1 /* 2 * ==================================================== 3 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. 4 * Copyright (c) 2008 Steven G. Kargl, David Schultz, Bruce D. Evans. 5 * 6 * Developed at SunSoft, a Sun Microsystems, Inc. business. 7 * Permission to use, copy, modify, and distribute this 8 * software is freely granted, provided that this notice 9 * is preserved. 10 * ==================================================== 11 */ 12 13 /* 14 * ld128 version of k_cos.c. See ../src/k_cos.c for most comments. 15 */ 16 17 #include "math_private.h" 18 19 /* 20 * Domain [-0.7854, 0.7854], range ~[-1.17e-39, 1.19e-39]: 21 * |cos(x) - c(x))| < 2**-129.3 22 * 23 * 113-bit precision requires more care than 64-bit precision, since 24 * simple methods give a minimax polynomial with coefficient for x^2 25 * that is 1 ulp below 0.5, but we want it to be precisely 0.5. See 26 * ../ld80/k_cosl.c for more details. 27 */ 28 static const double 29 one = 1.0; 30 static const long double 31 C1 = 4.16666666666666666666666666666666667e-02L, 32 C2 = -1.38888888888888888888888888888888834e-03L, 33 C3 = 2.48015873015873015873015873015446795e-05L, 34 C4 = -2.75573192239858906525573190949988493e-07L, 35 C5 = 2.08767569878680989792098886701451072e-09L, 36 C6 = -1.14707455977297247136657111139971865e-11L, 37 C7 = 4.77947733238738518870113294139830239e-14L, 38 C8 = -1.56192069685858079920640872925306403e-16L, 39 C9 = 4.11031762320473354032038893429515732e-19L, 40 C10= -8.89679121027589608738005163931958096e-22L, 41 C11= 1.61171797801314301767074036661901531e-24L, 42 C12= -2.46748624357670948912574279501044295e-27L; 43 44 long double 45 __kernel_cosl(long double x, long double y) 46 { 47 long double hz,z,r,w; 48 49 z = x*x; 50 r = z*(C1+z*(C2+z*(C3+z*(C4+z*(C5+z*(C6+z*(C7+ 51 z*(C8+z*(C9+z*(C10+z*(C11+z*C12))))))))))); 52 hz = 0.5*z; 53 w = one-hz; 54 return w + (((one-w)-hz) + (z*r-x*y)); 55 } 56