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/* Calculates the cube root function of _Decimal32 type x
Copyright (C) 1984, 1991 Stephen L. Moshier.
Copyright (C) 2006 IBM Corporation.
Copyright (C) 2001-2015 Free Software Foundation, Inc.
This file is part of the Decimal Floating Point C Library.
Author(s): Joseph Kerian <jkerian@us.ibm.com>
The Decimal Floating Point C Library is free software; you can
redistribute it and/or modify it under the terms of the GNU Lesser
General Public License version 2.1.
The Decimal Floating Point 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 version 2.1 for more details.
You should have received a copy of the GNU Lesser General Public
License version 2.1 along with the Decimal Floating Point C Library;
if not, write to the Free Software Foundation, Inc., 59 Temple Place,
Suite 330, Boston, MA 02111-1307 USA.
Please see libdfp/COPYING.txt for more information. */
#ifndef _DECIMAL_SIZE
# include <decimal32.h>
# define _DECIMAL_SIZE 32
#endif
#include <math.h>
#include <ieee754r_private.h>
#define FUNCTION_NAME cbrt
#include <dfpmacro.h>
/*
* Provided by the Cephes Math Library Release 2.2: January, 1991
* By Stephen L. Moshier
* Adapted for glibc October, 2001.
* Adapted for libdfp 2006, and donated to the FSF in 2007.
*
* 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
*/
/* Replace with:
* cbrt(10) and cbrt(100)
* and
* cbrt(-10) and cbrt(-100)
*
* used 'bc' to get these and then trunced by hand.
* echo 'scale=44;e(1/3*(l(10)))' | bc -l
* echo 'scale=44;e(1/3*(l(100)))' | bc -l
* echo 'scale=45;e(1/3*(l(1/10)))' | bc -l
* echo 'scale=45;e(1/3*(l(1/100)))' | bc -l
*/
static const _Decimal128
CBRT10 = 2.154434690031883721759293566519350495259345DL,
CBRT100 = 4.641588833612778892410076350919446576551349DL,
CBRT10I = 0.4641588833612778892410076350919446576551349DL,
CBRT100I = 0.2154434690031883721759293566519350495259345DL;
// CBRT2 = 1.259921049894873164767210607278228350570251DL,
// CBRT4 = 1.587401051968199474751705639272308260391493DL,
// CBRT2I= 0.7937005259840997373758528196361541301957467DL,
// CBRT4I= 0.6299605249474365823836053036391141752851257DL;
DEC_TYPE
INTERNAL_FUNCTION_NAME (DEC_TYPE x)
{
int e, rem, sign;
_Decimal128 z;
if (! FUNC_D(__isfinite) (x)) /* cbrt(x:x=inf/nan/-inf) = x+x (for sNaN) */
return x + x;
if (x == DFP_CONSTANT(0.0)) /* cbrt(0) = 0 */
return (x);
if (x > DFP_CONSTANT(0.0))
sign = 1;
else
{
sign = -1;
x = -x;
}
z = x;
/* extract power of 2, leaving mantissa between 0.5 and 1 */
x = FUNC_D(__frexp) (x, &e);
/* Approximate cube root of number between .5 and 1,
peak relative error = 1.2e-6 */
x = ((((1.3584464340920900529734e-1DL * x
- 6.3986917220457538402318e-1DL) * x
+ 1.2875551670318751538055e0DL) * x
- 1.4897083391357284957891e0DL) * x
+ 1.3304961236013647092521e0DL) * x + 3.7568280825958912391243e-1DL;
/* exponent divided by 3 */
if (e >= 0)
{
rem = e;
e /= 3;
rem -= 3 * e;
if (rem == 1)
//x *= CBRT2;
x *= CBRT10;
else if (rem == 2)
//x *= CBRT4;
x *= CBRT100;
}
else
{ /* argument less than 1 */
e = -e;
rem = e;
e /= 3;
rem -= 3 * e;
if (rem == 1)
//x *= CBRT2I;
x *= CBRT10I;
else if (rem == 2)
//x *= CBRT4I;
x *= CBRT100I;
e = -e;
}
/* multiply by power of 2 */
x = FUNC_D(__ldexp) (x, e);
/* Newton iteration */
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333DL;
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333DL;
x -= (x - (z / (x * x))) * 0.3333333333333333333333333333333333333333DL;
if (sign < 0)
x = -x;
return (x);
}
weak_alias (INTERNAL_FUNCTION_NAME, EXTERNAL_FUNCTION_NAME)
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