Formal verification of division and square root implementations, an Oracle report

Oracle has developed new implementations for integer division and floating-point division and square root. Our task was to verify the correctness of the new designs by formally proving equivalence between the RTL for these designs and their specifications in the SPARC ISA and in the IEEE 754 Standard on floating-point arithmetic. Performing such verifications involved many steps, which we describe in this paper. The contributions of this paper are two-fold. First, this paper describes Oracle's methodology for abstracting from low-level Verilog to a high-level algorithm using the latest open-source tools. Second, this paper describes the use of interval arithmetic in the error analysis of each algorithm. Our verification efforts proved that the designs had no errors, resulted in various improvements, and reduced the lookup tables by approximately 50% (division) and 75% (square root).