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132 lines
3.5 KiB
C
132 lines
3.5 KiB
C
/* mpz_primorial_ui(RES, N) -- Set RES to N# the product of primes <= N.
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Contributed to the GNU project by Marco Bodrato.
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Copyright 2012, 2015, 2016, 2021 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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/* TODO: Remove duplicated constants / macros / static functions...
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*/
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/*************************************************************/
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/* Section macros: common macros, for swing/fac/bin (&sieve) */
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/*************************************************************/
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#define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I) \
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do { \
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if ((PR) > (MAX_PR)) { \
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(VEC)[(I)++] = (PR); \
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(PR) = (P); \
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} else \
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(PR) *= (P); \
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} while (0)
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/*********************************************************/
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/* Section sieve: sieving functions and tools for primes */
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/*********************************************************/
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#if WANT_ASSERT
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/* n_to_bit (n) = ((n-1)&(-CNST_LIMB(2)))/3U-1 */
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static mp_limb_t
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n_to_bit (mp_limb_t n) { return ((n-5)|1)/3U; }
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static mp_size_t
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primesieve_size (mp_limb_t n) { return n_to_bit(n) / GMP_LIMB_BITS + 1; }
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#endif
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/*********************************************************/
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/* Section primorial: implementation */
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/*********************************************************/
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void
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mpz_primorial_ui (mpz_ptr res, unsigned long n)
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{
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ASSERT (n <= GMP_NUMB_MAX);
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if (n < 5)
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{
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/* The smallest 5 results for primorial are stored */
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/* in a 15-bits constant (five octal digits) */
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MPZ_NEWALLOC (res, 1)[0] = (066211 >> (n * 3)) & 7;
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SIZ (res) = 1;
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}
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else
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{
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mp_limb_t *sieve, *factors;
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mp_size_t size, j;
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mp_limb_t prod;
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TMP_DECL;
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/* Try to estimate the result size, to avoid */
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/* resizing, and to initially store the sieve. */
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size = n / GMP_NUMB_BITS;
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size = size + (size >> 1) + 1;
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ASSERT (size >= primesieve_size (n));
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sieve = MPZ_NEWALLOC (res, size);
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size = (gmp_primesieve (sieve, n) + 1) / log_n_max (n) + 1;
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TMP_MARK;
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factors = TMP_ALLOC_LIMBS (size);
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j = 0;
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prod = 6;
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/* Store primes from 5 to n */
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{
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mp_limb_t max_prod;
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max_prod = GMP_NUMB_MAX / n;
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/* Loop on sieved primes. */
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for (mp_limb_t i = 4, *sp = sieve; i < n; i += GMP_LIMB_BITS * 3)
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for (mp_limb_t b = i, x = ~ *(sp++); x != 0; b += 3, x >>= 1)
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if (x & 1)
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{
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mp_limb_t prime = b | 1;
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FACTOR_LIST_STORE (prime, prod, max_prod, factors, j);
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}
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}
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if (j != 0)
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{
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factors[j++] = prod;
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mpz_prodlimbs (res, factors, j);
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}
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else
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{
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PTR (res)[0] = prod;
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SIZ (res) = 1;
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}
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TMP_FREE;
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}
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}
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