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) 1991-2024 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 <https://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 mpn_mod_1 (mp_srcptr dividend_ptr, mp_size_t dividend_size,
  41            mp_limb_t divisor_limb)
  42 {
  43   mp_size_t i;
  44   mp_limb_t n1, n0, r;
  45   mp_limb_t dummy __attribute__ ((unused));
  46
  47   /* Botch: Should this be handled at all?  Rely on callers?  */
  48   if (dividend_size == 0)
  49     return 0;
  50
  51   /* If multiplication is much faster than division, and the
  52      dividend is large, pre-invert the divisor, and use
  53      only multiplications in the inner loop.  */
  54
  55   /* This test should be read:
  56        Does it ever help to use udiv_qrnnd_preinv?
  57          && Does what we save compensate for the inversion overhead?  */
  58   if (UDIV_TIME > (2 * UMUL_TIME + 6)
  59       && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
  60     {
  61       int normalization_steps;
  62
  63       count_leading_zeros (normalization_steps, divisor_limb);
  64       if (normalization_steps != 0)
  65         {
  66           mp_limb_t divisor_limb_inverted;
  67
  68           divisor_limb <<= normalization_steps;
  69
  70           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
  71              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
  72              most significant bit (with weight 2**N) implicit.  */
  73
  74           /* Special case for DIVISOR_LIMB == 100...000.  */
  75           if (divisor_limb << 1 == 0)
  76             divisor_limb_inverted = ~(mp_limb_t) 0;
  77           else
  78             udiv_qrnnd (divisor_limb_inverted, dummy,
  79                         -divisor_limb, 0, divisor_limb);
  80
  81           n1 = dividend_ptr[dividend_size - 1];
  82           r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
  83
  84           /* Possible optimization:
  85              if (r == 0
  86              && divisor_limb > ((n1 << normalization_steps)
  87                              | (dividend_ptr[dividend_size - 2] >> ...)))
  88              ...one division less... */
  89
  90           for (i = dividend_size - 2; i >= 0; i--)
  91             {
  92               n0 = dividend_ptr[i];
  93               udiv_qrnnd_preinv (dummy, r, r,
  94                                  ((n1 << normalization_steps)
  95                                   | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
  96                                  divisor_limb, divisor_limb_inverted);
  97               n1 = n0;
  98             }
  99           udiv_qrnnd_preinv (dummy, r, r,
 100                              n1 << normalization_steps,
 101                              divisor_limb, divisor_limb_inverted);
 102           return r >> normalization_steps;
 103         }
 104       else
 105         {
 106           mp_limb_t divisor_limb_inverted;
 107
 108           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
 109              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
 110              most significant bit (with weight 2**N) implicit.  */
 111
 112           /* Special case for DIVISOR_LIMB == 100...000.  */
 113           if (divisor_limb << 1 == 0)
 114             divisor_limb_inverted = ~(mp_limb_t) 0;
 115           else
 116             udiv_qrnnd (divisor_limb_inverted, dummy,
 117                         -divisor_limb, 0, divisor_limb);
 118
 119           i = dividend_size - 1;
 120           r = dividend_ptr[i];
 121
 122           if (r >= divisor_limb)
 123             r = 0;
 124           else
 125             i--;
 126
 127           for (; i >= 0; i--)
 128             {
 129               n0 = dividend_ptr[i];
 130               udiv_qrnnd_preinv (dummy, r, r,
 131                                  n0, divisor_limb, divisor_limb_inverted);
 132             }
 133           return r;
 134         }
 135     }
 136   else
 137     {
 138       if (UDIV_NEEDS_NORMALIZATION)
 139         {
 140           int normalization_steps;
 141
 142           count_leading_zeros (normalization_steps, divisor_limb);
 143           if (normalization_steps != 0)
 144             {
 145               divisor_limb <<= normalization_steps;
 146
 147               n1 = dividend_ptr[dividend_size - 1];
 148               r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
 149
 150               /* Possible optimization:
 151                  if (r == 0
 152                  && divisor_limb > ((n1 << normalization_steps)
 153                                  | (dividend_ptr[dividend_size - 2] >> ...)))
 154                  ...one division less... */
 155
 156               for (i = dividend_size - 2; i >= 0; i--)
 157                 {
 158                   n0 = dividend_ptr[i];
 159                   udiv_qrnnd (dummy, r, r,
 160                               ((n1 << normalization_steps)
 161                                | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 162                               divisor_limb);
 163                   n1 = n0;
 164                 }
 165               udiv_qrnnd (dummy, r, r,
 166                           n1 << normalization_steps,
 167                           divisor_limb);
 168               return r >> normalization_steps;
 169             }
 170         }
 171       /* No normalization needed, either because udiv_qrnnd doesn't require
 172          it, or because DIVISOR_LIMB is already normalized.  */
 173
 174       i = dividend_size - 1;
 175       r = dividend_ptr[i];
 176
 177       if (r >= divisor_limb)
 178         r = 0;
 179       else
 180         i--;
 181
 182       for (; i >= 0; i--)
 183         {
 184           n0 = dividend_ptr[i];
 185           udiv_qrnnd (dummy, r, r, n0, divisor_limb);
 186         }
 187       return r;
 188     }
 189 }