This paper addresses the problem of computational error modeling and analysis. Choosing different word-lengths for each functional unit in hardware implementations of numerical algorithms always results in an optimization problem of trading computational error with implementation costs. In this study, a symbolic noise analysis method is introduced for high-level synthesis, which is based on symbolic modeling of the error bounds where the error symbols are considered to be specified with a probability distribution function over a known range. The ability to combine word-length optimization with high-level synthesis parameters and costs to minimize the overall design cost is demonstrated using case studies.
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