1/* Compute cubic root of double value.
2 Copyright (C) 1997-2023 Free Software Foundation, Inc.
3 This file is part of the GNU C Library.
4
5 The GNU C Library is free software; you can redistribute it and/or
6 modify it under the terms of the GNU Lesser General Public
7 License as published by the Free Software Foundation; either
8 version 2.1 of the License, or (at your option) any later version.
9
10 The GNU C Library is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 Lesser General Public License for more details.
14
15 You should have received a copy of the GNU Lesser General Public
16 License along with the GNU C Library; if not, see
17 <https://www.gnu.org/licenses/>. */
18
19#include <math.h>
20#include <libm-alias-double.h>
21
22
23#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
24#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
25
26static const double factor[5] =
27{
28 1.0 / SQR_CBRT2,
29 1.0 / CBRT2,
30 1.0,
31 CBRT2,
32 SQR_CBRT2
33};
34
35
36double
37__cbrt (double x)
38{
39 double xm, ym, u, t2;
40 int xe;
41
42 /* Reduce X. XM now is an range 1.0 to 0.5. */
43 xm = __frexp (fabs (x), &xe);
44
45 /* If X is not finite or is null return it (with raising exceptions
46 if necessary.
47 Note: *Our* version of `frexp' sets XE to zero if the argument is
48 Inf or NaN. This is not portable but faster. */
49 if (xe == 0 && fpclassify (x) <= FP_ZERO)
50 return x + x;
51
52 u = (0.354895765043919860
53 + ((1.50819193781584896
54 + ((-2.11499494167371287
55 + ((2.44693122563534430
56 + ((-1.83469277483613086
57 + (0.784932344976639262 - 0.145263899385486377 * xm)
58 * xm)
59 * xm))
60 * xm))
61 * xm))
62 * xm));
63
64 t2 = u * u * u;
65
66 ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
67
68 return __ldexp (x > 0.0 ? ym : -ym, xe / 3);
69}
70libm_alias_double (__cbrt, cbrt)
71