source/libs/gmp/gmp-src/mpn/generic/dive_1.c

   1 /* mpn_divexact_1 -- mpn by limb exact division.
   2
   3    THE FUNCTIONS IN THIS FILE ARE FOR INTERNAL USE ONLY.  THEY'RE ALMOST
   4    CERTAIN TO BE SUBJECT TO INCOMPATIBLE CHANGES OR DISAPPEAR COMPLETELY IN
   5    FUTURE GNU MP RELEASES.
   6
   7 Copyright 2000-2003, 2005, 2013 Free Software Foundation, Inc.
   8
   9 This file is part of the GNU MP Library.
  10
  11 The GNU MP Library is free software; you can redistribute it and/or modify
  12 it under the terms of either:
  13
  14   * the GNU Lesser General Public License as published by the Free
  15     Software Foundation; either version 3 of the License, or (at your
  16     option) any later version.
  17
  18 or
  19
  20   * the GNU General Public License as published by the Free Software
  21     Foundation; either version 2 of the License, or (at your option) any
  22     later version.
  23
  24 or both in parallel, as here.
  25
  26 The GNU MP Library is distributed in the hope that it will be useful, but
  27 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  28 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  29 for more details.
  30
  31 You should have received copies of the GNU General Public License and the
  32 GNU Lesser General Public License along with the GNU MP Library.  If not,
  33 see https://www.gnu.org/licenses/.  */
  34
  35 #include "gmp.h"
  36 #include "gmp-impl.h"
  37 #include "longlong.h"
  38
  39
  40
  41 /* Divide a={src,size} by d=divisor and store the quotient in q={dst,size}.
  42    q will only be correct if d divides a exactly.
  43
  44    A separate loop is used for shift==0 because n<<GMP_LIMB_BITS doesn't
  45    give zero on all CPUs (for instance it doesn't on the x86s).  This
  46    separate loop might run faster too, helping odd divisors.
  47
  48    Possibilities:
  49
  50    mpn_divexact_1c could be created, accepting and returning c.  This would
  51    let a long calculation be done piece by piece.  Currently there's no
  52    particular need for that, and not returning c means that a final umul can
  53    be skipped.
  54
  55    Another use for returning c would be letting the caller know whether the
  56    division was in fact exact.  It would work just to return the carry bit
  57    "c=(l>s)" and let the caller do a final umul if interested.
  58
  59    When the divisor is even, the factors of two could be handled with a
  60    separate mpn_rshift, instead of shifting on the fly.  That might be
  61    faster on some CPUs and would mean just the shift==0 style loop would be
  62    needed.
  63
  64    If n<<GMP_LIMB_BITS gives zero on a particular CPU then the separate
  65    shift==0 loop is unnecessary, and could be eliminated if there's no great
  66    speed difference.
  67
  68    It's not clear whether "/" is the best way to handle size==1.  Alpha gcc
  69    2.95 for instance has a poor "/" and might prefer the modular method.
  70    Perhaps a tuned parameter should control this.
  71
  72    If src[size-1] < divisor then dst[size-1] will be zero, and one divide
  73    step could be skipped.  A test at last step for s<divisor (or ls in the
  74    even case) might be a good way to do that.  But if this code is often
  75    used with small divisors then it might not be worth bothering  */
  76
  77 void
  78 mpn_divexact_1 (mp_ptr dst, mp_srcptr src, mp_size_t size, mp_limb_t divisor)
  79 {
  80   mp_size_t  i;
  81   mp_limb_t  c, h, l, ls, s, s_next, inverse, dummy;
  82   unsigned   shift;
  83
  84   ASSERT (size >= 1);
  85   ASSERT (divisor != 0);
  86   ASSERT (MPN_SAME_OR_SEPARATE_P (dst, src, size));
  87   ASSERT_MPN (src, size);
  88   ASSERT_LIMB (divisor);
  89
  90   if ((divisor & 1) == 0)
  91     {
  92       count_trailing_zeros (shift, divisor);
  93       divisor >>= shift;
  94     }
  95   else
  96     shift = 0;
  97
  98   binvert_limb (inverse, divisor);
  99   divisor <<= GMP_NAIL_BITS;
 100
 101   if (shift != 0)
 102     {
 103       c = 0;
 104
 105       s = src[0];
 106
 107       for (i = 1; i < size; i++)
 108         {
 109           s_next = src[i];
 110           ls = ((s >> shift) | (s_next << (GMP_NUMB_BITS-shift))) & GMP_NUMB_MASK;
 111           s = s_next;
 112
 113           SUBC_LIMB (c, l, ls, c);
 114
 115           l = (l * inverse) & GMP_NUMB_MASK;
 116           dst[i - 1] = l;
 117
 118           umul_ppmm (h, dummy, l, divisor);
 119           c += h;
 120         }
 121       while (i < size);
 122
 123       ls = s >> shift;
 124       l = ls - c;
 125       l = (l * inverse) & GMP_NUMB_MASK;
 126       dst[size - 1] = l;
 127     }
 128   else
 129     {
 130       s = src[0];
 131
 132       l = (s * inverse) & GMP_NUMB_MASK;
 133       dst[0] = l;
 134       c = 0;
 135
 136       for (i = 1; i < size; i++)
 137         {
 138           umul_ppmm (h, dummy, l, divisor);
 139           c += h;
 140
 141           s = src[i];
 142           SUBC_LIMB (c, l, s, c);
 143
 144           l = (l * inverse) & GMP_NUMB_MASK;
 145           dst[i] = l;
 146         }
 147     }
 148 }