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

   1 /* mpz_fac_ui(RESULT, N) -- Set RESULT to N!.
   2
   3 Contributed to the GNU project by Marco Bodrato.
   4
   5 Copyright 1991, 1993-1995, 2000-2003, 2011, 2012 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 #define FACTOR_LIST_STORE(P, PR, MAX_PR, VEC, I)                \
  37   do {                                                          \
  38     if ((PR) > (MAX_PR)) {                                      \
  39       (VEC)[(I)++] = (PR);                                      \
  40       (PR) = (P);                                               \
  41     } else                                                      \
  42       (PR) *= (P);                                              \
  43   } while (0)
  44
  45 #if TUNE_PROGRAM_BUILD
  46 #define FACTORS_PER_LIMB (GMP_NUMB_BITS / (LOG2C(FAC_DSC_THRESHOLD_LIMIT-1)+1))
  47 #else
  48 #define FACTORS_PER_LIMB (GMP_NUMB_BITS / (LOG2C(FAC_ODD_THRESHOLD)+1))
  49 #endif
  50
  51 /* Computes n!, the factorial of n.
  52    WARNING: it assumes that n fits in a limb!
  53  */
  54 void
  55 mpz_fac_ui (mpz_ptr x, unsigned long n)
  56 {
  57   static const mp_limb_t table[] = { ONE_LIMB_FACTORIAL_TABLE };
  58
  59   ASSERT (n <= GMP_NUMB_MAX);
  60
  61   if (n < numberof (table))
  62     {
  63       PTR (x)[0] = table[n];
  64       SIZ (x) = 1;
  65     }
  66   else if (BELOW_THRESHOLD (n, FAC_ODD_THRESHOLD))
  67     {
  68       mp_limb_t prod, max_prod;
  69       mp_size_t j;
  70       mp_ptr    factors;
  71       TMP_SDECL;
  72
  73       TMP_SMARK;
  74       factors = TMP_SALLOC_LIMBS (2 + (n - numberof (table)) / FACTORS_PER_LIMB);
  75
  76       factors[0] = table[numberof (table)-1];
  77       j = 1;
  78       prod = n;
  79 #if TUNE_PROGRAM_BUILD
  80       max_prod = GMP_NUMB_MAX / FAC_DSC_THRESHOLD_LIMIT;
  81 #else
  82       max_prod = GMP_NUMB_MAX / (FAC_ODD_THRESHOLD | 1);
  83 #endif
  84       while (--n >= numberof (table))
  85         FACTOR_LIST_STORE (n, prod, max_prod, factors, j);
  86
  87       factors[j++] = prod;
  88       mpz_prodlimbs (x, factors, j);
  89
  90       TMP_SFREE;
  91     }
  92   else
  93     {
  94       mp_limb_t count;
  95       mpz_oddfac_1 (x, n, 0);
  96       if (n <= TABLE_LIMIT_2N_MINUS_POPC_2N)
  97         count = __gmp_fac2cnt_table[n / 2 - 1];
  98       else
  99         {
 100           popc_limb (count, n);
 101           count = n - count;
 102         }
 103       mpz_mul_2exp (x, x, count);
 104     }
 105 }
 106
 107 #undef FACTORS_PER_LIMB
 108 #undef FACTOR_LIST_STORE