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/* Compute cubic root of double value.
Copyright (C) 1997-2020 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Dirk Alboth <dirka@uni-paderborn.de> and
Ulrich Drepper <drepper@cygnus.com>, 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
The GNU C Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public
License along with the GNU C Library; if not, see
<https://www.gnu.org/licenses/>. */
#include <math.h>
#include <libm-alias-double.h>
#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
static const double factor[5] =
{
1.0 / SQR_CBRT2,
1.0 / CBRT2,
1.0,
CBRT2,
SQR_CBRT2
};
double
__cbrt (double x)
{
double xm, ym, u, t2;
int xe;
/* Reduce X. XM now is an range 1.0 to 0.5. */
xm = __frexp (fabs (x), &xe);
/* If X is not finite or is null return it (with raising exceptions
if necessary.
Note: *Our* version of `frexp' sets XE to zero if the argument is
Inf or NaN. This is not portable but faster. */
if (xe == 0 && fpclassify (x) <= FP_ZERO)
return x + x;
u = (0.354895765043919860
+ ((1.50819193781584896
+ ((-2.11499494167371287
+ ((2.44693122563534430
+ ((-1.83469277483613086
+ (0.784932344976639262 - 0.145263899385486377 * xm)
* xm)
* xm))
* xm))
* xm))
* xm));
t2 = u * u * u;
ym = u * (t2 + 2.0 * xm) / (2.0 * t2 + xm) * factor[2 + xe % 3];
return __ldexp (x > 0.0 ? ym : -ym, xe / 3);
}
libm_alias_double (__cbrt, cbrt)
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