1/* Compute cubic root of double value.
2 Copyright (C) 1997-2020 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4 Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
5 Ulrich Drepper <drepper@cygnus.com>, 1997.
6
7 The GNU C Library is free software; you can redistribute it and/or
8 modify it under the terms of the GNU Lesser General Public
9 License as published by the Free Software Foundation; either
10 version 2.1 of the License, or (at your option) any later version.
11
12 The GNU C Library is distributed in the hope that it will be useful,
13 but WITHOUT ANY WARRANTY; without even the implied warranty of
14 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
15 Lesser General Public License for more details.
16
17 You should have received a copy of the GNU Lesser General Public
18 License along with the GNU C Library; if not, see
19 <https://www.gnu.org/licenses/>. */
20
21#include <math.h>
22#include <libm-alias-ldouble.h>
23
24
25#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
26#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
27
28/* We don't use long double values here since U need not be computed
29 with full precision. */
30static const double factor[5] =
31{
32 1.0 / SQR_CBRT2,
33 1.0 / CBRT2,
34 1.0,
35 CBRT2,
36 SQR_CBRT2
37};
38
39static const long double third = 0.3333333333333333333333333L;
40
41long double
42__cbrtl (long double x)
43{
44 long double xm, u;
45 int xe;
46
47 /* Reduce X. XM now is an range 1.0 to 0.5. */
48 xm = __frexpl (fabsl (x), &xe);
49
50 /* If X is not finite or is null return it (with raising exceptions
51 if necessary.
52 Note: *Our* version of `frexp' sets XE to zero if the argument is
53 Inf or NaN. This is not portable but faster. */
54 if (xe == 0 && fpclassify (x) <= FP_ZERO)
55 return x + x;
56
57 u = (((-1.34661104733595206551E-1 * xm
58 + 5.46646013663955245034E-1) * xm
59 - 9.54382247715094465250E-1) * xm
60 + 1.13999833547172932737E0) * xm
61 + 4.02389795645447521269E-1;
62
63 u *= factor[2 + xe % 3];
64 u = __ldexpl (x > 0.0 ? u : -u, xe / 3);
65
66 u -= (u - (x / (u * u))) * third;
67 u -= (u - (x / (u * u))) * third;
68 return u;
69}
70libm_alias_ldouble (__cbrt, cbrt)
71