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 | pub fn tan(x: f64) -> f64 { |
44 | let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120 |
45 | |
46 | let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff; |
47 | /* |x| ~< pi/4 */ |
48 | if ix <= 0x3fe921fb { |
49 | if ix < 0x3e400000 { |
50 | /* |x| < 2**-27 */ |
51 | /* raise inexact if x!=0 and underflow if subnormal */ |
52 | force_eval!(if ix < 0x00100000 { |
53 | x / x1p120 as f64 |
54 | } else { |
55 | x + x1p120 as f64 |
56 | }); |
57 | return x; |
58 | } |
59 | return k_tan(x, 0.0, 0); |
60 | } |
61 | |
62 | /* tan(Inf or NaN) is NaN */ |
63 | if ix >= 0x7ff00000 { |
64 | return x - x; |
65 | } |
66 | |
67 | /* argument reduction */ |
68 | let (n, y0, y1) = rem_pio2(x); |
69 | k_tan(y0, y1, n & 1) |
70 | } |
71 | |