Re: range error - or "How to take the factorial of a huge

[Jim Witte]

2.
Work with logs of expressions.
  The MathWorld page on Stirling's approximation gives a formula for 
(log n!) as well. The first formula gives an *exect* (I think) 
derivation for ln n! as

ln n! = sum(k=1..n, ln k)

which is approximately (by changing that summation to an integral from 
1..n and simplifying it, to give

ln n! ~ n ln n - n

It also gives an (exact) integral definition of factorial:

n! = integral(0, infinity, ( exp(-x)*(x^n) ), dx)

So you could write an definite-integration function, taking a small 
slice parameter for dx, and sum the integrand term:  This would be 
something around the following

function integrand (x, n)
        reuturn (exp(-x) * x^n)
end integrand
function fact (n)
        put 0 into min
        put 100 into max
        put 0.001 into dx
        put min into x
        put 0 into sum
        add integrand(x, n) to sum
        add dx to x
        if (x>max) then
                return sum
        end if
end fact
since exp(-x) gets very small as x gets large, 100 should provide a 
reasonable maximum.  I don't know how small dx should really be.  I 
don't know how much better (or worse) this is compared to the foluma I 
quoted earlier.

Jim

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