[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...
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See also [Factorial using event loop]
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[Category Concept] | [Arts and crafts of Tcl-Tk programming]