mingw-w64-crt/math/cbrtf.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 <math.h>
#include "cephes_mconf.h"

static const float CBRT2 = 1.25992104989487316477;
static const float CBRT4 = 1.58740105196819947475;

float cbrtf (float x)
{
int e, rem, sign;
float z;
if (!isfinite (x) || x == 0.0F )
  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 = frexpf( x, &e );

/* Approximate cube root of number between .5 and 1,
 * peak relative error = 9.2e-6
 */
x = (((-0.13466110473359520655053  * x
      + 0.54664601366395524503440 ) * x
      - 0.95438224771509446525043 ) * x
      + 1.1399983354717293273738  ) * x
      + 0.40238979564544752126924;

/* 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;
	}


/* argument less than 1 */

else
	{
	e = -e;
	rem = e;
	e /= 3;
	rem -= 3*e;
	if( rem == 1 )
		x /= CBRT2;
	else if( rem == 2 )
		x /= CBRT4;
	e = -e;
	}

/* multiply by power of 2 */
x = ldexpf( x, e );

/* Newton iteration */
x -= ( x - (z/(x*x)) ) * 0.333333333333;

if( sign < 0 )
	x = -x;
return(x);
}