github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpz/bin_ui.c (about)

     1  /* mpz_bin_ui - compute n over k.
     2  
     3  Copyright 1998-2002, 2012, 2013 Free Software Foundation, Inc.
     4  
     5  This file is part of the GNU MP Library.
     6  
     7  The GNU MP Library is free software; you can redistribute it and/or modify
     8  it under the terms of either:
     9  
    10    * the GNU Lesser General Public License as published by the Free
    11      Software Foundation; either version 3 of the License, or (at your
    12      option) any later version.
    13  
    14  or
    15  
    16    * the GNU General Public License as published by the Free Software
    17      Foundation; either version 2 of the License, or (at your option) any
    18      later version.
    19  
    20  or both in parallel, as here.
    21  
    22  The GNU MP Library is distributed in the hope that it will be useful, but
    23  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
    24  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    25  for more details.
    26  
    27  You should have received copies of the GNU General Public License and the
    28  GNU Lesser General Public License along with the GNU MP Library.  If not,
    29  see https://www.gnu.org/licenses/.  */
    30  
    31  #include "gmp.h"
    32  #include "gmp-impl.h"
    33  #include "longlong.h"
    34  
    35  
    36  /* This is a poor implementation.  Look at bin_uiui.c for improvement ideas.
    37     In fact consider calling mpz_bin_uiui() when the arguments fit, leaving
    38     the code here only for big n.
    39  
    40     The identity bin(n,k) = (-1)^k * bin(-n+k-1,k) can be found in Knuth vol
    41     1 section 1.2.6 part G. */
    42  
    43  
    44  #define DIVIDE()                                                              \
    45    do {                                                                        \
    46      ASSERT (SIZ(r) > 0);                                                      \
    47      MPN_DIVREM_OR_DIVEXACT_1 (PTR(r), PTR(r), (mp_size_t) SIZ(r), kacc);      \
    48      SIZ(r) -= (PTR(r)[SIZ(r)-1] == 0);                                        \
    49    } while (0)
    50  
    51  void
    52  mpz_bin_ui (mpz_ptr r, mpz_srcptr n, unsigned long int k)
    53  {
    54    mpz_t      ni;
    55    mp_limb_t  i;
    56    mpz_t      nacc;
    57    mp_limb_t  kacc;
    58    mp_size_t  negate;
    59  
    60    if (SIZ (n) < 0)
    61      {
    62        /* bin(n,k) = (-1)^k * bin(-n+k-1,k), and set ni = -n+k-1 - k = -n-1 */
    63        mpz_init (ni);
    64        mpz_add_ui (ni, n, 1L);
    65        mpz_neg (ni, ni);
    66        negate = (k & 1);   /* (-1)^k */
    67      }
    68    else
    69      {
    70        /* bin(n,k) == 0 if k>n
    71  	 (no test for this under the n<0 case, since -n+k-1 >= k there) */
    72        if (mpz_cmp_ui (n, k) < 0)
    73  	{
    74  	  SIZ (r) = 0;
    75  	  return;
    76  	}
    77  
    78        /* set ni = n-k */
    79        mpz_init (ni);
    80        mpz_sub_ui (ni, n, k);
    81        negate = 0;
    82      }
    83  
    84    /* Now wanting bin(ni+k,k), with ni positive, and "negate" is the sign (0
    85       for positive, 1 for negative). */
    86    SIZ (r) = 1; PTR (r)[0] = 1;
    87  
    88    /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller.  In this case it's
    89       whether ni+k-k < k meaning ni<k, and if so change to denominator ni+k-k
    90       = ni, and new ni of ni+k-ni = k.  */
    91    if (mpz_cmp_ui (ni, k) < 0)
    92      {
    93        unsigned long  tmp;
    94        tmp = k;
    95        k = mpz_get_ui (ni);
    96        mpz_set_ui (ni, tmp);
    97      }
    98  
    99    kacc = 1;
   100    mpz_init_set_ui (nacc, 1L);
   101  
   102    for (i = 1; i <= k; i++)
   103      {
   104        mp_limb_t k1, k0;
   105  
   106  #if 0
   107        mp_limb_t nacclow;
   108        int c;
   109  
   110        nacclow = PTR(nacc)[0];
   111        for (c = 0; (((kacc | nacclow) & 1) == 0); c++)
   112  	{
   113  	  kacc >>= 1;
   114  	  nacclow >>= 1;
   115  	}
   116        mpz_div_2exp (nacc, nacc, c);
   117  #endif
   118  
   119        mpz_add_ui (ni, ni, 1L);
   120        mpz_mul (nacc, nacc, ni);
   121        umul_ppmm (k1, k0, kacc, i << GMP_NAIL_BITS);
   122        if (k1 != 0)
   123  	{
   124  	  /* Accumulator overflow.  Perform bignum step.  */
   125  	  mpz_mul (r, r, nacc);
   126  	  SIZ (nacc) = 1; PTR (nacc)[0] = 1;
   127  	  DIVIDE ();
   128  	  kacc = i;
   129  	}
   130        else
   131  	{
   132  	  /* Save new products in accumulators to keep accumulating.  */
   133  	  kacc = k0 >> GMP_NAIL_BITS;
   134  	}
   135      }
   136  
   137    mpz_mul (r, r, nacc);
   138    DIVIDE ();
   139    SIZ(r) = (SIZ(r) ^ -negate) + negate;
   140  
   141    mpz_clear (nacc);
   142    mpz_clear (ni);
   143  }