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Annotation of OpenXM_contrib/gmp/mpz/bin_uiui.c, Revision 1.1

1.1     ! maekawa     1: /* mpz_bin_uiui - compute n over k.
        !             2:
        !             3: Copyright (C) 1998, 1999, 2000 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 the GNU Lesser General Public License as published by
        !             9: the Free Software Foundation; either version 2.1 of the License, or (at your
        !            10: option) any later version.
        !            11:
        !            12: The GNU MP Library is distributed in the hope that it will be useful, but
        !            13: WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
        !            14: or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
        !            15: License for more details.
        !            16:
        !            17: You should have received a copy of the GNU Lesser General Public License
        !            18: along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
        !            19: the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
        !            20: MA 02111-1307, USA. */
        !            21:
        !            22: #include "gmp.h"
        !            23: #include "gmp-impl.h"
        !            24: #include "longlong.h"
        !            25:
        !            26:
        !            27: /* Avoid reallocs by rounding up any new size */
        !            28: #define ROUNDUP_MASK  15
        !            29:
        !            30: /* Enhancement: use mpn_divexact_1 when it exists */
        !            31: #define MULDIV()                                                \
        !            32:   MPZ_REALLOC (r, (SIZ(r)+1)|ROUNDUP_MASK);                     \
        !            33:   PTR(r)[SIZ(r)] = mpn_mul_1 (PTR(r), PTR(r), SIZ(r), nacc);    \
        !            34:   ASSERT_NOCARRY (mpn_divrem_1 (PTR(r), (mp_size_t) 0,          \
        !            35:                                 PTR(r), SIZ(r)+1, kacc));       \
        !            36:   SIZ(r) += (PTR(r)[SIZ(r)] != 0);
        !            37:
        !            38: void
        !            39: #if __STDC__
        !            40: mpz_bin_uiui (mpz_ptr r, unsigned long int n, unsigned long int k)
        !            41: #else
        !            42: mpz_bin_uiui (r, n, k)
        !            43:      mpz_ptr r;
        !            44:      unsigned long int n;
        !            45:      unsigned long int k;
        !            46: #endif
        !            47: {
        !            48:   unsigned long int  i, j;
        !            49:   mp_limb_t          nacc, kacc;
        !            50:   unsigned long int  cnt;
        !            51:
        !            52:   /* bin(n,k) = 0 if k>n. */
        !            53:   if (n < k)
        !            54:     {
        !            55:       mpz_set_ui (r, 0);
        !            56:       return;
        !            57:     }
        !            58:
        !            59:   /* Rewrite bin(n,k) as bin(n,n-k) if that is smaller. */
        !            60:   k = MIN (k, n-k);
        !            61:
        !            62:   /* bin(n,0) = 1 */
        !            63:   if (k == 0)
        !            64:     {
        !            65:       mpz_set_ui (r, 1);
        !            66:       return;
        !            67:     }
        !            68:
        !            69:   j = n - k + 1;
        !            70:   mpz_set_ui (r, j);
        !            71:
        !            72:   /* Initialize accumulators.  */
        !            73:   nacc = 1;
        !            74:   kacc = 1;
        !            75:
        !            76:   cnt = 0;
        !            77:   for (i = 2; i <= k; i++)
        !            78:     {
        !            79:       mp_limb_t n1, n0, k1, k0;
        !            80:
        !            81:       j++;
        !            82: #if 0
        !            83:       /* Remove common multiples of 2.  This will allow us to accumulate
        !            84:          more in nacc and kacc before we need a bignum step.  It would make
        !            85:          sense to cancel factors of 3, 5, etc too, but this would be best
        !            86:          handled by sieving out factors.  Alternatively, we could perform a
        !            87:          gcd of the accumulators just as they have overflown, and keep
        !            88:          accumulating until the gcd doesn't remove a significant factor.  */
        !            89:       while (((nacc | kacc) & 1) == 0)
        !            90:         {
        !            91:           nacc >>= 1;
        !            92:           kacc >>= 1;
        !            93:         }
        !            94: #else
        !            95:       cnt = ((nacc | kacc) & 1) ^ 1;
        !            96:       nacc >>= cnt;
        !            97:       kacc >>= cnt;
        !            98: #endif
        !            99:       /* Accumulate next multiples.  */
        !           100:       umul_ppmm (n1, n0, nacc, j);
        !           101:       umul_ppmm (k1, k0, kacc, i);
        !           102:       if (n1 != 0)
        !           103:         {
        !           104:           /* Accumulator overflow.  Perform bignum step.  */
        !           105:           MULDIV ();
        !           106:           nacc = j;
        !           107:           kacc = i;
        !           108:         }
        !           109:       else
        !           110:         {
        !           111:           if (k1 != 0) abort ();
        !           112:           /* Save new products in accumulators to keep accumulating.  */
        !           113:           nacc = n0;
        !           114:           kacc = k0;
        !           115:         }
        !           116:     }
        !           117:
        !           118:   /* Take care of whatever is left in accumulators.  */
        !           119:   MULDIV ();
        !           120: }