trig_const/
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
12// sin(x)
13// Return sine function of x.
14//
15// kernel function:
16//      k_sin            ... sine function on [-pi/4,pi/4]
17//      k_cos            ... cose 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
42use crate::{k_cos::k_cos, k_sin::k_sin, rem_pio2::rem_pio2};
43
44/// Sine
45///
46/// ```
47/// # use trig_const::sin;
48/// # use core::f64::consts::PI;
49/// # fn float_eq(lhs: f64, rhs: f64) { assert!((lhs - rhs).abs() < 0.0001, "lhs: {}, rhs: {}", lhs, rhs); }
50/// const SIN_PI: f64 = sin(PI);
51/// float_eq(SIN_PI, 0.0);
52/// ```
53pub const fn sin(x: f64) -> f64 {
54    /* High word of x. */
55    let ix = (f64::to_bits(x) >> 32) as u32 & 0x7fffffff;
56
57    /* |x| ~< pi/4 */
58    if ix <= 0x3fe921fb {
59        if ix < 0x3e500000 {
60            /* |x| < 2**-26 */
61            /* raise inexact if x != 0 and underflow if subnormal*/
62            return x;
63        }
64        return k_sin(x, 0.0, 0);
65    }
66
67    /* sin(Inf or NaN) is NaN */
68    if ix >= 0x7ff00000 {
69        return f64::NAN;
70    }
71
72    /* argument reduction needed */
73    let (n, y0, y1) = rem_pio2(x);
74    match n & 3 {
75        0 => k_sin(y0, y1, 1),
76        1 => k_cos(y0, y1),
77        2 => -k_sin(y0, y1, 1),
78        _ => -k_cos(y0, y1),
79    }
80}
trig_const/sin.rs

trig_const/
sin.rs
