| Austin Schuh | dace2a6 | 2020-08-18 10:56:48 -0700 | [diff] [blame^] | 1 | /* mpz_2fac_ui(RESULT, N) -- Set RESULT to N!!. |
| 2 | |
| 3 | Contributed to the GNU project by Marco Bodrato. |
| 4 | |
| 5 | Copyright 2012, 2015, 2018 Free Software Foundation, Inc. |
| 6 | |
| 7 | This file is part of the GNU MP Library. |
| 8 | |
| 9 | The GNU MP Library is free software; you can redistribute it and/or modify |
| 10 | it under the terms of either: |
| 11 | |
| 12 | * the GNU Lesser General Public License as published by the Free |
| 13 | Software Foundation; either version 3 of the License, or (at your |
| 14 | option) any later version. |
| 15 | |
| 16 | or |
| 17 | |
| 18 | * the GNU General Public License as published by the Free Software |
| 19 | Foundation; either version 2 of the License, or (at your option) any |
| 20 | later version. |
| 21 | |
| 22 | or both in parallel, as here. |
| 23 | |
| 24 | The GNU MP Library is distributed in the hope that it will be useful, but |
| 25 | WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY |
| 26 | or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| 27 | for more details. |
| 28 | |
| 29 | You should have received copies of the GNU General Public License and the |
| 30 | GNU Lesser General Public License along with the GNU MP Library. If not, |
| 31 | see https://www.gnu.org/licenses/. */ |
| 32 | |
| 33 | #include "gmp-impl.h" |
| 34 | |
| 35 | #define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I) \ |
| 36 | do { \ |
| 37 | if ((PR) > (MAX_PR)) { \ |
| 38 | (VEC)[(I)++] = (PR); \ |
| 39 | (PR) = (P); \ |
| 40 | } else \ |
| 41 | (PR) *= (P); \ |
| 42 | } while (0) |
| 43 | |
| 44 | #define FAC_2DSC_THRESHOLD ((FAC_DSC_THRESHOLD << 1) | (FAC_DSC_THRESHOLD & 1)) |
| 45 | #define FACTORS_PER_LIMB (GMP_NUMB_BITS / (LOG2C(FAC_2DSC_THRESHOLD-1)+1)) |
| 46 | |
| 47 | /* Computes n!!, the 2-multi-factorial of n. (aka double-factorial or semi-factorial) |
| 48 | WARNING: it assumes that n fits in a limb! |
| 49 | */ |
| 50 | void |
| 51 | mpz_2fac_ui (mpz_ptr x, unsigned long n) |
| 52 | { |
| 53 | ASSERT (n <= GMP_NUMB_MAX); |
| 54 | |
| 55 | if ((n & 1) == 0) { /* n is even, n = 2k, (2k)!! = k! 2^k */ |
| 56 | mp_limb_t count; |
| 57 | |
| 58 | if ((n <= TABLE_LIMIT_2N_MINUS_POPC_2N) & (n != 0)) |
| 59 | count = __gmp_fac2cnt_table[n / 2 - 1]; |
| 60 | else |
| 61 | { |
| 62 | popc_limb (count, n); /* popc(n) == popc(k) */ |
| 63 | count = n - count; /* n - popc(n) == k + k - popc(k) */ |
| 64 | } |
| 65 | mpz_oddfac_1 (x, n >> 1, 0); |
| 66 | mpz_mul_2exp (x, x, count); |
| 67 | } else { /* n is odd */ |
| 68 | if (n <= ODD_DOUBLEFACTORIAL_TABLE_LIMIT) { |
| 69 | MPZ_NEWALLOC (x, 1)[0] = __gmp_odd2fac_table[n >> 1]; |
| 70 | SIZ (x) = 1; |
| 71 | } else if (BELOW_THRESHOLD (n, FAC_2DSC_THRESHOLD)) { /* odd basecase, */ |
| 72 | mp_limb_t *factors, prod, max_prod; |
| 73 | mp_size_t j; |
| 74 | TMP_SDECL; |
| 75 | |
| 76 | /* FIXME: we might alloc a fixed amount 1+FAC_2DSC_THRESHOLD/FACTORS_PER_LIMB */ |
| 77 | TMP_SMARK; |
| 78 | factors = TMP_SALLOC_LIMBS (1 + n / (2 * FACTORS_PER_LIMB)); |
| 79 | |
| 80 | factors[0] = ODD_DOUBLEFACTORIAL_TABLE_MAX; |
| 81 | j = 1; |
| 82 | prod = n; |
| 83 | |
| 84 | max_prod = GMP_NUMB_MAX / FAC_2DSC_THRESHOLD; |
| 85 | while ((n -= 2) > ODD_DOUBLEFACTORIAL_TABLE_LIMIT) |
| 86 | FACTOR_LIST_STORE (n, prod, max_prod, factors, j); |
| 87 | |
| 88 | factors[j++] = prod; |
| 89 | mpz_prodlimbs (x, factors, j); |
| 90 | |
| 91 | TMP_SFREE; |
| 92 | } else { /* for the asymptotically fast odd case, let oddfac do the job. */ |
| 93 | mpz_oddfac_1 (x, n, 1); |
| 94 | } |
| 95 | } |
| 96 | } |
| 97 | |
| 98 | #undef FACTORS_PER_LIMB |
| 99 | #undef FACTOR_LIST_STORE |
| 100 | #undef FAC_2DSC_THRESHOLD |