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Annotation of OpenXM_contrib/gmp/mpn/generic/mul.c, Revision 1.1

1.1     ! maekawa     1: /* mpn_mul -- Multiply two natural numbers.
        !             2:
        !             3: Copyright (C) 1991, 1993, 1994, 1996 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 Library General Public License as published by
        !             9: the Free Software Foundation; either version 2 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 Library General Public
        !            15: License for more details.
        !            16:
        !            17: You should have received a copy of the GNU Library 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:
        !            25: /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
        !            26:    and v (pointed to by VP, with VSIZE limbs), and store the result at
        !            27:    PRODP.  USIZE + VSIZE limbs are always stored, but if the input
        !            28:    operands are normalized.  Return the most significant limb of the
        !            29:    result.
        !            30:
        !            31:    NOTE: The space pointed to by PRODP is overwritten before finished
        !            32:    with U and V, so overlap is an error.
        !            33:
        !            34:    Argument constraints:
        !            35:    1. USIZE >= VSIZE.
        !            36:    2. PRODP != UP and PRODP != VP, i.e. the destination
        !            37:       must be distinct from the multiplier and the multiplicand.  */
        !            38:
        !            39: /* If KARATSUBA_THRESHOLD is not already defined, define it to a
        !            40:    value which is good on most machines.  */
        !            41: #ifndef KARATSUBA_THRESHOLD
        !            42: #define KARATSUBA_THRESHOLD 32
        !            43: #endif
        !            44:
        !            45: mp_limb_t
        !            46: #if __STDC__
        !            47: mpn_mul (mp_ptr prodp,
        !            48:         mp_srcptr up, mp_size_t usize,
        !            49:         mp_srcptr vp, mp_size_t vsize)
        !            50: #else
        !            51: mpn_mul (prodp, up, usize, vp, vsize)
        !            52:      mp_ptr prodp;
        !            53:      mp_srcptr up;
        !            54:      mp_size_t usize;
        !            55:      mp_srcptr vp;
        !            56:      mp_size_t vsize;
        !            57: #endif
        !            58: {
        !            59:   mp_ptr prod_endp = prodp + usize + vsize - 1;
        !            60:   mp_limb_t cy;
        !            61:   mp_ptr tspace;
        !            62:   TMP_DECL (marker);
        !            63:
        !            64:   if (vsize < KARATSUBA_THRESHOLD)
        !            65:     {
        !            66:       /* Handle simple cases with traditional multiplication.
        !            67:
        !            68:         This is the most critical code of the entire function.  All
        !            69:         multiplies rely on this, both small and huge.  Small ones arrive
        !            70:         here immediately.  Huge ones arrive here as this is the base case
        !            71:         for Karatsuba's recursive algorithm below.  */
        !            72:       mp_size_t i;
        !            73:       mp_limb_t cy_limb;
        !            74:       mp_limb_t v_limb;
        !            75:
        !            76:       if (vsize == 0)
        !            77:        return 0;
        !            78:
        !            79:       /* Multiply by the first limb in V separately, as the result can be
        !            80:         stored (not added) to PROD.  We also avoid a loop for zeroing.  */
        !            81:       v_limb = vp[0];
        !            82:       if (v_limb <= 1)
        !            83:        {
        !            84:          if (v_limb == 1)
        !            85:            MPN_COPY (prodp, up, usize);
        !            86:          else
        !            87:            MPN_ZERO (prodp, usize);
        !            88:          cy_limb = 0;
        !            89:        }
        !            90:       else
        !            91:        cy_limb = mpn_mul_1 (prodp, up, usize, v_limb);
        !            92:
        !            93:       prodp[usize] = cy_limb;
        !            94:       prodp++;
        !            95:
        !            96:       /* For each iteration in the outer loop, multiply one limb from
        !            97:         U with one limb from V, and add it to PROD.  */
        !            98:       for (i = 1; i < vsize; i++)
        !            99:        {
        !           100:          v_limb = vp[i];
        !           101:          if (v_limb <= 1)
        !           102:            {
        !           103:              cy_limb = 0;
        !           104:              if (v_limb == 1)
        !           105:                cy_limb = mpn_add_n (prodp, prodp, up, usize);
        !           106:            }
        !           107:          else
        !           108:            cy_limb = mpn_addmul_1 (prodp, up, usize, v_limb);
        !           109:
        !           110:          prodp[usize] = cy_limb;
        !           111:          prodp++;
        !           112:        }
        !           113:       return cy_limb;
        !           114:     }
        !           115:
        !           116:   TMP_MARK (marker);
        !           117:
        !           118:   tspace = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
        !           119:   MPN_MUL_N_RECURSE (prodp, up, vp, vsize, tspace);
        !           120:
        !           121:   prodp += vsize;
        !           122:   up += vsize;
        !           123:   usize -= vsize;
        !           124:   if (usize >= vsize)
        !           125:     {
        !           126:       mp_ptr tp = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
        !           127:       do
        !           128:        {
        !           129:          MPN_MUL_N_RECURSE (tp, up, vp, vsize, tspace);
        !           130:          cy = mpn_add_n (prodp, prodp, tp, vsize);
        !           131:          mpn_add_1 (prodp + vsize, tp + vsize, vsize, cy);
        !           132:          prodp += vsize;
        !           133:          up += vsize;
        !           134:          usize -= vsize;
        !           135:        }
        !           136:       while (usize >= vsize);
        !           137:     }
        !           138:
        !           139:   /* True: usize < vsize.  */
        !           140:
        !           141:   /* Make life simple: Recurse.  */
        !           142:
        !           143:   if (usize != 0)
        !           144:     {
        !           145:       mpn_mul (tspace, vp, vsize, up, usize);
        !           146:       cy = mpn_add_n (prodp, prodp, tspace, vsize);
        !           147:       mpn_add_1 (prodp + vsize, tspace + vsize, usize, cy);
        !           148:     }
        !           149:
        !           150:   TMP_FREE (marker);
        !           151:   return *prod_endp;
        !           152: }