Profile-directed specialisation of custom floating-point hardware

We present a methodology for generating floating-point arithmetic hardware designs which are, for suitable applications, much reduced in size, while still retaining performance and IEEE-754 compliance. Our system uses three key parts: a profiling tool, a set of customisable floating-point units and a selection of system integration methods. We use a profiling tool for floating-point behaviour to identify arithmetic operations where fundamental elements of IEEE-754 floating-point may be compromised, without generating erroneous results in the common case. In the uncommon case, we use simple detection logic to determine when operands lie outside the range of capabilities of the optimised hardware. Out-of-range operations are handled by a separate, fully capable, floatingpoint implementation, either on-chip or by returning calculations to a host processor. We present methods of system integration to achieve this errorcorrection. Thus the system suffers no compromise in IEEE-754 compliance, even when the synthesised hardware would generate erroneous results. In particular, we identify from input operands the shift amounts required for input operand alignment and post-operation normalisation. For operations where these are small, we synthesise hardware with reduced-size barrel-shifters. We also propose optimisations to take advantage of other profile-exposed behaviours, including removing the hardware required to swap operands in a floating-point adder or subtractor, and reducing the exponent range to fit observed values. We present profiling results for a range of applications, including a selection of computational science programs, Spec FP 95 benchmarks and the FFMPEG media processing tool, indicating which would be amenable to our method. Selected applications which demonstrate potential for optimisation are then taken through to a hardware implementation. We show up to a 45% decrease in hardware size for a floating-point datapath, with a correctable error-rate of less then 3%, even with non-profiled datasets