xref: /illumos-gate/usr/src/lib/libm/common/Q/atan2l.c (revision d8849d7dee03b84a3fa281ec65eb9e3d86d3756b)
1 /*
2  * CDDL HEADER START
3  *
4  * The contents of this file are subject to the terms of the
5  * Common Development and Distribution License (the "License").
6  * You may not use this file except in compliance with the License.
7  *
8  * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9  * or http://www.opensolaris.org/os/licensing.
10  * See the License for the specific language governing permissions
11  * and limitations under the License.
12  *
13  * When distributing Covered Code, include this CDDL HEADER in each
14  * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15  * If applicable, add the following below this CDDL HEADER, with the
16  * fields enclosed by brackets "[]" replaced with your own identifying
17  * information: Portions Copyright [yyyy] [name of copyright owner]
18  *
19  * CDDL HEADER END
20  */
21 
22 /*
23  * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24  */
25 /*
26  * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27  * Use is subject to license terms.
28  */
29 
30 /*
31  * atan2l(y,x)
32  *
33  * Method :
34  *	1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
35  *	2. Reduce x to positive by (if x and y are unexceptional):
36  *		ARG (x+iy) = arctan(y/x)	   ... if x > 0,
37  *		ARG (x+iy) = pi - arctan[y/(-x)]   ... if x < 0,
38  *
39  * Special cases:
40  *
41  *	ATAN2((anything), NaN ) is NaN;
42  *	ATAN2(NAN , (anything) ) is NaN;
43  *	ATAN2(+-0, +(anything but NaN)) is +-0  ;
44  *	ATAN2(+-0, -(anything but NaN)) is +-PI ;
45  *	ATAN2(+-(anything but 0 and NaN), 0) is +-PI/2;
46  *	ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
47  *	ATAN2(+-(anything but INF and NaN), -INF) is +-PI;
48  *	ATAN2(+-INF,+INF ) is +-PI/4 ;
49  *	ATAN2(+-INF,-INF ) is +-3PI/4;
50  *	ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-PI/2;
51  *
52  * Constants:
53  * The hexadecimal values are the intended ones for the following constants.
54  * The decimal values may be used, provided that the compiler will convert
55  * from decimal to binary accurately enough to produce the hexadecimal values
56  * shown.
57  */
58 
59 #pragma weak __atan2l = atan2l
60 
61 #include "libm.h"
62 #include "longdouble.h"
63 
64 static const long double
65 	zero	=  0.0L,
66 	tiny	=  1.0e-40L,
67 	one	=  1.0L,
68 	half	=  0.5L,
69 	PI3o4	=  2.356194490192344928846982537459627163148L,
70 	PIo4	=  0.785398163397448309615660845819875721049L,
71 	PIo2	=  1.570796326794896619231321691639751442099L,
72 	PI	=  3.141592653589793238462643383279502884197L,
73 	PI_lo	=  8.671810130123781024797044026043351968762e-35L;
74 
75 long double
76 atan2l(long double y, long double x)
77 {
78 	long double t, z;
79 	int k, m, signy, signx;
80 
81 	if (x != x || y != y)
82 		return (x + y);	/* return NaN if x or y is NAN */
83 	signy = signbitl(y);
84 	signx = signbitl(x);
85 	if (x == one)
86 		return (atanl(y));
87 	/* Ensure sign indicators are boolean */
88 	m = (signy != 0) + (signx != 0) + (signx != 0);
89 
90 	/* when y = 0 */
91 	if (y == zero)
92 		switch (m) {
93 		case 0:
94 			return (y);	/* atan(+0,+anything) */
95 		case 1:
96 			return (y);	/* atan(-0,+anything) */
97 		case 2:
98 			return (PI + tiny);	/* atan(+0,-anything) */
99 		case 3:
100 			return (-PI - tiny);	/* atan(-0,-anything) */
101 		}
102 
103 	/* when x = 0 */
104 	if (x == zero)
105 		return (signy != 0 ? -PIo2 - tiny : PIo2 + tiny);
106 
107 	/* when x is INF */
108 	if (!finitel(x)) {
109 		if (!finitel(y)) {
110 			switch (m) {
111 			case 0:
112 				return (PIo4 + tiny);	/* atan(+INF,+INF) */
113 			case 1:
114 				return (-PIo4 - tiny);	/* atan(-INF,+INF) */
115 			case 2:
116 				return (PI3o4 + tiny);	/* atan(+INF,-INF) */
117 			case 3:
118 				return (-PI3o4 - tiny);	/* atan(-INF,-INF) */
119 			}
120 		} else {
121 			switch (m) {
122 			case 0:
123 				return (zero);	/* atan(+...,+INF) */
124 			case 1:
125 				return (-zero);	/* atan(-...,+INF) */
126 			case 2:
127 				return (PI + tiny);	/* atan(+...,-INF) */
128 			case 3:
129 				return (-PI - tiny);	/* atan(-...,-INF) */
130 			}
131 		}
132 	}
133 	/* when y is INF */
134 	if (!finitel(y))
135 		return (signy != 0 ? -PIo2 - tiny : PIo2 + tiny);
136 
137 	/* compute y/x */
138 	x = fabsl(x);
139 	y = fabsl(y);
140 	t = PI_lo;
141 	k = (ilogbl(y) - ilogbl(x));
142 
143 	if (k > 120)
144 		z = PIo2 + half * t;
145 	else if (m > 1 && k < -120)
146 		z = zero;
147 	else
148 		z = atanl(y / x);
149 
150 	switch (m) {
151 	case 0:
152 		return (z);	/* atan(+,+) */
153 	case 1:
154 		return (-z);	/* atan(-,+) */
155 	case 2:
156 		return (PI - (z - t));	/* atan(+,-) */
157 	case 3:
158 		return ((z - t) - PI);	/* atan(-,-) */
159 	}
160 	/* NOTREACHED */
161 	return (0.0L);
162 }
163