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)]
tan(x: f64) -> f6443 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