source/libs/gmp/gmp-src/mpn/generic/divrem_2.c

   1 /* mpn_divrem_2 -- Divide natural numbers, producing both remainder and
   2    quotient.  The divisor is two limbs.
   3
   4    THIS FILE CONTAINS INTERNAL FUNCTIONS WITH MUTABLE INTERFACES.  IT IS ONLY
   5    SAFE TO REACH THEM THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS ALMOST
   6    GUARANTEED THAT THEY'LL CHANGE OR DISAPPEAR IN A FUTURE GNU MP RELEASE.
   7
   8
   9 Copyright 1993-1996, 1999-2002 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 either:
  15
  16   * the GNU Lesser General Public License as published by the Free
  17     Software Foundation; either version 3 of the License, or (at your
  18     option) any later version.
  19
  20 or
  21
  22   * the GNU General Public License as published by the Free Software
  23     Foundation; either version 2 of the License, or (at your option) any
  24     later version.
  25
  26 or both in parallel, as here.
  27
  28 The GNU MP Library is distributed in the hope that it will be useful, but
  29 WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
  30 or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public License
  31 for more details.
  32
  33 You should have received copies of the GNU General Public License and the
  34 GNU Lesser General Public License along with the GNU MP Library.  If not,
  35 see https://www.gnu.org/licenses/.  */
  36
  37 #include "gmp.h"
  38 #include "gmp-impl.h"
  39 #include "longlong.h"
  40
  41
  42 /* Divide num {np,nn} by den {dp,2} and write the nn-2 least significant
  43    quotient limbs at qp and the 2 long remainder at np.  If qxn is non-zero,
  44    generate that many fraction bits and append them after the other quotient
  45    limbs.  Return the most significant limb of the quotient, this is always 0
  46    or 1.
  47
  48    Preconditions:
  49    1. The most significant bit of the divisor must be set.
  50    2. qp must either not overlap with the input operands at all, or
  51       qp >= np + 2 must hold true.  (This means that it's possible to put
  52       the quotient in the high part of {np,nn}, right above the remainder.
  53    3. nn >= 2, even if qxn is non-zero.  */
  54
  55 mp_limb_t
  56 mpn_divrem_2 (mp_ptr qp, mp_size_t qxn,
  57               mp_ptr np, mp_size_t nn,
  58               mp_srcptr dp)
  59 {
  60   mp_limb_t most_significant_q_limb;
  61   mp_size_t i;
  62   mp_limb_t r1, r0, d1, d0;
  63   gmp_pi1_t di;
  64
  65   ASSERT (nn >= 2);
  66   ASSERT (qxn >= 0);
  67   ASSERT (dp[1] & GMP_NUMB_HIGHBIT);
  68   ASSERT (! MPN_OVERLAP_P (qp, nn-2+qxn, np, nn) || qp >= np+2);
  69   ASSERT_MPN (np, nn);
  70   ASSERT_MPN (dp, 2);
  71
  72   np += nn - 2;
  73   d1 = dp[1];
  74   d0 = dp[0];
  75   r1 = np[1];
  76   r0 = np[0];
  77
  78   most_significant_q_limb = 0;
  79   if (r1 >= d1 && (r1 > d1 || r0 >= d0))
  80     {
  81 #if GMP_NAIL_BITS == 0
  82       sub_ddmmss (r1, r0, r1, r0, d1, d0);
  83 #else
  84       r0 = r0 - d0;
  85       r1 = r1 - d1 - (r0 >> GMP_LIMB_BITS - 1);
  86       r0 &= GMP_NUMB_MASK;
  87 #endif
  88       most_significant_q_limb = 1;
  89     }
  90
  91   invert_pi1 (di, d1, d0);
  92
  93   qp += qxn;
  94
  95   for (i = nn - 2 - 1; i >= 0; i--)
  96     {
  97       mp_limb_t n0, q;
  98       n0 = np[-1];
  99       udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di.inv32);
 100       np--;
 101       qp[i] = q;
 102     }
 103
 104   if (UNLIKELY (qxn != 0))
 105     {
 106       qp -= qxn;
 107       for (i = qxn - 1; i >= 0; i--)
 108         {
 109           mp_limb_t q;
 110           udiv_qr_3by2 (q, r1, r0, r1, r0, CNST_LIMB(0), d1, d0, di.inv32);
 111           qp[i] = q;
 112         }
 113     }
 114
 115   np[1] = r1;
 116   np[0] = r0;
 117
 118   return most_significant_q_limb;
 119 }