1/*
2 * Copyright (c) 1998, 2004, Oracle and/or its affiliates. All rights reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26/* __ieee754_atan2(y,x)
27 * Method :
28 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
29 * 2. Reduce x to positive by (if x and y are unexceptional):
30 * ARG (x+iy) = arctan(y/x) ... if x > 0,
31 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
32 *
33 * Special cases:
34 *
35 * ATAN2((anything), NaN ) is NaN;
36 * ATAN2(NAN , (anything) ) is NaN;
37 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
38 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
39 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
40 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
41 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
42 * ATAN2(+-INF,+INF ) is +-pi/4 ;
43 * ATAN2(+-INF,-INF ) is +-3pi/4;
44 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
45 *
46 * Constants:
47 * The hexadecimal values are the intended ones for the following
48 * constants. The decimal values may be used, provided that the
49 * compiler will convert from decimal to binary accurately enough
50 * to produce the hexadecimal values shown.
51 */
52
53#include "fdlibm.h"
54
55#ifdef __STDC__
56static const double
57#else
58static double
59#endif
60tiny = 1.0e-300,
61zero = 0.0,
62pi_o_4 = 7.8539816339744827900E-01, /* 0x3FE921FB, 0x54442D18 */
63pi_o_2 = 1.5707963267948965580E+00, /* 0x3FF921FB, 0x54442D18 */
64pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
65pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
66
67#ifdef __STDC__
68 double __ieee754_atan2(double y, double x)
69#else
70 double __ieee754_atan2(y,x)
71 double y,x;
72#endif
73{
74 double z;
75 int k,m,hx,hy,ix,iy;
76 unsigned lx,ly;
77
78 hx = __HI(x); ix = hx&0x7fffffff;
79 lx = __LO(x);
80 hy = __HI(y); iy = hy&0x7fffffff;
81 ly = __LO(y);
82 if(((ix|((lx|-lx)>>31))>0x7ff00000)||
83 ((iy|((ly|-ly)>>31))>0x7ff00000)) /* x or y is NaN */
84 return x+y;
85 if(((hx-0x3ff00000)|lx)==0) return atan(y); /* x=1.0 */
86 m = ((hy>>31)&1)|((hx>>30)&2); /* 2*sign(x)+sign(y) */
87
88 /* when y = 0 */
89 if((iy|ly)==0) {
90 switch(m) {
91 case 0:
92 case 1: return y; /* atan(+-0,+anything)=+-0 */
93 case 2: return pi+tiny;/* atan(+0,-anything) = pi */
94 case 3: return -pi-tiny;/* atan(-0,-anything) =-pi */
95 }
96 }
97 /* when x = 0 */
98 if((ix|lx)==0) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
99
100 /* when x is INF */
101 if(ix==0x7ff00000) {
102 if(iy==0x7ff00000) {
103 switch(m) {
104 case 0: return pi_o_4+tiny;/* atan(+INF,+INF) */
105 case 1: return -pi_o_4-tiny;/* atan(-INF,+INF) */
106 case 2: return 3.0*pi_o_4+tiny;/*atan(+INF,-INF)*/
107 case 3: return -3.0*pi_o_4-tiny;/*atan(-INF,-INF)*/
108 }
109 } else {
110 switch(m) {
111 case 0: return zero ; /* atan(+...,+INF) */
112 case 1: return -1.0*zero ; /* atan(-...,+INF) */
113 case 2: return pi+tiny ; /* atan(+...,-INF) */
114 case 3: return -pi-tiny ; /* atan(-...,-INF) */
115 }
116 }
117 }
118 /* when y is INF */
119 if(iy==0x7ff00000) return (hy<0)? -pi_o_2-tiny: pi_o_2+tiny;
120
121 /* compute y/x */
122 k = (iy-ix)>>20;
123 if(k > 60) z=pi_o_2+0.5*pi_lo; /* |y/x| > 2**60 */
124 else if(hx<0&&k<-60) z=0.0; /* |y|/x < -2**60 */
125 else z=atan(fabs(y/x)); /* safe to do y/x */
126 switch (m) {
127 case 0: return z ; /* atan(+,+) */
128 case 1: __HI(z) ^= 0x80000000;
129 return z ; /* atan(-,+) */
130 case 2: return pi-(z-pi_lo);/* atan(+,-) */
131 default: /* case 3 */
132 return (z-pi_lo)-pi;/* atan(-,-) */
133 }
134}
135