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322 lines
9.0 KiB
C
322 lines
9.0 KiB
C
/* primesieve (BIT_ARRAY, N) -- Fills the BIT_ARRAY with a mask for primes up to N.
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Contributed to the GNU project by Marco Bodrato.
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THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.
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IT IS ONLY SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.
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IN FACT, IT IS ALMOST GUARANTEED THAT IT WILL CHANGE OR
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DISAPPEAR IN A FUTURE GNU MP RELEASE.
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Copyright 2010-2012, 2015, 2016, 2021, 2022 Free Software Foundation, Inc.
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This file is part of the GNU MP Library.
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The GNU MP Library is free software; you can redistribute it and/or modify
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it under the terms of either:
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* the GNU Lesser General Public License as published by the Free
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Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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or
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* the GNU General Public License as published by the Free Software
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Foundation; either version 2 of the License, or (at your option) any
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later version.
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or both in parallel, as here.
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The GNU MP Library is distributed in the hope that it will be useful, but
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WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
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or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received copies of the GNU General Public License and the
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GNU Lesser General Public License along with the GNU MP Library. If not,
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see https://www.gnu.org/licenses/. */
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#include "gmp-impl.h"
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#if 0
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static mp_limb_t
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bit_to_n (mp_limb_t bit) { return (bit*3+4)|1; }
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#endif
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/* id_to_n (x) = bit_to_n (x-1) = (id*3+1)|1*/
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static mp_limb_t
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id_to_n (mp_limb_t id) { return id*3+1+(id&1); }
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/* n_fto_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */
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static mp_limb_t
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n_fto_bit (mp_limb_t n) { return ((n-5)|1)/3U; }
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/* n_cto_bit (n) = ((n-2)&(-CNST_LIMB(2)))/3U */
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static mp_limb_t
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n_cto_bit (mp_limb_t n) { return (n|1)/3U-1; }
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#if 0
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static mp_size_t
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primesieve_size (mp_limb_t n) { return n_fto_bit(n) / GMP_LIMB_BITS + 1; }
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#endif
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#define SET_OFF1(m1, m2, M1, M2, off, BITS) \
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if (off) { \
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if (off < GMP_LIMB_BITS) { \
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m1 = (M1 >> off) | (M2 << (GMP_LIMB_BITS - off)); \
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if (off <= BITS - GMP_LIMB_BITS) { \
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m2 = M1 << (BITS - GMP_LIMB_BITS - off) \
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| M2 >> off; \
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} else { \
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m1 |= M1 << (BITS - off); \
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m2 = M1 >> (off + GMP_LIMB_BITS - BITS); \
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} \
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} else { \
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m1 = M1 << (BITS - off) \
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| M2 >> (off - GMP_LIMB_BITS); \
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m2 = M2 << (BITS - off) \
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| M1 >> (off + GMP_LIMB_BITS - BITS); \
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} \
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} else { \
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m1 = M1; m2 = M2; \
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}
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#define SET_OFF2(m1, m2, m3, M1, M2, M3, off, BITS) \
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if (off) { \
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if (off <= GMP_LIMB_BITS) { \
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m1 = M2 << (GMP_LIMB_BITS - off); \
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m2 = M3 << (GMP_LIMB_BITS - off); \
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if (off != GMP_LIMB_BITS) { \
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m1 |= (M1 >> off); \
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m2 |= (M2 >> off); \
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} \
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if (off <= BITS - 2 * GMP_LIMB_BITS) { \
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m3 = M1 << (BITS - 2 * GMP_LIMB_BITS - off) \
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| M3 >> off; \
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} else { \
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m2 |= M1 << (BITS - GMP_LIMB_BITS - off); \
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m3 = M1 >> (off + 2 * GMP_LIMB_BITS - BITS); \
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} \
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} else if (off < 2 *GMP_LIMB_BITS) { \
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m1 = M2 >> (off - GMP_LIMB_BITS) \
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| M3 << (2 * GMP_LIMB_BITS - off); \
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if (off <= BITS - GMP_LIMB_BITS) { \
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m2 = M3 >> (off - GMP_LIMB_BITS) \
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| M1 << (BITS - GMP_LIMB_BITS - off); \
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m3 = M2 << (BITS - GMP_LIMB_BITS - off); \
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if (off != BITS - GMP_LIMB_BITS) { \
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m3 |= M1 >> (off + 2 * GMP_LIMB_BITS - BITS); \
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} \
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} else { \
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m1 |= M1 << (BITS - off); \
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m2 = M2 << (BITS - off) \
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| M1 >> (GMP_LIMB_BITS - BITS + off); \
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m3 = M2 >> (GMP_LIMB_BITS - BITS + off); \
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} \
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} else { \
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m1 = M1 << (BITS - off) \
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| M3 >> (off - 2 * GMP_LIMB_BITS); \
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m2 = M2 << (BITS - off) \
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| M1 >> (off + GMP_LIMB_BITS - BITS); \
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m3 = M3 << (BITS - off) \
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| M2 >> (off + GMP_LIMB_BITS - BITS); \
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} \
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} else { \
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m1 = M1; m2 = M2; m3 = M3; \
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}
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#define ROTATE1(m1, m2, BITS) \
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do { \
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mp_limb_t __tmp; \
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__tmp = m1 >> (2 * GMP_LIMB_BITS - BITS); \
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m1 = (m1 << (BITS - GMP_LIMB_BITS)) | m2; \
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m2 = __tmp; \
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} while (0)
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#define ROTATE2(m1, m2, m3, BITS) \
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do { \
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mp_limb_t __tmp; \
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__tmp = m2 >> (3 * GMP_LIMB_BITS - BITS); \
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m2 = m2 << (BITS - GMP_LIMB_BITS * 2) \
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| m1 >> (3 * GMP_LIMB_BITS - BITS); \
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m1 = m1 << (BITS - GMP_LIMB_BITS * 2) | m3; \
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m3 = __tmp; \
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} while (0)
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static mp_limb_t
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fill_bitpattern (mp_ptr bit_array, mp_size_t limbs, mp_limb_t offset)
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{
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#ifdef SIEVE_2MSK2
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mp_limb_t m11, m12, m21, m22, m23;
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{ /* correctly handle offset == 0... */
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mp_limb_t off1 = offset % (11 * 5 * 2);
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SET_OFF1 (m11, m12, SIEVE_MASK1, SIEVE_MASKT, off1, 11 * 5 * 2);
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offset %= 13 * 7 * 2;
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SET_OFF2 (m21, m22, m23, SIEVE_2MSK1, SIEVE_2MSK2, SIEVE_2MSKT, offset, 13 * 7 * 2);
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}
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/* THINK: Consider handling odd values of 'limbs' outside the loop,
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to have a single exit condition. */
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do {
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bit_array[0] = m11 | m21;
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if (--limbs == 0)
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break;
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ROTATE1 (m11, m12, 11 * 5 * 2);
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bit_array[1] = m11 | m22;
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bit_array += 2;
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ROTATE1 (m11, m12, 11 * 5 * 2);
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ROTATE2 (m21, m22, m23, 13 * 7 * 2);
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} while (--limbs != 0);
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return n_cto_bit (13 + 1);
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#else
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#ifdef SIEVE_MASK2
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mp_limb_t mask, mask2, tail;
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{ /* correctly handle offset == 0... */
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offset %= 7 * 5 * 2;
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SET_OFF2 (mask, mask2, tail, SIEVE_MASK1, SIEVE_MASK2, SIEVE_MASKT, offset, 7 * 5 * 2);
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}
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/* THINK: Consider handling odd values of 'limbs' outside the loop,
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to have a single exit condition. */
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do {
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bit_array[0] = mask;
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if (--limbs == 0)
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break;
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bit_array[1] = mask2;
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bit_array += 2;
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ROTATE2 (mask, mask2, tail, 7 * 5 * 2);
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} while (--limbs != 0);
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return n_cto_bit (7 + 1);
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#else
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MPN_FILL (bit_array, limbs, CNST_LIMB(0));
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return 0;
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#endif
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#endif
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}
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static void
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block_resieve (mp_ptr bit_array, mp_size_t limbs, mp_limb_t offset,
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mp_srcptr sieve)
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{
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mp_size_t bits, off = offset;
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mp_limb_t mask, i;
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ASSERT (limbs > 0);
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bits = limbs * GMP_LIMB_BITS - 1;
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i = fill_bitpattern (bit_array, limbs, offset);
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ASSERT (i < GMP_LIMB_BITS);
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mask = CNST_LIMB(1) << i;
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do {
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++i;
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if ((*sieve & mask) == 0)
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{
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mp_size_t step, lindex;
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mp_limb_t lmask;
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unsigned maskrot;
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step = id_to_n(i);
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/* lindex = n_to_bit(id_to_n(i)*id_to_n(i)); */
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lindex = i*(step+1)-1+(-(i&1)&(i+1));
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/* lindex = i*(step+1+(i&1))-1+(i&1); */
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if (lindex > bits + off)
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break;
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step <<= 1;
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maskrot = step % GMP_LIMB_BITS;
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if (lindex < off)
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lindex += step * ((off - lindex - 1) / step + 1);
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lindex -= off;
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lmask = CNST_LIMB(1) << (lindex % GMP_LIMB_BITS);
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for ( ; lindex <= bits; lindex += step) {
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bit_array[lindex / GMP_LIMB_BITS] |= lmask;
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lmask = lmask << maskrot | lmask >> (GMP_LIMB_BITS - maskrot);
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};
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/* lindex = n_to_bit(id_to_n(i)*bit_to_n(i)); */
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lindex = i*(i*3+6)+(i&1);
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if (lindex < off)
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lindex += step * ((off - lindex - 1) / step + 1);
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lindex -= off;
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lmask = CNST_LIMB(1) << (lindex % GMP_LIMB_BITS);
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for ( ; lindex <= bits; lindex += step) {
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bit_array[lindex / GMP_LIMB_BITS] |= lmask;
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lmask = lmask << maskrot | lmask >> (GMP_LIMB_BITS - maskrot);
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};
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}
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mask = mask << 1 | mask >> (GMP_LIMB_BITS-1);
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sieve += mask & 1;
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} while (1);
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}
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#define BLOCK_SIZE 2048
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/* Fills bit_array with the characteristic function of composite
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numbers up to the parameter n. I.e. a bit set to "1" represents a
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composite, a "0" represents a prime.
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The primesieve_size(n) limbs pointed to by bit_array are
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overwritten. The returned value counts prime integers in the
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interval [4, n]. Note that n > 4.
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Even numbers and multiples of 3 are excluded "a priori", only
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numbers equivalent to +/- 1 mod 6 have their bit in the array.
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Once sieved, if the bit b is ZERO it represent a prime, the
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represented prime is bit_to_n(b), if the LSbit is bit 0, or
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id_to_n(b), if you call "1" the first bit.
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*/
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mp_limb_t
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gmp_primesieve (mp_ptr bit_array, mp_limb_t n)
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{
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mp_size_t size;
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mp_limb_t bits;
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static mp_limb_t presieved[] = {PRIMESIEVE_INIT_TABLE};
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ASSERT (n > 4);
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bits = n_fto_bit(n);
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size = bits / GMP_LIMB_BITS + 1;
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for (mp_size_t j = 0, lim = MIN (size, PRIMESIEVE_NUMBEROF_TABLE);
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j < lim; ++j)
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bit_array [j] = presieved [j]; /* memcopy? */
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if (size > PRIMESIEVE_NUMBEROF_TABLE) {
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mp_size_t off;
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off = size > 2 * BLOCK_SIZE ? BLOCK_SIZE + (size % BLOCK_SIZE) : size;
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block_resieve (bit_array + PRIMESIEVE_NUMBEROF_TABLE,
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off - PRIMESIEVE_NUMBEROF_TABLE,
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GMP_LIMB_BITS * PRIMESIEVE_NUMBEROF_TABLE, bit_array);
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for (; off < size; off += BLOCK_SIZE)
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block_resieve (bit_array + off, BLOCK_SIZE, off * GMP_LIMB_BITS, bit_array);
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}
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if ((bits + 1) % GMP_LIMB_BITS != 0)
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bit_array[size-1] |= MP_LIMB_T_MAX << ((bits + 1) % GMP_LIMB_BITS);
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return size * GMP_LIMB_BITS - mpn_popcount (bit_array, size);
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}
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#undef BLOCK_SIZE
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#undef SIEVE_MASK1
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#undef SIEVE_MASK2
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#undef SIEVE_MASKT
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#undef SIEVE_2MSK1
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#undef SIEVE_2MSK2
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#undef SIEVE_2MSKT
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#undef SET_OFF1
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#undef SET_OFF2
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#undef ROTATE1
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#undef ROTATE2
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