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
12use 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
43/// The tangent of `x` (f64).
44///
45/// `x` is specified in radians.
46#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
47pub fn tan(x: f64) -> f64 {
48 let x1p120 = f32::from_bits(0x7b800000); // 0x1p120f === 2 ^ 120
49
50 let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
51 /* |x| ~< pi/4 */
52 if ix <= 0x3fe921fb {
53 if ix < 0x3e400000 {
54 /* |x| < 2**-27 */
55 /* raise inexact if x!=0 and underflow if subnormal */
56 force_eval!(if ix < 0x00100000 {
57 x / x1p120 as f64
58 } else {
59 x + x1p120 as f64
60 });
61 return x;
62 }
63 return k_tan(x, 0.0, 0);
64 }
65
66 /* tan(Inf or NaN) is NaN */
67 if ix >= 0x7ff00000 {
68 return x - x;
69 }
70
71 /* argument reduction */
72 let (n, y0, y1) = rem_pio2(x);
73 k_tan(y0, y1, n & 1)
74}
75