I have a recursion factorial
recursive.factorial <- function(x) {
if (x == 0) return (1)
else return (x * recursive.factorial(x-1))
}
Just curious what can be the largest x here in my recursive.factorial v.s the build-int factorial() function in R? is there a way to check with that
The bit-span of computer numeric values seems much more likely to be the problem than the "computer memory" by which I am assuming you meant the address space of RAM. The largest value for an integer that can be represented without approximation in R (and any software package using the usual IEEE standard) is 2^53 - 1. There are other packages (some of them available as R packages) that can support arbitrary precision numerics. The ?Recall functions is a more stable methods of doing recursion, although it is not optimized in R. The integer.max is set at the precison obtainable with 2 bytes:
2^32-1
[1] 4294967295
And the more recently introduced "long integers" max out at the limits of the mantissa of floating point "doubles".
> 2^53-1
[1] 9.007199e+15
> print( 2^53-1, digits=18)
[1] 9007199254740991
So as soon as you get a value of factorial(n) that is larger than that limit you only get an approximation and when you exceed the limits of the exponentiation for a "double" numeric, you get "Inf". My version of factorial seems to have the same breaking point as yours:
> fact <- function(n)
+ if(n==0) { 1} else{ (n) *Recall(n-1)}
> fact (170)
[1] 7.257416e+306
> fact (171)
[1] Inf
Here's another way of thinking about calculating factorial:
> exp( sum(log(1:15)))
[1] 1.307674e+12
> factorial(15)
[1] 1.307674e+12
The "Stirling's approximation" is often used to speed up calculations of factorial. For more accurate values you can install either the gmp or the Rmpfr packages.