| /* From: @(#)k_cos.c 1.3 95/01/18 */ |
| /* |
| * ==================================================== |
| * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
| * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. |
| * |
| * 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. |
| * ==================================================== |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| /* |
| * ld128 version of k_cos.c. See ../src/k_cos.c for most comments. |
| */ |
| |
| #include "math_private.h" |
| |
| /* |
| * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]: |
| * |cos(x) - c(x))| < 2**-122.0 |
| * |
| * 113-bit precision requires more care than 64-bit precision, since |
| * simple methods give a minimax polynomial with coefficient for x^2 |
| * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See |
| * ../ld80/k_cosl.c for more details. |
| */ |
| static const double |
| one = 1.0; |
| |
| static const long double |
| C1 = 0.04166666666666666666666666666666658424671L, |
| C2 = -0.001388888888888888888888888888863490893732L, |
| C3 = 0.00002480158730158730158730158600795304914210L, |
| C4 = -0.2755731922398589065255474947078934284324e-6L, |
| C5 = 0.2087675698786809897659225313136400793948e-8L, |
| C6 = -0.1147074559772972315817149986812031204775e-10L, |
| C7 = 0.4779477332386808976875457937252120293400e-13L; |
| |
| static const double |
| C8 = -0.1561920696721507929516718307820958119868e-15, |
| C9 = 0.4110317413744594971475941557607804508039e-18, |
| C10 = -0.8896592467191938803288521958313920156409e-21, |
| C11 = 0.1601061435794535138244346256065192782581e-23; |
| |
| long double |
| __kernel_cosl(long double x, long double y) |
| { |
| long double hz,z,r,w; |
| |
| z = x*x; |
| r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ |
| z*(C8+z*(C9+z*(C10+z*C11)))))))))); |
| hz = 0.5*z; |
| w = one-hz; |
| return w + (((one-w)-hz) + (z*r-x*y)); |
| } |