/*

 * IBM Accurate Mathematical Library

 * written by International Business Machines Corp.

 * Copyright (C) 2001-2018 Free Software Foundation, Inc.

 *

 * This program 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.

 *

 * This program 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 this program; if not, see <http://www.gnu.org/licenses/>.

 */

/******************************************************************/

/*                                                                */

/* MODULE_NAME:mpatan.c                                           */

/*                                                                */

/* FUNCTIONS:mpatan                                               */

/*                                                                */

/* FILES NEEDED: mpa.h endian.h mpatan.h                          */

/*               mpa.c                                            */

/*                                                                */

/* Multi-Precision Atan function subroutine, for precision p >= 4.*/

/* The relative error of the result is bounded by 34.32*r**(1-p), */

/* where r=2**24.                                                 */

/******************************************************************/

#include "endian.h"

#include "mpa.h"

#include <math.h>

#ifndef SECTION

# define SECTION

#endif

#include "mpatan.h"

void

SECTION

__mpatan (mp_no *x, mp_no *y, int p)

{

  int i, m, n;

  double dx;

  mp_no mptwoim1 =

  {

    0,

    {

      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,

      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,

      0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0

    }

  };

  mp_no mps, mpsm, mpt, mpt1, mpt2, mpt3;

  /* Choose m and initiate mptwoim1.  */

  if (EX > 0)

    m = 7;

  else if (EX < 0)

    m = 0;

  else

    {

      __mp_dbl (x, &dx, p);

      dx = fabs (dx);

      for (m = 6; m > 0; m--)

	{

	  if (dx > __atan_xm[m].d)

	    break;

	}

    }

  mptwoim1.e = 1;

  mptwoim1.d[0] = 1;

  /* Reduce x m times.  */

  __sqr (x, &mpsm, p);

  if (m == 0)

    __cpy (x, &mps, p);

  else

    {

      for (i = 0; i < m; i++)

	{

	  __add (&__mpone, &mpsm, &mpt1, p);

	  __mpsqrt (&mpt1, &mpt2, p);

	  __add (&mpt2, &mpt2, &mpt1, p);

	  __add (&__mptwo, &mpsm, &mpt2, p);

	  __add (&mpt1, &mpt2, &mpt3, p);

	  __dvd (&mpsm, &mpt3, &mpt1, p);

	  __cpy (&mpt1, &mpsm, p);

	}

      __mpsqrt (&mpsm, &mps, p);

      mps.d[0] = X[0];

    }

  /* Evaluate a truncated power series for Atan(s).  */

  n = __atan_np[p];

  mptwoim1.d[1] = __atan_twonm1[p].d;

  __dvd (&mpsm, &mptwoim1, &mpt, p);

  for (i = n - 1; i > 1; i--)

    {

      mptwoim1.d[1] -= 2;

      __dvd (&mpsm, &mptwoim1, &mpt1, p);

      __mul (&mpsm, &mpt, &mpt2, p);

      __sub (&mpt1, &mpt2, &mpt, p);

    }

  __mul (&mps, &mpt, &mpt1, p);

  __sub (&mps, &mpt1, &mpt, p);

  /* Compute Atan(x).  */

  mptwoim1.d[1] = 1 << m;

  __mul (&mptwoim1, &mpt, y, p);

}