xref: /openbsd/lib/libm/src/ld128/k_cosl.c (revision a6445c1d)
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  */
30 static const double
31 one = 1.0;
32 
33 static const long double
34 C1 =  0.04166666666666666666666666666666658424671L,
35 C2 = -0.001388888888888888888888888888863490893732L,
36 C3 =  0.00002480158730158730158730158600795304914210L,
37 C4 = -0.2755731922398589065255474947078934284324e-6L,
38 C5 =  0.2087675698786809897659225313136400793948e-8L,
39 C6 = -0.1147074559772972315817149986812031204775e-10L,
40 C7 =  0.4779477332386808976875457937252120293400e-13L;
41 
42 static const double
43 C8 = -0.1561920696721507929516718307820958119868e-15,
44 C9 =  0.4110317413744594971475941557607804508039e-18,
45 C10 = -0.8896592467191938803288521958313920156409e-21,
46 C11 =  0.1601061435794535138244346256065192782581e-23;
47 
48 long 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