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-double.h>
23
24
25#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
26#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
27
28static const double factor[5] =
29{
30 1.0 / SQR_CBRT2,
31 1.0 / CBRT2,
32 1.0,
33 CBRT2,
34 SQR_CBRT2
35};
36
37
38double
39__cbrt (double x)
40{
41 double xm, ym, u, t2;
42 int xe;
43
44 /* Reduce X. XM now is an range 1.0 to 0.5. */
45 xm = __frexp (fabs (x), &xe);
46
47 /* If X is not finite or is null return it (with raising exceptions
48 if necessary.
49 Note: *Our* version of `frexp' sets XE to zero if the argument is
50 Inf or NaN. This is not portable but faster. */
51 if (xe == 0 && fpclassify (x) <= FP_ZERO)
52 return x + x;
53
54 u = (0.354895765043919860
55 + ((1.50819193781584896
56 + ((-2.11499494167371287
57 + ((2.44693122563534430
58 + ((-1.83469277483613086
59 + (0.784932344976639262 - 0.145263899385486377 * xm)
60 * xm)
61 * xm))
62 * xm))
63 * xm))
64 * xm));
65
66 t2 = u * u * u;
67
68 ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
69
70 return __ldexp (x > 0.0 ? ym : -ym, xe / 3);
71}
72libm_alias_double (__cbrt, cbrt)
73