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, 1993, 1994, 1996 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, write to
  25 the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston,
  26 MA 02111-1307, USA. */
  27
  28 #include <gmp.h>
  29 #include "gmp-impl.h"
  30 #include "longlong.h"
  31
  32 #ifndef UMUL_TIME
  33 #define UMUL_TIME 1
  34 #endif
  35
  36 #ifndef UDIV_TIME
  37 #define UDIV_TIME UMUL_TIME
  38 #endif
  39
  40 /* FIXME: We should be using invert_limb (or invert_normalized_limb)
  41    here (not udiv_qrnnd).  */
  42
  43 mp_limb_t
  44 #if __STDC__
  45 mpn_divmod_1 (mp_ptr quot_ptr,
  46               mp_srcptr dividend_ptr, mp_size_t dividend_size,
  47               mp_limb_t divisor_limb)
  48 #else
  49 mpn_divmod_1 (quot_ptr, dividend_ptr, dividend_size, divisor_limb)
  50      mp_ptr quot_ptr;
  51      mp_srcptr dividend_ptr;
  52      mp_size_t dividend_size;
  53      mp_limb_t divisor_limb;
  54 #endif
  55 {
  56   mp_size_t i;
  57   mp_limb_t n1, n0, r;
  58   int dummy;
  59
  60   /* ??? Should this be handled at all?  Rely on callers?  */
  61   if (dividend_size == 0)
  62     return 0;
  63
  64   /* If multiplication is much faster than division, and the
  65      dividend is large, pre-invert the divisor, and use
  66      only multiplications in the inner loop.  */
  67
  68   /* This test should be read:
  69        Does it ever help to use udiv_qrnnd_preinv?
  70          && Does what we save compensate for the inversion overhead?  */
  71   if (UDIV_TIME > (2 * UMUL_TIME + 6)
  72       && (UDIV_TIME - (2 * UMUL_TIME + 6)) * dividend_size > UDIV_TIME)
  73     {
  74       int normalization_steps;
  75
  76       count_leading_zeros (normalization_steps, divisor_limb);
  77       if (normalization_steps != 0)
  78         {
  79           mp_limb_t divisor_limb_inverted;
  80
  81           divisor_limb <<= normalization_steps;
  82
  83           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
  84              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
  85              most significant bit (with weight 2**N) implicit.  */
  86
  87           /* Special case for DIVISOR_LIMB == 100...000.  */
  88           if (divisor_limb << 1 == 0)
  89             divisor_limb_inverted = ~(mp_limb_t) 0;
  90           else
  91             udiv_qrnnd (divisor_limb_inverted, dummy,
  92                         -divisor_limb, 0, divisor_limb);
  93
  94           n1 = dividend_ptr[dividend_size - 1];
  95           r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
  96
  97           /* Possible optimization:
  98              if (r == 0
  99              && divisor_limb > ((n1 << normalization_steps)
 100                              | (dividend_ptr[dividend_size - 2] >> ...)))
 101              ...one division less... */
 102
 103           for (i = dividend_size - 2; i >= 0; i--)
 104             {
 105               n0 = dividend_ptr[i];
 106               udiv_qrnnd_preinv (quot_ptr[i + 1], r, r,
 107                                  ((n1 << normalization_steps)
 108                                   | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 109                                  divisor_limb, divisor_limb_inverted);
 110               n1 = n0;
 111             }
 112           udiv_qrnnd_preinv (quot_ptr[0], r, r,
 113                              n1 << normalization_steps,
 114                              divisor_limb, divisor_limb_inverted);
 115           return r >> normalization_steps;
 116         }
 117       else
 118         {
 119           mp_limb_t divisor_limb_inverted;
 120
 121           /* Compute (2**2N - 2**N * DIVISOR_LIMB) / DIVISOR_LIMB.  The
 122              result is a (N+1)-bit approximation to 1/DIVISOR_LIMB, with the
 123              most significant bit (with weight 2**N) implicit.  */
 124
 125           /* Special case for DIVISOR_LIMB == 100...000.  */
 126           if (divisor_limb << 1 == 0)
 127             divisor_limb_inverted = ~(mp_limb_t) 0;
 128           else
 129             udiv_qrnnd (divisor_limb_inverted, dummy,
 130                         -divisor_limb, 0, divisor_limb);
 131
 132           i = dividend_size - 1;
 133           r = dividend_ptr[i];
 134
 135           if (r >= divisor_limb)
 136             r = 0;
 137           else
 138             {
 139               quot_ptr[i] = 0;
 140               i--;
 141             }
 142
 143           for (; i >= 0; i--)
 144             {
 145               n0 = dividend_ptr[i];
 146               udiv_qrnnd_preinv (quot_ptr[i], r, r,
 147                                  n0, divisor_limb, divisor_limb_inverted);
 148             }
 149           return r;
 150         }
 151     }
 152   else
 153     {
 154       if (UDIV_NEEDS_NORMALIZATION)
 155         {
 156           int normalization_steps;
 157
 158           count_leading_zeros (normalization_steps, divisor_limb);
 159           if (normalization_steps != 0)
 160             {
 161               divisor_limb <<= normalization_steps;
 162
 163               n1 = dividend_ptr[dividend_size - 1];
 164               r = n1 >> (BITS_PER_MP_LIMB - normalization_steps);
 165
 166               /* Possible optimization:
 167                  if (r == 0
 168                  && divisor_limb > ((n1 << normalization_steps)
 169                                  | (dividend_ptr[dividend_size - 2] >> ...)))
 170                  ...one division less... */
 171
 172               for (i = dividend_size - 2; i >= 0; i--)
 173                 {
 174                   n0 = dividend_ptr[i];
 175                   udiv_qrnnd (quot_ptr[i + 1], r, r,
 176                               ((n1 << normalization_steps)
 177                                | (n0 >> (BITS_PER_MP_LIMB - normalization_steps))),
 178                               divisor_limb);
 179                   n1 = n0;
 180                 }
 181               udiv_qrnnd (quot_ptr[0], r, r,
 182                           n1 << normalization_steps,
 183                           divisor_limb);
 184               return r >> normalization_steps;
 185             }
 186         }
 187       /* No normalization needed, either because udiv_qrnnd doesn't require
 188          it, or because DIVISOR_LIMB is already normalized.  */
 189
 190       i = dividend_size - 1;
 191       r = dividend_ptr[i];
 192
 193       if (r >= divisor_limb)
 194         r = 0;
 195       else
 196         {
 197           quot_ptr[i] = 0;
 198           i--;
 199         }
 200
 201       for (; i >= 0; i--)
 202         {
 203           n0 = dividend_ptr[i];
 204           udiv_qrnnd (quot_ptr[i], r, r, n0, divisor_limb);
 205         }
 206       return r;
 207     }
 208 }