1/* origin: FreeBSD /usr/src/lib/msun/src/e_atan2.c */
2/*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 *
6 * Developed at SunSoft, a Sun Microsystems, Inc. business.
7 * Permission to use, copy, modify, and distribute this
8 * software is freely granted, provided that this notice
9 * is preserved.
10 * ====================================================
11 *
12 */
13/* atan2(y,x)
14 * Method :
15 * 1. Reduce y to positive by atan2(y,x)=-atan2(-y,x).
16 * 2. Reduce x to positive by (if x and y are unexceptional):
17 * ARG (x+iy) = arctan(y/x) ... if x > 0,
18 * ARG (x+iy) = pi - arctan[y/(-x)] ... if x < 0,
19 *
20 * Special cases:
21 *
22 * ATAN2((anything), NaN ) is NaN;
23 * ATAN2(NAN , (anything) ) is NaN;
24 * ATAN2(+-0, +(anything but NaN)) is +-0 ;
25 * ATAN2(+-0, -(anything but NaN)) is +-pi ;
26 * ATAN2(+-(anything but 0 and NaN), 0) is +-pi/2;
27 * ATAN2(+-(anything but INF and NaN), +INF) is +-0 ;
28 * ATAN2(+-(anything but INF and NaN), -INF) is +-pi;
29 * ATAN2(+-INF,+INF ) is +-pi/4 ;
30 * ATAN2(+-INF,-INF ) is +-3pi/4;
31 * ATAN2(+-INF, (anything but,0,NaN, and INF)) is +-pi/2;
32 *
33 * Constants:
34 * The hexadecimal values are the intended ones for the following
35 * constants. The decimal values may be used, provided that the
36 * compiler will convert from decimal to binary accurately enough
37 * to produce the hexadecimal values shown.
38 */
39
40#include "libm.h"
41
42static const double
43pi = 3.1415926535897931160E+00, /* 0x400921FB, 0x54442D18 */
44pi_lo = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
45
46double atan2(double y, double x)
47{
48 double z;
49 uint32_t m,lx,ly,ix,iy;
50
51 if (isnan(x) || isnan(y))
52 return x+y;
53 EXTRACT_WORDS(ix, lx, x);
54 EXTRACT_WORDS(iy, ly, y);
55 if ((ix-0x3ff00000 | lx) == 0) /* x = 1.0 */
56 return atan(y);
57 m = ((iy>>31)&1) | ((ix>>30)&2); /* 2*sign(x)+sign(y) */
58 ix = ix & 0x7fffffff;
59 iy = iy & 0x7fffffff;
60
61 /* when y = 0 */
62 if ((iy|ly) == 0) {
63 switch(m) {
64 case 0:
65 case 1: return y; /* atan(+-0,+anything)=+-0 */
66 case 2: return pi; /* atan(+0,-anything) = pi */
67 case 3: return -pi; /* atan(-0,-anything) =-pi */
68 }
69 }
70 /* when x = 0 */
71 if ((ix|lx) == 0)
72 return m&1 ? -pi/2 : pi/2;
73 /* when x is INF */
74 if (ix == 0x7ff00000) {
75 if (iy == 0x7ff00000) {
76 switch(m) {
77 case 0: return pi/4; /* atan(+INF,+INF) */
78 case 1: return -pi/4; /* atan(-INF,+INF) */
79 case 2: return 3*pi/4; /* atan(+INF,-INF) */
80 case 3: return -3*pi/4; /* atan(-INF,-INF) */
81 }
82 } else {
83 switch(m) {
84 case 0: return 0.0; /* atan(+...,+INF) */
85 case 1: return -0.0; /* atan(-...,+INF) */
86 case 2: return pi; /* atan(+...,-INF) */
87 case 3: return -pi; /* atan(-...,-INF) */
88 }
89 }
90 }
91 /* |y/x| > 0x1p64 */
92 if (ix+(64<<20) < iy || iy == 0x7ff00000)
93 return m&1 ? -pi/2 : pi/2;
94
95 /* z = atan(|y/x|) without spurious underflow */
96 if ((m&2) && iy+(64<<20) < ix) /* |y/x| < 0x1p-64, x<0 */
97 z = 0;
98 else
99 z = atan(fabs(y/x));
100 switch (m) {
101 case 0: return z; /* atan(+,+) */
102 case 1: return -z; /* atan(-,+) */
103 case 2: return pi - (z-pi_lo); /* atan(+,-) */
104 default: /* case 3 */
105 return (z-pi_lo) - pi; /* atan(-,-) */
106 }
107}