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, 2015, 2021 Free
       6  Software Foundation, Inc.
       7  
       8  This file is part of the GNU MP Library.
       9  
      10  The GNU MP Library is free software; you can redistribute it and/or modify
      11  it under the terms of either:
      12  
      13    * the GNU Lesser General Public License as published by the Free
      14      Software Foundation; either version 3 of the License, or (at your
      15      option) any later version.
      16  
      17  or
      18  
      19    * the GNU General Public License as published by the Free Software
      20      Foundation; either version 2 of the License, or (at your option) any
      21      later version.
      22  
      23  or both in parallel, as here.
      24  
      25  The GNU MP Library is distributed in the hope that it will be useful, but
      26  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
      27  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
      28  for more details.
      29  
      30  You should have received copies of the GNU General Public License and the
      31  GNU Lesser General Public License along with the GNU MP Library.  If not,
      32  see https://www.gnu.org/licenses/.  */
      33  
      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        MPZ_NEWALLOC (x, 1)[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        mp_limb_t fac, diff = n - numberof (table);
      72        TMP_SDECL;
      73  
      74        TMP_SMARK;
      75        factors = TMP_SALLOC_LIMBS (2 + diff / FACTORS_PER_LIMB);
      76  
      77        factors[0] = table[numberof (table)-1];
      78        j = 1;
      79        if ((diff & 1) == 0)
      80  	{
      81  	  prod = n;
      82  	  /* if (diff != 0) */
      83  	    fac = --n * numberof (table);
      84  	}
      85        else
      86  	{
      87  	  prod = n * numberof (table);
      88  	  fac = prod + --diff;
      89  	}
      90  
      91  #if TUNE_PROGRAM_BUILD
      92        max_prod = GMP_NUMB_MAX / (FAC_DSC_THRESHOLD_LIMIT * FAC_DSC_THRESHOLD_LIMIT);
      93  #else
      94        max_prod = GMP_NUMB_MAX /
      95  	(((FAC_ODD_THRESHOLD + numberof (table) + 1) / 2) *
      96  	 ((FAC_ODD_THRESHOLD + numberof (table)) / 2));
      97  #endif
      98        for (;diff != 0; fac += (diff -= 2))
      99  	FACTOR_LIST_STORE (fac, prod, max_prod, factors, j);
     100  
     101        factors[j++] = prod;
     102        mpz_prodlimbs (x, factors, j);
     103  
     104        TMP_SFREE;
     105      }
     106    else
     107      {
     108        mp_limb_t count;
     109        mpz_oddfac_1 (x, n, 0);
     110        if (n <= TABLE_LIMIT_2N_MINUS_POPC_2N)
     111  	count = __gmp_fac2cnt_table[n / 2 - 1];
     112        else
     113  	{
     114  	  popc_limb (count, n);
     115  	  count = n - count;
     116  	}
     117        mpz_mul_2exp (x, x, count);
     118      }
     119  }
     120  
     121  #undef FACTORS_PER_LIMB
     122  #undef FACTOR_LIST_STORE