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/* mpz_primorial_ui(RESULT, N) -- Set RESULT 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 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.h"
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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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#define LOOP_ON_SIEVE_CONTINUE(prime,end,sieve) \
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__max_i = (end); \
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\
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do { \
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++__i; \
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if (((sieve)[__index] & __mask) == 0) \
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{ \
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(prime) = id_to_n(__i)
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#define LOOP_ON_SIEVE_BEGIN(prime,start,end,off,sieve) \
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do { \
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mp_limb_t __mask, __index, __max_i, __i; \
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\
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__i = (start)-(off); \
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__index = __i / GMP_LIMB_BITS; \
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__mask = CNST_LIMB(1) << (__i % GMP_LIMB_BITS); \
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__i += (off); \
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\
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LOOP_ON_SIEVE_CONTINUE(prime,end,sieve)
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#define LOOP_ON_SIEVE_STOP \
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} \
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__mask = __mask << 1 | __mask >> (GMP_LIMB_BITS-1); \
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__index += __mask & 1; \
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} while (__i <= __max_i) \
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#define LOOP_ON_SIEVE_END \
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LOOP_ON_SIEVE_STOP; \
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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 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_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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#if WANT_ASSERT
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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 x, unsigned long n)
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{
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static const mp_limb_t table[] = { 1, 1, 2, 6, 6 };
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ASSERT (n <= GMP_NUMB_MAX);
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if (n < numberof (table))
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{
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PTR (x)[0] = table[n];
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SIZ (x) = 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;
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mp_limb_t prod;
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mp_limb_t j;
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TMP_DECL;
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size = 1 + n / GMP_NUMB_BITS + n / (2*GMP_NUMB_BITS);
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ASSERT (size >= primesieve_size (n));
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sieve = MPZ_NEWALLOC (x, 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 = table[numberof (table)-1];
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/* Store primes from 5 to n */
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{
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mp_limb_t prime, max_prod;
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max_prod = GMP_NUMB_MAX / n;
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LOOP_ON_SIEVE_BEGIN (prime, n_to_bit(numberof (table)), n_to_bit (n), 0, sieve);
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FACTOR_LIST_STORE (prime, prod, max_prod, factors, j);
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LOOP_ON_SIEVE_END;
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}
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if (LIKELY (j != 0))
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{
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factors[j++] = prod;
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mpz_prodlimbs (x, factors, j);
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}
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else
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{
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PTR (x)[0] = prod;
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SIZ (x) = 1;
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}
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TMP_FREE;
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}
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}
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