/* mpz_nextprime(p,t) - compute the next prime > t and store that in p.

Copyright 1999-2001, 2008, 2009, 2012 Free Software Foundation, Inc.

Contributed to the GNU project by Niels Möller and Torbjorn Granlund.

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/.  */

#include "gmp-impl.h"

#include "longlong.h"

static const unsigned char primegap[] =

{

  2,2,4,2,4,2,4,6,2,6,4,2,4,6,6,2,6,4,2,6,4,6,8,4,2,4,2,4,14,4,6,

  2,10,2,6,6,4,6,6,2,10,2,4,2,12,12,4,2,4,6,2,10,6,6,6,2,6,4,2,10,14,4,2,

  4,14,6,10,2,4,6,8,6,6,4,6,8,4,8,10,2,10,2,6,4,6,8,4,2,4,12,8,4,8,4,6,

  12,2,18,6,10,6,6,2,6,10,6,6,2,6,6,4,2,12,10,2,4,6,6,2,12,4,6,8,10,8,10,8,

  6,6,4,8,6,4,8,4,14,10,12,2,10,2,4,2,10,14,4,2,4,14,4,2,4,20,4,8,10,8,4,6,

  6,14,4,6,6,8,6,12

};

#define NUMBER_OF_PRIMES 167

void

mpz_nextprime (mpz_ptr p, mpz_srcptr n)

{

  unsigned short *moduli;

  unsigned long difference;

  int i;

  unsigned prime_limit;

  unsigned long prime;

  mp_size_t pn;

  mp_bitcnt_t nbits;

  unsigned incr;

  TMP_SDECL;

  /* First handle tiny numbers */

  if (mpz_cmp_ui (n, 2) < 0)

    {

      mpz_set_ui (p, 2);

      return;

    }

  mpz_add_ui (p, n, 1);

  mpz_setbit (p, 0);

  if (mpz_cmp_ui (p, 7) <= 0)

    return;

  pn = SIZ(p);

  MPN_SIZEINBASE_2EXP(nbits, PTR(p), pn, 1);

  if (nbits / 2 >= NUMBER_OF_PRIMES)

    prime_limit = NUMBER_OF_PRIMES - 1;

  else

    prime_limit = nbits / 2;

  TMP_SMARK;

  /* Compute residues modulo small odd primes */

  moduli = TMP_SALLOC_TYPE (prime_limit, unsigned short);

  for (;;)

    {

      /* FIXME: Compute lazily? */

      prime = 3;

      for (i = 0; i < prime_limit; i++)

  {

    moduli[i] = mpz_tdiv_ui (p, prime);

    prime += primegap[i];

  }

#define INCR_LIMIT 0x10000  /* deep science */

      for (difference = incr = 0; incr < INCR_LIMIT; difference += 2)

  {

    /* First check residues */

    prime = 3;

    for (i = 0; i < prime_limit; i++)

      {

        unsigned r;

        /* FIXME: Reduce moduli + incr and store back, to allow for

     division-free reductions.  Alternatively, table primes[]'s

     inverses (mod 2^16).  */

        r = (moduli[i] + incr) % prime;

        prime += primegap[i];

        if (r == 0)

    goto next;

      }

    mpz_add_ui (p, p, difference);

    difference = 0;

    /* Miller-Rabin test */

    if (mpz_millerrabin (p, 25))

      goto done;

  next:;

    incr += 2;

  }

      mpz_add_ui (p, p, difference);

      difference = 0;

    }

 done:

  TMP_SFREE;

}