1// origin: FreeBSD /usr/src/lib/msun/src/s_cos.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_cos, k_sin, rem_pio2};
13
14// cos(x)
15// Return cosine function of x.
16//
17// kernel function:
18// k_sin ... sine function on [-pi/4,pi/4]
19// k_cos ... cosine function on [-pi/4,pi/4]
20// rem_pio2 ... argument reduction routine
21//
22// Method.
23// Let S,C and T denote the sin, cos and tan respectively on
24// [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
25// in [-pi/4 , +pi/4], and let n = k mod 4.
26// We have
27//
28// n sin(x) cos(x) tan(x)
29// ----------------------------------------------------------
30// 0 S C T
31// 1 C -S -1/T
32// 2 -S -C T
33// 3 -C S -1/T
34// ----------------------------------------------------------
35//
36// Special cases:
37// Let trig be any of sin, cos, or tan.
38// trig(+-INF) is NaN, with signals;
39// trig(NaN) is that NaN;
40//
41// Accuracy:
42// TRIG(x) returns trig(x) nearly rounded
43//
44
45/// The cosine of `x` (f64).
46///
47/// `x` is specified in radians.
48#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
49pub fn cos(x: f64) -> f64 {
50 let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
51
52 /* |x| ~< pi/4 */
53 if ix <= 0x3fe921fb {
54 if ix < 0x3e46a09e {
55 /* if x < 2**-27 * sqrt(2) */
56 /* raise inexact if x != 0 */
57 if x as i32 == 0 {
58 return 1.0;
59 }
60 }
61 return k_cos(x, 0.0);
62 }
63
64 /* cos(Inf or NaN) is NaN */
65 if ix >= 0x7ff00000 {
66 return x - x;
67 }
68
69 /* argument reduction needed */
70 let (n, y0, y1) = rem_pio2(x);
71 match n & 3 {
72 0 => k_cos(y0, y1),
73 1 => -k_sin(y0, y1, 1),
74 2 => -k_cos(y0, y1),
75 _ => k_sin(y0, y1, 1),
76 }
77}
78