*PBHD: An Efficient Graph Representation for Floating Point Circuit Verification

BMDs, HDDs, and K*BMDs provide compact representations for functions which map Boolean vectors into integer values, but not floating point values. In this paper, we propose a new data structure, called Multiplicative Power Binary Hybrid Diagrams (*PBHDs), to provide a compact representation for functions that map Boolean vectors into integer or floating point values. The size of the graph to represent the IEEE floating point encoding is linear with the word size. The complexity of floating point multiplication grows linearly with the word size. The complexity of floating point addition grows exponentially with the size of the exponent part, but linearly with the size of the mantissa part. We applied *PBHDs to verify integer multipliers and floating point multipliers before the rounding stage, based on a hierarchical verification approach. For integer multipliers, our results are at least 6 times faster than *BMD’s. Previous attempts at verifying floating point multipliers required manual intervention. We verified floating point multipliers before the rounding stage automatically. This research is sponsored by the Defense Advanced Research Projects Agency (DARPA) under contract number DABT63-96-C-0071. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of DARPA or the U.S. Goverment.