152 lines
4.3 KiB
C
152 lines
4.3 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2010 Fredrik Johansson
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Copyright (C) 2010 William Hart
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******************************************************************************/
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#include "arith.h"
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#if FLINT64
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#define LARGEST_ULONG_PRIMORIAL 52
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#else
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#define LARGEST_ULONG_PRIMORIAL 28
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#endif
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/* Only those with odd index */
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const ulong ULONG_PRIMORIALS[] =
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{
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UWORD(6),UWORD(30),UWORD(210),UWORD(210),UWORD(2310),UWORD(30030),UWORD(30030),UWORD(510510),UWORD(9699690),UWORD(9699690),
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UWORD(223092870),UWORD(223092870),UWORD(223092870)
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#if FLINT64
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,UWORD(6469693230),UWORD(200560490130),UWORD(200560490130),UWORD(200560490130),UWORD(7420738134810),
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UWORD(7420738134810),UWORD(304250263527210),UWORD(13082761331670030),UWORD(13082761331670030),
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UWORD(614889782588491410), UWORD(614889782588491410), UWORD(614889782588491410)
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#endif
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};
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#define PROD_LIMBS_DIRECT_CUTOFF 50
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mp_size_t mpn_prod_limbs_direct(mp_limb_t * result, const mp_limb_t * factors,
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mp_size_t n)
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{
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mp_size_t k, len;
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mp_limb_t top;
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if (n < 1)
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{
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result[0] = UWORD(1);
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return 1;
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}
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result[0] = factors[0];
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len = 1;
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for (k=1; k<n; k++)
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{
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top = mpn_mul_1(result, result, len, factors[k]);
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if (top)
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{
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result[len] = top;
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len++;
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}
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}
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return len;
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}
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mp_size_t mpn_prod_limbs_balanced(mp_limb_t * result, mp_limb_t * scratch,
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const mp_limb_t * factors, mp_size_t n, ulong bits)
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{
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mp_size_t an, bn, alen, blen, len;
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mp_limb_t top;
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if (n < PROD_LIMBS_DIRECT_CUTOFF)
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return mpn_prod_limbs_direct(result, factors, n);
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an = n/2;
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bn = n - an;
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alen = mpn_prod_limbs_balanced(scratch, result, factors, an, bits);
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blen = mpn_prod_limbs_balanced(scratch + alen, result, factors + an, bn, bits);
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len = alen + blen;
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if (alen <= blen)
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top = mpn_mul(result, scratch + alen, blen, scratch, alen);
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else
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top = mpn_mul(result, scratch, alen, scratch + alen, blen);
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if (!top)
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len--;
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return len;
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}
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/*
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Set result to the product of the given factors, return the
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length of the result. It is assumed that no factors are zero.
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bits must be set to some bound on the bit size of the entries
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in factors. If no bound is known, simply use FLINT_BITS.
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*/
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mp_size_t mpn_prod_limbs(mp_limb_t * result, const mp_limb_t * factors,
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mp_size_t n, ulong bits)
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{
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mp_size_t len, limbs;
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mp_limb_t * scratch;
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if (n < PROD_LIMBS_DIRECT_CUTOFF)
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return mpn_prod_limbs_direct(result, factors, n);
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limbs = (n * bits - 1)/FLINT_BITS + 2;
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scratch = flint_malloc(sizeof(mp_limb_t) * limbs);
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len = mpn_prod_limbs_balanced(result, scratch, factors, n, bits);
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flint_free(scratch);
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return len;
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}
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void arith_primorial(fmpz_t res, slong n)
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{
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mp_size_t len, pi;
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ulong bits;
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__mpz_struct * mpz_ptr;
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const mp_limb_t * primes;
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if (n <= LARGEST_ULONG_PRIMORIAL)
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{
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if (n <= 2)
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fmpz_set_ui(res, 1 + (n==2));
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else
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fmpz_set_ui(res, ULONG_PRIMORIALS[(n-1)/2-1]);
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return;
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}
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pi = n_prime_pi(n);
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primes = n_primes_arr_readonly(pi);
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bits = FLINT_BIT_COUNT(primes[pi - 1]);
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mpz_ptr = _fmpz_promote(res);
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mpz_realloc2(mpz_ptr, pi*bits);
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len = mpn_prod_limbs(mpz_ptr->_mp_d, primes, pi, bits);
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mpz_ptr->_mp_size = len;
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}
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