k_sin.c revision 141296 
1
2/* @(#)k_sin.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14#ifndef lint
15static char rcsid[] = "$FreeBSD: head/lib/msun/src/k_sin.c 141296 2005-02-04 18:26:06Z das $";
16#endif
17
18/* __kernel_sin( x, y, iy)
19 * kernel sin function on [-pi/4, pi/4], 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. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
27 *	3. sin(x) is approximated by a polynomial of degree 13 on
28 *	   [0,pi/4]
29 *		  	         3            13
30 *	   	sin(x) ~ x + S1*x + ... + S6*x
31 *	   where
32 *
33 * 	|sin(x)         2     4     6     8     10     12  |     -58
34 * 	|----- - (1+S1*x +S2*x +S3*x +S4*x +S5*x  +S6*x   )| <= 2
35 * 	|  x 					           |
36 *
37 *	4. sin(x+y) = sin(x) + sin'(x')*y
38 *		    ~ sin(x) + (1-x*x/2)*y
39 *	   For better accuracy, let
40 *		     3      2      2      2      2
41 *		r = x *(S2+x *(S3+x *(S4+x *(S5+x *S6))))
42 *	   then                   3    2
43 *		sin(x) = x + (S1*x + (x *(r-y/2)+y))
44 */
45
46#include "math.h"
47#include "math_private.h"
48
49static const double
50half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
51S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
52S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
53S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
54S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
55S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
56S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
57
58double
59__kernel_sin(double x, double y, int iy)
60{
61	double z,r,v;
62	int32_t ix;
63	GET_HIGH_WORD(ix,x);
64	ix &= 0x7fffffff;			/* high word of x */
65	if(ix<0x3e400000)			/* |x| < 2**-27 */
66	   {if((int)x==0) return x;}		/* generate inexact */
67	z	=  x*x;
68	v	=  z*x;
69	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
70	if(iy==0) return x+v*(S1+z*r);
71	else      return x-((z*(half*y-v*r)-y)-v*S1);
72}
73