Quelle primesieve.c Sprache: 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 2010-2012, 2015, 2016, 2021, 2022 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/.  */

#include "gmp-impl.h"

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

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

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

#define SET_OFF1(m1, m2, M1, M2, off, BITS)  \
  if (off) {      \
    if (off < GMP_LIMB_BITS) {    \
      m1 = (M1 >> off) | (M2 << (GMP_LIMB_BITS - off)); \
      if (off <= BITS - GMP_LIMB_BITS) {  \
m2 = M1 << (BITS - GMP_LIMB_BITS - off)  \
   | M2 >> off;     \
      } else {      \
m1 |= M1 << (BITS - off);   \
m2 = M1 >> (off + GMP_LIMB_BITS - BITS); \
      }       \
    } else {      \
      m1 = M1 << (BITS - off)    \
| M2 >> (off - GMP_LIMB_BITS);   \
      m2 = M2 << (BITS - off)    \
| M1 >> (off + GMP_LIMB_BITS - BITS);  \
    }       \
  } else {      \
    m1 = M1; m2 = M2;     \
  }

#define SET_OFF2(m1, m2, m3, M1, M2, M3, off, BITS) \
  if (off) {      \
    if (off <= GMP_LIMB_BITS) {    \
      m1 = M2 << (GMP_LIMB_BITS - off);   \
      m2 = M3 << (GMP_LIMB_BITS - off);   \
      if (off != GMP_LIMB_BITS) {   \
m1 |= (M1 >> off);    \
m2 |= (M2 >> off);    \
      }       \
      if (off <= BITS - 2 * GMP_LIMB_BITS) {  \
m3 = M1 << (BITS - 2 * GMP_LIMB_BITS - off) \
   | M3 >> off;     \
      } else {      \
m2 |= M1 << (BITS - GMP_LIMB_BITS - off); \
m3 = M1 >> (off + 2 * GMP_LIMB_BITS - BITS); \
      }       \
    } else if (off < 2 *GMP_LIMB_BITS) {  \
      m1 = M2 >> (off - GMP_LIMB_BITS)   \
| M3 << (2 * GMP_LIMB_BITS - off);  \
      if (off <= BITS - GMP_LIMB_BITS) {  \
m2 = M3 >> (off - GMP_LIMB_BITS)  \
   | M1 << (BITS - GMP_LIMB_BITS - off);  \
m3 = M2 << (BITS - GMP_LIMB_BITS - off); \
if (off != BITS - GMP_LIMB_BITS) {  \
   m3 |= M1 >> (off + 2 * GMP_LIMB_BITS - BITS); \
}      \
      } else {      \
m1 |= M1 << (BITS - off);   \
m2 = M2 << (BITS - off)    \
   | M1 >> (GMP_LIMB_BITS - BITS + off);  \
m3 = M2 >> (GMP_LIMB_BITS - BITS + off); \
      }       \
    } else {      \
      m1 = M1 << (BITS - off)    \
| M3 >> (off - 2 * GMP_LIMB_BITS);  \
      m2 = M2 << (BITS - off)    \
| M1 >> (off + GMP_LIMB_BITS - BITS);  \
      m3 = M3 << (BITS - off)    \
| M2 >> (off + GMP_LIMB_BITS - BITS);  \
    }       \
  } else {      \
    m1 = M1; m2 = M2; m3 = M3;    \
  }

#define ROTATE1(m1, m2, BITS)   \
  do {      \
    mp_limb_t __tmp;    \
    __tmp = m1 >> (2 * GMP_LIMB_BITS - BITS); \
    m1 = (m1 << (BITS - GMP_LIMB_BITS)) | m2; \
    m2 = __tmp;     \
  } while (0)

#define ROTATE2(m1, m2, m3, BITS)  \
  do {      \
    mp_limb_t __tmp;    \
    __tmp = m2 >> (3 * GMP_LIMB_BITS - BITS); \
    m2 = m2 << (BITS - GMP_LIMB_BITS * 2) \
      | m1 >> (3 * GMP_LIMB_BITS - BITS); \
    m1 = m1 << (BITS - GMP_LIMB_BITS * 2) | m3; \
    m3 = __tmp;     \
  } while (0)

static mp_limb_t
fill_bitpattern (mp_ptr bit_array, mp_size_t limbs, mp_limb_t offset)
{
#ifdef SIEVE_2MSK2
  mp_limb_t m11, m12, m21, m22, m23;

  { /* correctly handle offset == 0... */
    mp_limb_t off1 = offset % (11 * 5 * 2);
    SET_OFF1 (m11, m12, SIEVE_MASK1, SIEVE_MASKT, off1, 11 * 5 * 2);
    offset %= 13 * 7 * 2;
    SET_OFF2 (m21, m22, m23, SIEVE_2MSK1, SIEVE_2MSK2, SIEVE_2MSKT, offset, 13 * 7 * 2);
  }
  /* THINK: Consider handling odd values of 'limbs' outside the loop,
     to have a single exit condition. */
  do {
    bit_array[0] = m11 | m21;
    if (--limbs == 0)
      break;
    ROTATE1 (m11, m12, 11 * 5 * 2);
    bit_array[1] = m11 | m22;
    bit_array += 2;
    ROTATE1 (m11, m12, 11 * 5 * 2);
    ROTATE2 (m21, m22, m23, 13 * 7 * 2);
  } while (--limbs != 0);
  return n_cto_bit (13 + 1);
#else
#ifdef SIEVE_MASK2
  mp_limb_t mask, mask2, tail;

  { /* correctly handle offset == 0... */
    offset %= 7 * 5 * 2;
    SET_OFF2 (mask, mask2, tail, SIEVE_MASK1, SIEVE_MASK2, SIEVE_MASKT, offset, 7 * 5 * 2);
  }
  /* THINK: Consider handling odd values of 'limbs' outside the loop,
     to have a single exit condition. */
  do {
    bit_array[0] = mask;
    if (--limbs == 0)
      break;
    bit_array[1] = mask2;
    bit_array += 2;
    ROTATE2 (mask, mask2, tail, 7 * 5 * 2);
  } while (--limbs != 0);
  return n_cto_bit (7 + 1);
#else
  MPN_FILL (bit_array, limbs, CNST_LIMB(0));
  return 0;
#endif
#endif
}

static void
block_resieve (mp_ptr bit_array, mp_size_t limbs, mp_limb_t offset,
        mp_srcptr sieve)
{
  mp_size_t bits, off = offset;
  mp_limb_t mask, i;

  ASSERT (limbs > 0);

  bits = limbs * GMP_LIMB_BITS - 1;

  i = fill_bitpattern (bit_array, limbs, offset);

  ASSERT (i < GMP_LIMB_BITS);

  mask = CNST_LIMB(1) << i;
  do {
    ++i;
    if ((*sieve & 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 + off)
   break;

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

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

lindex -= off;

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

lindex -= off;

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);
      sieve += mask & 1;
  } while (1);
}

#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" represents a
   composite, a "0" represents 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;
  static mp_limb_t presieved[] = {PRIMESIEVE_INIT_TABLE};

  ASSERT (n > 4);

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

  for (mp_size_t j = 0, lim = MIN (size, PRIMESIEVE_NUMBEROF_TABLE);
       j < lim; ++j)
    bit_array [j] = presieved [j]; /* memcopy? */

  if (size > PRIMESIEVE_NUMBEROF_TABLE) {
    mp_size_t off;
    off = size > 2 * BLOCK_SIZE ? BLOCK_SIZE + (size % BLOCK_SIZE) : size;
    block_resieve (bit_array + PRIMESIEVE_NUMBEROF_TABLE,
     off - PRIMESIEVE_NUMBEROF_TABLE,
     GMP_LIMB_BITS * PRIMESIEVE_NUMBEROF_TABLE, bit_array);
    for (; off < size; off += BLOCK_SIZE)
      block_resieve (bit_array + off, BLOCK_SIZE, off * GMP_LIMB_BITS, bit_array);
  }

  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 SIEVE_MASK1
#undef SIEVE_MASK2
#undef SIEVE_MASKT
#undef SIEVE_2MSK1
#undef SIEVE_2MSK2
#undef SIEVE_2MSKT
#undef SET_OFF1
#undef SET_OFF2
#undef ROTATE1
#undef ROTATE2

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