stdlib/mul.c

   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 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
  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 }