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 /*
27 * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
28 * Use is subject to license terms.
29 */
30
31 /*
32 * atan2l(y,x)
33 *
34 * Method :
35 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
36 * 2. Reduce x to positive by (if x and y are unexceptional):
37 * ARG (x+iy) = arctan(y/x) ... if x > 0,
38 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
39 *
40 * Special cases:
41 *
42 * ATAN2((anything), NaN ) is NaN;
43 * ATAN2(NAN , (anything) ) is NaN;
44 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
45 * ATAN2(+-0, -(anything but NaN)) is +-PI ;
46 * ATAN2(+-(anything but 0 and NaN), 0) is +-PI/2;
47 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
48 * ATAN2(+-(anything but INF and NaN), -INF) is +-PI;
49 * ATAN2(+-INF,+INF ) is +-PI/4 ;
50 * ATAN2(+-INF,-INF ) is +-3PI/4;
51 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-PI/2;
52 *
53 * Constants:
54 * The hexadecimal values are the intended ones for the following constants.
55 * The decimal values may be used, provided that the compiler will convert
56 * from decimal to binary accurately enough to produce the hexadecimal values
57 * shown.
58 */
59
60 #pragma weak __atan2l = atan2l
61
62 #include "libm.h"
63 #include "longdouble.h"
64
65 static const long double 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
84 signy = signbitl(y);
85 signx = signbitl(x);
86
87 if (x == one)
88 return (atanl(y));
89
90 /* Ensure sign indicators are boolean */
91 m = (signy != 0) + (signx != 0) + (signx != 0);
92
93 /* when y = 0 */
94 if (y == zero) {
95 switch (m) {
96 case 0:
97 return (y); /* atan(+0,+anything) */
98 case 1:
99 return (y); /* atan(-0,+anything) */
100 case 2:
101 return (PI + tiny); /* atan(+0,-anything) */
102 case 3:
103 return (-PI - tiny); /* atan(-0,-anything) */
104 }
105 }
106
107 /* when x = 0 */
108 if (x == zero)
109 return (signy != 0 ? -PIo2 - tiny : PIo2 + tiny);
110
111 /* when x is INF */
112 if (!finitel(x)) {
113 if (!finitel(y)) {
114 switch (m) {
115 case 0:
116 return (PIo4 + tiny); /* atan(+INF,+INF) */
117 case 1:
118 return (-PIo4 - tiny); /* atan(-INF,+INF) */
119 case 2:
120 return (PI3o4 + tiny); /* atan(+INF,-INF) */
121 case 3:
122 return (-PI3o4 - tiny); /* atan(-INF,-INF) */
123 }
124 } else {
125 switch (m) {
126 case 0:
127 return (zero); /* atan(+...,+INF) */
128 case 1:
129 return (-zero); /* atan(-...,+INF) */
130 case 2:
131 return (PI + tiny); /* atan(+...,-INF) */
132 case 3:
133 return (-PI - tiny); /* atan(-...,-INF) */
134 }
135 }
136 }
137
138 /* when y is INF */
139 if (!finitel(y))
140 return (signy != 0 ? -PIo2 - tiny : PIo2 + tiny);
141
142 /* compute y/x */
143 x = fabsl(x);
144 y = fabsl(y);
145 t = PI_lo;
146 k = (ilogbl(y) - ilogbl(x));
147
148 if (k > 120)
149 z = PIo2 + half * t;
150 else if (m > 1 && k < -120)
151 z = zero;
152 else
153 z = atanl(y / x);
154
155 switch (m) {
156 case 0:
157 return (z); /* atan(+,+) */
158 case 1:
159 return (-z); /* atan(-,+) */
160 case 2:
161 return (PI - (z - t)); /* atan(+,-) */
162 case 3:
163 return ((z - t) - PI); /* atan(-,-) */
164 }
165
166 /* NOTREACHED */
167 return (0.0L);
168 }