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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 [itex]\mathcal{O}(n^2)[/itex] or [itex]\mathcal{O}(n^2\log n)[/itex] 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 [itex]\mathcal{O}(n^2\log n)\textrm{-ish}[/itex] 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.
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 [itex]\mathcal{O}(n^2)[/itex] or [itex]\mathcal{O}(n^2\log n)[/itex] 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 [itex]\mathcal{O}(n^2\log n)\textrm{-ish}[/itex] 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.