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-ldouble.h>
21
22
23#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
24#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
25
26/* We don't use long double values here since U need not be computed
27 with full precision. */
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
37static const long double third = 0.3333333333333333333333333L;
38
39long double
40__cbrtl (long double x)
41{
42 long double xm, u;
43 int xe;
44
45 /* Reduce X. XM now is an range 1.0 to 0.5. */
46 xm = __frexpl (fabsl (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 = (((-1.34661104733595206551E-1 * xm
56 + 5.46646013663955245034E-1) * xm
57 - 9.54382247715094465250E-1) * xm
58 + 1.13999833547172932737E0) * xm
59 + 4.02389795645447521269E-1;
60
61 u *= factor[2 + xe % 3];
62 u = __ldexpl (x > 0.0 ? u : -u, xe / 3);
63
64 u -= (u - (x / (u * u))) * third;
65 u -= (u - (x / (u * u))) * third;
66 return u;
67}
68libm_alias_ldouble (__cbrt, cbrt)
69