source/libs/gmp/gmp-src/mpn/generic/toom54_mul.c

   1 /* Implementation of the algorithm for Toom-Cook 4.5-way.
   2
   3    Contributed to the GNU project by Marco Bodrato.
   4
   5    THE FUNCTION IN THIS FILE IS INTERNAL WITH A MUTABLE INTERFACE.  IT IS ONLY
   6    SAFE TO REACH IT THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   7    GUARANTEED THAT IT WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
   8
   9 Copyright 2009, 2012 Free Software Foundation, Inc.
  10
  11 This file is part of the GNU MP Library.
  12
  13 The GNU MP Library is free software; you can redistribute it and/or modify
  14 it under the terms of either:
  15
  16   * the GNU Lesser General Public License as published by the Free
  17     Software Foundation; either version 3 of the License, or (at your
  18     option) any later version.
  19
  20 or
  21
  22   * the GNU General Public License as published by the Free Software
  23     Foundation; either version 2 of the License, or (at your option) any
  24     later version.
  25
  26 or both in parallel, as here.
  27
  28 The GNU MP Library is distributed in the hope that it will be useful, but
  29 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  30 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  31 for more details.
  32
  33 You should have received copies of the GNU General Public License and the
  34 GNU Lesser General Public License along with the GNU MP Library.  If not,
  35 see https://www.gnu.org/licenses/.  */
  36
  37 #include "gmp.h"
  38 #include "gmp-impl.h"
  39
  40
  41 /* Toom-4.5, the splitting 5x4 unbalanced version.
  42    Evaluate in: infinity, +4, -4, +2, -2, +1, -1, 0.
  43
  44   <--s-><--n--><--n--><--n--><--n-->
  45    ____ ______ ______ ______ ______
  46   |_a4_|__a3__|__a2__|__a1__|__a0__|
  47           |b3_|__b2__|__b1__|__b0__|
  48           <-t-><--n--><--n--><--n-->
  49
  50 */
  51 #define TOOM_54_MUL_N_REC(p, a, b, n, ws)               \
  52   do {  mpn_mul_n (p, a, b, n);                         \
  53   } while (0)
  54
  55 #define TOOM_54_MUL_REC(p, a, na, b, nb, ws)            \
  56   do {  mpn_mul (p, a, na, b, nb);                      \
  57   } while (0)
  58
  59 void
  60 mpn_toom54_mul (mp_ptr pp,
  61                 mp_srcptr ap, mp_size_t an,
  62                 mp_srcptr bp, mp_size_t bn, mp_ptr scratch)
  63 {
  64   mp_size_t n, s, t;
  65   int sign;
  66
  67   /***************************** decomposition *******************************/
  68 #define a4  (ap + 4 * n)
  69 #define b3  (bp + 3 * n)
  70
  71   ASSERT (an >= bn);
  72   n = 1 + (4 * an >= 5 * bn ? (an - 1) / (size_t) 5 : (bn - 1) / (size_t) 4);
  73
  74   s = an - 4 * n;
  75   t = bn - 3 * n;
  76
  77   ASSERT (0 < s && s <= n);
  78   ASSERT (0 < t && t <= n);
  79   /* Required by mpn_toom_interpolate_8pts. */
  80   ASSERT ( s + t >= n );
  81   ASSERT ( s + t > 4);
  82   ASSERT ( n > 2);
  83
  84 #define   r8    pp                              /* 2n   */
  85 #define   r7    scratch                         /* 3n+1 */
  86 #define   r5    (pp + 3*n)                      /* 3n+1 */
  87 #define   v0    (pp + 3*n)                      /* n+1 */
  88 #define   v1    (pp + 4*n+1)                    /* n+1 */
  89 #define   v2    (pp + 5*n+2)                    /* n+1 */
  90 #define   v3    (pp + 6*n+3)                    /* n+1 */
  91 #define   r3    (scratch + 3 * n + 1)           /* 3n+1 */
  92 #define   r1    (pp + 7*n)                      /* s+t <= 2*n */
  93 #define   ws    (scratch + 6 * n + 2)           /* ??? */
  94
  95   /* Alloc also 3n+1 limbs for ws... mpn_toom_interpolate_8pts may
  96      need all of them, when DO_mpn_sublsh_n usea a scratch  */
  97   /********************** evaluation and recursive calls *********************/
  98   /* $\pm4$ */
  99   sign = mpn_toom_eval_pm2exp (v2, v0, 4, ap, n, s, 2, pp)
 100        ^ mpn_toom_eval_pm2exp (v3, v1, 3, bp, n, t, 2, pp);
 101   TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-4)*B(-4) */
 102   TOOM_54_MUL_N_REC(r3, v2, v3, n + 1, ws); /* A(+4)*B(+4) */
 103   mpn_toom_couple_handling (r3, 2*n+1, pp, sign, n, 2, 4);
 104
 105   /* $\pm1$ */
 106   sign = mpn_toom_eval_pm1 (v2, v0, 4, ap, n, s,    pp)
 107        ^ mpn_toom_eval_dgr3_pm1 (v3, v1, bp, n, t,    pp);
 108   TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-1)*B(-1) */
 109   TOOM_54_MUL_N_REC(r7, v2, v3, n + 1, ws); /* A(1)*B(1) */
 110   mpn_toom_couple_handling (r7, 2*n+1, pp, sign, n, 0, 0);
 111
 112   /* $\pm2$ */
 113   sign = mpn_toom_eval_pm2 (v2, v0, 4, ap, n, s, pp)
 114        ^ mpn_toom_eval_dgr3_pm2 (v3, v1, bp, n, t, pp);
 115   TOOM_54_MUL_N_REC(pp, v0, v1, n + 1, ws); /* A(-2)*B(-2) */
 116   TOOM_54_MUL_N_REC(r5, v2, v3, n + 1, ws); /* A(+2)*B(+2) */
 117   mpn_toom_couple_handling (r5, 2*n+1, pp, sign, n, 1, 2);
 118
 119   /* A(0)*B(0) */
 120   TOOM_54_MUL_N_REC(pp, ap, bp, n, ws);
 121
 122   /* Infinity */
 123   if (s > t) {
 124     TOOM_54_MUL_REC(r1, a4, s, b3, t, ws);
 125   } else {
 126     TOOM_54_MUL_REC(r1, b3, t, a4, s, ws);
 127   };
 128
 129   mpn_toom_interpolate_8pts (pp, n, r3, r7, s + t, ws);
 130
 131 #undef a4
 132 #undef b3
 133 #undef r1
 134 #undef r3
 135 #undef r5
 136 #undef v0
 137 #undef v1
 138 #undef v2
 139 #undef v3
 140 #undef r7
 141 #undef r8
 142 #undef ws
 143 }