/* derived from /netlib/fdlibm */ /* @(#)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. */ #include "fdlibm.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;	int ix;	ix = __HI(x)&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 {	        __HI(qx) = ix-0x00200000;	/* x/4 */	        __LO(qx) = 0;	    }	    hz = 0.5*z-qx;	    a  = one-qx;	    return a - (hz - (z*r-x*y));	}}