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
45 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
46 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
47 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
48 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
49 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
50 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
51 
__sin(double x,double y,int iy)52 double __sin(double x, double y, int iy)
53 {
54 	double_t z,r,v,w;
55 
56 	z = x*x;
57 	w = z*z;
58 	r = S2 + z*(S3 + z*S4) + z*w*(S5 + z*S6);
59 	v = z*x;
60 	if (iy == 0)
61 		return x + v*(S1 + z*r);
62 	else
63 		return x - ((z*(0.5*y - v*r) - y) - v*S1);
64 }
65