Higher radix floating-point representations for FPGA-based arithmetic

FPGA implementations of floating-point operators have historically been designed to use binary floating-point representations. The general computing world settled on binary floating-point representations over three decades ago, and more recently, the FPGA community followed their example. Binary representations were chosen to maximize numerical accuracy per bit of data, however, the unique nature of FPGA-based computation makes numerical accuracy per unit of FPGA resources a more important measure of the usefulness of a given floating-point representation. In this paper, we show that higher radix floating-point representations are well suited to FPGA-based computations, especially high precision calculations which require the support of denormalized numbers. Higher radix representations use FPGA resources more efficiently. For example, a hexadecimal floating-point adder has a 30% smaller area-time product than its binary counterpart, while still delivering equal worst-case and better average-case numerical accuracy. Contrary to established belief, higher radix representations are useful for FPGA applications requiring IEEE 754 compliance, since they can deliver superior numerical performance while still using less FPGA resources.