# Help me choose an arbitrary precision program

1. Mar 17, 2008

### CRGreathouse

This is a crosspost from General Math; I wasn't sure what place was more appropriate.

I'm looking for a tool to solve a problem I've been working on. In particular, I want something that implements subquadratic trig functions -- in my case I'm looking for the tangent. I've been using Pari, but its tangent routine seems to be $\mathcal{O}(n^2)$ or $\mathcal{O}(n^2\log n)$ based on timing, and for high precision this simply takes too long. 10,000 digits in Pari takes half a second, but 100,000 takes more than a minute, and ten million takes over a week, which isn't feasible.

Any suggestions? Can anyone test their preferred platform (Math'ca, Maple, etc.) to see how long these take? I was testing tan(1) if you want comparability. I tested Maxima, but it seemed to be inappropriate for the task: it uses an $\mathcal{O}(n^2\log n)\textrm{-ish}$ algorithm, and took at least 30 times longer than Pari.

I could use a stand-alone system like Mathematica or a library, whatever I can find. I will need programming ability (too many problems to type by hand), but that shouldn't be hard to find.