github.com/aergoio/aergo@v1.3.1/libtool/src/gmp-6.1.2/mpn/generic/mod_1_3.c (about)

     1  /* mpn_mod_1s_3p (ap, n, b, cps)
     2     Divide (ap,,n) by b.  Return the single-limb remainder.
     3     Requires that d < B / 3.
     4  
     5     Contributed to the GNU project by Torbjorn Granlund.
     6     Based on a suggestion by Peter L. Montgomery.
     7  
     8     THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
     9     SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
    10     GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
    11  
    12  Copyright 2008-2010, 2013 Free Software Foundation, Inc.
    13  
    14  This file is part of the GNU MP Library.
    15  
    16  The GNU MP Library is free software; you can redistribute it and/or modify
    17  it under the terms of either:
    18  
    19    * the GNU Lesser General Public License as published by the Free
    20      Software Foundation; either version 3 of the License, or (at your
    21      option) any later version.
    22  
    23  or
    24  
    25    * the GNU General Public License as published by the Free Software
    26      Foundation; either version 2 of the License, or (at your option) any
    27      later version.
    28  
    29  or both in parallel, as here.
    30  
    31  The GNU MP Library is distributed in the hope that it will be useful, but
    32  WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
    33  or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
    34  for more details.
    35  
    36  You should have received copies of the GNU General Public License and the
    37  GNU Lesser General Public License along with the GNU MP Library.  If not,
    38  see https://www.gnu.org/licenses/.  */
    39  
    40  #include "gmp.h"
    41  #include "gmp-impl.h"
    42  #include "longlong.h"
    43  
    44  void
    45  mpn_mod_1s_3p_cps (mp_limb_t cps[6], mp_limb_t b)
    46  {
    47    mp_limb_t bi;
    48    mp_limb_t B1modb, B2modb, B3modb, B4modb;
    49    int cnt;
    50  
    51    ASSERT (b <= (~(mp_limb_t) 0) / 3);
    52  
    53    count_leading_zeros (cnt, b);
    54  
    55    b <<= cnt;
    56    invert_limb (bi, b);
    57  
    58    cps[0] = bi;
    59    cps[1] = cnt;
    60  
    61    B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));
    62    ASSERT (B1modb <= b);		/* NB: not fully reduced mod b */
    63    cps[2] = B1modb >> cnt;
    64  
    65    udiv_rnnd_preinv (B2modb, B1modb, CNST_LIMB(0), b, bi);
    66    cps[3] = B2modb >> cnt;
    67  
    68    udiv_rnnd_preinv (B3modb, B2modb, CNST_LIMB(0), b, bi);
    69    cps[4] = B3modb >> cnt;
    70  
    71    udiv_rnnd_preinv (B4modb, B3modb, CNST_LIMB(0), b, bi);
    72    cps[5] = B4modb >> cnt;
    73  
    74  #if WANT_ASSERT
    75    {
    76      int i;
    77      b = cps[2];
    78      for (i = 3; i <= 5; i++)
    79        {
    80  	b += cps[i];
    81  	ASSERT (b >= cps[i]);
    82        }
    83    }
    84  #endif
    85  }
    86  
    87  mp_limb_t
    88  mpn_mod_1s_3p (mp_srcptr ap, mp_size_t n, mp_limb_t b, const mp_limb_t cps[6])
    89  {
    90    mp_limb_t rh, rl, bi, ph, pl, ch, cl, r;
    91    mp_limb_t B1modb, B2modb, B3modb, B4modb;
    92    mp_size_t i;
    93    int cnt;
    94  
    95    ASSERT (n >= 1);
    96  
    97    B1modb = cps[2];
    98    B2modb = cps[3];
    99    B3modb = cps[4];
   100    B4modb = cps[5];
   101  
   102    /* We compute n mod 3 in a tricky way, which works except for when n is so
   103       close to the maximum size that we don't need to support it.  The final
   104       cast to int is a workaround for HP cc.  */
   105    switch ((int) ((mp_limb_t) n * MODLIMB_INVERSE_3 >> (GMP_NUMB_BITS - 2)))
   106      {
   107      case 0:
   108        umul_ppmm (ph, pl, ap[n - 2], B1modb);
   109        add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[n - 3]);
   110        umul_ppmm (rh, rl, ap[n - 1], B2modb);
   111        add_ssaaaa (rh, rl, rh, rl, ph, pl);
   112        n -= 3;
   113        break;
   114      case 2:	/* n mod 3 = 1 */
   115        rh = 0;
   116        rl = ap[n - 1];
   117        n -= 1;
   118        break;
   119      case 1:	/* n mod 3 = 2 */
   120        rh = ap[n - 1];
   121        rl = ap[n - 2];
   122        n -= 2;
   123        break;
   124      }
   125  
   126    for (i = n - 3; i >= 0; i -= 3)
   127      {
   128        /* rr = ap[i]				< B
   129  	    + ap[i+1] * (B mod b)		<= (B-1)(b-1)
   130  	    + ap[i+2] * (B^2 mod b)		<= (B-1)(b-1)
   131  	    + LO(rr)  * (B^3 mod b)		<= (B-1)(b-1)
   132  	    + HI(rr)  * (B^4 mod b)		<= (B-1)(b-1)
   133        */
   134        umul_ppmm (ph, pl, ap[i + 1], B1modb);
   135        add_ssaaaa (ph, pl, ph, pl, CNST_LIMB(0), ap[i + 0]);
   136  
   137        umul_ppmm (ch, cl, ap[i + 2], B2modb);
   138        add_ssaaaa (ph, pl, ph, pl, ch, cl);
   139  
   140        umul_ppmm (ch, cl, rl, B3modb);
   141        add_ssaaaa (ph, pl, ph, pl, ch, cl);
   142  
   143        umul_ppmm (rh, rl, rh, B4modb);
   144        add_ssaaaa (rh, rl, rh, rl, ph, pl);
   145      }
   146  
   147    umul_ppmm (rh, cl, rh, B1modb);
   148    add_ssaaaa (rh, rl, rh, rl, CNST_LIMB(0), cl);
   149  
   150    cnt = cps[1];
   151    bi = cps[0];
   152  
   153    r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
   154    udiv_rnnd_preinv (r, r, rl << cnt, b, bi);
   155  
   156    return r >> cnt;
   157  }