/* 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, 2011, 2012 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 either:

  * the GNU Lesser General Public License as published by the Free

    Software Foundation; either version 3 of the License, or (at your

    option) any later version.

or

  * the GNU General Public License as published by the Free Software

    Foundation; either version 2 of the License, or (at your option) any

    later version.

or both in parallel, as here.

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 General Public License

for more details.

You should have received copies of the GNU General Public License and the

GNU Lesser General Public License along with the GNU MP Library.  If not,

see https://www.gnu.org/licenses/.  */

#include "gmp.h"

#include "gmp-impl.h"

#include "longlong.h"

mp_limb_t

mpn_udiv_w_sdiv (mp_limb_t *rp, mp_limb_t a1, mp_limb_t a0, mp_limb_t 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 >> (GMP_LIMB_BITS - 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 << (GMP_LIMB_BITS - 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 << (GMP_LIMB_BITS - 1);

	}

    }

  else

    {

      b1 = d >> 1;			/* d/2, between 2^30 and 2^31 - 1 */

      c1 = a1 >> 1;			/* A/2 */

      c0 = (a1 << (GMP_LIMB_BITS - 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 = -CNST_LIMB(1);

	      r = a0 + d;

	    }

	  else

	    {

	      q = -CNST_LIMB(2);

	      r = a0 + 2*d;

	    }

	}

    }

  *rp = r;

  return q;

}