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From: kj on 23 Jan 2010 17:55


Before I go off to re-invent a thoroughly invented wheel, I thought
I'd ask around for some existing module for computing binomial
coefficient, hypergeometric coefficients, and other factorial-based
combinatorial indices. I'm looking for something that can handle
fairly large factorials (on the order of 10000!), using floating-point
approximations as needed, and is smart about optimizations,
memoizations, etc.

TIA!

~K

From: idrevetnom on 24 Jan 2010 03:09

Maybe this could be of interest :


http://tnt.math.metro-u.ac.jp/nzmath/manual/modules/combinatorial.html


hope this helps Id

From: Dave Angel on 24 Jan 2010 07:07
kj wrote:
> Before I go off to re-invent a thoroughly invented wheel, I thought
> I'd ask around for some existing module for computing binomial
> coefficient, hypergeometric coefficients, and other factorial-based
> combinatorial indices. I'm looking for something that can handle
> fairly large factorials (on the order of 10000!), using floating-point
> approximations as needed, and is smart about optimizations,
> memoizations, etc.
>
> TIA!
>
> ~K
>
>
You do realize that a standard. python floating point number cannot
possibly approximate a number like 10000! Better use longs.

I'd check out the gamma function, which matches factorial for integer
arguments (plus or minus 1).

DaveA

From: Alf P. Steinbach on 24 Jan 2010 07:55
* Dave Angel:
> kj wrote:
>> Before I go off to re-invent a thoroughly invented wheel, I thought
>> I'd ask around for some existing module for computing binomial
>> coefficient, hypergeometric coefficients, and other factorial-based
>> combinatorial indices. I'm looking for something that can handle
>> fairly large factorials (on the order of 10000!), using floating-point
>> approximations as needed, and is smart about optimizations,
>> memoizations, etc.
>>
>> TIA!
>>
>> ~K
>>
>>
> You do realize that a standard. python floating point number cannot
> possibly approximate a number like 10000!

I think what kj is looking for, provided she/he is knowledgable about the
subject, is code that does something like

>>> from math import *
>>> log_fac = 0
>>> for i in range( 1, 10000+1 ):
... log_fac += log( i, 10 )
...
>>> print( "10000! = {}e{}".format( 10**(log_fac % 1), int( log_fac ) ) )
10000! = 2.84625968062e35659
>>> _

which turned out to be accurate to 10 digits.


> Better use longs.

That would involve incredible overhead. E.g., how many bytes for the number
above? Those bytes translate into arithmetic overhead.


> I'd check out the gamma function, which matches factorial for integer
> arguments (plus or minus 1).

Or, e.g., logarithms... ;-)


Cheers & hth.,

- Alf
From: Dave Angel on 24 Jan 2010 16:11
Alf P. Steinbach wrote:
> <div class="moz-text-flowed" style="font-family: -moz-fixed">* Dave
> Angel:
>> kj wrote:
>>> Before I go off to re-invent a thoroughly invented wheel, I thought
>>> I'd ask around for some existing module for computing binomial
>>> coefficient, hypergeometric coefficients, and other factorial-based
>>> combinatorial indices. I'm looking for something that can handle
>>> fairly large factorials (on the order of 10000!), using floating-point
>>> approximations as needed, and is smart about optimizations,
>>> memoizations, etc.
>>>
>>> TIA!
>>>
>>> ~K
>>>
>>>
>> You do realize that a standard. python floating point number cannot
>> possibly approximate a number like 10000!
>
> I think what kj is looking for, provided she/he is knowledgable about
> the subject, is code that does something like
>
> >>> from math import *
> >>> log_fac = 0
> >>> for i in range( 1, 10000+1 ):
> ... log_fac += log( i, 10 )
> ...
> >>> print( "10000! = {}e{}".format( 10**(log_fac % 1), int( log_fac
> ) ) )
> 10000! = 2.84625968062e35659
> >>> _
>
> which turned out to be accurate to 10 digits.
>
>
>> Better use longs.
>
> That would involve incredible overhead. E.g., how many bytes for the
> number above? Those bytes translate into arithmetic overhead.
>
About 14k.
>
>> I'd check out the gamma function, which matches factorial for integer
>> arguments (plus or minus 1).
>
> Or, e.g., logarithms... ;-)
>
>
> Cheers & hth.,
>
> - Alf
>
I didn't think of simply summing the logs. I did have some
optimizations in mind for the multiply of the longs. If you do lots of
partial products, you can do a good bit of the work with smaller
numbers, and only get to longs when those partial products get big
enough. You could also use scaling when the numbers do start getting
bigger.

But I still think there must be code for the gamma function that would
be quicker. But I haven't chased that lead.

DaveA
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