Iterative refinement algorithm for computing exp(x) with arbitrary precision

algorithms numerical-methods special-functions

Solution 1:

There is an algorithm for computing $\log_2(x)$ that might suit you. Combine that with the spigot algorithm for $e$, and you can get $\ln(x)$. From there, you can use Newton-Raphson to get $\exp(x)$.

I don't know if this roundabout way ends up doing any better than just recomputing.

Related

Every finite commutative ring with no zero divisors contains a multiplicative identity?
Group $\mathbb Q^*$ as direct product/sum
Why is $\frac{1}{\infty } \approx 0 $ and $ \frac{1}{0} = {\infty}$?
Probability of winning in a die rolling game with six players
Equality of two notions of tensor products over a commutative ring
For what $n$ can $\pm 1\pm 2\pm 3 ... \pm (n-1) \pm n = n+1$?
On the integral $\int_{0}^{1/2}\frac{\text{Li}_3(1-z)}{\sqrt{z(1-z)}}\,dz$
Cancellation problem: $R\not\cong S$ but $R[t]\cong S[t]$ (Danielewski surfaces)
Normalizing every Sylow p-subgroup versus centralizing every Sylow p-subgroup
Solve $\dfrac{1}{1+\frac{1}{1+\ddots}}$
How to know if its permutation or combination in a specific exercise?
Different ways to come up with $1+2+3+\cdots +n=\frac{n(n+1)}{2}$