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Log of factorial of large numbers

version (3.58 KB) by Yvan Lengwiler
computes log10 of the factorial

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Updated 10 May 2007

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This function computes log10 of the factorial. Unlike FACTORIAL, it is not limited to arguments less than 171.

Two methods are implemented, one based on the gamma function (thank you, John), as well as a direct sum. The user can choose between the two methods. The gamma method is superior and is therefore the default choice.

The function returns the log10 of the factorial, the mantissa and the exponent of the factorial, as well as a string representing the factorial.

For instance
[L,M,X,S] = logfactorial(1E6)
L = 5.5657e+006 % log10(N!)
M = 8.2639 % mantissa
X = 5565708 % exponent
S = '8.26393e+5565708' % N! as a string

The function accepts scalars or arrays as inputs.

LOGFACTORIAL is the result of a seqeunce of improvements that were suggested by John D'Errico and Urs Schwarz in their discussion of another FEX file, LARGEFACTORIAL. LOGFACTORIAL is preferrable for two reasons:

1. The gamma-based code is much faster than the direct sum code, which is the only one implemented in LARGEFACTORIAL.

2. LARGEFACTORIAL returns a string as the first argument, which is not very convenient to perform further computations. LOGFACTORIAL returns the log10 as the first argument, so for instance 10.^logfactorial(...) does make sense.

Cite As

Yvan Lengwiler (2020). Log of factorial of large numbers (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (2)

John D'Errico

For those who don't want to remember the use of gammaln as implemented inside, this adds a few extras too. It is complete, with good help.

Eelke Spaak

This allowed me to compute Fisher's exact test for contingency tables for large n. Excellent, thanks a lot!


More descriptive title. Correction of typo in the description.

MATLAB Release Compatibility
Created with R14SP3
Compatible with any release
Platform Compatibility
Windows macOS Linux

Inspired by: Factorial of large numbers