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 | use super::atan; |
41 | use super::fabs; |
42 | |
43 | const PI: f64 = 3.1415926535897931160E+00; /* 0x400921FB, 0x54442D18 */ |
44 | const 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)] |
52 | pub 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 ] |
119 | fn 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 | |