| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 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 |
| Elliott Hughes | 460ad74 | 2014-09-12 14:00:02 -0700 | [diff] [blame] | 8 | * software is freely granted, provided that this notice |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 9 | * is preserved. |
| 10 | * ==================================================== |
| 11 | */ |
| 12 | |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 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 | /* |
| Elliott Hughes | 99ef447 | 2022-01-12 17:51:20 -0800 | [diff] [blame] | 20 | * Domain [-0.7854, 0.7854], range ~[-1.17e-39, 1.19e-39]: |
| 21 | * |cos(x) - c(x))| < 2**-129.3 |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 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; |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 30 | static const long double |
| Elliott Hughes | 99ef447 | 2022-01-12 17:51:20 -0800 | [diff] [blame] | 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; |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 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+ |
| Elliott Hughes | 99ef447 | 2022-01-12 17:51:20 -0800 | [diff] [blame] | 51 | z*(C8+z*(C9+z*(C10+z*(C11+z*C12))))))))))); |
| Calin Juravle | 4d77c11 | 2014-03-14 17:56:46 +0000 | [diff] [blame] | 52 | hz = 0.5*z; |
| 53 | w = one-hz; |
| 54 | return w + (((one-w)-hz) + (z*r-x*y)); |
| 55 | } |