2014-02-28 08:00:53 -05:00
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/* mpz_2fac_ui(RESULT, N) -- Set RESULT to 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 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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2014-02-28 08:19:19 -05:00
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#include "mpir.h"
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2014-02-28 08:00:53 -05:00
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#include "gmp-impl.h"
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#if GMP_LIMB_BITS == 64
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#define TABLE_LIMIT_2N_MINUS_POPC_2N 81
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#define ODD_DOUBLEFACTORIAL_TABLE_MAX CNST_LIMB(0x57e22099c030d941)
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#define ODD_DOUBLEFACTORIAL_TABLE_LIMIT 33
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#else
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#define TABLE_LIMIT_2N_MINUS_POPC_2N 49
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#define ODD_DOUBLEFACTORIAL_TABLE_MAX CNST_LIMB(0x27065f73)
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#define ODD_DOUBLEFACTORIAL_TABLE_LIMIT (19)
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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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#define FAC_2DSC_THRESHOLD ((FAC_DSC_THRESHOLD << 1) | (FAC_DSC_THRESHOLD & 1))
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#define FACTORS_PER_LIMB (GMP_NUMB_BITS / (LOG2C(FAC_2DSC_THRESHOLD-1)+1))
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/* Computes n!!, the 2-multi-factorial of n. (aka double-factorial or semi-factorial)
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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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2014-02-28 14:33:27 -05:00
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mpz_2fac_ui (mpz_ptr x, mpir_ui n)
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2014-02-28 08:00:53 -05:00
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{
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ASSERT (n <= GMP_NUMB_MAX);
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if ((n & 1) == 0) { /* n is even, n = 2k, (2k)!! = k! 2^k */
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mp_limb_t count;
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if ((n <= TABLE_LIMIT_2N_MINUS_POPC_2N) & (n != 0))
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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); /* popc(n) == popc(k) */
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count = n - count; /* n - popc(n) == k + k - popc(k) */
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}
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mpz_oddfac_1 (x, n >> 1, 0);
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mpz_mul_2exp (x, x, count);
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} else { /* n is odd */
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if (n <= ODD_DOUBLEFACTORIAL_TABLE_LIMIT) {
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PTR (x)[0] = __gmp_odd2fac_table[n >> 1];
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SIZ (x) = 1;
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} else if (BELOW_THRESHOLD (n, FAC_2DSC_THRESHOLD)) { /* odd basecase, */
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mp_limb_t *factors, prod, max_prod, j;
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TMP_SDECL;
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/* FIXME: we might alloc a fixed ammount 1+FAC_2DSC_THRESHOLD/FACTORS_PER_LIMB */
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TMP_SMARK;
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factors = TMP_SALLOC_LIMBS (1 + n / (2 * FACTORS_PER_LIMB));
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factors[0] = ODD_DOUBLEFACTORIAL_TABLE_MAX;
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j = 1;
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prod = n;
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max_prod = GMP_NUMB_MAX / FAC_2DSC_THRESHOLD;
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while ((n -= 2) > ODD_DOUBLEFACTORIAL_TABLE_LIMIT)
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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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} else { /* for the asymptotically fast odd case, let oddfac do the job. */
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mpz_oddfac_1 (x, n, 1);
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}
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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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#undef FAC_2DSC_THRESHOLD
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