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) 1991-2020 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 <https://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 mpn_divmod_1 (mp_ptr quot_ptr,
  44               mp_srcptr dividend_ptr, mp_size_t dividend_size,
  45               mp_limb_t divisor_limb)
  46 {
  47   mp_size_t i;
  48   mp_limb_t n1, n0, r;
  49   mp_limb_t dummy __attribute__ ((unused));
  50
  51   /* ??? Should this be handled at all?  Rely on callers?  */
  52   if (dividend_size == 0)
  53     return 0;
  54
  55   /* If multiplication is much faster than division, and the
  56      dividend is large, pre-invert the divisor, and use
  57      only multiplications in the inner loop.  */
  58
  59   /* This test should be read:
  60        Does it ever help to use udiv_qrnnd_preinv?
  61          && Does what we save compensate for the inversion overhead?  */
  62   if (UDIV_TIME > (2 * UMUL_TIME + 6)
  63       && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
  64     {
  65       int normalization_steps;
  66
  67       count_leading_zeros (normalization_steps, divisor_limb);
  68       if (normalization_steps != 0)
  69         {
  70           mp_limb_t divisor_limb_inverted;
  71
  72           divisor_limb <<= normalization_steps;
  73
  74           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
  75              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
  76              most significant bit (with weight 2**N) implicit.  */
  77
  78           /* Special case for DIVISOR_LIMB == 100...000.  */
  79           if (divisor_limb << 1 == 0)
  80             divisor_limb_inverted = ~(mp_limb_t) 0;
  81           else
  82             udiv_qrnnd (divisor_limb_inverted, dummy,
  83                         -divisor_limb, 0, divisor_limb);
  84
  85           n1 = dividend_ptr[dividend_size - 1];
  86           r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
  87
  88           /* Possible optimization:
  89              if (r == 0
  90              && divisor_limb > ((n1 << normalization_steps)
  91                              | (dividend_ptr[dividend_size - 2] >> ...)))
  92              ...one division less... */
  93
  94           for (i = dividend_size - 2; i >= 0; i--)
  95             {
  96               n0 = dividend_ptr[i];
  97               udiv_qrnnd_preinv (quot_ptr[i + 1], r, r,
  98                                  ((n1 << normalization_steps)
  99                                   | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 100                                  divisor_limb, divisor_limb_inverted);
 101               n1 = n0;
 102             }
 103           udiv_qrnnd_preinv (quot_ptr[0], r, r,
 104                              n1 << normalization_steps,
 105                              divisor_limb, divisor_limb_inverted);
 106           return r >> normalization_steps;
 107         }
 108       else
 109         {
 110           mp_limb_t divisor_limb_inverted;
 111
 112           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
 113              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
 114              most significant bit (with weight 2**N) implicit.  */
 115
 116           /* Special case for DIVISOR_LIMB == 100...000.  */
 117           if (divisor_limb << 1 == 0)
 118             divisor_limb_inverted = ~(mp_limb_t) 0;
 119           else
 120             udiv_qrnnd (divisor_limb_inverted, dummy,
 121                         -divisor_limb, 0, divisor_limb);
 122
 123           i = dividend_size - 1;
 124           r = dividend_ptr[i];
 125
 126           if (r >= divisor_limb)
 127             r = 0;
 128           else
 129             {
 130               quot_ptr[i] = 0;
 131               i--;
 132             }
 133
 134           for (; i >= 0; i--)
 135             {
 136               n0 = dividend_ptr[i];
 137               udiv_qrnnd_preinv (quot_ptr[i], 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 (quot_ptr[i + 1], r, r,
 167                               ((n1 << normalization_steps)
 168                                | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 169                               divisor_limb);
 170                   n1 = n0;
 171                 }
 172               udiv_qrnnd (quot_ptr[0], 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         {
 188           quot_ptr[i] = 0;
 189           i--;
 190         }
 191
 192       for (; i >= 0; i--)
 193         {
 194           n0 = dividend_ptr[i];
 195           udiv_qrnnd (quot_ptr[i], r, r, n0, divisor_limb);
 196         }
 197       return r;
 198     }
 199 }