  The natural exponential function is widely used in modeling many engineering
and scientific systems. It is also an integral part of many neural network
activation function such as sigmoid, tanh, ELU, RBF etc. Dedicated hardware
accelerator and processors are designed for faster execution of such
applications. Such accelerators can immensely benefit from an optimal
implementation of exponential function. This can be achieved for most
applications with the knowledge that the exponential function for a negative
domain is more widely used than the positive domain. This paper presents an
optimized implementation of exponential function for variable precision fixed
point negative input. The implementation presented here significantly reduces
the number of multipliers and adders. This is further optimized using mixed
world-length implementation for the series expansion. The reduction in area and
power consumption is more than 30% and 50% respectively over previous
equivalent method.
