mpz_prevprime

[Niels Möller]

Seth Troisi <braintwo at gmail.com> writes:

> Did you still limit the trial division to prime_limit?

No, I used *all* tabulated primes (which makes it slower for smaller
inputs). It seems clear that setting prime_limit improves performance
for smaller numbers.

> I'd love to see your code so I can try to understand what I might not
> tested.

It intended to attach it, but list archive didn't quite like it...
Copied below.

Regards,
/Niels

/* 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"

#if 1
struct gmp_primes_dtab {
  mp_limb_t p;
  mp_limb_t binv;
  mp_limb_t lim;
};

static const struct gmp_primes_dtab dtab[] =
{
#define WANT_dtab
#define P(p,inv,lim) {p, inv,lim}
#include "trialdivtab.h"
#undef WANT_dtab
#undef P
};

#define DTAB_SIZE (sizeof (dtab) / sizeof (dtab[0]))

void
mpz_nextprime (mpz_ptr p, mpz_srcptr n)
{
  unsigned short *moduli;
  unsigned long difference;
  int i;
  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;

  if (SIZ(p) == 1) 
    {
      mp_limb_t pl = PTR(p)[0];
      if (pl < SMALLEST_OMITTED_PRIME) 
	{
	  /* Simple linear search */
	  for (i = 0; i < DTAB_SIZE; i++)
	    if (dtab[i].p >= pl) 
	      {
		PTR(p)[0] = dtab[i].p;
		return;
	      }
	  PTR(p)[0] = SMALLEST_OMITTED_PRIME;
	  return;
	}
      /* FIXME: Could check if pl < SMALLEST_OMITTED_PRIME^2, or
	 generally do single-limb sieving. */
    }
  TMP_SMARK;

  /* Compute residues modulo small odd primes */
  moduli = TMP_SALLOC_TYPE (DTAB_SIZE, unsigned short);

  for (;;)
    {
      /* FIXME: Compute lazily? */
      for (i = 0; i < DTAB_SIZE; i++)
	{
	  /* FIXME: Could speedup using ptab*/
	  moduli[i] = mpz_tdiv_ui (p, dtab[i].p);
	}

#define INCR_LIMIT 0x10000	/* deep science */

      for (difference = incr = 0; incr < INCR_LIMIT; difference += 2)
	{
	  /* First check divisibility based on prime list */
	  for (i = 0; i < DTAB_SIZE; i++)
	    {
	      if ((moduli[i] + incr) * dtab[i].binv <= dtab[i].lim)
		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;
}
#else
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;
}

#endif

-- 
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