/* @(#)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.
 * ====================================================
 */

/*
 * __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.
 */

#ifndef __FDLIBM_H__
#include "fdlibm.h"
#endif

double __kernel_cos(double x, double y)
{
	double a, hz, z, r, qx;
	int32_t ix;

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

	GET_HIGH_WORD(ix, x);
	ix &= IC(0x7fffffff);				/* ix = |x|'s high word */
	if (ix < IC(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 < IC(0x3FD33333))			/* if |x| < 0.3 */
		return one - (0.5 * z - (z * r - x * y));
	else
	{
		if (ix > IC(0x3fe90000))
		{								/* x > 0.78125 */
			qx = 0.28125;
		} else
		{
			INSERT_WORDS(qx, ix - IC(0x00200000), 0);	/* x/4 */
		}
		hz = 0.5 * z - qx;
		a = one - qx;
		return a - (hz - (z * r - x * y));
	}
}
