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. In fact, as Additional math functions points out, the float limit is at n>170, so an intermediate result in the Stirling formula must have busted at 144. For such few values it is most efficient to just look them up in a pre-built table, as Tcllib's math::factorial does.
Incidentally, playing with that, I noticed a bug: as table lookup is guarded with
if {$x <= [llength $factorialList]} {return [lindex $factorialList $x]}
that function has a blind spot at x=171: it returns "" (list index overrun, should test with < ;-) instead of throwing the error, which it does for x>171...
See also Factorial using event loop