source/libs/gmp/gmp-src/mpn/generic/mod_1_3.c

   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 }