1/* Compute cubic root of double value.
2 Copyright (C) 1997-2018 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 <http://www.gnu.org/licenses/>. */
20
21#include <math.h>
22#include <math_private.h>
23#include <libm-alias-double.h>
24
25
26#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
27#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
28
29static const double factor[5] =
30{
31 1.0 / SQR_CBRT2,
32 1.0 / CBRT2,
33 1.0,
34 CBRT2,
35 SQR_CBRT2
36};
37
38
39double
40__cbrt (double x)
41{
42 double xm, ym, u, t2;
43 int xe;
44
45 /* Reduce X. XM now is an range 1.0 to 0.5. */
46 xm = __frexp (fabs (x), &xe);
47
48 /* If X is not finite or is null return it (with raising exceptions
49 if necessary.
50 Note: *Our* version of `frexp' sets XE to zero if the argument is
51 Inf or NaN. This is not portable but faster. */
52 if (xe == 0 && fpclassify (x) <= FP_ZERO)
53 return x + x;
54
55 u = (0.354895765043919860
56 + ((1.50819193781584896
57 + ((-2.11499494167371287
58 + ((2.44693122563534430
59 + ((-1.83469277483613086
60 + (0.784932344976639262 - 0.145263899385486377 * xm)
61 * xm)
62 * xm))
63 * xm))
64 * xm))
65 * xm));
66
67 t2 = u * u * u;
68
69 ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
70
71 return __ldexp (x > 0.0 ? ym : -ym, xe / 3);
72}
73libm_alias_double (__cbrt, cbrt)
74