/src/moddable/xs/tools/fdlibm/k_sin.c
Line | Count | Source |
1 | | |
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 | | |
13 | | /* __kernel_sin( x, y, iy) |
14 | | * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854 |
15 | | * Input x is assumed to be bounded by ~pi/4 in magnitude. |
16 | | * Input y is the tail of x. |
17 | | * Input iy indicates whether y is 0. (if iy=0, y assume to be 0). |
18 | | * |
19 | | * Algorithm |
20 | | * 1. Since sin(-x) = -sin(x), we need only to consider positive x. |
21 | | * 2. Callers must return sin(-0) = -0 without calling here since our |
22 | | * odd polynomial is not evaluated in a way that preserves -0. |
23 | | * Callers may do the optimization sin(x) ~ x for tiny x. |
24 | | * 3. sin(x) is approximated by a polynomial of degree 13 on |
25 | | * [0,pi/4] |
26 | | * 3 13 |
27 | | * sin(x) ~ x + S1*x + ... + S6*x |
28 | | * where |
29 | | * |
30 | | * |sin(x) 2 4 6 8 10 12 | -58 |
31 | | * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2 |
32 | | * | x | |
33 | | * |
34 | | * 4. sin(x+y) = sin(x) + sin'(x')*y |
35 | | * ~ sin(x) + (1-x*x/2)*y |
36 | | * For better accuracy, let |
37 | | * 3 2 2 2 2 |
38 | | * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6)))) |
39 | | * then 3 2 |
40 | | * sin(x) = x + (S1*x + (x *(r-y/2)+y)) |
41 | | */ |
42 | | |
43 | | #include "math_private.h" |
44 | | |
45 | | static const double |
46 | | half = 5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */ |
47 | | S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */ |
48 | | S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */ |
49 | | S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */ |
50 | | S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */ |
51 | | S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */ |
52 | | S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */ |
53 | | |
54 | | double |
55 | | __kernel_sin(double x, double y, int iy) |
56 | 171k | { |
57 | 171k | double z,r,v,w; |
58 | | |
59 | 171k | z = x*x; |
60 | 171k | w = z*z; |
61 | 171k | r = S2+z*(S3+z*S4) + z*w*(S5+z*S6); |
62 | 171k | v = z*x; |
63 | 171k | if(iy==0) return x+v*(S1+z*r); |
64 | 169k | else return x-((z*(half*y-v*r)-y)-v*S1); |
65 | 171k | } |