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-impl.h"
      41  #include "longlong.h"
      42  
      43  mp_limb_t
      44  mpn_udiv_w_sdiv (mp_limb_t *rp, mp_limb_t a1, mp_limb_t a0, mp_limb_t d)
      45  {
      46    mp_limb_t q, r;
      47    mp_limb_t c0, c1, b1;
      48  
      49    ASSERT (d != 0);
      50    ASSERT (a1 < d);
      51  
      52    if ((mp_limb_signed_t) d >= 0)
      53      {
      54        if (a1 < d - a1 - (a0 >> (GMP_LIMB_BITS - 1)))
      55  	{
      56  	  /* dividend, divisor, and quotient are nonnegative */
      57  	  sdiv_qrnnd (q, r, a1, a0, d);
      58  	}
      59        else
      60  	{
      61  	  /* Compute c1*2^32 + c0 = a1*2^32 + a0 - 2^31*d */
      62  	  sub_ddmmss (c1, c0, a1, a0, d >> 1, d << (GMP_LIMB_BITS - 1));
      63  	  /* Divide (c1*2^32 + c0) by d */
      64  	  sdiv_qrnnd (q, r, c1, c0, d);
      65  	  /* Add 2^31 to quotient */
      66  	  q += (mp_limb_t) 1 << (GMP_LIMB_BITS - 1);
      67  	}
      68      }
      69    else
      70      {
      71        b1 = d >> 1;			/* d/2, between 2^30 and 2^31 - 1 */
      72        c1 = a1 >> 1;			/* A/2 */
      73        c0 = (a1 << (GMP_LIMB_BITS - 1)) + (a0 >> 1);
      74  
      75        if (a1 < b1)			/* A < 2^32*b1, so A/2 < 2^31*b1 */
      76  	{
      77  	  sdiv_qrnnd (q, r, c1, c0, b1); /* (A/2) / (d/2) */
      78  
      79  	  r = 2*r + (a0 & 1);		/* Remainder from A/(2*b1) */
      80  	  if ((d & 1) != 0)
      81  	    {
      82  	      if (r >= q)
      83  		r = r - q;
      84  	      else if (q - r <= d)
      85  		{
      86  		  r = r - q + d;
      87  		  q--;
      88  		}
      89  	      else
      90  		{
      91  		  r = r - q + 2*d;
      92  		  q -= 2;
      93  		}
      94  	    }
      95  	}
      96        else if (c1 < b1)			/* So 2^31 <= (A/2)/b1 < 2^32 */
      97  	{
      98  	  c1 = (b1 - 1) - c1;
      99  	  c0 = ~c0;			/* logical NOT */
     100  
     101  	  sdiv_qrnnd (q, r, c1, c0, b1); /* (A/2) / (d/2) */
     102  
     103  	  q = ~q;			/* (A/2)/b1 */
     104  	  r = (b1 - 1) - r;
     105  
     106  	  r = 2*r + (a0 & 1);		/* A/(2*b1) */
     107  
     108  	  if ((d & 1) != 0)
     109  	    {
     110  	      if (r >= q)
     111  		r = r - q;
     112  	      else if (q - r <= d)
     113  		{
     114  		  r = r - q + d;
     115  		  q--;
     116  		}
     117  	      else
     118  		{
     119  		  r = r - q + 2*d;
     120  		  q -= 2;
     121  		}
     122  	    }
     123  	}
     124        else				/* Implies c1 = b1 */
     125  	{				/* Hence a1 = d - 1 = 2*b1 - 1 */
     126  	  if (a0 >= -d)
     127  	    {
     128  	      q = -CNST_LIMB(1);
     129  	      r = a0 + d;
     130  	    }
     131  	  else
     132  	    {
     133  	      q = -CNST_LIMB(2);
     134  	      r = a0 + 2*d;
     135  	    }
     136  	}
     137      }
     138  
     139    *rp = r;
     140    return q;
     141  }