/* gmp_nextprime -- generate small primes reasonably efficiently for internal

   GMP needs.

   Contributed to the GNU project by Torbjorn Granlund.  Miscellaneous

   improvements by Martin Boij.

   THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY

   SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST

   GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2009 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify

it under the terms of either:

  * the GNU Lesser General Public License as published by the Free

    Software Foundation; either version 3 of the License, or (at your

    option) any later version.

or

  * the GNU General Public License as published by the Free Software

    Foundation; either version 2 of the License, or (at your option) any

    later version.

or both in parallel, as here.

The GNU MP Library is distributed in the hope that it will be useful, but

WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY

or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License

for more details.

You should have received copies of the GNU General Public License and the

GNU Lesser General Public License along with the GNU MP Library.  If not,

see https://www.gnu.org/licenses/.  */

/*

  Optimisation ideas:

  1. Unroll the sieving loops.  Should reach 1 write/cycle.  That would be a 2x

     improvement.

  2. Separate sieving with primes p < SIEVESIZE and p >= SIEVESIZE.  The latter

     will need at most one write, and thus not need any inner loop.

  3. For primes p >= SIEVESIZE, i.e., typically the majority of primes, we

     perform more than one division per sieving write.  That might dominate the

     entire run time for the nextprime function.  A incrementally initialised

     remainder table of Pi(65536) = 6542 16-bit entries could replace that

     division.

*/

#include "gmp-impl.h"

#include <string.h>   /* for memset */

unsigned long int

gmp_nextprime (gmp_primesieve_t *ps)

{

  unsigned long p, d, pi;

  unsigned char *sp;

  static unsigned char addtab[] =

    { 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,

      2,4,6,2,6,4,2,4,2,10,2,10 };

  unsigned char *addp = addtab;

  unsigned long ai;

  /* Look for already sieved primes.  A sentinel at the end of the sieving

     area allows us to use a very simple loop here.  */

  d = ps->d;

  sp = ps->s + d;

  while (*sp != 0)

    sp++;

  if (sp != ps->s + SIEVESIZE)

    {

      d = sp - ps->s;

      ps->d = d + 1;

      return ps->s0 + 2 * d;

    }

  /* Handle the number 2 separately.  */

  if (ps->s0 < 3)

    {

      ps->s0 = 3 - 2 * SIEVESIZE; /* Tricky */

      return 2;

    }

  /* Exhausted computed primes.  Resieve, then call ourselves recursively.  */

#if 0

  for (sp = ps->s; sp < ps->s + SIEVESIZE; sp++)

    *sp = 0;

#else

  memset (ps->s, 0, SIEVESIZE);

#endif

  ps->s0 += 2 * SIEVESIZE;

  /* Update sqrt_s0 as needed.  */

  while ((ps->sqrt_s0 + 1) * (ps->sqrt_s0 + 1) <= ps->s0 + 2 * SIEVESIZE - 1)

    ps->sqrt_s0++;

  pi = ((ps->s0 + 3) / 2) % 3;

  if (pi > 0)

    pi = 3 - pi;

  if (ps->s0 + 2 * pi <= 3)

    pi += 3;

  sp = ps->s + pi;

  while (sp < ps->s + SIEVESIZE)

    {

      *sp = 1, sp += 3;

    }

  pi = ((ps->s0 + 5) / 2) % 5;

  if (pi > 0)

    pi = 5 - pi;

  if (ps->s0 + 2 * pi <= 5)

    pi += 5;

  sp = ps->s + pi;

  while (sp < ps->s + SIEVESIZE)

    {

      *sp = 1, sp += 5;

    }

  pi = ((ps->s0 + 7) / 2) % 7;

  if (pi > 0)

    pi = 7 - pi;

  if (ps->s0 + 2 * pi <= 7)

    pi += 7;

  sp = ps->s + pi;

  while (sp < ps->s + SIEVESIZE)

    {

      *sp = 1, sp += 7;

    }

  p = 11;

  ai = 0;

  while (p <= ps->sqrt_s0)

    {

      pi = ((ps->s0 + p) / 2) % p;

      if (pi > 0)

  pi = p - pi;

      if (ps->s0 + 2 * pi <= p)

    pi += p;

      sp = ps->s + pi;

      while (sp < ps->s + SIEVESIZE)

  {

    *sp = 1, sp += p;

  }

      p += addp[ai];

      ai = (ai + 1) % 48;

    }

  ps->d = 0;

  return gmp_nextprime (ps);

}

void

gmp_init_primesieve (gmp_primesieve_t *ps)

{

  ps->s0 = 0;

  ps->sqrt_s0 = 0;

  ps->d = SIEVESIZE;

  ps->s[SIEVESIZE] = 0;    /* sentinel */

}