github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpn/generic/toom54_mul.c (about)

     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  }