I am looking for an efficient algorithm to compute $$f(x) = x^a, x\in[0, 1] \land a\,\text{constant}$$

If it helps, $a$ is either $2.2$, or $1/2.2$. Knowing valid values for $x$ and $a$ could make it possible to take some shortcuts a general pow function cannot make.

General tailor series expansion has some serious convergence problems when $x \to 0^+$, at least when $a < 1$.

I am looking for an efficient algorithm to compute $$f(x) = x^a, x\in[0, 1] \land a\,\text{constant}$$

If it helps, $a$ is either $2.2$, or $1/2.2$. Knowing valid values for $x$ and $a$ could make it possible to take some shortcuts a general pow function cannot make.

General tailor series expansion has some serious convergence problems when $x \to 0^+$, at least when $a < 1$.

• The algorithm must be faster than pow
• The maximum error on the specified interval must be less than or equal to $10^{-4}$.