gcc/gmp/mpz/nextprime.c

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

Copyright 1999, 2000, 2001, 2008, 2009 Free Software Foundation, Inc.

Contributed to the GNU project by Niels Möller and Torbjörn 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 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.

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 Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */

#include "gmp.h"
#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;
  int cnt;
  mp_size_t pn;
  unsigned long 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);
  count_leading_zeros (cnt, PTR(p)[pn - 1]);
  nbits = pn * GMP_NUMB_BITS - (cnt - GMP_NAIL_BITS);
  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 * sizeof moduli[0], unsigned short);

  for (;;)
    {
      /* FIXME: Compute lazily? */
      prime = 3;
      for (i = 0; i < prime_limit; i++)
	{
	  moduli[i] = mpz_fdiv_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, 10))
	    goto done;
	next:;
	  incr += 2;
	}
      mpz_add_ui (p, p, difference);
      difference = 0;
    }
 done:
  TMP_SFREE;
}