trig_const/
cos.rs

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
12// cos(x)
13// Return cosine function of x.
14//
15// kernel function:
16//      k_sin           ... sine function on [-pi/4,pi/4]
17//      k_cos           ... cosine function on [-pi/4,pi/4]
18//      rem_pio2        ... argument reduction routine
19//
20// Method.
21//      Let S,C and T denote the sin, cos and tan respectively on
22//      [-PI/4, +PI/4]. Reduce the argument x to y1+y2 = x-k*pi/2
23//      in [-pi/4 , +pi/4], and let n = k mod 4.
24//      We have
25//
26//          n        sin(x)      cos(x)        tan(x)
27//     ----------------------------------------------------------
28//          0          S           C             T
29//          1          C          -S            -1/T
30//          2         -S          -C             T
31//          3         -C           S            -1/T
32//     ----------------------------------------------------------
33//
34// Special cases:
35//      Let trig be any of sin, cos, or tan.
36//      trig(+-INF)  is NaN, with signals;
37//      trig(NaN)    is that NaN;
38//
39// Accuracy:
40//      TRIG(x) returns trig(x) nearly rounded
41//
42
43use crate::{k_cos::k_cos, k_sin::k_sin, rem_pio2::rem_pio2};
44
45/// Cosine
46///
47/// ```
48/// # use trig_const::cos;
49/// # use core::f64::consts::PI;
50/// const COS_PI: f64 = cos(PI);
51/// assert_eq!(COS_PI, -1.0);
52/// ```
53pub const fn cos(x: f64) -> f64 {
54    let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
55
56    /* |x| ~< pi/4 */
57    if ix <= 0x3fe921fb {
58        if ix < 0x3e46a09e {
59            /* if x < 2**-27 * sqrt(2) */
60            /* raise inexact if x != 0 */
61            if x as i32 == 0 {
62                return 1.0;
63            }
64        }
65        return k_cos(x, 0.0);
66    }
67
68    /* cos(Inf or NaN) is NaN */
69    if ix >= 0x7ff00000 {
70        return f64::NAN;
71    }
72
73    /* argument reduction needed */
74    let (n, y0, y1) = rem_pio2(x);
75    match n & 3 {
76        0 => k_cos(y0, y1),
77        1 => -k_sin(y0, y1, 1),
78        2 => -k_cos(y0, y1),
79        _ => k_sin(y0, y1, 1),
80    }
81}
trig_const/cos.rs

trig_const/
cos.rs
