k_cos_freeBSD.c   [plain text]

```
/* @(#)k_cos.c 1.3 95/01/18 */
/*
* ====================================================
* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
*
* Developed at SunSoft, a Sun Microsystems, Inc. business.
* Permission to use, copy, modify, and distribute this
* software is freely granted, provided that this notice
* is preserved.
* ====================================================
*/

#ifndef lint
static char rcsid[] = "\$FreeBSD: src/lib/msun/src/k_cos.c,v 1.8 2005/02/04 18:26:06 das Exp \$";
#endif

/*
* __kernel_cos( x,  y )
* kernel cos function on [-pi/4, pi/4], pi/4 ~ 0.785398164
* Input x is assumed to be bounded by ~pi/4 in magnitude.
* Input y is the tail of x.
*
* Algorithm
*	1. Since cos(-x) = cos(x), we need only to consider positive x.
*	2. if x < 2^-27 (hx<0x3e400000 0), return 1 with inexact if x!=0.
*	3. cos(x) is approximated by a polynomial of degree 14 on
*	   [0,pi/4]
*		  	                 4            14
*	   	cos(x) ~ 1 - x*x/2 + C1*x + ... + C6*x
*	   where the remez error is
*
* 	|              2     4     6     8     10    12     14 |     -58
* 	|cos(x)-(1-.5*x +C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  )| <= 2
* 	|    					               |
*
* 	               4     6     8     10    12     14
*	4. let r = C1*x +C2*x +C3*x +C4*x +C5*x  +C6*x  , then
*	       cos(x) = 1 - x*x/2 + r
*	   since cos(x+y) ~ cos(x) - sin(x)*y
*			  ~ cos(x) - x*y,
*	   a correction term is necessary in cos(x) and hence
*		cos(x+y) = 1 - (x*x/2 - (r - x*y))
*	   For better accuracy when x > 0.3, let qx = |x|/4 with
*	   the last 32 bits mask off, and if x > 0.78125, let qx = 0.28125.
*	   Then
*		cos(x+y) = (1-qx) - ((x*x/2-qx) - (r-x*y)).
*	   Note that 1-qx and (x*x/2-qx) is EXACT here, and the
*	   magnitude of the latter is at least a quarter of x*x/2,
*	   thus, reducing the rounding error in the subtraction.
*/

#include "math.h"
#include "math_private.h"

static const double
one =  1.00000000000000000000e+00, /* 0x3FF00000, 0x00000000 */
C1  =  4.16666666666666019037e-02, /* 0x3FA55555, 0x5555554C */
C2  = -1.38888888888741095749e-03, /* 0xBF56C16C, 0x16C15177 */
C3  =  2.48015872894767294178e-05, /* 0x3EFA01A0, 0x19CB1590 */
C4  = -2.75573143513906633035e-07, /* 0xBE927E4F, 0x809C52AD */
C5  =  2.08757232129817482790e-09, /* 0x3E21EE9E, 0xBDB4B1C4 */
C6  = -1.13596475577881948265e-11; /* 0xBDA8FAE9, 0xBE8838D4 */

double
__kernel_cos(double x, double y)
{
double a,hz,z,r,qx;
int32_t ix;
GET_HIGH_WORD(ix,x);
ix &= 0x7fffffff;			/* ix = |x|'s high word*/
if(ix<0x3e400000) {			/* if x < 2**27 */
if(((int)x)==0) return one;		/* generate inexact */
}
z  = x*x;
r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*C6)))));
if(ix < 0x3FD33333) 			/* if |x| < 0.3 */
return one - (0.5*z - (z*r - x*y));
else {
if(ix > 0x3fe90000) {		/* x > 0.78125 */
qx = 0.28125;
} else {
INSERT_WORDS(qx,ix-0x00200000,0);	/* x/4 */
}
hz = 0.5*z-qx;
a  = one-qx;
return a - (hz - (z*r-x*y));
}
}
```