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
40use super::{atan, fabs};
41
42const PI: f64 = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */
43const PI_LO: f64 = 1.2246467991473531772E-16; /* 0x3CA1A626, 0x33145C07 */
44
45/// Arctangent of y/x (f64)
46///
47/// Computes the inverse tangent (arc tangent) of `y/x`.
48/// Produces the correct result even for angles near pi/2 or -pi/2 (that is, when `x` is near 0).
49/// Returns a value in radians, in the range of -pi to pi.
50#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
51pub fn atan2(y: f64, x: f64) -> f64 {
52 if x.is_nan() || y.is_nan() {
53 return x + y;
54 }
55 let mut ix = (x.to_bits() >> 32) as u32;
56 let lx = x.to_bits() as u32;
57 let mut iy = (y.to_bits() >> 32) as u32;
58 let ly = y.to_bits() as u32;
59 if ((ix.wrapping_sub(0x3ff00000)) | lx) == 0 {
60 /* x = 1.0 */
61 return atan(y);
62 }
63 let m = ((iy >> 31) & 1) | ((ix >> 30) & 2); /* 2*sign(x)+sign(y) */
64 ix &= 0x7fffffff;
65 iy &= 0x7fffffff;
66
67 /* when y = 0 */
68 if (iy | ly) == 0 {
69 return match m {
70 0 | 1 => y, /* atan(+-0,+anything)=+-0 */
71 2 => PI, /* atan(+0,-anything) = PI */
72 _ => -PI, /* atan(-0,-anything) =-PI */
73 };
74 }
75 /* when x = 0 */
76 if (ix | lx) == 0 {
77 return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
78 }
79 /* when x is INF */
80 if ix == 0x7ff00000 {
81 if iy == 0x7ff00000 {
82 return match m {
83 0 => PI / 4.0, /* atan(+INF,+INF) */
84 1 => -PI / 4.0, /* atan(-INF,+INF) */
85 2 => 3.0 * PI / 4.0, /* atan(+INF,-INF) */
86 _ => -3.0 * PI / 4.0, /* atan(-INF,-INF) */
87 };
88 } else {
89 return match m {
90 0 => 0.0, /* atan(+...,+INF) */
91 1 => -0.0, /* atan(-...,+INF) */
92 2 => PI, /* atan(+...,-INF) */
93 _ => -PI, /* atan(-...,-INF) */
94 };
95 }
96 }
97 /* |y/x| > 0x1p64 */
98 if ix.wrapping_add(64 << 20) < iy || iy == 0x7ff00000 {
99 return if m & 1 != 0 { -PI / 2.0 } else { PI / 2.0 };
100 }
101
102 /* z = atan(|y/x|) without spurious underflow */
103 let z = if (m & 2 != 0) && iy.wrapping_add(64 << 20) < ix {
104 /* |y/x| < 0x1p-64, x<0 */
105 0.0
106 } else {
107 atan(fabs(y / x))
108 };
109 match m {
110 0 => z, /* atan(+,+) */
111 1 => -z, /* atan(-,+) */
112 2 => PI - (z - PI_LO), /* atan(+,-) */
113 _ => (z - PI_LO) - PI, /* atan(-,-) */
114 }
115}
116
117#[cfg(test)]
118mod tests {
119 use super::*;
120
121 #[test]
122 #[cfg_attr(x86_no_sse, ignore = "FIXME(i586): possible incorrect rounding")]
123 fn sanity_check() {
124 assert_eq!(atan2(0.0, 1.0), 0.0);
125 assert_eq!(atan2(0.0, -1.0), PI);
126 assert_eq!(atan2(-0.0, -1.0), -PI);
127 assert_eq!(atan2(3.0, 2.0), atan(3.0 / 2.0));
128 assert_eq!(atan2(2.0, -1.0), atan(2.0 / -1.0) + PI);
129 assert_eq!(atan2(-2.0, -1.0), atan(-2.0 / -1.0) - PI);
130 }
131}
132