Fast Factorial Algorithms
luschny.deA cached map will do best if you actualy need a fast factorial. There are very little entries before the numbers become pointlessly big.
To all commenting about the Sitrling formula, there is a separate page linked at the end for approximations http://www.luschny.de/math/factorial/approx/SimpleCases.html which contains many advanced options to compare for that.
I hoped this would help me solve some more Project Euler [1] problems. Unfortunately, the algorithms given are not explained in detail, so the learning experience is somewhat mediocre. Then again, I have ChatGPT to elucidate them for me.
This article [2] has some interesting details on the swinging factorial function n≀, but I can't seem to find the essay that it references: "Swing, divide and conquer the factorial", 2008.
No Stirling formula?
That one is an approximation rather than returning all millions of exact big integer digits though (the approximation is more useful for real life statistics etc..., but doesn't look like what this article is targeting)