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 #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 } 62