mpir/primesieve.c

/* primesieve (BIT_ARRAY, N) -- Fills the BIT_ARRAY with a mask for primes up to N.

Contributed to the GNU project by Marco Bodrato.

THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.
IT IS ONLY SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.
IN FACT, IT IS ALMOST GUARANTEED THAT IT WILL CHANGE OR
DISAPPEAR IN A FUTURE GNU MP RELEASE.

Copyright 2010, 2011, 2012 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 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"

/**************************************************************/
/* Section macros: common macros, for mswing/fac/bin (&sieve) */
/**************************************************************/

#define LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)			\
    __max_i = (end);						\
								\
    do {							\
      ++__i;							\
      if (((sieve)[__index] & __mask) == 0)			\
	{							\
	  (prime) = id_to_n(__i)

#define LOOP_ON_SIEVE_BEGIN(prime,start,end,off,sieve)		\
  do {								\
    mp_limb_t __mask, __index, __max_i, __i;			\
								\
    __i = (start)-(off);					\
    __index = __i / GMP_LIMB_BITS;				\
    __mask = CNST_LIMB(1) << (__i % GMP_LIMB_BITS);		\
    __i += (off);						\
								\
    LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)

#define LOOP_ON_SIEVE_STOP					\
	}							\
      __mask = __mask << 1 | __mask >> (GMP_LIMB_BITS-1);	\
      __index += __mask & 1;					\
    }  while (__i <= __max_i)					\

#define LOOP_ON_SIEVE_END					\
    LOOP_ON_SIEVE_STOP;						\
  } while (0)

/*********************************************************/
/* Section sieve: sieving functions and tools for primes */
/*********************************************************/

#if 0
static mp_limb_t
bit_to_n (mp_limb_t bit) { return (bit*3+4)|1; }
#endif

/* id_to_n (x) = bit_to_n (x-1) = (id*3+1)|1*/
static mp_limb_t
id_to_n  (mp_limb_t id)  { return id*3+1+(id&1); }

/* n_to_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */
static mp_limb_t
n_to_bit (mp_limb_t n) { return ((n-5)|1)/3U; }

#if 0
static mp_size_t
primesieve_size (mp_limb_t n) { return n_to_bit(n) / GMP_LIMB_BITS + 1; }
#endif

#if GMP_LIMB_BITS > 61
#define SIEVE_SEED CNST_LIMB(0x3294C9E069128480)
#define SEED_LIMIT 202
#else
#if GMP_LIMB_BITS > 30
#define SIEVE_SEED CNST_LIMB(0x69128480)
#define SEED_LIMIT 114
#else
#if GMP_LIMB_BITS > 15
#define SIEVE_SEED CNST_LIMB(0x8480)
#define SEED_LIMIT 54
#else
#if GMP_LIMB_BITS > 7
#define SIEVE_SEED CNST_LIMB(0x80)
#define SEED_LIMIT 34
#else
#define SIEVE_SEED CNST_LIMB(0x0)
#define SEED_LIMIT 24
#endif /* 7 */
#endif /* 15 */
#endif /* 30 */
#endif /* 61 */

static void
first_block_primesieve (mp_ptr bit_array, mp_limb_t n)
{
  mp_size_t bits, limbs;

  ASSERT (n > 4);

  bits  = n_to_bit(n);
  limbs = bits / GMP_LIMB_BITS + 1;

  /* FIXME: We can skip 5 too, filling with a 5-part pattern. */
  MPN_ZERO (bit_array, limbs);
  bit_array[0] = SIEVE_SEED;

  if ((bits + 1) % GMP_LIMB_BITS != 0)
    bit_array[limbs-1] |= MP_LIMB_T_MAX << ((bits + 1) % GMP_LIMB_BITS);

  if (n > SEED_LIMIT) {
    mp_limb_t mask, index, i;

    ASSERT (n > 49);

    mask = 1;
    index = 0;
    i = 1;
    do {
      if ((bit_array[index] & mask) == 0)
	{
	  mp_size_t step, lindex;
	  mp_limb_t lmask;
	  unsigned  maskrot;

	  step = id_to_n(i);
/*	  lindex = n_to_bit(id_to_n(i)*id_to_n(i)); */
	  lindex = i*(step+1)-1+(-(i&1)&(i+1));
/*	  lindex = i*(step+1+(i&1))-1+(i&1); */
	  if (lindex > bits)
	    break;

	  step <<= 1;
	  maskrot = step % GMP_LIMB_BITS;

	  lmask = CNST_LIMB(1) << (lindex % GMP_LIMB_BITS);
	  do {
	    bit_array[lindex / GMP_LIMB_BITS] |= lmask;
	    lmask = lmask << maskrot | lmask >> (GMP_LIMB_BITS - maskrot);
	    lindex += step;
	  } while (lindex <= bits);

/*	  lindex = n_to_bit(id_to_n(i)*bit_to_n(i)); */
	  lindex = i*(i*3+6)+(i&1);

	  lmask = CNST_LIMB(1) << (lindex % GMP_LIMB_BITS);
	  for ( ; lindex <= bits; lindex += step) {
	    bit_array[lindex / GMP_LIMB_BITS] |= lmask;
	    lmask = lmask << maskrot | lmask >> (GMP_LIMB_BITS - maskrot);
	  };
	}
      mask = mask << 1 | mask >> (GMP_LIMB_BITS-1);
      index += mask & 1;
      i++;
    } while (1);
  }
}

static void
block_resieve (mp_ptr bit_array, mp_size_t limbs, mp_limb_t offset,
		      mp_srcptr sieve, mp_limb_t sieve_bits)
{
  mp_size_t bits, step;

  ASSERT (limbs > 0);

  bits = limbs * GMP_LIMB_BITS - 1;

  /* FIXME: We can skip 5 too, filling with a 5-part pattern. */
  MPN_ZERO (bit_array, limbs);

  LOOP_ON_SIEVE_BEGIN(step,0,sieve_bits,0,sieve);
  {
    mp_size_t lindex;
    mp_limb_t lmask;
    unsigned  maskrot;

/*  lindex = n_to_bit(id_to_n(i)*id_to_n(i)); */
    lindex = __i*(step+1)-1+(-(__i&1)&(__i+1));
/*  lindex = __i*(step+1+(__i&1))-1+(__i&1); */
    if (lindex > bits + offset)
      break;

    step <<= 1;
    maskrot = step % GMP_LIMB_BITS;

    if (lindex < offset)
      lindex += step * ((offset - lindex - 1) / step + 1);

    lindex -= offset;

    lmask = CNST_LIMB(1) << (lindex % GMP_LIMB_BITS);
    for ( ; lindex <= bits; lindex += step) {
      bit_array[lindex / GMP_LIMB_BITS] |= lmask;
      lmask = lmask << maskrot | lmask >> (GMP_LIMB_BITS - maskrot);
    };

/*  lindex = n_to_bit(id_to_n(i)*bit_to_n(i)); */
    lindex = __i*(__i*3+6)+(__i&1);
    if (lindex > bits + offset)
      continue;

    if (lindex < offset)
      lindex += step * ((offset - lindex - 1) / step + 1);

    lindex -= offset;

    lmask = CNST_LIMB(1) << (lindex % GMP_LIMB_BITS);
    for ( ; lindex <= bits; lindex += step) {
      bit_array[lindex / GMP_LIMB_BITS] |= lmask;
      lmask = lmask << maskrot | lmask >> (GMP_LIMB_BITS - maskrot);
    };
  }
  LOOP_ON_SIEVE_END;
}

#define BLOCK_SIZE 2048

/* Fills bit_array with the characteristic function of composite
   numbers up to the parameter n. I.e. a bit set to "1" represent a
   composite, a "0" represent a prime.

   The primesieve_size(n) limbs pointed to by bit_array are
   overwritten. The returned value counts prime integers in the
   interval [4, n]. Note that n > 4.

   Even numbers and multiples of 3 are excluded "a priori", only
   numbers equivalent to +/- 1 mod 6 have their bit in the array.

   Once sieved, if the bit b is ZERO it represent a prime, the
   represented prime is bit_to_n(b), if the LSbit is bit 0, or
   id_to_n(b), if you call "1" the first bit.
 */

mp_limb_t
gmp_primesieve (mp_ptr bit_array, mp_limb_t n)
{
  mp_size_t size;
  mp_limb_t bits;

  ASSERT (n > 4);

  bits = n_to_bit(n);
  size = bits / GMP_LIMB_BITS + 1;

  if (size > BLOCK_SIZE * 2) {
    mp_size_t off;
    off = BLOCK_SIZE + (size % BLOCK_SIZE);
    first_block_primesieve (bit_array, id_to_n (off * GMP_LIMB_BITS));
    for ( ; off < size; off += BLOCK_SIZE)
      block_resieve (bit_array + off, BLOCK_SIZE, off * GMP_LIMB_BITS, bit_array, off * GMP_LIMB_BITS - 1);
  } else {
    first_block_primesieve (bit_array, n);
  }

  if ((bits + 1) % GMP_LIMB_BITS != 0)
    bit_array[size-1] |= MP_LIMB_T_MAX << ((bits + 1) % GMP_LIMB_BITS);


  return size * GMP_LIMB_BITS - mpn_popcount (bit_array, size);
}

#undef BLOCK_SIZE
#undef SEED_LIMIT
#undef SIEVE_SEED
#undef LOOP_ON_SIEVE_END
#undef LOOP_ON_SIEVE_STOP
#undef LOOP_ON_SIEVE_BEGIN
#undef LOOP_ON_SIEVE_CONTINUE