Evolutionary Functional Approximation of Circuits Implemented into FPGAs

functional approximation evolutionary algorithm equivalence FPGA synthesis

In many applications it is acceptable to allow a small error in the result if significant improvements are obtained in terms of performance, area or energy efficiency. Exploiting this principle is particularly important for FPGA-based solutions that are inherently subject to many resources- oriented constraints. This paper devises an automated method that enables to approximate circuit components which are often implemented in multiple instances in FPGA-based accelerators. The approximation process starts with a fully functional gate-level circuit, which is approximated by means of Cartesian Genetic Programming reflecting the error metric and constraints formulated by the user. The evolved circuits are then implemented for a particular FPGA by common FPGA synthesis and optimization tools. It is shown using five different FPGA tools, that the approximations obtained by CGP working at the gate level are preserved at the level look-up tables of FPGAs. The proposed method is evaluated in the task of 8-bit adder, 8-bit multiplier, 9-input median and 25-input median approximation.