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
12 const S1: f64 = -1.66666666666666324348e-01; /* 0xBFC55555, 0x55555549 */
13 const S2: f64 = 8.33333333332248946124e-03; /* 0x3F811111, 0x1110F8A6 */
14 const S3: f64 = -1.98412698298579493134e-04; /* 0xBF2A01A0, 0x19C161D5 */
15 const S4: f64 = 2.75573137070700676789e-06; /* 0x3EC71DE3, 0x57B1FE7D */
16 const S5: f64 = -2.50507602534068634195e-08; /* 0xBE5AE5E6, 0x8A2B9CEB */
17 const 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)]
k_sin(x: f64, y: f64, iy: i32) -> f6447 pub(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 {
53 x + v * (S1 + z * r)
54 } else {
55 x - ((z * (0.5 * y - v * r) - y) - v * S1)
56 }
57 }
58