Fast Factorial Algorithms

Summary

Link Content Algorithms A very short description of 21 algorithms for computing the factorial function n!. X Julia factorial *NEW* The factorial function based on the swinging factorial which in turn is computed via prime factorization implemented in Julia. Mini Library The factorial function, the binomial function, the double factorial, the swing numbers and an efficient prime number sieve implemented in Scala and GO. Browse Code Various algorithms implemented inJava, C# and C++. SageMath Implementations in SageMath. LISP Implementations in Lisp. Benchmarks Benchmark 2013: With MPIR 2.6 you can calculate 100.000.000! in less than a minute provided you use one of the fast algorithms described here. Conclusions Which algorithm should we choose? Download Download a test application and benchmark yourself. X Approximations A unique collection! Approximation formulas. Gamma quot Bounds for Gamma(x+1)/Gamma(x+1/2) Gamma shift Why is Gamma(n)=(n-1)! and not Gamma(n)=n! ? X Hadamard Hadamard's Gamma function and a new factorial function [MathJax version] History Not even Wikipedia knows this! The early history of the factorial function. Notation On the notation n! Binary Split For coders only. Go to the page of the day. Sage / Python Implementation of the swing algorithm. ‼ Double Factorial The fast double factorial function. Prime Factorial Primfakultaet ('The Primorial', in German.) Bibliography Bibliography on Inequalities for the Gamma function. X Bernoulli &Euler Exotic Applications: Inclusions for the Bernoulli and Euler numbers. Binomial Fast Binomial Function (Binomial Coefficients). Variations A combinatorial generalization of the factorial. X Stieltjes' CF On Stieltjes' Continued Fraction for theGamma Function. al-Haytham /Lagrange The ignorance of some western mathematicians.A deterministic factorial primality test. Factorial Digits Number of decimal digits of 10n! Calculator Calculate n! for n up to 9.999.999.999 . RPN-Factorial The retro-factorial page! Permut...