Numerical Data Representations for FPGA-Based Scientific Computing

Various means of addressing complexity associated with the analysis of data representation techniques, providing tutorial and survey content for established approaches and highlighting recent promising research directions, are discussed. In applications with simple control flow, such as most simple signal-processing computations, the precision of internal variables is directly related to the resulting accuracy of the computation. Software packages such as the Multiple-Precision Binary Floating- Point Library with Correct Rounding (MPFR) can be used to evaluate the quality of the result. The Cestac method uses multiple simulation runs via random rounding-mode switches to estimate the number of correct digits of the output for any finite-number representation. State-of-the-art solvers can handle hundreds of constraints within seconds, depending on the density of the correlations among the constraints.