev_prime_low = mpz_get_ui (prime);
       }
   }
   
   int
   main (int argc, char *argv[])
   {
   char *progname = argv[0];    char *progname = argv[0];
   mpz_t r0, r1;                 /* range */    mpz_t fr, to;
   mpz_t cur;    mpz_t fr2, to2;
   unsigned char *st;    unsigned long sieve_lim;
   unsigned long i, ii;    unsigned long est_n_primes;
   unsigned long nprimes = 0;    unsigned char *s;
   unsigned long last;    mpz_t tmp;
   int flag_print = 1;    mpz_t siev_sqr_lim;
   int flag_count = 0;  
   
   st = malloc (ST_SIZE);  
   
   while (argc != 1)    while (argc != 1)
     {      {
       if (strcmp (argv[1], "-c") == 0)        if (strcmp (argv[1], "-c") == 0)
Line 52  main (int argc, char **argv)
Line 121  main (int argc, char **argv)
           argv++;            argv++;
           argc--;            argc--;
         }          }
         else if (strcmp (argv[1], "-g") == 0)
           {
             flag_maxgap = 1;
             argv++;
             argc--;
           }
       else        else
         break;          break;
     }      }
   
   if (flag_count)    if (flag_count || flag_maxgap)
     flag_print--;               /* clear unless an explicit -p  */      flag_print--;               /* clear unless an explicit -p  */
   
   mpz_init (r0);    mpz_init (fr);
   mpz_init (r1);    mpz_init (to);
   mpz_init (cur);    mpz_init (fr2);
     mpz_init (to2);
   
   if (argc == 2)    if (argc == 3)
     {      {
       mpz_set_ui (r0, 2);        mpz_set_str (fr, argv[1], 0);
       mpz_set_str (r1, argv[1], 0);  
     }  
   else if (argc == 3)  
     {  
       mpz_set_str (r0, argv[1], 0);  
       if (argv[2][0] == '+')        if (argv[2][0] == '+')
         {          {
           mpz_set_str (r1, argv[2] + 1, 0);            mpz_set_str (to, argv[2] + 1, 0);
           mpz_add (r1, r1, r0);            mpz_add (to, to, fr);
         }          }
       else        else
         mpz_set_str (r1, argv[2], 0);          mpz_set_str (to, argv[2], 0);
     }      }
     else if (argc == 2)
       {
         mpz_set_ui (fr, 0);
         mpz_set_str (to, argv[1], 0);
       }
   else    else
     {      {
       fprintf (stderr, "usage: %s [-c] [-g] [from [+]]to\n", progname);        fprintf (stderr, "usage: %s [-c] [-p] [-g] [from [+]]to\n", progname);
       exit (1);        exit (1);
     }      }
   
   if (mpz_cmp_ui (r0, 2) < 0)    mpz_set (fr2, fr);
     mpz_set_ui (r0, 2);    if (mpz_cmp_ui (fr2, 3) < 0)
       {
         mpz_set_ui (fr2, 2);
         report (fr2);
         mpz_set_ui (fr2, 3);
       }
     mpz_setbit (fr2, 0);                          /* make odd */
     mpz_sub_ui (to2, to, 1);
     mpz_setbit (to2, 0);                          /* make odd */
   
   if ((mpz_get_ui (r0) & 1) == 0)    mpz_init (tmp);
     mpz_init (siev_sqr_lim);
   
     mpz_sqrt (tmp, to2);
   #define SIEVE_LIMIT 10000000
     if (mpz_cmp_ui (tmp, SIEVE_LIMIT) < 0)
     {      {
       if (mpz_cmp_ui (r0, 2) == 0)        sieve_lim = mpz_get_ui (tmp);
       }
     else
       {
         sieve_lim = SIEVE_LIMIT;
         mpz_sub (tmp, to2, fr2);
         if (mpz_cmp_ui (tmp, sieve_lim) < 0)
           sieve_lim = mpz_get_ui (tmp);   /* limit sieving for small ranges */
       }
     mpz_set_ui (siev_sqr_lim, sieve_lim + 1);
     mpz_mul_ui (siev_sqr_lim, siev_sqr_lim, sieve_lim + 1);
   
     est_n_primes = (size_t) (sieve_lim / log((double) sieve_lim) * 1.13) + 10;
     primes = malloc (est_n_primes * sizeof primes[0]);
     make_primelist (sieve_lim);
     assert (est_n_primes >= n_primes);
   
   #if DEBUG
     printf ("sieve_lim = %lu\n", sieve_lim);
     printf ("n_primes = %lu (3..%u)\n",
             n_primes, primes[n_primes - 1].prime);
   #endif
   
   #define S (1 << 15)             /* FIXME: Figure out L1 cache size */
     s = malloc (S/2);
     while (mpz_cmp (fr2, to2) <= 0)
       {
         unsigned long rsize;
         rsize = S;
         mpz_add_ui (tmp, fr2, rsize);
         if (mpz_cmp (tmp, to2) > 0)
         {          {
           if (flag_print)            mpz_sub (tmp, to2, fr2);
             puts ("2");            rsize = mpz_get_ui (tmp) + 2;
           nprimes++;  
         }          }
       mpz_add_ui (r0, r0, 1);  #if DEBUG
         printf ("Sieving region ["); mpz_out_str (stdout, 10, fr2);
         printf (","); mpz_add_ui (tmp, fr2, rsize - 2);
         mpz_out_str (stdout, 10, tmp); printf ("]\n");
   #endif
         sieve_region (s, fr2, rsize);
         find_primes (s, fr2, rsize / 2, siev_sqr_lim);
   
         mpz_add_ui (fr2, fr2, S);
     }      }
     free (s);
   
   mpz_set (cur, r0);    if (flag_count)
       printf ("Pi(interval) = %lu\n", total_primes);
   
   while (mpz_cmp (cur, r1) <= 0)    if (flag_maxgap)
       printf ("max gap: %lu\n", maxgap);
   
     return 0;
   }
   
   /* Find primes in region [fr,fr+rsize).  Requires that fr is odd and that
      rsize is even.  The sieving array s should be aligned for "long int" and
      have rsize/2 entries, rounded up to the nearest multiple of "long int".  */
   void
   sieve_region (unsigned char *s, mpz_t fr, unsigned long rsize)
   {
     unsigned long ssize = rsize / 2;
     unsigned long start, start2, prime;
     unsigned long i;
     mpz_t tmp;
   
     mpz_init (tmp);
   
   #if 0
     /* initialize sieving array */
     for (ii = 0; ii < (ssize + sizeof (long) - 1) / sizeof (long); ii++)
       ((long *) s) [ii] = ~0L;
   #else
     {
       signed long k;
       long *se = (long *) (s + ((ssize + sizeof (long) - 1) & -sizeof (long)));
       for (k = -((ssize + sizeof (long) - 1) / sizeof (long)); k < 0; k++)
         se[k] = ~0L;
     }
   #endif
   
     for (i = 0; i < n_primes; i++)
     {      {
       memset (st, 1, ST_SIZE);        prime = primes[i].prime;
       for (i = 3; i < MAX_S_PRIME; i += 2)  
         if (primes[i].rem >= 0)
         {          {
           unsigned long start;            start2 = primes[i].rem;
           start = mpz_tdiv_ui (cur, i);  
           if (start != 0)  
             start = i - start;  
   
           if (mpz_cmp_ui (cur, i - start) == 0)  
             start += i;  
           for (ii = start; ii < ST_SIZE; ii += i)  
             st[ii] = 0;  
         }          }
       last = 0;        else
       for (ii = 0; ii < ST_SIZE; ii += 2)  
         {          {
           if (st[ii] != 0)            mpz_set_ui (tmp, prime);
             mpz_mul_ui (tmp, tmp, prime);
             if (mpz_cmp (fr, tmp) <= 0)
             {              {
               mpz_add_ui (cur, cur, ii - last);                mpz_sub (tmp, tmp, fr);
               last = ii;                if (mpz_cmp_ui (tmp, 2 * ssize) > 0)
               if (mpz_cmp (cur, r1) > 0)                  break;          /* avoid overflow at next line, also speedup */
                 goto done;                start = mpz_get_ui (tmp);
               if (mpz_probab_prime_p (cur, 3))              }
             else
               {
                 start = (prime - mpz_tdiv_ui (fr, prime)) % prime;
                 if (start % 2 != 0)
                   start += prime;         /* adjust if even divisable */
               }
             start2 = start / 2;
           }
   
   #if 0
         for (ii = start2; ii < ssize; ii += prime)
           s[ii] = 0;
         primes[i].rem = ii - ssize;
   #else
         {
           signed long k;
           unsigned char *se = s + ssize; /* point just beyond sieving range */
           for (k = start2 - ssize; k < 0; k += prime)
             se[k] = 0;
           primes[i].rem = k;
         }
   #endif
       }
     mpz_clear (tmp);
   }
   
   /* Find primes in region [fr,fr+rsize), using the previously sieved s[].  */
   void
   find_primes (unsigned char *s, mpz_t  fr, unsigned long ssize,
                mpz_t siev_sqr_lim)
   {
     unsigned long j, ij;
     mpz_t tmp;
   
     mpz_init (tmp);
     for (j = 0; j < (ssize + sizeof (long) - 1) / sizeof (long); j++)
       {
         if (((long *) s) [j] != 0)
           {
             for (ij = 0; ij < sizeof (long); ij++)
               {
                 if (s[j * sizeof (long) + ij] != 0)
                 {                  {
                   nprimes++;                    if (j * sizeof (long) + ij >= ssize)
                   if (flag_print)                      goto out;
                     {                    mpz_add_ui (tmp, fr, (j * sizeof (long) + ij) * 2);
                       mpz_out_str (stdout, 10, cur); puts ("");                    if (mpz_cmp (tmp, siev_sqr_lim) < 0 ||
                     }                        mpz_probab_prime_p (tmp, 3))
                       report (tmp);
                 }                  }
             }              }
         }          }
       mpz_add_ui (cur, cur, ST_SIZE - last);  
     }      }
  done:   out:
   if (flag_count)    mpz_clear (tmp);
     printf ("Pi(interval) = %lu\n", nprimes);  }
   
   exit (0);  /* Generate a lits of primes and store in the global array primes[].  */
   void
   make_primelist (unsigned long maxprime)
   {
   #if 1
     unsigned char *s;
     unsigned long ssize = maxprime / 2;
     unsigned long i, ii, j;
   
     s = malloc (ssize);
     memset (s, ~0, ssize);
     for (i = 3; ; i += 2)
       {
         unsigned long isqr = i * i;
         if (isqr >= maxprime)
           break;
         if (s[i * i / 2 - 1] == 0)
           continue;                               /* only sieve with primes */
         for (ii = i * i / 2 - 1; ii < ssize; ii += i)
           s[ii] = 0;
       }
     n_primes = 0;
     for (j = 0; j < ssize; j++)
       {
         if (s[j] != 0)
           {
             primes[n_primes].prime = j * 2 + 3;
             primes[n_primes].rem = -1;
             n_primes++;
           }
       }
     /* FIXME: This should not be needed if fencepost errors were fixed... */
     if (primes[n_primes - 1].prime > maxprime)
       n_primes--;
     free (s);
   #else
     unsigned long i;
     n_primes = 0;
     for (i = 3; i <= maxprime; i += 2)
       {
         if (i < 7 || (i % 3 != 0 && i % 5 != 0 && i % 7 != 0))
           {
             primes[n_primes].prime = i;
             primes[n_primes].rem = -1;
             n_primes++;
           }
       }
   #endif
 }  }
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