# Combinatorical functions test
use math.rational: rat
use math.cf: fac, bc, euler1, stirling2
use functional: fix
use sys: exit

function error(s)
   print("Error in test-cf: test ", s, " failed.")
   exit(1)
end

Ba = fix({},|B,n| 1 if n==0 else
   1-rat(1,n+1)*(0..n-1).sum(|k| B(k)*bc(n+1,k)))

Bb = |n| rat(
   n*(0..n-1).sum(|k| (-1)^k*euler1(n-1,k)),
   2^n*(2^n-1)
)

Bc = |n| (0..n).sum(|k|
   rat((-1)^k*fac(k)*stirling2(n+1,k+1),k+1))

Bd = |n| rat(1,2) if n==1 else (0..n).sum(|k|
   rat((-1)^k*fac(k)*stirling2(n,k),k+1))

Be = |n| rat(n,2^(n+1)-2)*(0..n-1).sum(|k|
   rat(fac(k)*stirling2(n,k+1),(-2)^k))

# Bernoulli numbers test
N = 100

if (1..N).any(|n| Ba(n)!=Bb(n) or Bb(n)!=Bc(n))
   error("#1.1")
end

if (1..N).any(|n| Bb(n)!=Bd(n) or Bb(n)!=Be(n))
   error("#1.2")
end