contrib/gmp/nextprime.c

   1 /* gmp_nextprime -- generate small primes reasonably efficiently for internal
   2    GMP needs.
   3
   4    Contributed to the GNU project by Torbjorn Granlund.  Miscellaneous
   5    improvements by Martin Boij.
   6
   7    THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
   8    SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   9    GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
  10
  11 Copyright 2009 Free Software Foundation, Inc.
  12
  13 This file is part of the GNU MP Library.
  14
  15 The GNU MP Library is free software; you can redistribute it and/or modify
  16 it under the terms of the GNU Lesser General Public License as published by
  17 the Free Software Foundation; either version 3 of the License, or (at your
  18 option) any later version.
  19
  20 The GNU MP Library is distributed in the hope that it will be useful, but
  21 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  22 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  23 License for more details.
  24
  25 You should have received a copy of the GNU Lesser General Public License
  26 along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
  27
  28 /*
  29   Optimisation ideas:
  30
  31   1. Unroll the sieving loops.  Should reach 1 write/cycle.  That would be a 2x
  32      improvement.
  33
  34   2. Separate sieving with primes p < SIEVESIZE and p >= SIEVESIZE.  The latter
  35      will need at most one write, and thus not need any inner loop.
  36
  37   3. For primes p >= SIEVESIZE, i.e., typically the majority of primes, we
  38      perform more than one division per sieving write.  That might dominate the
  39      entire run time for the nextprime function.  A incrementally initialised
  40      remainder table of Pi(65536) = 6542 16-bit entries could replace that
  41      division.
  42 */
  43
  44 #include "gmp.h"
  45 #include "gmp-impl.h"
  46 #include <string.h>             /* for memset */
  47
  48
  49 unsigned long int
  50 gmp_nextprime (gmp_primesieve_t *ps)
  51 {
  52   unsigned long p, d, pi;
  53   unsigned char *sp;
  54   static unsigned char addtab[] =
  55     { 2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,8,6,4,6,2,4,6,2,6,6,4,
  56       2,4,6,2,6,4,2,4,2,10,2,10 };
  57   unsigned char *addp = addtab;
  58   unsigned long ai;
  59
  60   /* Look for already sieved primes.  A sentinel at the end of the sieving
  61      area allows us to use a very simple loop here.  */
  62   d = ps->d;
  63   sp = ps->s + d;
  64   while (*sp != 0)
  65     sp++;
  66   if (sp != ps->s + SIEVESIZE)
  67     {
  68       d = sp - ps->s;
  69       ps->d = d + 1;
  70       return ps->s0 + 2 * d;
  71     }
  72
  73   /* Handle the number 2 separately.  */
  74   if (ps->s0 < 3)
  75     {
  76       ps->s0 = 3 - 2 * SIEVESIZE; /* Tricky */
  77       return 2;
  78     }
  79
  80   /* Exhausted computed primes.  Resieve, then call ourselves recursively.  */
  81
  82 #if 0
  83   for (sp = ps->s; sp < ps->s + SIEVESIZE; sp++)
  84     *sp = 0;
  85 #else
  86   memset (ps->s, 0, SIEVESIZE);
  87 #endif
  88
  89   ps->s0 += 2 * SIEVESIZE;
  90
  91   /* Update sqrt_s0 as needed.  */
  92   while ((ps->sqrt_s0 + 1) * (ps->sqrt_s0 + 1) <= ps->s0 + 2 * SIEVESIZE - 1)
  93     ps->sqrt_s0++;
  94
  95   pi = ((ps->s0 + 3) / 2) % 3;
  96   if (pi > 0)
  97     pi = 3 - pi;
  98   if (ps->s0 + 2 * pi <= 3)
  99     pi += 3;
 100   sp = ps->s + pi;
 101   while (sp < ps->s + SIEVESIZE)
 102     {
 103       *sp = 1, sp += 3;
 104     }
 105
 106   pi = ((ps->s0 + 5) / 2) % 5;
 107   if (pi > 0)
 108     pi = 5 - pi;
 109   if (ps->s0 + 2 * pi <= 5)
 110     pi += 5;
 111   sp = ps->s + pi;
 112   while (sp < ps->s + SIEVESIZE)
 113     {
 114       *sp = 1, sp += 5;
 115     }
 116
 117   pi = ((ps->s0 + 7) / 2) % 7;
 118   if (pi > 0)
 119     pi = 7 - pi;
 120   if (ps->s0 + 2 * pi <= 7)
 121     pi += 7;
 122   sp = ps->s + pi;
 123   while (sp < ps->s + SIEVESIZE)
 124     {
 125       *sp = 1, sp += 7;
 126     }
 127
 128   p = 11;
 129   ai = 0;
 130   while (p <= ps->sqrt_s0)
 131     {
 132       pi = ((ps->s0 + p) / 2) % p;
 133       if (pi > 0)
 134         pi = p - pi;
 135       if (ps->s0 + 2 * pi <= p)
 136           pi += p;
 137       sp = ps->s + pi;
 138       while (sp < ps->s + SIEVESIZE)
 139         {
 140           *sp = 1, sp += p;
 141         }
 142       p += addp[ai];
 143       ai = (ai + 1) % 48;
 144     }
 145   ps->d = 0;
 146   return gmp_nextprime (ps);
 147 }
 148
 149 void
 150 gmp_init_primesieve (gmp_primesieve_t *ps)
 151 {
 152   ps->s0 = 0;
 153   ps->sqrt_s0 = 0;
 154   ps->d = SIEVESIZE;
 155   ps->s[SIEVESIZE] = 0;         /* sentinel */
 156 }