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Annotation of OpenXM_contrib/gmp/mpn/generic/mul.c, Revision 1.1.1.1

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: }