libm/math/
sin.rs

1// origin: FreeBSD /usr/src/lib/msun/src/s_sin.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// sin(x)
15// Return sine function of x.
16//
17// kernel function:
18//      k_sin            ... sine function on [-pi/4,pi/4]
19//      k_cos            ... cose 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/// The sine of `x` (f64).
45///
46/// `x` is specified in radians.
47#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
48pub fn sin(x: f64) -> f64 {
49    let x1p120 = f64::from_bits(0x4770000000000000); // 0x1p120f === 2 ^ 120
50
51    /* High word of x. */
52    let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
53
54    /* |x| ~< pi/4 */
55    if ix <= 0x3fe921fb {
56        if ix < 0x3e500000 {
57            /* |x| < 2**-26 */
58            /* raise inexact if x != 0 and underflow if subnormal*/
59            if ix < 0x00100000 {
60                force_eval!(x / x1p120);
61            } else {
62                force_eval!(x + x1p120);
63            }
64            return x;
65        }
66        return k_sin(x, 0.0, 0);
67    }
68
69    /* sin(Inf or NaN) is NaN */
70    if ix >= 0x7ff00000 {
71        return x - x;
72    }
73
74    /* argument reduction needed */
75    let (n, y0, y1) = rem_pio2(x);
76    match n & 3 {
77        0 => k_sin(y0, y1, 1),
78        1 => k_cos(y0, y1),
79        2 => -k_sin(y0, y1, 1),
80        _ => -k_cos(y0, y1),
81    }
82}
83
84#[test]
85fn test_near_pi() {
86    let x = f64::from_bits(0x400921fb000FD5DD); // 3.141592026217707
87    let sx = f64::from_bits(0x3ea50d15ced1a4a2); // 6.273720864039205e-7
88    let result = sin(x);
89    #[cfg(all(target_arch = "x86", not(target_feature = "sse2")))]
90    let result = force_eval!(result);
91    assert_eq!(result, sx);
92}
libm/math/sin.rs

libm/math/
sin.rs
