Hierarchical Verification of the Implementation of The IEEE-754 Table-Driven Floating-Point Exponential Function using HOL

The IEEE-754 floating-point standard, used in nearly all floating-point applications, is considered one of the most important standards. Deep datapath and algorithm complexity have made the verification of such floating-point units a very hard task. Most simulation and reachability analysis verification tools fail to verify a circuit with a deep datapath like most industrial floating-point units. Theorem proving, however, offers a better solution to handle such verification. In this report we have formalized and verified a hardware implementation of the IEEE-754 Table-Driven floating-point exponential function algorithm using the HOL theorem prover. The high ability of abstraction in the HOL verification system allows its use for the verification task over the whole design path of the circuit, starting from the gate level implementation of the circuit up to a higher level behavioral specification. To achieve this goal, we have used both hierarchical and modular approaches for modeling and verifying the floatingpoint exponential function in HOL.