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