stats.awk

# Returns NaN.
function nan() {
  return "+NaN" + 0
}

# Returns the binomial coefficient.
# It works, at least, when either n or k is a non-negative integer.
function binom(n, k,  tmp) {
  if (n == k || k == 0) {
    return 1
  }
  if (k > n - k && n - k >= 0) {
    k = n - k
  }
  tmp = 1
  while (n >= 1 && k >= 1) {
    tmp *= n / k
    n--
    k--
  }
  while (k >= 1) {
    tmp *= (n - k + 1) / k
    k--
  }
  while (n >= 1 && n > k) {
    tmp *= n / (n - k)
    n--
  }
  if (n == k || k == 0) {
    return tmp
  }
  if (n == 0) {
    k *= atan2(0, -1)
    return tmp *= sin(k) / k
  }
  return nan()  # unsupported
}