/* Compute cubic root of double value.
Copyright (C) 1997 Free Software Foundation, Inc.
This file is part of the GNU C Library.
Contributed by Dirk Alboth and
Ulrich Drepper , 1997.
The GNU C Library is free software; you can redistribute it and/or
modify it under the terms of the GNU Library General Public License as
published by the Free Software Foundation; either version 2 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
Library General Public License for more details.
You should have received a copy of the GNU Library General Public
License along with the GNU C Library; see the file COPYING.LIB. If not,
write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA. */
#include "math.h"
#include "math_private.h"
#define CBRT2 1.2599210498948731648 /* 2^(1/3) */
#define SQR_CBRT2 1.5874010519681994748 /* 2^(2/3) */
/* We don't use long double values here since U need not be computed
with full precision. */
static const double factor[5] =
{
1.0 / SQR_CBRT2,
1.0 / CBRT2,
1.0,
CBRT2,
SQR_CBRT2
};
long double
__cbrtl (long double x)
{
long double xm, ym, u, t2;
int xe;
/* Reduce X. XM now is an range 1.0 to 0.5. */
xm = __frexpl (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 = (0.338058687610520237
+ (1.67595307700780102
+ (-2.82414939754975962
+ (4.09559907378707839 +
(-4.11151425200350531
+ (2.65298938441952296 +
(-0.988553671195413709
+ 0.161617097923756032 * xm)
* 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 __ldexpl (x > 0.0 ? ym : -ym, xe / 3);
}
weak_alias (__cbrtl, cbrtl)