I would've done it using complex exponentiation. And the exponential function is very easy to estimate fast: instead of Taylor series, use: e^x=(1+x/n)^n pick

I would've done it using complex exponentiation. And the exponential function is very easy to estimate fast: instead of Taylor series, use: e^x=(1+x/n)^n pick n=2^N, and that's just a bit shift and N repeated multiplications. Probably much faster and accurate.