81 lines
1.6 KiB
C
81 lines
1.6 KiB
C
|
/**
|
||
|
|
* This file has no copyright assigned and is placed in the Public Domain.
|
||
|
|
* This file is part of the mingw-w64 runtime package.
|
||
|
|
* No warranty is given; refer to the file DISCLAIMER.PD within this package.
|
||
|
|
*/
|
||
|
|
#include <math.h>
|
||
|
|
|
||
|
|
static const long double CBRT2 = 1.2599210498948731647672L;
|
||
|
|
static const long double CBRT4 = 1.5874010519681994747517L;
|
||
|
|
static const long double CBRT2I = 0.79370052598409973737585L;
|
||
|
|
static const long double CBRT4I = 0.62996052494743658238361L;
|
||
|
|
|
||
|
|
long double cbrtl(long double x)
|
||
|
|
{
|
||
|
|
int e, rem, sign;
|
||
|
|
long double z;
|
||
|
|
|
||
|
|
if (!isfinite (x) || x == 0.0L)
|
||
|
|
return (x);
|
||
|
|
|
||
|
|
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)) )*0.3333333333333333333333L;
|
||
|
|
x -= ( x - (z/(x*x)) )*0.3333333333333333333333L;
|
||
|
|
|
||
|
|
if (sign < 0)
|
||
|
|
x = -x;
|
||
|
|
return (x);
|
||
|
|
}
|