"S.D.Mechveliani" wrote:
>
> Steve Bennett <[EMAIL PROTECTED]> writes to hugs-users...
>
> > [..]
> > Ok, maybe 111,111! is asking a bit much...but would it be possible to
> > write a factorial function that wouldn't stack overflow? Like it would
> > crash some other way...not enough memory, taking too long, etc etc?
> > Stack overflow just seems a little ungraceful :)
> >
> > (PS: if anyone knows of a way of estimating the value of a factorial,
> > I'd also appreciate that).
>
> (2n)! = (1*2n)*(2*(2n-1))*...*(n*n) >= n^n - if i do not mistake.
>
> In the calculus guides they, probably, prove something stronger.
> So, the number of bits in 111111! is more than
> 55000*(log_2 55000) > 15*55000
> Multiplying such numbers may cost a penny.
> I have heard, there exist good algorithms using the fast Fourie
> transformation: s*(log s) operations, s the number of digits in n.
> This is instead of more than s^2 of "usual" methods.
> See the book of Aho, Hopcroft, Ulman.
Here is a better one known as stirling's approximation
n! (approx)= (n/e)^n*sqrt(2*pi*n)
