Algorithm and Implementation Details for Complementary Error Function

The algorithm proposed in this article provides high accuracy and requires only double-precision arithmetic. The calculated value obtained by the algorithm is proved to be accurate to
$0.785 \cdot \text{ulp}$
as long as the result does not underflow. In the case of subnormal results the error does not exceed
$0.875 \cdot \text{ulp}$
. The testing results have also shown that the implementation of the proposed algorithm has reasonable computational time compared to other implementations.