mpir/mpn/generic/udiv_w_sdiv.c

/* mpn_udiv_w_sdiv -- implement udiv_qrnnd on machines with only signed
   division.

   Contributed by Peter L. Montgomery.

   THIS IS AN INTERNAL FUNCTION WITH A MUTABLE INTERFACE.  IT IS ONLY SAFE
   TO REACH THIS FUNCTION THROUGH DOCUMENTED INTERFACES.  IN FACT, IT IS
   ALMOST GUARANTEED THAT THIS FUNCTION WILL CHANGE OR DISAPPEAR IN A FUTURE
   GNU MP RELEASE.


Copyright 1992, 1994, 1996, 2000 Free Software Foundation, Inc.

This file is part of the GNU MP Library.

The GNU MP Library is free software; you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation; either version 2.1 of the License, or (at your
option) any later version.

The GNU MP Library is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
License for more details.

You should have received a copy of the GNU Lesser General Public License
along with the GNU MP Library; see the file COPYING.LIB.  If not, write to
the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston,
MA 02110-1301, USA. */

#include "gmp.h"
#include "gmp-impl.h"
#include "longlong.h"

mp_limb_t
mpn_udiv_w_sdiv (rp, a1, a0, d)
     mp_limb_t *rp, a1, a0, d;
{
  mp_limb_t q, r;
  mp_limb_t c0, c1, b1;

  ASSERT (d != 0);
  ASSERT (a1 < d);

  if ((mp_limb_signed_t) d >= 0)
    {
      if (a1 < d - a1 - (a0 >> (BITS_PER_MP_LIMB - 1)))
	{
	  /* dividend, divisor, and quotient are nonnegative */
	  sdiv_qrnnd (q, r, a1, a0, d);
	}
      else
	{
	  /* Compute c1*2^32 + c0 = a1*2^32 + a0 - 2^31*d */
	  sub_ddmmss (c1, c0, a1, a0, d >> 1, d << (BITS_PER_MP_LIMB - 1));
	  /* Divide (c1*2^32 + c0) by d */
	  sdiv_qrnnd (q, r, c1, c0, d);
	  /* Add 2^31 to quotient */
	  q += (mp_limb_t) 1 << (BITS_PER_MP_LIMB - 1);
	}
    }
  else
    {
      b1 = d >> 1;			/* d/2, between 2^30 and 2^31 - 1 */
      c1 = a1 >> 1;			/* A/2 */
      c0 = (a1 << (BITS_PER_MP_LIMB - 1)) + (a0 >> 1);

      if (a1 < b1)			/* A < 2^32*b1, so A/2 < 2^31*b1 */
	{
	  sdiv_qrnnd (q, r, c1, c0, b1); /* (A/2) / (d/2) */

	  r = 2*r + (a0 & 1);		/* Remainder from A/(2*b1) */
	  if ((d & 1) != 0)
	    {
	      if (r >= q)
		r = r - q;
	      else if (q - r <= d)
		{
		  r = r - q + d;
		  q--;
		}
	      else
		{
		  r = r - q + 2*d;
		  q -= 2;
		}
	    }
	}
      else if (c1 < b1)			/* So 2^31 <= (A/2)/b1 < 2^32 */
	{
	  c1 = (b1 - 1) - c1;
	  c0 = ~c0;			/* logical NOT */

	  sdiv_qrnnd (q, r, c1, c0, b1); /* (A/2) / (d/2) */

	  q = ~q;			/* (A/2)/b1 */
	  r = (b1 - 1) - r;

	  r = 2*r + (a0 & 1);		/* A/(2*b1) */

	  if ((d & 1) != 0)
	    {
	      if (r >= q)
		r = r - q;
	      else if (q - r <= d)
		{
		  r = r - q + d;
		  q--;
		}
	      else
		{
		  r = r - q + 2*d;
		  q -= 2;
		}
	    }
	}
      else				/* Implies c1 = b1 */
	{				/* Hence a1 = d - 1 = 2*b1 - 1 */
	  if (a0 >= -d)
	    {
	      q = -1;
	      r = a0 + d;
	    }
	  else
	    {
	      q = -2;
	      r = a0 + 2*d;
	    }
	}
    }

  *rp = r;
  return q;
}