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.
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.
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.
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/>. */
22 #include <math_private.h>
23 #include <libm-alias-ldouble.h>
26 #define CBRT2 1.2599210498948731648 /* 2^(1/3) */
27 #define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
29 /* We don't use long double values here since U need not be computed
30 with full precision. */
31 static const double factor
[5] =
40 static const long double third
= 0.3333333333333333333333333L;
43 __cbrtl (long double x
)
48 /* Reduce X. XM now is an range 1.0 to 0.5. */
49 xm
= __frexpl (fabsl (x
), &xe
);
51 /* If X is not finite or is null return it (with raising exceptions
53 Note: *Our* version of `frexp' sets XE to zero if the argument is
54 Inf or NaN. This is not portable but faster. */
55 if (xe
== 0 && fpclassify (x
) <= FP_ZERO
)
58 u
= (((-1.34661104733595206551E-1 * xm
59 + 5.46646013663955245034E-1) * xm
60 - 9.54382247715094465250E-1) * xm
61 + 1.13999833547172932737E0
) * xm
62 + 4.02389795645447521269E-1;
64 u
*= factor
[2 + xe
% 3];
65 u
= __ldexpl (x
> 0.0 ? u
: -u
, xe
/ 3);
67 u
-= (u
- (x
/ (u
* u
))) * third
;
68 u
-= (u
- (x
/ (u
* u
))) * third
;
71 libm_alias_ldouble (__cbrt
, cbrt
)