Richard Suchenwirth 2004-02-08 - Factorial (n!) is a popular function with super-exponential growth. Mathematically put,
0! = 1 n! = n (n-1)! if n >0, else undefined
In Tcl, we can have it pretty similarly:
proc fact n {expr {$n<2? 1: $n * [fact [incr n -1]]}}But this very soon crosses the limits of integers, giving wrong results.
Weekend reading in an older math book showed me the Stirling approximation to n! for large n (at Tcl's precisions, "large" is > 20 ...), so I built that in:
proc fact n {expr {
$n<2? 1:
$n>20? pow($n,$n)*exp(-$n)*sqrt(2*acos(-1)*$n):
wide($n)*[fact [incr n -1]]}
}Just in case somebody needs approximated large factorials... But for n>143 we reach the domain limit of floating point numbers, for which I can offer no way out :(
See also Factorial using event loop