The round function is just 4 SLOC:

    function q( state, val, numerator, denominator ) {
      // Continued Fraction mixed with Egyptian fraction "Continued Egyptian Fraction"
      // with denominator = val + pos / state[1]
      state[0] += numerator / denominator;
      state[0] = 1.0 / state[0];

      // Standard Continued Fraction with a_i = val, b_i = (a_i-1) + i + 1
      state[1] += val;
      state[1] = numerator / state[1];
    }