Math.Combinatorics.Factorial

The factorial numbers (http://oeis.org/A000142). For negative inputs, all functions return 0 (rather than throwing an exception or using Maybe).

Notable limits:

• 12! is the largest factorial that can fit into Int32.
• 20! is the largest factorial that can fit into Int64.
• 170! is the largest factorial that can fit into 64-bit Double.

Documentation

factorial :: (Integral a, Bits a) => Int -> a

Exact factorial numbers. For a fast approximation see math-functions:Numeric.SpecFunctions.factorial instead. The naive definition of the factorial numbers is:

 factorial n
     | n < 0     = 0
     | otherwise = product [1..n]

However, we use a fast algorithm based on the split-recursive form:

 factorial n =
     2^(n - popCount n) * product [(q k)^k | forall k, k >= 1]
     where
     q k = product [j | forall j, n*2^(-k) < j <= n*2^(-k+1), odd j]