// cube root approximation using 3 iterations of Newton's method (float)
static float newton_cbrt3f(float d)
{
float a = cbrt_5f(d);
a = cbrta_newtonf(a, d);
a = cbrta_newtonf(a, d);
return cbrta_newtonf(a, d);
}
static float
lab_f(const float x)
{
const float epsilon = 216.0f/24389.0f;
const float kappa = 24389.0f/27.0f;
if(x > epsilon)
{
// approximate cbrtf(x):
const float a = cbrt_5f(x);
return cbrta_halleyf(a, x);
}
else return (kappa*x + 16.0f)/116.0f;
}
// cube root approximation using 2 iterations of Halley's method (float)
static float halley_cbrt2f(float d)
{
float a = cbrt_5f(d);
a = cbrta_halleyf(a, d);
return cbrta_halleyf(a, d);
}