source/libs/gmp/gmp-src/mpn/generic/udiv_w_sdiv.c

   1 /* mpn_udiv_w_sdiv -- implement udiv_qrnnd on machines with only signed
   2    division.
   3
   4    Contributed by Peter L. Montgomery.
   5
   6    THIS IS AN INTERNAL FUNCTION WITH A MUTABLE INTERFACE.  IT IS ONLY SAFE
   7    TO REACH THIS FUNCTION THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS
   8    ALMOST GUARANTEED THAT THIS FUNCTION WILL CHANGE OR DISAPPEAR IN A FUTURE
   9    GNU MP RELEASE.
  10
  11
  12 Copyright 1992, 1994, 1996, 2000, 2011, 2012 Free Software Foundation, Inc.
  13
  14 This file is part of the GNU MP Library.
  15
  16 The GNU MP Library is free software; you can redistribute it and/or modify
  17 it under the terms of either:
  18
  19   * the GNU Lesser General Public License as published by the Free
  20     Software Foundation; either version 3 of the License, or (at your
  21     option) any later version.
  22
  23 or
  24
  25   * the GNU General Public License as published by the Free Software
  26     Foundation; either version 2 of the License, or (at your option) any
  27     later version.
  28
  29 or both in parallel, as here.
  30
  31 The GNU MP Library is distributed in the hope that it will be useful, but
  32 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  33 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  34 for more details.
  35
  36 You should have received copies of the GNU General Public License and the
  37 GNU Lesser General Public License along with the GNU MP Library.  If not,
  38 see https://www.gnu.org/licenses/.  */
  39
  40 #include "gmp.h"
  41 #include "gmp-impl.h"
  42 #include "longlong.h"
  43
  44 mp_limb_t
  45 mpn_udiv_w_sdiv (mp_limb_t *rp, mp_limb_t a1, mp_limb_t a0, mp_limb_t d)
  46 {
  47   mp_limb_t q, r;
  48   mp_limb_t c0, c1, b1;
  49
  50   ASSERT (d != 0);
  51   ASSERT (a1 < d);
  52
  53   if ((mp_limb_signed_t) d >= 0)
  54     {
  55       if (a1 < d - a1 - (a0 >> (GMP_LIMB_BITS - 1)))
  56         {
  57           /* dividend, divisor, and quotient are nonnegative */
  58           sdiv_qrnnd (q, r, a1, a0, d);
  59         }
  60       else
  61         {
  62           /* Compute c1*2^32 + c0 = a1*2^32 + a0 - 2^31*d */
  63           sub_ddmmss (c1, c0, a1, a0, d >> 1, d << (GMP_LIMB_BITS - 1));
  64           /* Divide (c1*2^32 + c0) by d */
  65           sdiv_qrnnd (q, r, c1, c0, d);
  66           /* Add 2^31 to quotient */
  67           q += (mp_limb_t) 1 << (GMP_LIMB_BITS - 1);
  68         }
  69     }
  70   else
  71     {
  72       b1 = d >> 1;                      /* d/2, between 2^30 and 2^31 - 1 */
  73       c1 = a1 >> 1;                     /* A/2 */
  74       c0 = (a1 << (GMP_LIMB_BITS - 1)) + (a0 >> 1);
  75
  76       if (a1 < b1)                      /* A < 2^32*b1, so A/2 < 2^31*b1 */
  77         {
  78           sdiv_qrnnd (q, r, c1, c0, b1); /* (A/2) / (d/2) */
  79
  80           r = 2*r + (a0 & 1);           /* Remainder from A/(2*b1) */
  81           if ((d & 1) != 0)
  82             {
  83               if (r >= q)
  84                 r = r - q;
  85               else if (q - r <= d)
  86                 {
  87                   r = r - q + d;
  88                   q--;
  89                 }
  90               else
  91                 {
  92                   r = r - q + 2*d;
  93                   q -= 2;
  94                 }
  95             }
  96         }
  97       else if (c1 < b1)                 /* So 2^31 <= (A/2)/b1 < 2^32 */
  98         {
  99           c1 = (b1 - 1) - c1;
 100           c0 = ~c0;                     /* logical NOT */
 101
 102           sdiv_qrnnd (q, r, c1, c0, b1); /* (A/2) / (d/2) */
 103
 104           q = ~q;                       /* (A/2)/b1 */
 105           r = (b1 - 1) - r;
 106
 107           r = 2*r + (a0 & 1);           /* A/(2*b1) */
 108
 109           if ((d & 1) != 0)
 110             {
 111               if (r >= q)
 112                 r = r - q;
 113               else if (q - r <= d)
 114                 {
 115                   r = r - q + d;
 116                   q--;
 117                 }
 118               else
 119                 {
 120                   r = r - q + 2*d;
 121                   q -= 2;
 122                 }
 123             }
 124         }
 125       else                              /* Implies c1 = b1 */
 126         {                               /* Hence a1 = d - 1 = 2*b1 - 1 */
 127           if (a0 >= -d)
 128             {
 129               q = -CNST_LIMB(1);
 130               r = a0 + d;
 131             }
 132           else
 133             {
 134               q = -CNST_LIMB(2);
 135               r = a0 + 2*d;
 136             }
 137         }
 138     }
 139
 140   *rp = r;
 141   return q;
 142 }