#  Binomial coefficient
#
#  Input:    tos-2    n
#
#      tos-1    k
#
#  Output:    Binomial coefficient on stack
#
#  binomial(n, k) = n! / k! / (n - k)!
#
#  The binomial coefficient vanishes for k < 0 or k > n. (A=B, p. 19)




Eval_binomial = ->
  push(cadr(p1))
  Eval()
  push(caddr(p1))
  Eval()
  binomial()

binomial = ->
  save()
  ybinomial()
  restore()

#define N p1
#define K p2

ybinomial = ->
  p2 = pop()
  p1 = pop()

  if (BINOM_check_args() == 0)
    push(zero)
    return

  push(p1)
  factorial()

  push(p2)
  factorial()

  divide()

  push(p1)
  push(p2)
  subtract()
  factorial()

  divide()

BINOM_check_args = ->
  if (isNumericAtom(p1) && lessp(p1, zero))
    return 0
  else if (isNumericAtom(p2) && lessp(p2, zero))
    return 0
  else if (isNumericAtom(p1) && isNumericAtom(p2) && lessp(p1, p2))
    return 0
  else
    return 1