Functional Verification of High Performance Adders in COQ

Abstract

Addition arithmetic design plays a crucial role in high performance digital systems. The paper proposes a systematic method to formalize and verify adders in a formal proof assistant COQ. The proposed approach succeeds in formalizing the gate-level implementations and verifying the functional correctness of the most important adders of interest in industry, in a faithful, scalable, and modularized way. The methodology can be extended to other adder architectures as well.

Scalable Verification of a Generic End-Around-Carry Adder for Floating-Point Units by Coq

“…Reference [15] helps to achieve the goal of this paper. It verifies basic adders by shallow embedding in a scalability, modularization, and fidelity way, thanks to the dependent type, module system, higher-order recursive function, and other features provided by the theorem prover Coq [16].…”

“…It verifies basic adders by shallow embedding in a scalability, modularization, and fidelity way, thanks to the dependent type, module system, higher-order recursive function, and other features provided by the theorem prover Coq [16]. This paper is an extension of [15] by supplementing the method to deal with arbitrary grouping of arbitrary input data-width, which makes the method more complete. The general architecture is then parameterized by the input data-width, grouping method and sub-components used.…”

“…2) Providing the grouping method and proving the method is valid, which is no more than splitting a natural number into nonoverlapped and nonoverflowed segments. 3) Providing correct sub-components used in the architecture and most kinds of sub-components can be picked up from [15] or other related works. Further optimization to this architecture may require additional equivalence proof for intermediate results, which would not be complex.…”

“…Further optimization to this architecture may require additional equivalence proof for intermediate results, which would not be complex. As discussed in [15], this verified architecture can also be used to help designing or automatically generating new correct implementations in the future. This paper has been carried out in the theorem prover Coq.…”

“…Detailed proof scripts can be found on Q. Wang's web page (http:// superwalter.github.io/dev/eacVeri-TCAD.zip). The advantages to use shallow embedding, dependent type, higher order function, and the module system have been mentioned in [15], therefore, we just addressed two of them, which are related to this paper. Dependent type provides faithful formalization of related data types and in advance error detection as discussed in [17], but it brings more work in the development as discussed in [17]- [19].…”