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123 lines
3.1 KiB
C
123 lines
3.1 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, 1993-1995, 2000-2003, 2011, 2012, 2015, 2021 Free
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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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#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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MPZ_NEWALLOC (x, 1)[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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mp_limb_t fac, diff = n - numberof (table);
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TMP_SDECL;
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TMP_SMARK;
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factors = TMP_SALLOC_LIMBS (2 + diff / FACTORS_PER_LIMB);
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factors[0] = table[numberof (table)-1];
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j = 1;
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if ((diff & 1) == 0)
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{
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prod = n;
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/* if (diff != 0) */
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fac = --n * numberof (table);
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}
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else
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{
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prod = n * numberof (table);
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fac = prod + --diff;
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}
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#if TUNE_PROGRAM_BUILD
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max_prod = GMP_NUMB_MAX / (FAC_DSC_THRESHOLD_LIMIT * FAC_DSC_THRESHOLD_LIMIT);
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#else
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max_prod = GMP_NUMB_MAX /
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(((FAC_ODD_THRESHOLD + numberof (table) + 1) / 2) *
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((FAC_ODD_THRESHOLD + numberof (table)) / 2));
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#endif
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for (;diff != 0; fac += (diff -= 2))
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FACTOR_LIST_STORE (fac, 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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