[PD] weird behavior of factorial in expr
oscar pablo di liscia
odiliscia at gmail.com
Fri Sep 18 03:12:29 CEST 2020
Thanks, so i will do.
I just wanted to be sure before.
El jueves, 17 de septiembre de 2020, Alexandre Torres Porres <
porres at gmail.com> escribió:
> hopefully you can open an issue on github please https://github.com/
> Em qui., 17 de set. de 2020 às 18:12, oscar pablo di liscia <
> odiliscia at gmail.com> 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.
>> Oscar Pablo Di Liscia
>> El jue., 17 sept. 2020 a las 4:24, Albert Rafetseder (<
>> albert.rafetseder+pd at univie.ac.at>) 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 
>>> 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 , and thus truncates the result, producing
>>> [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 
>>> * the Gamma function 
>>> * binomial coefficient without factorials 
>>>  https://en.wikipedia.org/wiki/Integer_overflow
>>>  https://en.wikipedia.org/wiki/Stirling%27s_approximation
>>>  https://en.wikipedia.org/wiki/Gamma_function
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Oscar Pablo Di Liscia
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