[R] Ratio of huge products

[David Winsemius]

On Dec 15, 2011, at 1:35 PM, Alberto Magni wrote:

> Hello everybody,
>
> I have to compute something in this form:
>
> x = prod(a:b) / prod(c:d),    where: a < c and b < d and obviously: a
> < b and c < d
>
> I cannot make assumptions on the relative position of c,b and a,d.
>
> The problem is that a,b,c,d are large and the products are huge (R  
> return Inf).

Well, R does have some limitations.

> Their ratio is less than 1 but significantly higher than 0: it is a
> non-tiny probability.
>
> I need to find a way to simplify this ratio.

x <- exp( sum(log(a:b)) -sum(log(c:d)) )

> The only way to solve this that I see is to decompose into prime
> factors all the
> numbers in the numerator and the denominator and to remove the ones  
> in common

Ewww. That does sound painful.

-- 

David Winsemius, MD
West Hartford, CT