I have gotten the 10-term "munafacmu34" version performing to near the limits of what's possible in a 32-digit floating-point (Dekker style double-double) numerics library. To answer your question *"How many divides is a '+a5*z^2' worth?"*, I'd say it's probably about a one-to-one tradeoff. In other words, if you add one term to a polynomial to save one divide in the "Gamma[x+1]=x Gamma[x]" iteration, that would be about a break-even. So if you can reduce the minimum argument by 2 via adding one term, that's a win. The bigger issue I'm dealing with is the transcendental operations. My Sinh() is doing an 8-step Taylor series (for 1/z <= 1/14), Exp() is a 16 to 20 step Taylor series, and Log() is a little slower than Exp(). Since we need about 5 of these transcendentals to use the approximation formula, that's where most the computation time is being spent. - Robert [1] See bibliography at mrob.com/pub/math/f161.html On Tue, Jan 10, 2012 at 19:14, Bill Gosper <billgosper@gmail.com> wrote:
(Sorry about (no subject).) Hmm, "only" 26 digits with seven b*ggerfactors on z>9:
http://gosper.org/munafacmu26.png
Note that the z^7 means we only need ~20 digit values for the seven b*ggerfactors, but it looks like we'll need > eight, ior larger "9" for quad (34digit) precision. How many divides is a "+a5*z^2" worth? --rwg
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com