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-impl.h"
      38  #include "longlong.h"
      39  
      40  
      41  /* Divide num {np,nn} by den {dp,2} and write the nn-2 least significant
      42     quotient limbs at qp and the 2 long remainder at np.  If qxn is non-zero,
      43     generate that many fraction bits and append them after the other quotient
      44     limbs.  Return the most significant limb of the quotient, this is always 0
      45     or 1.
      46  
      47     Preconditions:
      48     1. The most significant bit of the divisor must be set.
      49     2. qp must either not overlap with the input operands at all, or
      50        qp >= np + 2 must hold true.  (This means that it's possible to put
      51        the quotient in the high part of {np,nn}, right above the remainder.
      52     3. nn >= 2, even if qxn is non-zero.  */
      53  
      54  mp_limb_t
      55  mpn_divrem_2 (mp_ptr qp, mp_size_t qxn,
      56  	      mp_ptr np, mp_size_t nn,
      57  	      mp_srcptr dp)
      58  {
      59    mp_limb_t most_significant_q_limb;
      60    mp_size_t i;
      61    mp_limb_t r1, r0, d1, d0;
      62    gmp_pi1_t di;
      63  
      64    ASSERT (nn >= 2);
      65    ASSERT (qxn >= 0);
      66    ASSERT (dp[1] & GMP_NUMB_HIGHBIT);
      67    ASSERT (! MPN_OVERLAP_P (qp, nn-2+qxn, np, nn) || qp >= np+2);
      68    ASSERT_MPN (np, nn);
      69    ASSERT_MPN (dp, 2);
      70  
      71    np += nn - 2;
      72    d1 = dp[1];
      73    d0 = dp[0];
      74    r1 = np[1];
      75    r0 = np[0];
      76  
      77    most_significant_q_limb = 0;
      78    if (r1 >= d1 && (r1 > d1 || r0 >= d0))
      79      {
      80  #if GMP_NAIL_BITS == 0
      81        sub_ddmmss (r1, r0, r1, r0, d1, d0);
      82  #else
      83        r0 = r0 - d0;
      84        r1 = r1 - d1 - (r0 >> GMP_LIMB_BITS - 1);
      85        r0 &= GMP_NUMB_MASK;
      86  #endif
      87        most_significant_q_limb = 1;
      88      }
      89  
      90    invert_pi1 (di, d1, d0);
      91  
      92    qp += qxn;
      93  
      94    for (i = nn - 2 - 1; i >= 0; i--)
      95      {
      96        mp_limb_t n0, q;
      97        n0 = np[-1];
      98        udiv_qr_3by2 (q, r1, r0, r1, r0, n0, d1, d0, di.inv32);
      99        np--;
     100        qp[i] = q;
     101      }
     102  
     103    if (UNLIKELY (qxn != 0))
     104      {
     105        qp -= qxn;
     106        for (i = qxn - 1; i >= 0; i--)
     107  	{
     108  	  mp_limb_t q;
     109  	  udiv_qr_3by2 (q, r1, r0, r1, r0, CNST_LIMB(0), d1, d0, di.inv32);
     110  	  qp[i] = q;
     111  	}
     112      }
     113  
     114    np[1] = r1;
     115    np[0] = r0;
     116  
     117    return most_significant_q_limb;
     118  }