Efficient digital implementation of the sigmoid function for reprogrammable logic

Special attention must be paid to an efficient approximation of the sigmoid function in implementing FPGA-based reprogrammable hardware-based artificial neural networks. Four previously published piecewise linear and one piecewise second-order approximation of the sigmoid function are compared with SIG-sigmoid, a purely combinational approximation. The approximations are compared in terms of speed, required area resources and accuracy measured by average and maximum error. It is concluded that the best performance is achieved by SIG-sigmoid.