source/libs/gmp/gmp-src/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 either:
  17
  18   * the GNU Lesser General Public License as published by the Free
  19     Software Foundation; either version 3 of the License, or (at your
  20     option) any later version.
  21
  22 or
  23
  24   * the GNU General Public License as published by the Free Software
  25     Foundation; either version 2 of the License, or (at your option) any
  26     later version.
  27
  28 or both in parallel, as here.
  29
  30 The GNU MP Library is distributed in the hope that it will be useful, but
  31 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  32 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  33 for more details.
  34
  35 You should have received copies of the GNU General Public License and the
  36 GNU Lesser General Public License along with the GNU MP Library.  If not,
  37 see https://www.gnu.org/licenses/.  */
  38
  39 /*
  40   Optimisation ideas:
  41
  42   1. Unroll the sieving loops.  Should reach 1 write/cycle.  That would be a 2x
  43      improvement.
  44
  45   2. Separate sieving with primes p < SIEVESIZE and p >= SIEVESIZE.  The latter
  46      will need at most one write, and thus not need any inner loop.
  47
  48   3. For primes p >= SIEVESIZE, i.e., typically the majority of primes, we
  49      perform more than one division per sieving write.  That might dominate the
  50      entire run time for the nextprime function.  A incrementally initialised
  51      remainder table of Pi(65536) = 6542 16-bit entries could replace that
  52      division.
  53 */
  54
  55 #include "gmp.h"
  56 #include "gmp-impl.h"
  57 #include <string.h>             /* for memset */
  58
  59
  60 unsigned long int
  61 gmp_nextprime (gmp_primesieve_t *ps)
  62 {
  63   unsigned long p, d, pi;
  64   unsigned char *sp;
  65   static unsigned char addtab[] =
  66     { 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,
  67       2,4,6,2,6,4,2,4,2,10,2,10 };
  68   unsigned char *addp = addtab;
  69   unsigned long ai;
  70
  71   /* Look for already sieved primes.  A sentinel at the end of the sieving
  72      area allows us to use a very simple loop here.  */
  73   d = ps->d;
  74   sp = ps->s + d;
  75   while (*sp != 0)
  76     sp++;
  77   if (sp != ps->s + SIEVESIZE)
  78     {
  79       d = sp - ps->s;
  80       ps->d = d + 1;
  81       return ps->s0 + 2 * d;
  82     }
  83
  84   /* Handle the number 2 separately.  */
  85   if (ps->s0 < 3)
  86     {
  87       ps->s0 = 3 - 2 * SIEVESIZE; /* Tricky */
  88       return 2;
  89     }
  90
  91   /* Exhausted computed primes.  Resieve, then call ourselves recursively.  */
  92
  93 #if 0
  94   for (sp = ps->s; sp < ps->s + SIEVESIZE; sp++)
  95     *sp = 0;
  96 #else
  97   memset (ps->s, 0, SIEVESIZE);
  98 #endif
  99
 100   ps->s0 += 2 * SIEVESIZE;
 101
 102   /* Update sqrt_s0 as needed.  */
 103   while ((ps->sqrt_s0 + 1) * (ps->sqrt_s0 + 1) <= ps->s0 + 2 * SIEVESIZE - 1)
 104     ps->sqrt_s0++;
 105
 106   pi = ((ps->s0 + 3) / 2) % 3;
 107   if (pi > 0)
 108     pi = 3 - pi;
 109   if (ps->s0 + 2 * pi <= 3)
 110     pi += 3;
 111   sp = ps->s + pi;
 112   while (sp < ps->s + SIEVESIZE)
 113     {
 114       *sp = 1, sp += 3;
 115     }
 116
 117   pi = ((ps->s0 + 5) / 2) % 5;
 118   if (pi > 0)
 119     pi = 5 - pi;
 120   if (ps->s0 + 2 * pi <= 5)
 121     pi += 5;
 122   sp = ps->s + pi;
 123   while (sp < ps->s + SIEVESIZE)
 124     {
 125       *sp = 1, sp += 5;
 126     }
 127
 128   pi = ((ps->s0 + 7) / 2) % 7;
 129   if (pi > 0)
 130     pi = 7 - pi;
 131   if (ps->s0 + 2 * pi <= 7)
 132     pi += 7;
 133   sp = ps->s + pi;
 134   while (sp < ps->s + SIEVESIZE)
 135     {
 136       *sp = 1, sp += 7;
 137     }
 138
 139   p = 11;
 140   ai = 0;
 141   while (p <= ps->sqrt_s0)
 142     {
 143       pi = ((ps->s0 + p) / 2) % p;
 144       if (pi > 0)
 145         pi = p - pi;
 146       if (ps->s0 + 2 * pi <= p)
 147           pi += p;
 148       sp = ps->s + pi;
 149       while (sp < ps->s + SIEVESIZE)
 150         {
 151           *sp = 1, sp += p;
 152         }
 153       p += addp[ai];
 154       ai = (ai + 1) % 48;
 155     }
 156   ps->d = 0;
 157   return gmp_nextprime (ps);
 158 }
 159
 160 void
 161 gmp_init_primesieve (gmp_primesieve_t *ps)
 162 {
 163   ps->s0 = 0;
 164   ps->sqrt_s0 = 0;
 165   ps->d = SIEVESIZE;
 166   ps->s[SIEVESIZE] = 0;         /* sentinel */
 167 }