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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2021 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 <https://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);
}
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