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 long double t, z;
78 int k, m, signy, signx;
79
80 if (x != x || y != y)
81 return (x + y); /* return NaN if x or y is NAN */
82 signy = signbitl(y);
83 signx = signbitl(x);
84 if (x == one)
85 return (atanl(y));
86 m = signy + signx + signx;
87
88 /* when y = 0 */
89 if (y == zero)
90 switch (m) {
91 case 0:
92 return (y); /* atan(+0,+anything) */
93 case 1:
94 return (y); /* atan(-0,+anything) */
95 case 2:
96 return (PI + tiny); /* atan(+0,-anything) */
97 case 3:
98 return (-PI - tiny); /* atan(-0,-anything) */
99 }
100
101 /* when x = 0 */
102 if (x == zero)
103 return (signy == 1 ? -PIo2 - tiny : PIo2 + tiny);
104
105 /* when x is INF */
106 if (!finitel(x)) {
107 if (!finitel(y)) {
108 switch (m) {
109 case 0:
110 return (PIo4 + tiny); /* atan(+INF,+INF) */
111 case 1:
112 return (-PIo4 - tiny); /* atan(-INF,+INF) */
113 case 2:
114 return (PI3o4 + tiny); /* atan(+INF,-INF) */
115 case 3:
116 return (-PI3o4 - tiny); /* atan(-INF,-INF) */
117 }
118 } else {
119 switch (m) {
120 case 0:
121 return (zero); /* atan(+...,+INF) */
122 case 1:
123 return (-zero); /* atan(-...,+INF) */
124 case 2:
125 return (PI + tiny); /* atan(+...,-INF) */
126 case 3:
127 return (-PI - tiny); /* atan(-...,-INF) */
128 }
129 }
130 }
131 /* when y is INF */
132 if (!finitel(y))
133 return (signy == 1 ? -PIo2 - tiny : PIo2 + tiny);
134
135 /* compute y/x */
136 x = fabsl(x);
137 y = fabsl(y);
138 t = PI_lo;
139 k = (ilogbl(y) - ilogbl(x));
140
141 if (k > 120)
142 z = PIo2 + half * t;
143 else if (m > 1 && k < -120)
144 z = zero;
145 else
146 z = atanl(y / x);
147
148 switch (m) {
149 case 0:
150 return (z); /* atan(+,+) */
151 case 1:
152 return (-z); /* atan(-,+) */
153 case 2:
154 return (PI - (z - t)); /* atan(+,-) */
155 case 3:
156 return ((z - t) - PI); /* atan(-,-) */
157 }
158 /* NOTREACHED */
159 return 0.0L;
160 }