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/*
* IBM Accurate Mathematical Library
* written by International Business Machines Corp.
* Copyright (C) 2001-2022 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: atnat.c */
/* */
/* FUNCTIONS: uatan */
/* signArctan */
/* */
/* FILES NEEDED: dla.h endian.h mydefs.h atnat.h */
/* uatan.tbl */
/* */
/************************************************************************/
#include <dla.h>
#include "mydefs.h"
#include "uatan.tbl"
#include "atnat.h"
#include <fenv.h>
#include <float.h>
#include <libm-alias-double.h>
#include <math.h>
#include <fenv_private.h>
#include <math-underflow.h>
#define TWO52 0x1.0p52
/* Fix the sign of y and return */
static double
__signArctan (double x, double y)
{
return copysign (y, x);
}
/* atan with max ULP of ~0.523 based on random sampling. */
double
__atan (double x)
{
double cor, t1, t2, t3, u,
v, w, ww, y, yy, z;
int i, ux, dx;
mynumber num;
num.d = x;
ux = num.i[HIGH_HALF];
dx = num.i[LOW_HALF];
/* x=NaN */
if (((ux & 0x7ff00000) == 0x7ff00000)
&& (((ux & 0x000fffff) | dx) != 0x00000000))
return x + x;
/* Regular values of x, including denormals +-0 and +-INF */
SET_RESTORE_ROUND (FE_TONEAREST);
u = (x < 0) ? -x : x;
if (u < C)
{
if (u < B)
{
if (u < A)
{
math_check_force_underflow_nonneg (u);
return x;
}
else
{ /* A <= u < B */
v = x * x;
yy = d11.d + v * d13.d;
yy = d9.d + v * yy;
yy = d7.d + v * yy;
yy = d5.d + v * yy;
yy = d3.d + v * yy;
yy *= x * v;
y = x + yy;
/* Max ULP is 0.511. */
return y;
}
}
else
{ /* B <= u < C */
i = (TWO52 + 256 * u) - TWO52;
i -= 16;
z = u - cij[i][0].d;
yy = cij[i][5].d + z * cij[i][6].d;
yy = cij[i][4].d + z * yy;
yy = cij[i][3].d + z * yy;
yy = cij[i][2].d + z * yy;
yy *= z;
t1 = cij[i][1].d;
y = t1 + yy;
/* Max ULP is 0.56. */
return __signArctan (x, y);
}
}
else
{
if (u < D)
{ /* C <= u < D */
w = 1 / u;
EMULV (w, u, t1, t2);
ww = w * ((1 - t1) - t2);
i = (TWO52 + 256 * w) - TWO52;
i -= 16;
z = (w - cij[i][0].d) + ww;
yy = cij[i][5].d + z * cij[i][6].d;
yy = cij[i][4].d + z * yy;
yy = cij[i][3].d + z * yy;
yy = cij[i][2].d + z * yy;
yy = HPI1 - z * yy;
t1 = HPI - cij[i][1].d;
y = t1 + yy;
/* Max ULP is 0.503. */
return __signArctan (x, y);
}
else
{
if (u < E)
{ /* D <= u < E */
w = 1 / u;
v = w * w;
EMULV (w, u, t1, t2);
yy = d11.d + v * d13.d;
yy = d9.d + v * yy;
yy = d7.d + v * yy;
yy = d5.d + v * yy;
yy = d3.d + v * yy;
yy *= w * v;
ww = w * ((1 - t1) - t2);
ESUB (HPI, w, t3, cor);
yy = ((HPI1 + cor) - ww) - yy;
y = t3 + yy;
/* Max ULP is 0.5003. */
return __signArctan (x, y);
}
else
{
/* u >= E */
if (x > 0)
return HPI;
else
return MHPI;
}
}
}
}
#ifndef __atan
libm_alias_double (__atan, atan)
#endif
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