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, 1993, 1994, 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, write to
  22 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  23 MA 02111-1307, USA. */
  24
  25 #include <gmp.h>
  26 #include "gmp-impl.h"
  27 #include "longlong.h"
  28
  29 #ifndef UMUL_TIME
  30 #define UMUL_TIME 1
  31 #endif
  32
  33 #ifndef UDIV_TIME
  34 #define UDIV_TIME UMUL_TIME
  35 #endif
  36
  37 /* FIXME: We should be using invert_limb (or invert_normalized_limb)
  38    here (not udiv_qrnnd).  */
  39
  40 mp_limb_t
  41 #if __STDC__
  42 mpn_mod_1 (mp_srcptr dividend_ptr, mp_size_t dividend_size,
  43            mp_limb_t divisor_limb)
  44 #else
  45 mpn_mod_1 (dividend_ptr, dividend_size, divisor_limb)
  46      mp_srcptr dividend_ptr;
  47      mp_size_t dividend_size;
  48      mp_limb_t divisor_limb;
  49 #endif
  50 {
  51   mp_size_t i;
  52   mp_limb_t n1, n0, r;
  53   mp_limb_t dummy;
  54
  55   /* Botch: Should this be handled at all?  Rely on callers?  */
  56   if (dividend_size == 0)
  57     return 0;
  58
  59   /* If multiplication is much faster than division, and the
  60      dividend is large, pre-invert the divisor, and use
  61      only multiplications in the inner loop.  */
  62
  63   /* This test should be read:
  64        Does it ever help to use udiv_qrnnd_preinv?
  65          && Does what we save compensate for the inversion overhead?  */
  66   if (UDIV_TIME > (2 * UMUL_TIME + 6)
  67       && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
  68     {
  69       int normalization_steps;
  70
  71       count_leading_zeros (normalization_steps, divisor_limb);
  72       if (normalization_steps != 0)
  73         {
  74           mp_limb_t divisor_limb_inverted;
  75
  76           divisor_limb <<= normalization_steps;
  77
  78           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
  79              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
  80              most significant bit (with weight 2**N) implicit.  */
  81
  82           /* Special case for DIVISOR_LIMB == 100...000.  */
  83           if (divisor_limb << 1 == 0)
  84             divisor_limb_inverted = ~(mp_limb_t) 0;
  85           else
  86             udiv_qrnnd (divisor_limb_inverted, dummy,
  87                         -divisor_limb, 0, divisor_limb);
  88
  89           n1 = dividend_ptr[dividend_size - 1];
  90           r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
  91
  92           /* Possible optimization:
  93              if (r == 0
  94              && divisor_limb > ((n1 << normalization_steps)
  95                              | (dividend_ptr[dividend_size - 2] >> ...)))
  96              ...one division less... */
  97
  98           for (i = dividend_size - 2; i >= 0; i--)
  99             {
 100               n0 = dividend_ptr[i];
 101               udiv_qrnnd_preinv (dummy, r, r,
 102                                  ((n1 << normalization_steps)
 103                                   | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 104                                  divisor_limb, divisor_limb_inverted);
 105               n1 = n0;
 106             }
 107           udiv_qrnnd_preinv (dummy, r, r,
 108                              n1 << normalization_steps,
 109                              divisor_limb, divisor_limb_inverted);
 110           return r >> normalization_steps;
 111         }
 112       else
 113         {
 114           mp_limb_t divisor_limb_inverted;
 115
 116           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
 117              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
 118              most significant bit (with weight 2**N) implicit.  */
 119
 120           /* Special case for DIVISOR_LIMB == 100...000.  */
 121           if (divisor_limb << 1 == 0)
 122             divisor_limb_inverted = ~(mp_limb_t) 0;
 123           else
 124             udiv_qrnnd (divisor_limb_inverted, dummy,
 125                         -divisor_limb, 0, divisor_limb);
 126
 127           i = dividend_size - 1;
 128           r = dividend_ptr[i];
 129
 130           if (r >= divisor_limb)
 131             r = 0;
 132           else
 133             i--;
 134
 135           for (; i >= 0; i--)
 136             {
 137               n0 = dividend_ptr[i];
 138               udiv_qrnnd_preinv (dummy, r, r,
 139                                  n0, divisor_limb, divisor_limb_inverted);
 140             }
 141           return r;
 142         }
 143     }
 144   else
 145     {
 146       if (UDIV_NEEDS_NORMALIZATION)
 147         {
 148           int normalization_steps;
 149
 150           count_leading_zeros (normalization_steps, divisor_limb);
 151           if (normalization_steps != 0)
 152             {
 153               divisor_limb <<= normalization_steps;
 154
 155               n1 = dividend_ptr[dividend_size - 1];
 156               r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
 157
 158               /* Possible optimization:
 159                  if (r == 0
 160                  && divisor_limb > ((n1 << normalization_steps)
 161                                  | (dividend_ptr[dividend_size - 2] >> ...)))
 162                  ...one division less... */
 163
 164               for (i = dividend_size - 2; i >= 0; i--)
 165                 {
 166                   n0 = dividend_ptr[i];
 167                   udiv_qrnnd (dummy, r, r,
 168                               ((n1 << normalization_steps)
 169                                | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 170                               divisor_limb);
 171                   n1 = n0;
 172                 }
 173               udiv_qrnnd (dummy, r, r,
 174                           n1 << normalization_steps,
 175                           divisor_limb);
 176               return r >> normalization_steps;
 177             }
 178         }
 179       /* No normalization needed, either because udiv_qrnnd doesn't require
 180          it, or because DIVISOR_LIMB is already normalized.  */
 181
 182       i = dividend_size - 1;
 183       r = dividend_ptr[i];
 184
 185       if (r >= divisor_limb)
 186         r = 0;
 187       else
 188         i--;
 189
 190       for (; i >= 0; i--)
 191         {
 192           n0 = dividend_ptr[i];
 193           udiv_qrnnd (dummy, r, r, n0, divisor_limb);
 194         }
 195       return r;
 196     }
 197 }