125 lines
3.0 KiB
C
125 lines
3.0 KiB
C
/* mpz_mfac_uiui(RESULT, N, M) -- Set RESULT to N!^(M) = N(N-M)(N-2M)...
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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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#include "mpir.h"
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#include "gmp-impl.h"
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/*************************************************************/
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/* Section macros: common macros, for swing/fac/bin (&sieve) */
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/*************************************************************/
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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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/*********************************************************/
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/* Section oder factorials: */
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/*********************************************************/
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/* mpz_mfac_uiui (x, n, m) computes x = n!^(m) = n*(n-m)*(n-2m)*... */
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void
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mpz_mfac_uiui (mpz_ptr x, mpir_ui n, mpir_ui m)
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{
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ASSERT (n <= GMP_NUMB_MAX);
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ASSERT (m != 0);
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if (n < 3 || n - 3 < m - 1) { /* (n < 3 || n - 1 <= m || m == 0) */
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PTR (x)[0] = n + (n == 0);
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SIZ (x) = 1;
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} else { /* m < n - 1 < GMP_NUMB_MAX */
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mp_limb_t g, sn;
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mpz_t t;
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sn = n;
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g = mpn_gcd_1 (&sn, 1, m);
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if (g != 1) { n/=g; m/=g; }
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if (m <= 2) { /* fac or 2fac */
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if (m == 1) {
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if (g > 2) {
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mpz_init (t);
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mpz_fac_ui (t, n);
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sn = n;
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} else {
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if (g == 2)
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mpz_2fac_ui (x, n << 1);
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else
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mpz_fac_ui (x, n);
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return;
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}
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} else { /* m == 2 */
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if (g != 1) {
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mpz_init (t);
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mpz_2fac_ui (t, n);
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sn = n / 2 + 1;
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} else {
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mpz_2fac_ui (x, n);
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return;
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}
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}
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} else { /* m >= 3, gcd(n,m) = 1 */
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mp_limb_t *factors;
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mp_limb_t prod, max_prod, j;
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TMP_DECL;
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sn = n / m + 1;
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j = 0;
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prod = n;
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n -= m;
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max_prod = GMP_NUMB_MAX / n;
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TMP_MARK;
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factors = TMP_ALLOC_LIMBS (sn / log_n_max (n) + 2);
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for (; n > m; n -= m)
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FACTOR_LIST_STORE (n, prod, max_prod, factors, j);
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factors[j++] = n;
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factors[j++] = prod;
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if (g > 1) {
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mpz_init (t);
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mpz_prodlimbs (t, factors, j);
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} else
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mpz_prodlimbs (x, factors, j);
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TMP_FREE;
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}
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if (g > 1) {
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mpz_t p;
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mpz_init (p);
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mpz_ui_pow_ui (p, g, sn); /* g^sn */
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mpz_mul (x, p, t);
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mpz_clear (p);
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mpz_clear (t);
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}
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}
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}
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