glibc/sysdeps/ieee754/dbl-64/mpatan.c

/*
 * IBM Accurate Mathematical Library
 * written by International Business Machines Corp.
 * Copyright (C) 2001-2017 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);
}