115 lines
3.5 KiB
C
115 lines
3.5 KiB
C
/* mpz_fac_ui(RESULT, N) -- Set RESULT to N!.
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Contributed to the GNU project by Marco Bodrato.
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Copyright 1991, 1993, 1994, 1995, 2000, 2001, 2002, 2003, 2011, 2012
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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 the GNU Lesser General Public License as published by
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the Free Software Foundation; either version 3 of the License, or (at your
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option) any later version.
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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 Lesser General Public
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License for more details.
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You should have received a copy of the GNU Lesser General Public License
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along with the GNU MP Library. If not, see http://www.gnu.org/licenses/. */
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#include "mpir.h"
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#include "gmp-impl.h"
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#if GMP_LIMB_BITS == 64
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/* This table is 0!,1!,2!,3!,...,n! where n! has <= GMP_NUMB_BITS bits */
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#define ONE_LIMB_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1),CNST_LIMB(0x2),CNST_LIMB(0x6),CNST_LIMB(0x18),CNST_LIMB(0x78),CNST_LIMB(0x2d0),CNST_LIMB(0x13b0),CNST_LIMB(0x9d80),CNST_LIMB(0x58980),CNST_LIMB(0x375f00),CNST_LIMB(0x2611500),CNST_LIMB(0x1c8cfc00),CNST_LIMB(0x17328cc00),CNST_LIMB(0x144c3b2800),CNST_LIMB(0x13077775800),CNST_LIMB(0x130777758000),CNST_LIMB(0x1437eeecd8000),CNST_LIMB(0x16beecca730000),CNST_LIMB(0x1b02b9306890000),CNST_LIMB(0x21c3677c82b40000)
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#define TABLE_LIMIT_2N_MINUS_POPC_2N 81
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#else
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/* This table is 0!,1!,2!,3!,...,n! where n! has <= GMP_NUMB_BITS bits */
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#define ONE_LIMB_FACTORIAL_TABLE CNST_LIMB(0x1),CNST_LIMB(0x1),CNST_LIMB(0x2),CNST_LIMB(0x6),CNST_LIMB(0x18),CNST_LIMB(0x78),CNST_LIMB(0x2d0),CNST_LIMB(0x13b0),CNST_LIMB(0x9d80),CNST_LIMB(0x58980),CNST_LIMB(0x375f00),CNST_LIMB(0x2611500),CNST_LIMB(0x1c8cfc00)
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#define TABLE_LIMIT_2N_MINUS_POPC_2N 49
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#endif
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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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#if TUNE_PROGRAM_BUILD
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#define FACTORS_PER_LIMB (GMP_NUMB_BITS / (LOG2C(FAC_DSC_THRESHOLD_LIMIT-1)+1))
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#else
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#define FACTORS_PER_LIMB (GMP_NUMB_BITS / (LOG2C(FAC_ODD_THRESHOLD)+1))
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#endif
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/* Computes n!, the factorial of n.
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WARNING: it assumes that n fits in a limb!
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*/
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void
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mpz_fac_ui (mpz_ptr x, unsigned long n)
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{
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static const mp_limb_t table[] = { ONE_LIMB_FACTORIAL_TABLE };
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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 if (BELOW_THRESHOLD (n, FAC_ODD_THRESHOLD))
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{
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mp_limb_t prod, max_prod;
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mp_size_t j;
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mp_ptr factors;
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TMP_SDECL;
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TMP_SMARK;
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factors = TMP_SALLOC_LIMBS (2 + (n - numberof (table)) / FACTORS_PER_LIMB);
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factors[0] = table[numberof (table)-1];
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j = 1;
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prod = n;
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#if TUNE_PROGRAM_BUILD
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max_prod = GMP_NUMB_MAX / FAC_DSC_THRESHOLD_LIMIT;
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#else
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max_prod = GMP_NUMB_MAX / (FAC_ODD_THRESHOLD | 1);
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#endif
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while (--n >= numberof (table))
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FACTOR_LIST_STORE (n, prod, max_prod, factors, j);
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factors[j++] = prod;
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mpz_prodlimbs (x, factors, j);
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TMP_SFREE;
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}
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else
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{
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mp_limb_t count;
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mpz_oddfac_1 (x, n, 0);
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if (n <= TABLE_LIMIT_2N_MINUS_POPC_2N)
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count = __gmp_fac2cnt_table[n / 2 - 1];
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else
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{
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popc_limb (count, n);
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count = n - count;
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}
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mpz_mul_2exp (x, x, count);
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}
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}
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#undef FACTORS_PER_LIMB
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#undef FACTOR_LIST_STORE
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