1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
|
// origin: FreeBSD /usr/src/lib/msun/src/k_sin.c
//
// ====================================================
// Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
//
// Developed at SunSoft, a Sun Microsystems, Inc. business.
// Permission to use, copy, modify, and distribute this
// software is freely granted, provided that this notice
// is preserved.
// ====================================================
const S1: f64 = -1.66666666666666324348e-01; /* 0xBFC55555, 0x55555549 */
const S2: f64 = 8.33333333332248946124e-03; /* 0x3F811111, 0x1110F8A6 */
const S3: f64 = -1.98412698298579493134e-04; /* 0xBF2A01A0, 0x19C161D5 */
const S4: f64 = 2.75573137070700676789e-06; /* 0x3EC71DE3, 0x57B1FE7D */
const S5: f64 = -2.50507602534068634195e-08; /* 0xBE5AE5E6, 0x8A2B9CEB */
const S6: f64 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
// kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
// Input x is assumed to be bounded by ~pi/4 in magnitude.
// Input y is the tail of x.
// Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
//
// Algorithm
// 1. Since sin(-x) = -sin(x), we need only to consider positive x.
// 2. Callers must return sin(-0) = -0 without calling here since our
// odd polynomial is not evaluated in a way that preserves -0.
// Callers may do the optimization sin(x) ~ x for tiny x.
// 3. sin(x) is approximated by a polynomial of degree 13 on
// [0,pi/4]
// 3 13
// sin(x) ~ x + S1*x + ... + S6*x
// where
//
// |sin(x) 2 4 6 8 10 12 | -58
// |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
// | x |
//
// 4. sin(x+y) = sin(x) + sin'(x')*y
// ~ sin(x) + (1-x*x/2)*y
// For better accuracy, let
// 3 2 2 2 2
// r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
// then 3 2
// sin(x) = x + (S1*x + (x *(r-y/2)+y))
#[inline]
#[cfg_attr(all(test, assert_no_panic), no_panic::no_panic)]
pub(crate) fn k_sin(x: f64, y: f64, iy: i32) -> f64 {
let z = x * x;
let w = z * z;
let r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
let v = z * x;
if iy == 0 {
x + v * (S1 + z * r)
} else {
x - ((z * (0.5 * y - v * r) - y) - v * S1)
}
}
|
