source/libs/gmp/gmp-src/mpz/mfac_uiui.c

   1 /* mpz_mfac_uiui(RESULT, N, M) -- Set RESULT to N!^(M) = N(N-M)(N-2M)...
   2
   3 Contributed to the GNU project by Marco Bodrato.
   4
   5 Copyright 2012, 2013 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.h"
  34 #include "gmp-impl.h"
  35
  36 /*************************************************************/
  37 /* Section macros: common macros, for swing/fac/bin (&sieve) */
  38 /*************************************************************/
  39
  40 #define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I)                \
  41   do {                                                          \
  42     if ((PR) > (MAX_PR)) {                                      \
  43       (VEC)[(I)++] = (PR);                                      \
  44       (PR) = (P);                                               \
  45     } else                                                      \
  46       (PR) *= (P);                                              \
  47   } while (0)
  48
  49 /*********************************************************/
  50 /* Section oder factorials:                              */
  51 /*********************************************************/
  52
  53 /* mpz_mfac_uiui (x, n, m) computes x = n!^(m) = n*(n-m)*(n-2m)*...   */
  54
  55 void
  56 mpz_mfac_uiui (mpz_ptr x, unsigned long n, unsigned long m)
  57 {
  58   ASSERT (n <= GMP_NUMB_MAX);
  59   ASSERT (m != 0);
  60
  61   if ((n < 3) | (n - 3 < m - 1)) { /* (n < 3 || n - 1 <= m || m == 0) */
  62     PTR (x)[0] = n + (n == 0);
  63     SIZ (x) = 1;
  64   } else { /* m < n - 1 < GMP_NUMB_MAX */
  65     mp_limb_t g, sn;
  66     mpz_t     t;
  67
  68     sn = n;
  69     g = mpn_gcd_1 (&sn, 1, m);
  70     if (g > 1) { n/=g; m/=g; }
  71
  72     if (m <= 2) { /* fac or 2fac */
  73       if (m == 1) {
  74         if (g > 2) {
  75           mpz_init (t);
  76           mpz_fac_ui (t, n);
  77           sn = n;
  78         } else {
  79           if (g == 2)
  80             mpz_2fac_ui (x, n << 1);
  81           else
  82             mpz_fac_ui (x, n);
  83           return;
  84         }
  85       } else { /* m == 2 */
  86         if (g > 1) {
  87           mpz_init (t);
  88           mpz_2fac_ui (t, n);
  89           sn = n / 2 + 1;
  90         } else {
  91           mpz_2fac_ui (x, n);
  92           return;
  93         }
  94       }
  95     } else { /* m >= 3, gcd(n,m) = 1 */
  96       mp_limb_t *factors;
  97       mp_limb_t prod, max_prod, j;
  98       TMP_DECL;
  99
 100       sn = n / m + 1;
 101
 102       j = 0;
 103       prod = n;
 104       n -= m;
 105       max_prod = GMP_NUMB_MAX / n;
 106
 107       if (g > 1)
 108         factors = MPZ_NEWALLOC (x, sn / log_n_max (n) + 2);
 109       else {
 110         TMP_MARK;
 111         factors = TMP_ALLOC_LIMBS (sn / log_n_max (n) + 2);
 112       }
 113
 114       for (; n > m; n -= m)
 115         FACTOR_LIST_STORE (n, prod, max_prod, factors, j);
 116
 117       factors[j++] = n;
 118       factors[j++] = prod;
 119
 120       if (g > 1) {
 121         mpz_init (t);
 122         mpz_prodlimbs (t, factors, j);
 123       } else {
 124         mpz_prodlimbs (x, factors, j);
 125         TMP_FREE;
 126         return;
 127       }
 128     }
 129
 130     {
 131       mpz_t p;
 132
 133       mpz_init (p);
 134       mpz_ui_pow_ui (p, g, sn); /* g^sn */
 135       mpz_mul (x, p, t);
 136       mpz_clear (p);
 137       mpz_clear (t);
 138     }
 139   }
 140 }