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/* Compute cubic root of long double value.
Copyright (C) 2012-2018 Free Software Foundation, Inc.
Cephes Math Library Release 2.2: January, 1991
Copyright 1984, 1991 by Stephen L. Moshier
Adapted for glibc October, 2001.
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 3 of the License, or
(at your option) any later version.
This program 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 General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <https://www.gnu.org/licenses/>. */
#include <config.h>
/* Specification. */
#include <math.h>
#if HAVE_SAME_LONG_DOUBLE_AS_DOUBLE
long double
cbrtl (long double x)
{
return cbrt (x);
}
#else
/* Code based on glibc/sysdeps/ieee754/ldbl-128/s_cbrtl.c. */
/* cbrtl.c
*
* Cube root, long double precision
*
*
*
* SYNOPSIS:
*
* long double x, y, cbrtl();
*
* y = cbrtl( x );
*
*
*
* DESCRIPTION:
*
* Returns the cube root of the argument, which may be negative.
*
* Range reduction involves determining the power of 2 of
* the argument. A polynomial of degree 2 applied to the
* mantissa, and multiplication by the cube root of 1, 2, or 4
* approximates the root to within about 0.1%. Then Newton's
* iteration is used three times to converge to an accurate
* result.
*
*
*
* ACCURACY:
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE -8,8 100000 1.3e-34 3.9e-35
* IEEE exp(+-707) 100000 1.3e-34 4.3e-35
*
*/
static const long double CBRT2 = 1.259921049894873164767210607278228350570251L;
static const long double CBRT4 = 1.587401051968199474751705639272308260391493L;
static const long double CBRT2I = 0.7937005259840997373758528196361541301957467L;
static const long double CBRT4I = 0.6299605249474365823836053036391141752851257L;
long double
cbrtl (long double x)
{
if (isfinite (x) && x != 0.0L)
{
int e, rem, sign;
long double z;
if (x > 0)
sign = 1;
else
{
sign = -1;
x = -x;
}
z = x;
/* extract power of 2, leaving mantissa between 0.5 and 1 */
x = frexpl (x, &e);
/* Approximate cube root of number between .5 and 1,
peak relative error = 1.2e-6 */
x = ((((1.3584464340920900529734e-1L * x
- 6.3986917220457538402318e-1L) * x
+ 1.2875551670318751538055e0L) * x
- 1.4897083391357284957891e0L) * x
+ 1.3304961236013647092521e0L) * x + 3.7568280825958912391243e-1L;
/* exponent divided by 3 */
if (e >= 0)
{
rem = e;
e /= 3;
rem -= 3 * e;
if (rem == 1)
x *= CBRT2;
else if (rem == 2)
x *= CBRT4;
}
else
{ /* argument less than 1 */
e = -e;
rem = e;
e /= 3;
rem -= 3 * e;
if (rem == 1)
x *= CBRT2I;
else if (rem == 2)
x *= CBRT4I;
e = -e;
}
/* multiply by power of 2 */
x = ldexpl (x, e);
/* Newton iteration */
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333L;
if (sign < 0)
x = -x;
return x;
}
else
{
# ifdef __sgi /* so that when x == -0.0L, the result is -0.0L not +0.0L */
return x;
# else
return x + x;
# endif
}
}
#endif
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