stdlib/mul.c

   1 /* mpn_mul -- Multiply two natural numbers.
   2
   3 Copyright (C) 1991-2023 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 <https://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 mpn_mul (mp_ptr prodp,
  46          mp_srcptr up, mp_size_t usize,
  47          mp_srcptr vp, mp_size_t vsize)
  48 {
  49   mp_ptr prod_endp = prodp + usize + vsize - 1;
  50   mp_limb_t cy;
  51   mp_ptr tspace;
  52   TMP_DECL (marker);
  53
  54   if (vsize < KARATSUBA_THRESHOLD)
  55     {
  56       /* Handle simple cases with traditional multiplication.
  57
  58          This is the most critical code of the entire function.  All
  59          multiplies rely on this, both small and huge.  Small ones arrive
  60          here immediately.  Huge ones arrive here as this is the base case
  61          for Karatsuba's recursive algorithm below.  */
  62       mp_size_t i;
  63       mp_limb_t cy_limb;
  64       mp_limb_t v_limb;
  65
  66       if (vsize == 0)
  67         return 0;
  68
  69       /* Multiply by the first limb in V separately, as the result can be
  70          stored (not added) to PROD.  We also avoid a loop for zeroing.  */
  71       v_limb = vp[0];
  72       if (v_limb <= 1)
  73         {
  74           if (v_limb == 1)
  75             MPN_COPY (prodp, up, usize);
  76           else
  77             MPN_ZERO (prodp, usize);
  78           cy_limb = 0;
  79         }
  80       else
  81         cy_limb = mpn_mul_1 (prodp, up, usize, v_limb);
  82
  83       prodp[usize] = cy_limb;
  84       prodp++;
  85
  86       /* For each iteration in the outer loop, multiply one limb from
  87          U with one limb from V, and add it to PROD.  */
  88       for (i = 1; i < vsize; i++)
  89         {
  90           v_limb = vp[i];
  91           if (v_limb <= 1)
  92             {
  93               cy_limb = 0;
  94               if (v_limb == 1)
  95                 cy_limb = mpn_add_n (prodp, prodp, up, usize);
  96             }
  97           else
  98             cy_limb = mpn_addmul_1 (prodp, up, usize, v_limb);
  99
 100           prodp[usize] = cy_limb;
 101           prodp++;
 102         }
 103       return cy_limb;
 104     }
 105
 106   TMP_MARK (marker);
 107
 108   tspace = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
 109   MPN_MUL_N_RECURSE (prodp, up, vp, vsize, tspace);
 110
 111   prodp += vsize;
 112   up += vsize;
 113   usize -= vsize;
 114   if (usize >= vsize)
 115     {
 116       mp_ptr tp = (mp_ptr) TMP_ALLOC (2 * vsize * BYTES_PER_MP_LIMB);
 117       do
 118         {
 119           MPN_MUL_N_RECURSE (tp, up, vp, vsize, tspace);
 120           cy = mpn_add_n (prodp, prodp, tp, vsize);
 121           mpn_add_1 (prodp + vsize, tp + vsize, vsize, cy);
 122           prodp += vsize;
 123           up += vsize;
 124           usize -= vsize;
 125         }
 126       while (usize >= vsize);
 127     }
 128
 129   /* True: usize < vsize.  */
 130
 131   /* Make life simple: Recurse.  */
 132
 133   if (usize != 0)
 134     {
 135       mpn_mul (tspace, vp, vsize, up, usize);
 136       cy = mpn_add_n (prodp, prodp, tspace, vsize);
 137       mpn_add_1 (prodp + vsize, tspace + vsize, usize, cy);
 138     }
 139
 140   TMP_FREE (marker);
 141   return *prod_endp;
 142 }