hopefully you can open an issue on github please https://github.com/pure-data/pure-data/issues
Em qui., 17 de set. de 2020 às 18:12, oscar pablo di liscia < [email protected]> escreveu: > Hello Albert: > Many thanks for your kind response and your advice. I want factorial to > work on some combinatorial stuff. > I just wanted to check if I was doing something wrong with the use of > "expr". IMHO, the advantage > of "expr" is that I can have "packed" in just one object a complete > formula including > operator precedences. > Best > > > Oscar Pablo Di Liscia > > > El jue., 17 sept. 2020 a las 4:24, Albert Rafetseder (< > [email protected]>) escribió: > >> Hi Oscar, >> >> > the "fact" (factorial) function does not seem to work properly in the >> > "expr" external when called with an argument greater than 12. >> >> the problem in [expr fact(...)] looks like an integer overflow. See [1] >> for conceptual details, TL;DR: Factorials produce huge numbers very >> quickly, but the implementation of `fact` reserves too little space to >> store the result's digits [2], and thus truncates the result, producing >> garbage: >> >> [expr fact(12)] is 4.79002e+08, just about right >> [expr fact(13)] is 1.93205e+09, clearly *not* the above times 13 >> [expr fact(14)] is 1.27895e+09, even smaller than the previous result >> (...) >> [expr fact(17)] is a negative number altogether >> >> I can't comment on the efficiency your implementation as I'm not too >> well versed in Pd. I'd speculate it won't suffer [expr fact]'s numerical >> problems since AFAIK, patches use floats as the default number format, >> basically allowing for larger numbers to be stored. >> >> The usual suggestion for avoiding numerical problems with factorials is >> to re-think what the numbers are used for -- Taylor series? >> combinatorials of n-choose-k kind? something else? -- and use an >> appropriate alternative such as: >> >> * Stirling's approximation [3] >> * the Gamma function [4] >> * binomial coefficient without factorials [5] >> >> Cheers, >> Albert. >> >> [1] https://en.wikipedia.org/wiki/Integer_overflow >> [2] >> >> https://github.com/pure-data/pure-data/blob/2af4b5d/src/x_vexp_fun.c#L913-L928 >> [3] https://en.wikipedia.org/wiki/Stirling%27s_approximation >> [4] https://en.wikipedia.org/wiki/Gamma_function >> [5] >> >> https://en.wikipedia.org/wiki/Binomial_coefficient#Binomial_coefficient_in_programming_languages >> > _______________________________________________ > [email protected] mailing list > UNSUBSCRIBE and account-management -> > https://lists.puredata.info/listinfo/pd-list >
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