1 /* From: @(#)k_cos.c 1.3 95/01/18 */
2 /*
3 * ====================================================
4 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
5 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans.
6 *
7 * Developed at SunSoft, a Sun Microsystems, Inc. business.
8 * Permission to use, copy, modify, and distribute this
9 * software is freely granted, provided that this notice
10 * is preserved.
11 * ====================================================
12 */
13
14 //__FBSDID("$FreeBSD: src/lib/msun/ld128/k_cosl.c,v 1.1 2008/02/17 07:32:31 das Exp $");
15
16 /*
17 * ld128 version of k_cos.c. See ../src/k_cos.c for most comments.
18 */
19
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
__kernel_cosl(long double x,long double y)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*((long double)C8+z*((long double)C9+z*((long double)C10+z*(long double)C11))))))))));
56 hz = 0.5L*z;
57 w = (long double)one-hz;
58 return w + ((((long double)one-w)-hz) + (z*r-x*y));
59 }
60
