source/libs/gmp/gmp-src/mpn/generic/diveby3.c

   1 /* mpn_divexact_by3c -- mpn exact division by 3.
   2
   3 Copyright 2000-2003, 2008 Free Software Foundation, Inc.
   4
   5 This file is part of the GNU MP Library.
   6
   7 The GNU MP Library is free software; you can redistribute it and/or modify
   8 it under the terms of either:
   9
  10   * the GNU Lesser General Public License as published by the Free
  11     Software Foundation; either version 3 of the License, or (at your
  12     option) any later version.
  13
  14 or
  15
  16   * the GNU General Public License as published by the Free Software
  17     Foundation; either version 2 of the License, or (at your option) any
  18     later version.
  19
  20 or both in parallel, as here.
  21
  22 The GNU MP Library is distributed in the hope that it will be useful, but
  23 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  24 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  25 for more details.
  26
  27 You should have received copies of the GNU General Public License and the
  28 GNU Lesser General Public License along with the GNU MP Library.  If not,
  29 see https://www.gnu.org/licenses/.  */
  30
  31 #include "gmp.h"
  32 #include "gmp-impl.h"
  33
  34 #if DIVEXACT_BY3_METHOD == 0
  35
  36 mp_limb_t
  37 mpn_divexact_by3c (mp_ptr rp, mp_srcptr up, mp_size_t un, mp_limb_t c)
  38 {
  39   mp_limb_t r;
  40   r = mpn_bdiv_dbm1c (rp, up, un, GMP_NUMB_MASK / 3, GMP_NUMB_MASK / 3 * c);
  41
  42   /* Possible bdiv_dbm1 return values are C * (GMP_NUMB_MASK / 3), 0 <= C < 3.
  43      We want to return C.  We compute the remainder mod 4 and notice that the
  44      inverse of (2^(2k)-1)/3 mod 4 is 1.  */
  45   return r & 3;
  46 }
  47
  48 #endif
  49
  50 #if DIVEXACT_BY3_METHOD == 1
  51
  52 /* The algorithm here is basically the same as mpn_divexact_1, as described
  53    in the manual.  Namely at each step q = (src[i]-c)*inverse, and new c =
  54    borrow(src[i]-c) + high(divisor*q).  But because the divisor is just 3,
  55    high(divisor*q) can be determined with two comparisons instead of a
  56    multiply.
  57
  58    The "c += ..."s add the high limb of 3*l to c.  That high limb will be 0,
  59    1 or 2.  Doing two separate "+="s seems to give better code on gcc (as of
  60    2.95.2 at least).
  61
  62    It will be noted that the new c is formed by adding three values each 0
  63    or 1.  But the total is only 0, 1 or 2.  When the subtraction src[i]-c
  64    causes a borrow, that leaves a limb value of either 0xFF...FF or
  65    0xFF...FE.  The multiply by MODLIMB_INVERSE_3 gives 0x55...55 or
  66    0xAA...AA respectively, and in those cases high(3*q) is only 0 or 1
  67    respectively, hence a total of no more than 2.
  68
  69    Alternatives:
  70
  71    This implementation has each multiply on the dependent chain, due to
  72    "l=s-c".  See below for alternative code which avoids that.  */
  73
  74 mp_limb_t
  75 mpn_divexact_by3c (mp_ptr restrict rp, mp_srcptr restrict up, mp_size_t un, mp_limb_t c)
  76 {
  77   mp_limb_t  l, q, s;
  78   mp_size_t  i;
  79
  80   ASSERT (un >= 1);
  81   ASSERT (c == 0 || c == 1 || c == 2);
  82   ASSERT (MPN_SAME_OR_SEPARATE_P (rp, up, un));
  83
  84   i = 0;
  85   do
  86     {
  87       s = up[i];
  88       SUBC_LIMB (c, l, s, c);
  89
  90       q = (l * MODLIMB_INVERSE_3) & GMP_NUMB_MASK;
  91       rp[i] = q;
  92
  93       c += (q >= GMP_NUMB_CEIL_MAX_DIV3);
  94       c += (q >= GMP_NUMB_CEIL_2MAX_DIV3);
  95     }
  96   while (++i < un);
  97
  98   ASSERT (c == 0 || c == 1 || c == 2);
  99   return c;
 100 }
 101
 102
 103 #endif
 104
 105 #if DIVEXACT_BY3_METHOD == 2
 106
 107 /* The following alternative code re-arranges the quotient calculation from
 108    (src[i]-c)*inverse to instead
 109
 110        q = src[i]*inverse - c*inverse
 111
 112    thereby allowing src[i]*inverse to be scheduled back as far as desired,
 113    making full use of multiplier throughput and leaving just some carry
 114    handing on the dependent chain.
 115
 116    The carry handling consists of determining the c for the next iteration.
 117    This is the same as described above, namely look for any borrow from
 118    src[i]-c, and at the high of 3*q.
 119
 120    high(3*q) is done with two comparisons as above (in c2 and c3).  The
 121    borrow from src[i]-c is incorporated into those by noting that if there's
 122    a carry then then we have src[i]-c == 0xFF..FF or 0xFF..FE, in turn
 123    giving q = 0x55..55 or 0xAA..AA.  Adding 1 to either of those q values is
 124    enough to make high(3*q) come out 1 bigger, as required.
 125
 126    l = -c*inverse is calculated at the same time as c, since for most chips
 127    it can be more conveniently derived from separate c1/c2/c3 values than
 128    from a combined c equal to 0, 1 or 2.
 129
 130    The net effect is that with good pipelining this loop should be able to
 131    run at perhaps 4 cycles/limb, depending on available execute resources
 132    etc.
 133
 134    Usage:
 135
 136    This code is not used by default, since we really can't rely on the
 137    compiler generating a good software pipeline, nor on such an approach
 138    even being worthwhile on all CPUs.
 139
 140    Itanium is one chip where this algorithm helps though, see
 141    mpn/ia64/diveby3.asm.  */
 142
 143 mp_limb_t
 144 mpn_divexact_by3c (mp_ptr restrict rp, mp_srcptr restrict up, mp_size_t un, mp_limb_t cy)
 145 {
 146   mp_limb_t  s, sm, cl, q, qx, c2, c3;
 147   mp_size_t  i;
 148
 149   ASSERT (un >= 1);
 150   ASSERT (cy == 0 || cy == 1 || cy == 2);
 151   ASSERT (MPN_SAME_OR_SEPARATE_P (rp, up, un));
 152
 153   cl = cy == 0 ? 0 : cy == 1 ? -MODLIMB_INVERSE_3 : -2*MODLIMB_INVERSE_3;
 154
 155   for (i = 0; i < un; i++)
 156     {
 157       s = up[i];
 158       sm = (s * MODLIMB_INVERSE_3) & GMP_NUMB_MASK;
 159
 160       q = (cl + sm) & GMP_NUMB_MASK;
 161       rp[i] = q;
 162       qx = q + (s < cy);
 163
 164       c2 = qx >= GMP_NUMB_CEIL_MAX_DIV3;
 165       c3 = qx >= GMP_NUMB_CEIL_2MAX_DIV3 ;
 166
 167       cy = c2 + c3;
 168       cl = (-c2 & -MODLIMB_INVERSE_3) + (-c3 & -MODLIMB_INVERSE_3);
 169     }
 170
 171   return cy;
 172 }
 173
 174 #endif