1 
2 /* @(#)k_sin.c 5.1 93/09/24 */
3 /*
4  * ====================================================
5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6  *
7  * Developed at SunPro, 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 /* __kernel_sin( x, y, iy)
15  * kernel sin function on [-pi/4, pi/4], pi/4 ~ 0.7854
16  * Input x is assumed to be bounded by ~pi/4 in magnitude.
17  * Input y is the tail of x.
18  * Input iy indicates whether y is 0. (if iy=0, y assume to be 0).
19  *
20  * Algorithm
21  *	1. Since sin(-x) = -sin(x), we need only to consider positive x.
22  *	2. if x < 2^-27 (hx<0x3e400000 0), return x with inexact if x!=0.
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 "fdlibm.h"
43 
44 #ifndef _DOUBLE_IS_32BITS
45 
46 #ifdef __STDC__
47 static const double
48 #else
49 static double
50 #endif
51 half =  5.00000000000000000000e-01, /* 0x3FE00000, 0x00000000 */
52 S1  = -1.66666666666666324348e-01, /* 0xBFC55555, 0x55555549 */
53 S2  =  8.33333333332248946124e-03, /* 0x3F811111, 0x1110F8A6 */
54 S3  = -1.98412698298579493134e-04, /* 0xBF2A01A0, 0x19C161D5 */
55 S4  =  2.75573137070700676789e-06, /* 0x3EC71DE3, 0x57B1FE7D */
56 S5  = -2.50507602534068634195e-08, /* 0xBE5AE5E6, 0x8A2B9CEB */
57 S6  =  1.58969099521155010221e-10; /* 0x3DE5D93A, 0x5ACFD57C */
58 
59 #ifdef __STDC__
__kernel_sin(double x,double y,int iy)60 	double __kernel_sin(double x, double y, int iy)
61 #else
62 	double __kernel_sin(x, y, iy)
63 	double x,y; int iy;		/* iy=0 if y is zero */
64 #endif
65 {
66 	double z,r,v;
67 	__int32_t ix;
68 	GET_HIGH_WORD(ix,x);
69 	ix &= 0x7fffffff;			/* high word of x */
70 	if(ix<0x3e400000)			/* |x| < 2**-27 */
71 	   {if((int)x==0) return x;}		/* generate inexact */
72 	z	=  x*x;
73 	v	=  z*x;
74 	r	=  S2+z*(S3+z*(S4+z*(S5+z*S6)));
75 	if(iy==0) return x+v*(S1+z*r);
76 	else      return x-((z*(half*y-v*r)-y)-v*S1);
77 }
78 
79 #endif /* defined(_DOUBLE_IS_32BITS) */
80