mingw-w64-crt/math/cbrtl.c

/**
 * This file has no copyright assigned and is placed in the Public Domain.
 * This file is part of the w64 mingw-runtime package.
 * No warranty is given; refer to the file DISCLAIMER within this package.
 */
#include "cephes_mconf.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;

extern long double ldexpl(long double,int);

long double cbrtl(x)
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);
}