NoverK

Fast and accurate N over K

N over K

A fast and stable computation of: n! / (k! * (n-k)!)

This is the number of combinations, if k elements are chosen out of n without

repetitions and order.

[c, OF] = NoverK(n, k)

INPUT:

n, k: Scalars with real integer values, floating point or integer types.

OUTPUT:

c: Result as same type as the inputs.

OF: Logical flag, true on overflow.

NOTES:

- Alternatives:

prod(((n-k+1):n) ./ (1:k)) 3 times slower, less accurate

nchoosek(n, k) 20 times slower, less accurate:

nchoosek(61, 17) 536830054536826 (14 valid digits only)

NoverK(61, 17) 536830054536825

The accuracy and overflow handling was the main reason to write this function.

Tested: Matlab 2009a (no U/INT64!), 2015b(32/64), 2016b, 2018b, Win10