Choice of base revisited
Bryan Catanzaro, Brent Nelson · 2005
The general computing world settled on radix 2 floating point representations over three decades ago. The analyses which led to this choice were all based on the underlying premise that the goal of a floating-point representation is to maximize numerical accuracy per bit of data. However, the unique nature of FPGA-based computations makes numerical accuracy per unit of FPGA resources a more important measure by which to judge the usefulness of a given floating point representation. Due to the high cost of shifters as implemented on FPGAs, higher radix floating-point representations are uniquely 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 radix 16 adder requires 20% less LUTs than its radix 2 counterpart, while delivering equal worst-case and better average case numerical accuracy.