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Revision 1.11, Sun May 26 22:01:53 2002 UTC (12 years, 3 months ago) by wiz
Branch: MAIN
CVS Tags: yamt-pf42-baseX, yamt-pf42-base4, yamt-pf42-base3, yamt-pf42-base2, yamt-pf42-base, yamt-pf42, yamt-pagecache-tag8, yamt-pagecache-base9, yamt-pagecache-base8, yamt-pagecache-base7, yamt-pagecache-base6, yamt-pagecache-base5, yamt-pagecache-base4, yamt-pagecache-base3, yamt-pagecache-base2, yamt-pagecache-base, yamt-pagecache, wrstuden-revivesa-base-3, wrstuden-revivesa-base-2, wrstuden-revivesa-base-1, wrstuden-revivesa-base, wrstuden-revivesa, wrstuden-fixsa-newbase, wrstuden-fixsa-base-1, wrstuden-fixsa-base, wrstuden-fixsa, tls-maxphys-base, tls-maxphys, tls-earlyentropy-base, tls-earlyentropy, riastradh-xf86-video-intel-2-7-1-pre-2-21-15, riastradh-drm2-base3, riastradh-drm2-base2, riastradh-drm2-base1, riastradh-drm2-base, riastradh-drm2, netbsd-7-base, netbsd-7, netbsd-6-base, netbsd-6-1-RELEASE, netbsd-6-1-RC4, netbsd-6-1-RC3, netbsd-6-1-RC2, netbsd-6-1-RC1, netbsd-6-1-4-RELEASE, netbsd-6-1-3-RELEASE, netbsd-6-1-2-RELEASE, netbsd-6-1-1-RELEASE, netbsd-6-1, netbsd-6-0-RELEASE, netbsd-6-0-RC2, netbsd-6-0-RC1, netbsd-6-0-5-RELEASE, netbsd-6-0-4-RELEASE, netbsd-6-0-3-RELEASE, netbsd-6-0-2-RELEASE, netbsd-6-0-1-RELEASE, netbsd-6-0, netbsd-6, netbsd-5-base, netbsd-5-2-RELEASE, netbsd-5-2-RC1, netbsd-5-2-2-RELEASE, netbsd-5-2-1-RELEASE, netbsd-5-2, netbsd-5-1-RELEASE, netbsd-5-1-RC4, netbsd-5-1-RC3, netbsd-5-1-RC2, netbsd-5-1-RC1, netbsd-5-1-4-RELEASE, netbsd-5-1-3-RELEASE, netbsd-5-1-2-RELEASE, netbsd-5-1-1-RELEASE, netbsd-5-1, netbsd-5-0-RELEASE, netbsd-5-0-RC4, netbsd-5-0-RC3, netbsd-5-0-RC2, netbsd-5-0-RC1, netbsd-5-0-2-RELEASE, netbsd-5-0-1-RELEASE, netbsd-5-0, netbsd-5, netbsd-4-base, netbsd-4-0-RELEASE, netbsd-4-0-RC5, netbsd-4-0-RC4, netbsd-4-0-RC3, netbsd-4-0-RC2, netbsd-4-0-RC1, netbsd-4-0-1-RELEASE, netbsd-4-0, netbsd-4, netbsd-3-base, netbsd-3-1-RELEASE, netbsd-3-1-RC4, netbsd-3-1-RC3, netbsd-3-1-RC2, netbsd-3-1-RC1, netbsd-3-1-1-RELEASE, netbsd-3-1, netbsd-3-0-RELEASE, netbsd-3-0-RC6, netbsd-3-0-RC5, netbsd-3-0-RC4, netbsd-3-0-RC3, netbsd-3-0-RC2, netbsd-3-0-RC1, netbsd-3-0-3-RELEASE, netbsd-3-0-2-RELEASE, netbsd-3-0-1-RELEASE, netbsd-3-0, netbsd-3, netbsd-2-base, netbsd-2-1-RELEASE, netbsd-2-1-RC6, netbsd-2-1-RC5, netbsd-2-1-RC4, netbsd-2-1-RC3, netbsd-2-1-RC2, netbsd-2-1-RC1, netbsd-2-1, netbsd-2-0-base, netbsd-2-0-RELEASE, netbsd-2-0-RC5, netbsd-2-0-RC4, netbsd-2-0-RC3, netbsd-2-0-RC2, netbsd-2-0-RC1, netbsd-2-0-3-RELEASE, netbsd-2-0-2-RELEASE, netbsd-2-0-1-RELEASE, netbsd-2-0, netbsd-2, mjf-devfs2-base, mjf-devfs2, matt-premerge-20091211, matt-nb6-plus-nbase, matt-nb6-plus-base, matt-nb6-plus, matt-nb5-pq3-base, matt-nb5-pq3, matt-nb5-mips64-u2-k2-k4-k7-k8-k9, matt-nb5-mips64-u1-k1-k5, matt-nb5-mips64-premerge-20101231, matt-nb5-mips64-premerge-20091211, matt-nb5-mips64-k15, matt-nb5-mips64, matt-nb4-mips64-k7-u2a-k9b, matt-mips64-premerge-20101231, matt-mips64-base2, matt-mips64-base, matt-mips64, matt-armv6-prevmlocking, matt-armv6-nbase, matt-armv6-base, matt-armv6, keiichi-mipv6-base, keiichi-mipv6, jym-xensuspend-nbase, jym-xensuspend-base, jym-xensuspend, hpcarm-cleanup-nbase, hpcarm-cleanup-base, hpcarm-cleanup, fvdl_fs64_base, cube-autoconf-base, cube-autoconf, cherry-xenmp-base, cherry-xenmp, bouyer-quota2-nbase, bouyer-quota2-base, bouyer-quota2, agc-symver-base, agc-symver, abandoned-netbsd-4-base, abandoned-netbsd-4, HEAD
Changes since 1.10: +3 -11 lines

__STDC__ is always defined on NetBSD.

/* @(#)k_cos.c 5.1 93/09/24 */
/*
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunPro, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include <sys/cdefs.h>
#if defined(LIBM_SCCS) && !defined(lint)
__RCSID("$NetBSD: k_cos.c,v 1.11 2002/05/26 22:01:53 wiz 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));
	}
}