libm/math/
k_sin.rs

1// origin: FreeBSD /usr/src/lib/msun/src/k_sin.c
2//
3// ====================================================
4// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5//
6// Developed at SunSoft, 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
12const S1: f64 = -1.66666666666666324348e-01; /* 0xBFC55555, 0x55555549 */
13const S2: f64 = 8.33333333332248946124e-03; /* 0x3F811111, 0x1110F8A6 */
14const S3: f64 = -1.98412698298579493134e-04; /* 0xBF2A01A0, 0x19C161D5 */
15const S4: f64 = 2.75573137070700676789e-06; /* 0x3EC71DE3, 0x57B1FE7D */
16const S5: f64 = -2.50507602534068634195e-08; /* 0xBE5AE5E6, 0x8A2B9CEB */
17const S6: f64 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
18
19// kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
20// Input x is assumed to be bounded by ~pi/4 in magnitude.
21// Input y is the tail of x.
22// Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
23//
24// Algorithm
25//      1. Since sin(-x) = -sin(x), we need only to consider positive x.
26//      2. Callers must return sin(-0) = -0 without calling here since our
27//         odd polynomial is not evaluated in a way that preserves -0.
28//         Callers may do the optimization sin(x) ~ x for tiny x.
29//      3. sin(x) is approximated by a polynomial of degree 13 on
30//         [0,pi/4]
31//                               3            13
32//              sin(x) ~ x + S1*x + ... + S6*x
33//         where
34//
35//      |sin(x)         2     4     6     8     10     12  |     -58
36//      |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
37//      |  x                                               |
38//
39//      4. sin(x+y) = sin(x) + sin'(x')*y
40//                  ~ sin(x) + (1-x*x/2)*y
41//         For better accuracy, let
42//                   3      2      2      2      2
43//              r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
44//         then                   3    2
45//              sin(x) = x + (S1*x + (x *(r-y/2)+y))
46#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
47pub(crate) fn k_sin(x: f64, y: f64, iy: i32) -> f64 {
48    let z = x * x;
49    let w = z * z;
50    let r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
51    let v = z * x;
52    if iy == 0 { x + v * (S1 + z * r) } else { x - ((z * (0.5 * y - v * r) - y) - v * S1) }
53}
libm/math/k_sin.rs

libm/math/
k_sin.rs
