1/*	$OpenBSD: k_cosl.c,v 1.1 2008/12/09 20:00:35 martynas Exp $	*/
2/* From: @(#)k_cos.c 1.3 95/01/18 */
3/*
4 * ====================================================
5 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
6 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
7 *
8 * Developed at SunSoft, a Sun Microsystems, Inc. business.
9 * Permission to use, copy, modify, and distribute this
10 * software is freely granted, provided that this notice
11 * is preserved.
12 * ====================================================
13 */
14
15/*
16 * ld128 version of k_cos.c.  See ../k_cos.c for most comments.
17 */
18
19#include "math_private.h"
20
21/*
22 * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]:
23 * |cos(x) - c(x))| < 2**-122.0
24 *
25 * 113-bit precision requires more care than 64-bit precision, since
26 * simple methods give a minimax polynomial with coefficient for x^2
27 * that is 1 ulp below 0.5, but we want it to be precisely 0.5.  See
28 * ../ld80/k_cosl.c for more details.
29 */
30static const double
31one = 1.0;
32
33static const long double
34C1 =  0.04166666666666666666666666666666658424671L,
35C2 = -0.001388888888888888888888888888863490893732L,
36C3 =  0.00002480158730158730158730158600795304914210L,
37C4 = -0.2755731922398589065255474947078934284324e-6L,
38C5 =  0.2087675698786809897659225313136400793948e-8L,
39C6 = -0.1147074559772972315817149986812031204775e-10L,
40C7 =  0.4779477332386808976875457937252120293400e-13L;
41
42static const double
43C8 = -0.1561920696721507929516718307820958119868e-15,
44C9 =  0.4110317413744594971475941557607804508039e-18,
45C10 = -0.8896592467191938803288521958313920156409e-21,
46C11 =  0.1601061435794535138244346256065192782581e-23;
47
48long double
49__kernel_cosl(long double x, long double y)
50{
51	long double hz,z,r,w;
52
53	z  = x*x;
54	r  = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+
55	    z*(C8+z*(C9+z*(C10+z*C11))))))))));
56	hz = 0.5*z;
57	w  = one-hz;
58	return w + (((one-w)-hz) + (z*r-x*y));
59}
60