/*

  Factorial / Gamma function

  maxCount = 5
  code = factorial((N + (N + 1))) = [[[1],6],[[2],120],[[3],5040],[[4],362880],[[5],39916800],[[6],622702080
 
  Cf http://hakank.org/jgap/gamma_test.conf

  Note: This blows up. It's very easy to get something like this
  f = !(!(N))

  But using factorial_restricted works:
  [program = N - N + factorial_restricted(N + (1 + N)),res = 51090942171709440000,count = 8]
  [program = factorial_restricted(N + N + 1),res = 51090942171709440000,count = 7]
  [program = factorial_restricted(1 + (N + N)),res = 51090942171709440000,count = 6]
  [program = factorial_restricted(N + (N + 1)),res = 51090942171709440000,count = 5]
  [program = factorial_restricted(N + (1 + N)) + N * (1 - 1) * 1,res = 51090942171709440000,count = 3]
  [program = factorial_restricted(2 * N + factorial_restricted(1)),res = 51090942171709440000,count = 3]
  [program = factorial_restricted(N + (1 + N)) * 1,res = 51090942171709440000,count = 2]
  [program = factorial_restricted(N * 2 + 1),res = 51090942171709440000,count = 1]

  resultMap = [51090942171709440000 = 8]


*/
data(factorial_test,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  Data =  [ [[N],factorial(2*N+1)] : N in 1..9],
  println(data=Data),
  Unknown = [10], 
  Vars = ['N'],
  % Ops = [+,-,*,!],
  Ops = [+,-,*,factorial_restricted], 
  Constants = 1..2,
  MaxSize = 6,
  Params = new_map([debug=false]).