An FPGA-specific Approach to Floating-Point Accumulation and Sum-of-Products

This article studies two common situations where the flexibility of FPGAs allows one to design application-specific floating-point operators which are more efficient and more accurate than those offered by processors and GPUs. First, for applications involving the addition of a large number of floating-point values, an ad-hoc accumulator is proposed. By tailoring its parameters to the numerical requirements of the application, it can be made arbitrarily accurate, at an area cost comparable to that of a standard floating-point adder, and at a higher frequency The second example is the sum-of-product operation, which is the building block of matrix computations. A novel architecture is proposed that feeds the previous accumulator out of a floating-point multiplier whose rounding logic has been removed, again improving the area/accuracy tradeoff. These architectures are implemented within the FloPoCo generator, freely available under the LGPL.