stdlib/divrem.c

   1 /* mpn_divrem -- Divide natural numbers, producing both remainder and
   2    quotient.
   3
   4 Copyright (C) 1993-2015 Free Software Foundation, Inc.
   5
   6 This file is part of the GNU MP Library.
   7
   8 The GNU MP Library is free software; you can redistribute it and/or modify
   9 it under the terms of the GNU Lesser General Public License as published by
  10 the Free Software Foundation; either version 2.1 of the License, or (at your
  11 option) any later version.
  12
  13 The GNU MP Library is distributed in the hope that it will be useful, but
  14 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  15 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
  16 License for more details.
  17
  18 You should have received a copy of the GNU Lesser General Public License
  19 along with the GNU MP Library; see the file COPYING.LIB.  If not, see
  20 <http://www.gnu.org/licenses/>.  */
  21
  22 #include <gmp.h>
  23 #include "gmp-impl.h"
  24 #include "longlong.h"
  25
  26 /* Divide num (NP/NSIZE) by den (DP/DSIZE) and write
  27    the NSIZE-DSIZE least significant quotient limbs at QP
  28    and the DSIZE long remainder at NP.  If QEXTRA_LIMBS is
  29    non-zero, generate that many fraction bits and append them after the
  30    other quotient limbs.
  31    Return the most significant limb of the quotient, this is always 0 or 1.
  32
  33    Preconditions:
  34    0. NSIZE >= DSIZE.
  35    1. The most significant bit of the divisor must be set.
  36    2. QP must either not overlap with the input operands at all, or
  37       QP + DSIZE >= NP must hold true.  (This means that it's
  38       possible to put the quotient in the high part of NUM, right after the
  39       remainder in NUM.
  40    3. NSIZE >= DSIZE, even if QEXTRA_LIMBS is non-zero.  */
  41
  42 mp_limb_t
  43 #if __STDC__
  44 mpn_divrem (mp_ptr qp, mp_size_t qextra_limbs,
  45             mp_ptr np, mp_size_t nsize,
  46             mp_srcptr dp, mp_size_t dsize)
  47 #else
  48 mpn_divrem (qp, qextra_limbs, np, nsize, dp, dsize)
  49      mp_ptr qp;
  50      mp_size_t qextra_limbs;
  51      mp_ptr np;
  52      mp_size_t nsize;
  53      mp_srcptr dp;
  54      mp_size_t dsize;
  55 #endif
  56 {
  57   mp_limb_t most_significant_q_limb = 0;
  58
  59   switch (dsize)
  60     {
  61     case 0:
  62       /* We are asked to divide by zero, so go ahead and do it!  (To make
  63          the compiler not remove this statement, return the value.)  */
  64       return 1 / dsize;
  65
  66     case 1:
  67       {
  68         mp_size_t i;
  69         mp_limb_t n1;
  70         mp_limb_t d;
  71
  72         d = dp[0];
  73         n1 = np[nsize - 1];
  74
  75         if (n1 >= d)
  76           {
  77             n1 -= d;
  78             most_significant_q_limb = 1;
  79           }
  80
  81         qp += qextra_limbs;
  82         for (i = nsize - 2; i >= 0; i--)
  83           udiv_qrnnd (qp[i], n1, n1, np[i], d);
  84         qp -= qextra_limbs;
  85
  86         for (i = qextra_limbs - 1; i >= 0; i--)
  87           udiv_qrnnd (qp[i], n1, n1, 0, d);
  88
  89         np[0] = n1;
  90       }
  91       break;
  92
  93     case 2:
  94       {
  95         mp_size_t i;
  96         mp_limb_t n1, n0, n2;
  97         mp_limb_t d1, d0;
  98
  99         np += nsize - 2;
 100         d1 = dp[1];
 101         d0 = dp[0];
 102         n1 = np[1];
 103         n0 = np[0];
 104
 105         if (n1 >= d1 && (n1 > d1 || n0 >= d0))
 106           {
 107             sub_ddmmss (n1, n0, n1, n0, d1, d0);
 108             most_significant_q_limb = 1;
 109           }
 110
 111         for (i = qextra_limbs + nsize - 2 - 1; i >= 0; i--)
 112           {
 113             mp_limb_t q;
 114             mp_limb_t r;
 115
 116             if (i >= qextra_limbs)
 117               np--;
 118             else
 119               np[0] = 0;
 120
 121             if (n1 == d1)
 122               {
 123                 /* Q should be either 111..111 or 111..110.  Need special
 124                    treatment of this rare case as normal division would
 125                    give overflow.  */
 126                 q = ~(mp_limb_t) 0;
 127
 128                 r = n0 + d1;
 129                 if (r < d1)     /* Carry in the addition? */
 130                   {
 131                     add_ssaaaa (n1, n0, r - d0, np[0], 0, d0);
 132                     qp[i] = q;
 133                     continue;
 134                   }
 135                 n1 = d0 - (d0 != 0);
 136                 n0 = -d0;
 137               }
 138             else
 139               {
 140                 udiv_qrnnd (q, r, n1, n0, d1);
 141                 umul_ppmm (n1, n0, d0, q);
 142               }
 143
 144             n2 = np[0];
 145           q_test:
 146             if (n1 > r || (n1 == r && n0 > n2))
 147               {
 148                 /* The estimated Q was too large.  */
 149                 q--;
 150
 151                 sub_ddmmss (n1, n0, n1, n0, 0, d0);
 152                 r += d1;
 153                 if (r >= d1)    /* If not carry, test Q again.  */
 154                   goto q_test;
 155               }
 156
 157             qp[i] = q;
 158             sub_ddmmss (n1, n0, r, n2, n1, n0);
 159           }
 160         np[1] = n1;
 161         np[0] = n0;
 162       }
 163       break;
 164
 165     default:
 166       {
 167         mp_size_t i;
 168         mp_limb_t dX, d1, n0;
 169
 170         np += nsize - dsize;
 171         dX = dp[dsize - 1];
 172         d1 = dp[dsize - 2];
 173         n0 = np[dsize - 1];
 174
 175         if (n0 >= dX)
 176           {
 177             if (n0 > dX || mpn_cmp (np, dp, dsize - 1) >= 0)
 178               {
 179                 mpn_sub_n (np, np, dp, dsize);
 180                 n0 = np[dsize - 1];
 181                 most_significant_q_limb = 1;
 182               }
 183           }
 184
 185         for (i = qextra_limbs + nsize - dsize - 1; i >= 0; i--)
 186           {
 187             mp_limb_t q;
 188             mp_limb_t n1, n2;
 189             mp_limb_t cy_limb;
 190
 191             if (i >= qextra_limbs)
 192               {
 193                 np--;
 194                 n2 = np[dsize];
 195               }
 196             else
 197               {
 198                 n2 = np[dsize - 1];
 199                 MPN_COPY_DECR (np + 1, np, dsize);
 200                 np[0] = 0;
 201               }
 202
 203             if (n0 == dX)
 204               /* This might over-estimate q, but it's probably not worth
 205                  the extra code here to find out.  */
 206               q = ~(mp_limb_t) 0;
 207             else
 208               {
 209                 mp_limb_t r;
 210
 211                 udiv_qrnnd (q, r, n0, np[dsize - 1], dX);
 212                 umul_ppmm (n1, n0, d1, q);
 213
 214                 while (n1 > r || (n1 == r && n0 > np[dsize - 2]))
 215                   {
 216                     q--;
 217                     r += dX;
 218                     if (r < dX) /* I.e. "carry in previous addition?"  */
 219                       break;
 220                     n1 -= n0 < d1;
 221                     n0 -= d1;
 222                   }
 223               }
 224
 225             /* Possible optimization: We already have (q * n0) and (1 * n1)
 226                after the calculation of q.  Taking advantage of that, we
 227                could make this loop make two iterations less.  */
 228
 229             cy_limb = mpn_submul_1 (np, dp, dsize, q);
 230
 231             if (n2 != cy_limb)
 232               {
 233                 mpn_add_n (np, np, dp, dsize);
 234                 q--;
 235               }
 236
 237             qp[i] = q;
 238             n0 = np[dsize - 1];
 239           }
 240       }
 241     }
 242
 243   return most_significant_q_limb;
 244 }