Centaur technology media unit verification case study: Floating-point addition

Abstract

We have verified floating-point addition/subtraction instructions for the media unit from Centaur's 64-bit, X86-compatible microprocessor. This unit implements over one hundred instructions, with the most complex being floating-point addition/subtraction. This media unit can add/subtract four pairs of floating-point numbers every clock cycle with an industry-leading two-cycle latency. Using the ACL2 theorem proving system, we model the media unit by translating its Verilog design into an HDL that we have deeply embedded in the ACL2 logic. We specify the addition/subtraction instructions as integer-based ACL2 functions. Using a combination of AIG- and BDD-based symbolic simulation, case splitting, and theorem proving, we produce a mechanically checked theorem in ACL2 for each instruction examined stating that the hardware model yields the same result as the instruction specification. In pursuit of these verifications, we implemented a formal HDL and symbolic simulation framework, including formally verified BDD and AIG operators, within the ACL2 theorem proving system. The HDL includes an extensible interpreter capable of performing concrete and symbolic simulations as well as non-functional analyses. We know of no other symbolic simulation-based floating-point verification that is performed within a single formal system and produces a theorem in that system without relying on unverified external tools. © 2009 Springer Berlin Heidelberg.