/build/cargo-vendor-dir/libm-0.2.8/src/math/tan.rs
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1 | | // origin: FreeBSD /usr/src/lib/msun/src/s_tan.c */ |
2 | | // |
3 | | // ==================================================== |
4 | | // Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
5 | | // |
6 | | // Developed at SunPro, 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 | | use super::{k_tan, rem_pio2}; |
13 | | |
14 | | // tan(x) |
15 | | // Return tangent function of x. |
16 | | // |
17 | | // kernel function: |
18 | | // k_tan ... tangent function on [-pi/4,pi/4] |
19 | | // rem_pio2 ... argument reduction routine |
20 | | // |
21 | | // Method. |
22 | | // Let S,C and T denote the sin, cos and tan respectively on |
23 | | // [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2 |
24 | | // in [-pi/4 , +pi/4], and let n = k mod 4. |
25 | | // We have |
26 | | // |
27 | | // n sin(x) cos(x) tan(x) |
28 | | // ---------------------------------------------------------- |
29 | | // 0 S C T |
30 | | // 1 C -S -1/T |
31 | | // 2 -S -C T |
32 | | // 3 -C S -1/T |
33 | | // ---------------------------------------------------------- |
34 | | // |
35 | | // Special cases: |
36 | | // Let trig be any of sin, cos, or tan. |
37 | | // trig(+-INF) is NaN, with signals; |
38 | | // trig(NaN) is that NaN; |
39 | | // |
40 | | // Accuracy: |
41 | | // TRIG(x) returns trig(x) nearly rounded |
42 | | #[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)] |
43 | 0 | pub fn tan(x: f64) -> f64 { |
44 | 0 | let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120 |
45 | 0 |
|
46 | 0 | let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff; |
47 | 0 | /* |x| ~< pi/4 */ |
48 | 0 | if ix <= 0x3fe921fb { |
49 | 0 | if ix < 0x3e400000 { |
50 | | /* |x| < 2**-27 */ |
51 | | /* raise inexact if x!=0 and underflow if subnormal */ |
52 | 0 | force_eval!(if ix < 0x00100000 { |
53 | 0 | x / x1p120 as f64 |
54 | | } else { |
55 | 0 | x + x1p120 as f64 |
56 | | }); |
57 | 0 | return x; |
58 | 0 | } |
59 | 0 | return k_tan(x, 0.0, 0); |
60 | 0 | } |
61 | 0 |
|
62 | 0 | /* tan(Inf or NaN) is NaN */ |
63 | 0 | if ix >= 0x7ff00000 { |
64 | 0 | return x - x; |
65 | 0 | } |
66 | 0 |
|
67 | 0 | /* argument reduction */ |
68 | 0 | let (n, y0, y1) = rem_pio2(x); |
69 | 0 | k_tan(y0, y1, n & 1) |
70 | 0 | } |