atan2l.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* CDDL HEADER START
*
* The contents of this file are subject to the terms of the
* Common Development and Distribution License (the "License").
* You may not use this file except in compliance with the License.
*
* You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
* or http://www.opensolaris.org/os/licensing.
* See the License for the specific language governing permissions
* and limitations under the License.
*
* When distributing Covered Code, include this CDDL HEADER in each
* file and include the License file at usr/src/OPENSOLARIS.LICENSE.
* If applicable, add the following below this CDDL HEADER, with the
* fields enclosed by brackets "[]" replaced with your own identifying
* information: Portions Copyright [yyyy] [name of copyright owner]
*
* CDDL HEADER END
*/
/*
* Copyright 2011 Nexenta Systems, Inc. All rights reserved.
*/
/*
* Copyright 2006 Sun Microsystems, Inc. All rights reserved.
* Use is subject to license terms.
*/
/*
* atan2l(y,x)
*
* Method :
* 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
* 2. Reduce x to positive by (if x and y are unexceptional):
* ARG (x+iy) = arctan(y/x) ... if x > 0,
* ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
*
* Special cases:
*
* ATAN2((anything), NaN ) is NaN;
* ATAN2(NAN , (anything) ) is NaN;
* ATAN2(+-0, +(anything but NaN)) is +-0 ;
* ATAN2(+-0, -(anything but NaN)) is +-PI ;
* ATAN2(+-(anything but 0 and NaN), 0) is +-PI/2;
* ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
* ATAN2(+-(anything but INF and NaN), -INF) is +-PI;
* ATAN2(+-INF,+INF ) is +-PI/4 ;
* ATAN2(+-INF,-INF ) is +-3PI/4;
* ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-PI/2;
*
* Constants:
* The hexadecimal values are the intended ones for the following constants.
* The decimal values may be used, provided that the compiler will convert
* from decimal to binary accurately enough to produce the hexadecimal values
* shown.
*/
#pragma weak atan2l = __atan2l
#include "libm.h"
#include "longdouble.h"
static const long double
zero = 0.0L,
tiny = 1.0e-40L,
one = 1.0L,
half = 0.5L,
PI3o4 = 2.356194490192344928846982537459627163148L,
PIo4 = 0.785398163397448309615660845819875721049L,
PIo2 = 1.570796326794896619231321691639751442099L,
PI = 3.141592653589793238462643383279502884197L,
PI_lo = 8.671810130123781024797044026043351968762e-35L;
long double
atan2l(long double y, long double x) {
long double t, z;
int k, m, signy, signx;
if (x != x || y != y)
return (x + y); /* return NaN if x or y is NAN */
signy = signbitl(y);
signx = signbitl(x);
if (x == one)
return (atanl(y));
m = signy + signx + signx;
/* when y = 0 */
if (y == zero)
switch (m) {
case 0:
return (y); /* atan(+0,+anything) */
case 1:
return (y); /* atan(-0,+anything) */
case 2:
return (PI + tiny); /* atan(+0,-anything) */
case 3:
return (-PI - tiny); /* atan(-0,-anything) */
}
/* when x = 0 */
if (x == zero)
return (signy == 1 ? -PIo2 - tiny : PIo2 + tiny);
/* when x is INF */
if (!finitel(x)) {
if (!finitel(y)) {
switch (m) {
case 0:
return (PIo4 + tiny); /* atan(+INF,+INF) */
case 1:
return (-PIo4 - tiny); /* atan(-INF,+INF) */
case 2:
return (PI3o4 + tiny); /* atan(+INF,-INF) */
case 3:
return (-PI3o4 - tiny); /* atan(-INF,-INF) */
}
} else {
switch (m) {
case 0:
return (zero); /* atan(+...,+INF) */
case 1:
return (-zero); /* atan(-...,+INF) */
case 2:
return (PI + tiny); /* atan(+...,-INF) */
case 3:
return (-PI - tiny); /* atan(-...,-INF) */
}
}
}
/* when y is INF */
if (!finitel(y))
return (signy == 1 ? -PIo2 - tiny : PIo2 + tiny);
/* compute y/x */
x = fabsl(x);
y = fabsl(y);
t = PI_lo;
k = (ilogbl(y) - ilogbl(x));
if (k > 120)
z = PIo2 + half * t;
else if (m > 1 && k < -120)
z = zero;
else
z = atanl(y / x);
switch (m) {
case 0:
return (z); /* atan(+,+) */
case 1:
return (-z); /* atan(-,+) */
case 2:
return (PI - (z - t)); /* atan(+,-) */
case 3:
return ((z - t) - PI); /* atan(-,-) */
}
/* NOTREACHED */
return 0.0L;
}