class MoreMath::ContinuedFraction

def call(x = nil, epsilon: 1E-16, max_iterations: 1 << 31)

iterations using the Wallis-method with scaling.
accuracy +epsilon+ and +max_iterations+ as the maximum number of
Evaluates the continued fraction for the value +x+ (if any) with the 
def call(x = nil, epsilon: 1E-16, max_iterations: 1 << 31)
  c_0, c_1 = 1.0, a(0, x)
  c_1 == nil and return 0 / 0.0
  d_0, d_1 = 0.0, 1.0
  result = c_1 / d_1
  n = 0
  error = 1 / 0.0
  $DEBUG and warn "n=%u, a=%f, b=nil, c=%f, d=%f result=%f, error=nil" %
    [ n, c_1, c_1, d_1, result ]
  while n < max_iterations and error > epsilon
    n += 1
    a_n, b_n = a(n, x), b(n, x)
    a_n and b_n or break
    c_2 = a_n * c_1 + b_n * c_0
    d_2 = a_n * d_1 + b_n * d_0
    if c_2.infinite? or d_2.infinite?
      if a_n != 0
        c_2 = c_1 + (b_n / a_n * c_0)
        d_2 = d_1 + (b_n / a_n * d_0)
      elsif b_n != 0
        c_2 = (a_n / b_n * c_1) + c_0
        d_2 = (a_n / b_n * d_1) + d_0
      else
        raise Errno::ERANGE
      end
    end
    r = c_2 / d_2
    error = (r / result - 1).abs
    result = r
    $DEBUG and warn "n=%u, a=%f, b=%f, c=%f, d=%f, result=%f, error=%.16f" %
      [ n, a_n, b_n, c_1, d_1, result, error ]
    c_0, c_1 = c_1, c_2
    d_0, d_1 = d_1, d_2
  end
  n >= max_iterations and raise Errno::ERANGE
  result
end