Accurate Floating Point Arithmetic through Hardware Error-Free Transformations

Manouk V. Manoukian, George A. Constantinides

Abstract: This paper presents a hardware approach to performing accurate floating point addition and multiplication using the idea of error-free transformations. Specialized iterative algorithms are implemented for computing arbitrarily accurate sums and dot products. The results of a Xilinx Virtex 6 implementation are given, area and performance are compared against standard floating point units and it is shown that the time×area product can be improved by a factor of 4 and 6 over software error-free addition and multiplication. Furthermore, it is illustrated that a number of area and performance trade-offs can be made when calculating vector sums and dot products.