**In one easy sentence**: I improved a (Python) software tool that’s used to further improve digital circuits that perform numerical computations.

Project Supervisor: Prof. George A. Constantinides

# Abstract

During high-level synthesis (HLS) more often than not, standard discrete-arithmetic units are used to synthesise C-like arithmetic programs onto a field-programmable gate array (FPGA). In this project, I expand on the open-source HLS tool `Structural Optimisation of Arithmetic Programs’ (SOAP) to consider fused arithmetic units.

SOAP rewrites a program to produce a set of equivalent programs that are Pareto-optimal in resource usage (area), numerical accuracy and latency. In this project, just the area and numerical accuracy of individual arithmetic expressions are evaluated. The fused units implemented are the 3-input adder, fused multiply-add (FMA) and constant multiplier, all acting on floating-point numbers. SOAP’s power of expression transformation is harnessed to expose non-obvious uses of these fused units.

Improvements achieved in some of the inner expressions of PolyBench and Livermore Loops, for single-precision floating-point, are up to 1.13× in area without degrading accuracy, and up to 1.4× in numerical accuracy at an area cost of up to 2.6×. It is shown that the accuracy improvement can be arbitrarily large under certain conditions.