| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 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 |
| Elliott Hughes | 460ad74 | 2014-09-12 14:00:02 -0700 | [diff] [blame^] | 9 | * software is freely granted, provided that this notice |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 10 | * is preserved. |
| 11 | * ==================================================== |
| 12 | */ |
| 13 | |
| 14 | #include <sys/cdefs.h> |
| 15 | __FBSDID("$FreeBSD$"); |
| 16 | |
| 17 | /* |
| 18 | * ld128 version of k_cos.c. See ../src/k_cos.c for most comments. |
| 19 | */ |
| 20 | |
| 21 | #include "math_private.h" |
| 22 | |
| 23 | /* |
| 24 | * Domain [-0.7854, 0.7854], range ~[-1.80e-37, 1.79e-37]: |
| 25 | * |cos(x) - c(x))| < 2**-122.0 |
| 26 | * |
| 27 | * 113-bit precision requires more care than 64-bit precision, since |
| 28 | * simple methods give a minimax polynomial with coefficient for x^2 |
| 29 | * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See |
| 30 | * ../ld80/k_cosl.c for more details. |
| 31 | */ |
| 32 | static const double |
| 33 | one = 1.0; |
| 34 | |
| 35 | static const long double |
| 36 | C1 = 0.04166666666666666666666666666666658424671L, |
| 37 | C2 = -0.001388888888888888888888888888863490893732L, |
| 38 | C3 = 0.00002480158730158730158730158600795304914210L, |
| 39 | C4 = -0.2755731922398589065255474947078934284324e-6L, |
| 40 | C5 = 0.2087675698786809897659225313136400793948e-8L, |
| 41 | C6 = -0.1147074559772972315817149986812031204775e-10L, |
| 42 | C7 = 0.4779477332386808976875457937252120293400e-13L; |
| 43 | |
| 44 | static const double |
| 45 | C8 = -0.1561920696721507929516718307820958119868e-15, |
| 46 | C9 = 0.4110317413744594971475941557607804508039e-18, |
| 47 | C10 = -0.8896592467191938803288521958313920156409e-21, |
| 48 | C11 = 0.1601061435794535138244346256065192782581e-23; |
| 49 | |
| 50 | long double |
| 51 | __kernel_cosl(long double x, long double y) |
| 52 | { |
| 53 | long double hz,z,r,w; |
| 54 | |
| 55 | z = x*x; |
| 56 | r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ |
| 57 | z*(C8+z*(C9+z*(C10+z*C11)))))))))); |
| 58 | hz = 0.5*z; |
| 59 | w = one-hz; |
| 60 | return w + (((one-w)-hz) + (z*r-x*y)); |
| 61 | } |