contrib/gmp/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
   7    THE FUNCTIONS IN THIS FILE ARE INTERNAL WITH MUTABLE INTERFACES.  IT IS ONLY
   8    SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   9    GUARANTEED THAT THEY WILL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
  10
  11 Copyright 2008, 2009 Free Software Foundation, Inc.
  12
  13 This file is part of the GNU MP Library.
  14
  15 The GNU MP Library is free software; you can redistribute it and/or modify
  16 it under the terms of the GNU Lesser General Public License as published by
  17 the Free Software Foundation; either version 3 of the License, or (at your
  18 option) any later version.
  19
  20 The GNU MP Library is distributed in the hope that it will be useful, but
  21 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  22 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  23 License for more details.
  24
  25 You should have received a copy of the GNU Lesser General Public License
  26 along with the GNU MP Library.  If not, see http://www.gnu.org/licenses/.  */
  27
  28 #include "gmp.h"
  29 #include "gmp-impl.h"
  30 #include "longlong.h"
  31
  32 void
  33 mpn_mod_1s_3p_cps (mp_limb_t cps[6], mp_limb_t b)
  34 {
  35   mp_limb_t bi;
  36   mp_limb_t B1modb, B2modb, B3modb, B4modb;
  37   int cnt;
  38
  39   ASSERT (b <= GMP_NUMB_MAX / 3);
  40
  41   count_leading_zeros (cnt, b);
  42
  43   b <<= cnt;
  44   invert_limb (bi, b);
  45
  46   B1modb = -b * ((bi >> (GMP_LIMB_BITS-cnt)) | (CNST_LIMB(1) << cnt));
  47   ASSERT (B1modb <= b);         /* NB: not fully reduced mod b */
  48   udiv_rnd_preinv (B2modb, B1modb, b, bi);
  49   udiv_rnd_preinv (B3modb, B2modb, b, bi);
  50   udiv_rnd_preinv (B4modb, B3modb, b, bi);
  51
  52   cps[0] = bi;
  53   cps[1] = cnt;
  54   cps[2] = B1modb >> cnt;
  55   cps[3] = B2modb >> cnt;
  56   cps[4] = B3modb >> cnt;
  57   cps[5] = B4modb >> cnt;
  58 }
  59
  60 mp_limb_t
  61 mpn_mod_1s_3p (mp_srcptr ap, mp_size_t n, mp_limb_t b, mp_limb_t cps[6])
  62 {
  63   mp_limb_t rh, rl, bi, q, ph, pl, ch, cl, r;
  64   mp_limb_t B1modb, B2modb, B3modb, B4modb;
  65   mp_size_t i;
  66   int cnt;
  67
  68   B1modb = cps[2];
  69   B2modb = cps[3];
  70   B3modb = cps[4];
  71   B4modb = cps[5];
  72
  73   umul_ppmm (ph, pl, ap[n - 2], B1modb);
  74   add_ssaaaa (ph, pl, ph, pl, 0, ap[n - 3]);
  75   umul_ppmm (ch, cl, ap[n - 1], B2modb);
  76   add_ssaaaa (rh, rl, ph, pl, ch, cl);
  77
  78   for (i = n - 6; i >= 0; i -= 3)
  79     {
  80       /* rr = ap[i]                             < B
  81             + ap[i+1] * (B mod b)               <= (B-1)(b-1)
  82             + ap[i+2] * (B^2 mod b)             <= (B-1)(b-1)
  83             + LO(rr)  * (B^3 mod b)             <= (B-1)(b-1)
  84             + HI(rr)  * (B^4 mod b)             <= (B-1)(b-1)
  85       */
  86       umul_ppmm (ph, pl, ap[i + 1], B1modb);
  87       add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 0]);
  88
  89       umul_ppmm (ch, cl, ap[i + 2], B2modb);
  90       add_ssaaaa (ph, pl, ph, pl, ch, cl);
  91
  92       umul_ppmm (ch, cl, rl, B3modb);
  93       add_ssaaaa (ph, pl, ph, pl, ch, cl);
  94
  95       umul_ppmm (rh, rl, rh, B4modb);
  96       add_ssaaaa (rh, rl, rh, rl, ph, pl);
  97     }
  98
  99   if (i >= -2)
 100     {
 101       umul_ppmm (ph, pl, rl, B1modb);
 102       add_ssaaaa (ph, pl, ph, pl, 0, ap[i + 2]);
 103       umul_ppmm (rh, rl, rh, B2modb);
 104       add_ssaaaa (rh, rl, rh, rl, ph, pl);
 105       if (i >= -1)
 106         {
 107           umul_ppmm (ph, pl, rl, B1modb);
 108           add_ssaaaa (ph, pl, ph, pl, 0, ap[0]);
 109           umul_ppmm (rh, rl, rh, B2modb);
 110           add_ssaaaa (rh, rl, rh, rl, ph, pl);
 111         }
 112     }
 113
 114   bi = cps[0];
 115   cnt = cps[1];
 116
 117 #if 1
 118   umul_ppmm (rh, cl, rh, B1modb);
 119   add_ssaaaa (rh, rl, rh, rl, 0, cl);
 120   r = (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt));
 121 #else
 122   udiv_qrnnd_preinv (q, r, rh >> (GMP_LIMB_BITS - cnt),
 123                      (rh << cnt) | (rl >> (GMP_LIMB_BITS - cnt)), b, bi);
 124   ASSERT (q <= 3);      /* optimize for small quotient? */
 125 #endif
 126
 127   udiv_qrnnd_preinv (q, r, r, rl << cnt, b, bi);
 128
 129   return r >> cnt;
 130 }