stdlib/mul.c

   1 /* mpn_mul -- Multiply two natural numbers.
   2
   3 Copyright (C) 1991-2013 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 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, see
  19 <http://www.gnu.org/licenses/>.  */
  20
  21 #include <gmp.h>
  22 #include "gmp-impl.h"
  23
  24 /* Multiply the natural numbers u (pointed to by UP, with USIZE limbs)
  25    and v (pointed to by VP, with VSIZE limbs), and store the result at
  26    PRODP.  USIZE + VSIZE limbs are always stored, but if the input
  27    operands are normalized.  Return the most significant limb of the
  28    result.
  29
  30    NOTE: The space pointed to by PRODP is overwritten before finished
  31    with U and V, so overlap is an error.
  32
  33    Argument constraints:
  34    1. USIZE >= VSIZE.
  35    2. PRODP != UP and PRODP != VP, i.e. the destination
  36       must be distinct from the multiplier and the multiplicand.  */
  37
  38 /* If KARATSUBA_THRESHOLD is not already defined, define it to a
  39    value which is good on most machines.  */
  40 #ifndef KARATSUBA_THRESHOLD
  41 #define KARATSUBA_THRESHOLD 32
  42 #endif
  43
  44 mp_limb_t
  45 #if __STDC__
  46 mpn_mul (mp_ptr prodp,
  47          mp_srcptr up, mp_size_t usize,
  48          mp_srcptr vp, mp_size_t vsize)
  49 #else
  50 mpn_mul (prodp, up, usize, vp, vsize)
  51      mp_ptr prodp;
  52      mp_srcptr up;
  53      mp_size_t usize;
  54      mp_srcptr vp;
  55      mp_size_t vsize;
  56 #endif
  57 {
  58   mp_ptr prod_endp = prodp + usize + vsize - 1;
  59   mp_limb_t cy;
  60   mp_ptr tspace;
  61   TMP_DECL (marker);
  62
  63   if (vsize < KARATSUBA_THRESHOLD)
  64     {
  65       /* Handle simple cases with traditional multiplication.
  66
  67          This is the most critical code of the entire function.  All
  68          multiplies rely on this, both small and huge.  Small ones arrive
  69          here immediately.  Huge ones arrive here as this is the base case
  70          for Karatsuba's recursive algorithm below.  */
  71       mp_size_t i;
  72       mp_limb_t cy_limb;
  73       mp_limb_t v_limb;
  74
  75       if (vsize == 0)
  76         return 0;
  77
  78       /* Multiply by the first limb in V separately, as the result can be
  79          stored (not added) to PROD.  We also avoid a loop for zeroing.  */
  80       v_limb = vp[0];
  81       if (v_limb <= 1)
  82         {
  83           if (v_limb == 1)
  84             MPN_COPY (prodp, up, usize);
  85           else
  86             MPN_ZERO (prodp, usize);
  87           cy_limb = 0;
  88         }
  89       else
  90         cy_limb = mpn_mul_1 (prodp, up, usize, v_limb);
  91
  92       prodp[usize] = cy_limb;
  93       prodp++;
  94
  95       /* For each iteration in the outer loop, multiply one limb from
  96          U with one limb from V, and add it to PROD.  */
  97       for (i = 1; i < vsize; i++)
  98         {
  99           v_limb = vp[i];
 100           if (v_limb <= 1)
 101             {
 102               cy_limb = 0;
 103               if (v_limb == 1)
 104                 cy_limb = mpn_add_n (prodp, prodp, up, usize);
 105             }
 106           else
 107             cy_limb = mpn_addmul_1 (prodp, up, usize, v_limb);
 108
 109           prodp[usize] = cy_limb;
 110           prodp++;
 111         }
 112       return cy_limb;
 113     }
 114
 115   TMP_MARK (marker);
 116
 117   tspace = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
 118   MPN_MUL_N_RECURSE (prodp, up, vp, vsize, tspace);
 119
 120   prodp += vsize;
 121   up += vsize;
 122   usize -= vsize;
 123   if (usize >= vsize)
 124     {
 125       mp_ptr tp = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
 126       do
 127         {
 128           MPN_MUL_N_RECURSE (tp, up, vp, vsize, tspace);
 129           cy = mpn_add_n (prodp, prodp, tp, vsize);
 130           mpn_add_1 (prodp + vsize, tp + vsize, vsize, cy);
 131           prodp += vsize;
 132           up += vsize;
 133           usize -= vsize;
 134         }
 135       while (usize >= vsize);
 136     }
 137
 138   /* True: usize < vsize.  */
 139
 140   /* Make life simple: Recurse.  */
 141
 142   if (usize != 0)
 143     {
 144       mpn_mul (tspace, vp, vsize, up, usize);
 145       cy = mpn_add_n (prodp, prodp, tspace, vsize);
 146       mpn_add_1 (prodp + vsize, tspace + vsize, usize, cy);
 147     }
 148
 149   TMP_FREE (marker);
 150   return *prod_endp;
 151 }