Approximation of Elementary Functions by Polynomials and Rational Functions - Some Results for FPGA Based Implementations

Abstract

The hardware evaluation of elementary functions such as exp(x) and sin(x) is advantageous due to the performance that can be reached when compared with software solutions. Such evaluations can be done by computing simple functions thal approximate the targeted elementary functions. Actual microprocessors and specific processors like the digital signal processors include computing capabilities for some elementary functions but they could be inappropriate for some situations. Due to the great impact that Field Programmable Gate Arrays (FPGA) have in a wide range of hardware applications, specially in areas where hardware customization can improve the overall performance, the implementation of these functions in FPGA devices is worth considering. The reconfigurabllity they offer increases the flexibility and the power of such custom computing machines. Implementations of common elementary functions using single precision floating point arithmetic are described and the correspondent results are presented.