k_cos.c revision b07e1d9fd8d9e4e03698e0bd9bf77154c5390326 
1
2/* @(#)k_cos.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/*
15 * __kernel_cos( x,  y )
16 * kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
17 * Input x is assumed to be bounded by ~pi/4 in magnitude.
18 * Input y is the tail of x.
19 *
20 * Algorithm
21 *	1. Since ieee_cos(-x) = ieee_cos(x), we need only to consider positive x.
22 *	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
23 *	3. ieee_cos(x) is approximated by a polynomial of degree 14 on
24 *	   [0,pi/4]
25 *		  	                 4            14
26 *	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
27 *	   where the remez error is
28 *
29 * 	|              2     4     6     8     10    12     14 |     -58
30 * 	|ieee_cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
31 * 	|    					               |
32 *
33 * 	               4     6     8     10    12     14
34 *	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
35 *	       ieee_cos(x) = 1 - x*x/2 + r
36 *	   since ieee_cos(x+y) ~ ieee_cos(x) - ieee_sin(x)*y
37 *			  ~ ieee_cos(x) - x*y,
38 *	   a correction term is necessary in ieee_cos(x) and hence
39 *		cos(x+y) = 1 - (x*x/2 - (r - x*y))
40 *	   For better accuracy when x > 0.3, let qx = |x|/4 with
41 *	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
42 *	   Then
43 *		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
44 *	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
45 *	   magnitude of the latter is at least a quarter of x*x/2,
46 *	   thus, reducing the rounding error in the subtraction.
47 */
48
49#include "fdlibm.h"
50
51#ifdef __STDC__
52static const double
53#else
54static double
55#endif
56one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
57C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
58C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
59C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
60C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
61C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
62C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */
63
64#ifdef __STDC__
65	double __kernel_cos(double x, double y)
66#else
67	double __kernel_cos(x, y)
68	double x,y;
69#endif
70{
71	double a,hz,z,r,qx;
72	int ix;
73	ix = __HI(x)&0x7fffffff;	/* ix = |x|'s high word*/
74	if(ix<0x3e400000) {			/* if x < 2**27 */
75	    if(((int)x)==0) return one;		/* generate inexact */
76	}
77	z  = x*x;
78	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
79	if(ix < 0x3FD33333) 			/* if |x| < 0.3 */
80	    return one - (0.5*z - (z*r - x*y));
81	else {
82	    if(ix > 0x3fe90000) {		/* x > 0.78125 */
83		qx = 0.28125;
84	    } else {
85	        __HI(qx) = ix-0x00200000;	/* x/4 */
86	        __LO(qx) = 0;
87	    }
88	    hz = 0.5*z-qx;
89	    a  = one-qx;
90	    return a - (hz - (z*r-x*y));
91	}
92}
93