stdlib/divmod_1.c

   1 /* mpn_divmod_1(quot_ptr, dividend_ptr, dividend_size, divisor_limb) --
   2    Divide (DIVIDEND_PTR,,DIVIDEND_SIZE) by DIVISOR_LIMB.
   3    Write DIVIDEND_SIZE limbs of quotient at QUOT_PTR.
   4    Return the single-limb remainder.
   5    There are no constraints on the value of the divisor.
   6
   7    QUOT_PTR and DIVIDEND_PTR might point to the same limb.
   8
   9 Copyright (C) 1991-2013 Free Software Foundation, Inc.
  10
  11 This file is part of the GNU MP Library.
  12
  13 The GNU MP Library is free software; you can redistribute it and/or modify
  14 it under the terms of the GNU Lesser General Public License as published by
  15 the Free Software Foundation; either version 2.1 of the License, or (at your
  16 option) any later version.
  17
  18 The GNU MP Library is distributed in the hope that it will be useful, but
  19 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  20 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  21 License for more details.
  22
  23 You should have received a copy of the GNU Lesser General Public License
  24 along with the GNU MP Library; see the file COPYING.LIB.  If not, see
  25 <http://www.gnu.org/licenses/>.  */
  26
  27 #include <gmp.h>
  28 #include "gmp-impl.h"
  29 #include "longlong.h"
  30
  31 #ifndef UMUL_TIME
  32 #define UMUL_TIME 1
  33 #endif
  34
  35 #ifndef UDIV_TIME
  36 #define UDIV_TIME UMUL_TIME
  37 #endif
  38
  39 /* FIXME: We should be using invert_limb (or invert_normalized_limb)
  40    here (not udiv_qrnnd).  */
  41
  42 mp_limb_t
  43 #if __STDC__
  44 mpn_divmod_1 (mp_ptr quot_ptr,
  45               mp_srcptr dividend_ptr, mp_size_t dividend_size,
  46               mp_limb_t divisor_limb)
  47 #else
  48 mpn_divmod_1 (quot_ptr, dividend_ptr, dividend_size, divisor_limb)
  49      mp_ptr quot_ptr;
  50      mp_srcptr dividend_ptr;
  51      mp_size_t dividend_size;
  52      mp_limb_t divisor_limb;
  53 #endif
  54 {
  55   mp_size_t i;
  56   mp_limb_t n1, n0, r;
  57   mp_limb_t dummy __attribute__ ((unused));
  58
  59   /* ??? Should this be handled at all?  Rely on callers?  */
  60   if (dividend_size == 0)
  61     return 0;
  62
  63   /* If multiplication is much faster than division, and the
  64      dividend is large, pre-invert the divisor, and use
  65      only multiplications in the inner loop.  */
  66
  67   /* This test should be read:
  68        Does it ever help to use udiv_qrnnd_preinv?
  69          && Does what we save compensate for the inversion overhead?  */
  70   if (UDIV_TIME > (2 * UMUL_TIME + 6)
  71       && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
  72     {
  73       int normalization_steps;
  74
  75       count_leading_zeros (normalization_steps, divisor_limb);
  76       if (normalization_steps != 0)
  77         {
  78           mp_limb_t divisor_limb_inverted;
  79
  80           divisor_limb <<= normalization_steps;
  81
  82           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
  83              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
  84              most significant bit (with weight 2**N) implicit.  */
  85
  86           /* Special case for DIVISOR_LIMB == 100...000.  */
  87           if (divisor_limb << 1 == 0)
  88             divisor_limb_inverted = ~(mp_limb_t) 0;
  89           else
  90             udiv_qrnnd (divisor_limb_inverted, dummy,
  91                         -divisor_limb, 0, divisor_limb);
  92
  93           n1 = dividend_ptr[dividend_size - 1];
  94           r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
  95
  96           /* Possible optimization:
  97              if (r == 0
  98              && divisor_limb > ((n1 << normalization_steps)
  99                              | (dividend_ptr[dividend_size - 2] >> ...)))
 100              ...one division less... */
 101
 102           for (i = dividend_size - 2; i >= 0; i--)
 103             {
 104               n0 = dividend_ptr[i];
 105               udiv_qrnnd_preinv (quot_ptr[i + 1], r, r,
 106                                  ((n1 << normalization_steps)
 107                                   | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 108                                  divisor_limb, divisor_limb_inverted);
 109               n1 = n0;
 110             }
 111           udiv_qrnnd_preinv (quot_ptr[0], r, r,
 112                              n1 << normalization_steps,
 113                              divisor_limb, divisor_limb_inverted);
 114           return r >> normalization_steps;
 115         }
 116       else
 117         {
 118           mp_limb_t divisor_limb_inverted;
 119
 120           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
 121              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
 122              most significant bit (with weight 2**N) implicit.  */
 123
 124           /* Special case for DIVISOR_LIMB == 100...000.  */
 125           if (divisor_limb << 1 == 0)
 126             divisor_limb_inverted = ~(mp_limb_t) 0;
 127           else
 128             udiv_qrnnd (divisor_limb_inverted, dummy,
 129                         -divisor_limb, 0, divisor_limb);
 130
 131           i = dividend_size - 1;
 132           r = dividend_ptr[i];
 133
 134           if (r >= divisor_limb)
 135             r = 0;
 136           else
 137             {
 138               quot_ptr[i] = 0;
 139               i--;
 140             }
 141
 142           for (; i >= 0; i--)
 143             {
 144               n0 = dividend_ptr[i];
 145               udiv_qrnnd_preinv (quot_ptr[i], r, r,
 146                                  n0, divisor_limb, divisor_limb_inverted);
 147             }
 148           return r;
 149         }
 150     }
 151   else
 152     {
 153       if (UDIV_NEEDS_NORMALIZATION)
 154         {
 155           int normalization_steps;
 156
 157           count_leading_zeros (normalization_steps, divisor_limb);
 158           if (normalization_steps != 0)
 159             {
 160               divisor_limb <<= normalization_steps;
 161
 162               n1 = dividend_ptr[dividend_size - 1];
 163               r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
 164
 165               /* Possible optimization:
 166                  if (r == 0
 167                  && divisor_limb > ((n1 << normalization_steps)
 168                                  | (dividend_ptr[dividend_size - 2] >> ...)))
 169                  ...one division less... */
 170
 171               for (i = dividend_size - 2; i >= 0; i--)
 172                 {
 173                   n0 = dividend_ptr[i];
 174                   udiv_qrnnd (quot_ptr[i + 1], r, r,
 175                               ((n1 << normalization_steps)
 176                                | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 177                               divisor_limb);
 178                   n1 = n0;
 179                 }
 180               udiv_qrnnd (quot_ptr[0], r, r,
 181                           n1 << normalization_steps,
 182                           divisor_limb);
 183               return r >> normalization_steps;
 184             }
 185         }
 186       /* No normalization needed, either because udiv_qrnnd doesn't require
 187          it, or because DIVISOR_LIMB is already normalized.  */
 188
 189       i = dividend_size - 1;
 190       r = dividend_ptr[i];
 191
 192       if (r >= divisor_limb)
 193         r = 0;
 194       else
 195         {
 196           quot_ptr[i] = 0;
 197           i--;
 198         }
 199
 200       for (; i >= 0; i--)
 201         {
 202           n0 = dividend_ptr[i];
 203           udiv_qrnnd (quot_ptr[i], r, r, n0, divisor_limb);
 204         }
 205       return r;
 206     }
 207 }