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 /* __sin( x, y, iy)
13 * kernel sin function on ~[-pi/4, pi/4] (except on -0), pi/4 ~ 0.7854
14 * Input x is assumed to be bounded by ~pi/4 in magnitude.
15 * Input y is the tail of x.
16 * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
17 *
18 * Algorithm
19 * 1. Since sin(-x) = -sin(x), we need only to consider positive x.
20 * 2. Callers must return sin(-0) = -0 without calling here since our
21 * odd polynomial is not evaluated in a way that preserves -0.
22 * Callers may do the optimization sin(x) ~ x for tiny x.
23 * 3. sin(x) is approximated by a polynomial of degree 13 on
24 * [0,pi/4]
25 * 3 13
26 * sin(x) ~ x + S1*x + ... + S6*x
27 * where
28 *
29 * |sin(x) 2 4 6 8 10 12 | -58
30 * |----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x +S6*x )| <= 2
31 * | x |
32 *
33 * 4. sin(x+y) = sin(x) + sin'(x')*y
34 * ~ sin(x) + (1-x*x/2)*y
35 * For better accuracy, let
36 * 3 2 2 2 2
37 * r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
38 * then 3 2
39 * sin(x) = x + (S1*x + (x *(r-y/2)+y))
40 */
41
42 #include "libm.h"
43
44 static const double S1 = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
45 S2 = 8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
46 S3 = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
47 S4 = 2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
48 S5 = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
49 S6 = 1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
50
__sin(double x,double y,int iy)51 double __sin(double x, double y, int iy) {
52 double_t z, r, v, w;
53
54 z = x * x;
55 w = z * z;
56 r = S2 + z * (S3 + z * S4) + z * w * (S5 + z * S6);
57 v = z * x;
58 if (iy == 0)
59 return x + v * (S1 + z * r);
60 else
61 return x - ((z * (0.5 * y - v * r) - y) - v * S1);
62 }
63