1 | /* origin: FreeBSD /usr/src/lib/msun/src/s_atanf.c */ |
2 | /* |
3 | * Conversion to float by Ian Lance Taylor, Cygnus Support, ian@cygnus.com. |
4 | */ |
5 | /* |
6 | * ==================================================== |
7 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
8 | * |
9 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
10 | * Permission to use, copy, modify, and distribute this |
11 | * software is freely granted, provided that this notice |
12 | * is preserved. |
13 | * ==================================================== |
14 | */ |
15 | |
16 | use super::fabsf; |
17 | |
18 | const ATAN_HI: [f32; 4] = [ |
19 | 4.6364760399e-01, /* atan(0.5)hi 0x3eed6338 */ |
20 | 7.8539812565e-01, /* atan(1.0)hi 0x3f490fda */ |
21 | 9.8279368877e-01, /* atan(1.5)hi 0x3f7b985e */ |
22 | 1.5707962513e+00, /* atan(inf)hi 0x3fc90fda */ |
23 | ]; |
24 | |
25 | const ATAN_LO: [f32; 4] = [ |
26 | 5.0121582440e-09, /* atan(0.5)lo 0x31ac3769 */ |
27 | 3.7748947079e-08, /* atan(1.0)lo 0x33222168 */ |
28 | 3.4473217170e-08, /* atan(1.5)lo 0x33140fb4 */ |
29 | 7.5497894159e-08, /* atan(inf)lo 0x33a22168 */ |
30 | ]; |
31 | |
32 | const A_T: [f32; 5] = [ |
33 | 3.3333328366e-01, |
34 | -1.9999158382e-01, |
35 | 1.4253635705e-01, |
36 | -1.0648017377e-01, |
37 | 6.1687607318e-02, |
38 | ]; |
39 | |
40 | /// Arctangent (f32) |
41 | /// |
42 | /// Computes the inverse tangent (arc tangent) of the input value. |
43 | /// Returns a value in radians, in the range of -pi/2 to pi/2. |
44 | #[cfg_attr (all(test, assert_no_panic), no_panic::no_panic)] |
45 | pub fn atanf(mut x: f32) -> f32 { |
46 | let x1p_120 = f32::from_bits(0x03800000); // 0x1p-120 === 2 ^ (-120) |
47 | |
48 | let z: f32; |
49 | |
50 | let mut ix = x.to_bits(); |
51 | let sign = (ix >> 31) != 0; |
52 | ix &= 0x7fffffff; |
53 | |
54 | if ix >= 0x4c800000 { |
55 | /* if |x| >= 2**26 */ |
56 | if x.is_nan() { |
57 | return x; |
58 | } |
59 | z = i!(ATAN_HI, 3) + x1p_120; |
60 | return if sign { -z } else { z }; |
61 | } |
62 | let id = if ix < 0x3ee00000 { |
63 | /* |x| < 0.4375 */ |
64 | if ix < 0x39800000 { |
65 | /* |x| < 2**-12 */ |
66 | if ix < 0x00800000 { |
67 | /* raise underflow for subnormal x */ |
68 | force_eval!(x * x); |
69 | } |
70 | return x; |
71 | } |
72 | -1 |
73 | } else { |
74 | x = fabsf(x); |
75 | if ix < 0x3f980000 { |
76 | /* |x| < 1.1875 */ |
77 | if ix < 0x3f300000 { |
78 | /* 7/16 <= |x| < 11/16 */ |
79 | x = (2. * x - 1.) / (2. + x); |
80 | 0 |
81 | } else { |
82 | /* 11/16 <= |x| < 19/16 */ |
83 | x = (x - 1.) / (x + 1.); |
84 | 1 |
85 | } |
86 | } else if ix < 0x401c0000 { |
87 | /* |x| < 2.4375 */ |
88 | x = (x - 1.5) / (1. + 1.5 * x); |
89 | 2 |
90 | } else { |
91 | /* 2.4375 <= |x| < 2**26 */ |
92 | x = -1. / x; |
93 | 3 |
94 | } |
95 | }; |
96 | /* end of argument reduction */ |
97 | z = x * x; |
98 | let w = z * z; |
99 | /* break sum from i=0 to 10 aT[i]z**(i+1) into odd and even poly */ |
100 | let s1 = z * (i!(A_T, 0) + w * (i!(A_T, 2) + w * i!(A_T, 4))); |
101 | let s2 = w * (i!(A_T, 1) + w * i!(A_T, 3)); |
102 | if id < 0 { |
103 | return x - x * (s1 + s2); |
104 | } |
105 | let id = id as usize; |
106 | let z = i!(ATAN_HI, id) - ((x * (s1 + s2) - i!(ATAN_LO, id)) - x); |
107 | if sign { |
108 | -z |
109 | } else { |
110 | z |
111 | } |
112 | } |
113 | |