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)]
atan2(y: f64, x: f64) -> f6452 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]
sanity_check()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