PWL approximation of hyperbolic tangent and the first derivative for VLSI implementation

Hyperbolic tangent function is approximated using piecewise linear approximation. This approximation can be used in any embedded hardware architecture where occupied chip space is a challenging factor. The presented recursive algorithm makes a trade-off between circuit delay and accuracy, where low memory consumption is required. In the presented centered linear approximation, hyperbolic tangent and its first derivative is approximated and optimized using maximum error and mean square error of the approximation. Hyperbolic tangent approximation using maximum error shows better results while the first derivative of hyperbolic tangent is better approximated using mean square error. It is demonstrated that a mean square error of 0.02 can be achieved after specific number of iterations in the approximation of hyperbolic tangent.