stdlib/mod_1.c

   1 /* mpn_mod_1(dividend_ptr, dividend_size, divisor_limb) --
   2    Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
   3    Return the single-limb remainder.
   4    There are no constraints on the value of the divisor.
   5
   6 Copyright (C) 1991-2014 Free Software Foundation, Inc.
   7
   8 This file is part of the GNU MP Library.
   9
  10 The GNU MP Library is free software; you can redistribute it and/or modify
  11 it under the terms of the GNU Lesser General Public License as published by
  12 the Free Software Foundation; either version 2.1 of the License, or (at your
  13 option) any later version.
  14
  15 The GNU MP Library is distributed in the hope that it will be useful, but
  16 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  17 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  18 License for more details.
  19
  20 You should have received a copy of the GNU Lesser General Public License
  21 along with the GNU MP Library; see the file COPYING.LIB.  If not, see
  22 <http://www.gnu.org/licenses/>.  */
  23
  24 #include <gmp.h>
  25 #include "gmp-impl.h"
  26 #include "longlong.h"
  27
  28 #ifndef UMUL_TIME
  29 #define UMUL_TIME 1
  30 #endif
  31
  32 #ifndef UDIV_TIME
  33 #define UDIV_TIME UMUL_TIME
  34 #endif
  35
  36 /* FIXME: We should be using invert_limb (or invert_normalized_limb)
  37    here (not udiv_qrnnd).  */
  38
  39 mp_limb_t
  40 #if __STDC__
  41 mpn_mod_1 (mp_srcptr dividend_ptr, mp_size_t dividend_size,
  42            mp_limb_t divisor_limb)
  43 #else
  44 mpn_mod_1 (dividend_ptr, dividend_size, divisor_limb)
  45      mp_srcptr dividend_ptr;
  46      mp_size_t dividend_size;
  47      mp_limb_t divisor_limb;
  48 #endif
  49 {
  50   mp_size_t i;
  51   mp_limb_t n1, n0, r;
  52   mp_limb_t dummy __attribute__ ((unused));
  53
  54   /* Botch: Should this be handled at all?  Rely on callers?  */
  55   if (dividend_size == 0)
  56     return 0;
  57
  58   /* If multiplication is much faster than division, and the
  59      dividend is large, pre-invert the divisor, and use
  60      only multiplications in the inner loop.  */
  61
  62   /* This test should be read:
  63        Does it ever help to use udiv_qrnnd_preinv?
  64          && Does what we save compensate for the inversion overhead?  */
  65   if (UDIV_TIME > (2 * UMUL_TIME + 6)
  66       && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
  67     {
  68       int normalization_steps;
  69
  70       count_leading_zeros (normalization_steps, divisor_limb);
  71       if (normalization_steps != 0)
  72         {
  73           mp_limb_t divisor_limb_inverted;
  74
  75           divisor_limb <<= normalization_steps;
  76
  77           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
  78              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
  79              most significant bit (with weight 2**N) implicit.  */
  80
  81           /* Special case for DIVISOR_LIMB == 100...000.  */
  82           if (divisor_limb << 1 == 0)
  83             divisor_limb_inverted = ~(mp_limb_t) 0;
  84           else
  85             udiv_qrnnd (divisor_limb_inverted, dummy,
  86                         -divisor_limb, 0, divisor_limb);
  87
  88           n1 = dividend_ptr[dividend_size - 1];
  89           r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
  90
  91           /* Possible optimization:
  92              if (r == 0
  93              && divisor_limb > ((n1 << normalization_steps)
  94                              | (dividend_ptr[dividend_size - 2] >> ...)))
  95              ...one division less... */
  96
  97           for (i = dividend_size - 2; i >= 0; i--)
  98             {
  99               n0 = dividend_ptr[i];
 100               udiv_qrnnd_preinv (dummy, r, r,
 101                                  ((n1 << normalization_steps)
 102                                   | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 103                                  divisor_limb, divisor_limb_inverted);
 104               n1 = n0;
 105             }
 106           udiv_qrnnd_preinv (dummy, r, r,
 107                              n1 << normalization_steps,
 108                              divisor_limb, divisor_limb_inverted);
 109           return r >> normalization_steps;
 110         }
 111       else
 112         {
 113           mp_limb_t divisor_limb_inverted;
 114
 115           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
 116              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
 117              most significant bit (with weight 2**N) implicit.  */
 118
 119           /* Special case for DIVISOR_LIMB == 100...000.  */
 120           if (divisor_limb << 1 == 0)
 121             divisor_limb_inverted = ~(mp_limb_t) 0;
 122           else
 123             udiv_qrnnd (divisor_limb_inverted, dummy,
 124                         -divisor_limb, 0, divisor_limb);
 125
 126           i = dividend_size - 1;
 127           r = dividend_ptr[i];
 128
 129           if (r >= divisor_limb)
 130             r = 0;
 131           else
 132             i--;
 133
 134           for (; i >= 0; i--)
 135             {
 136               n0 = dividend_ptr[i];
 137               udiv_qrnnd_preinv (dummy, r, r,
 138                                  n0, divisor_limb, divisor_limb_inverted);
 139             }
 140           return r;
 141         }
 142     }
 143   else
 144     {
 145       if (UDIV_NEEDS_NORMALIZATION)
 146         {
 147           int normalization_steps;
 148
 149           count_leading_zeros (normalization_steps, divisor_limb);
 150           if (normalization_steps != 0)
 151             {
 152               divisor_limb <<= normalization_steps;
 153
 154               n1 = dividend_ptr[dividend_size - 1];
 155               r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
 156
 157               /* Possible optimization:
 158                  if (r == 0
 159                  && divisor_limb > ((n1 << normalization_steps)
 160                                  | (dividend_ptr[dividend_size - 2] >> ...)))
 161                  ...one division less... */
 162
 163               for (i = dividend_size - 2; i >= 0; i--)
 164                 {
 165                   n0 = dividend_ptr[i];
 166                   udiv_qrnnd (dummy, r, r,
 167                               ((n1 << normalization_steps)
 168                                | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 169                               divisor_limb);
 170                   n1 = n0;
 171                 }
 172               udiv_qrnnd (dummy, r, r,
 173                           n1 << normalization_steps,
 174                           divisor_limb);
 175               return r >> normalization_steps;
 176             }
 177         }
 178       /* No normalization needed, either because udiv_qrnnd doesn't require
 179          it, or because DIVISOR_LIMB is already normalized.  */
 180
 181       i = dividend_size - 1;
 182       r = dividend_ptr[i];
 183
 184       if (r >= divisor_limb)
 185         r = 0;
 186       else
 187         i--;
 188
 189       for (; i >= 0; i--)
 190         {
 191           n0 = dividend_ptr[i];
 192           udiv_qrnnd (dummy, r, r, n0, divisor_limb);
 193         }
 194       return r;
 195     }
 196 }