A Spanning Tree Carry Lookahead Adder
IEEE Transactions on Computers - Special issue on computer arithmetic
Parallel computing using the prefix problem
Parallel computing using the prefix problem
Mechanical Verification of Adder Circuits using Rewrite RuleLaboratory
Formal Methods in System Design
Journal of the ACM (JACM)
Computer Arithmetic Algorithms
Computer Arithmetic Algorithms
ARITH '01 Proceedings of the 15th IEEE Symposium on Computer Arithmetic
A Regular Layout for Parallel Adders
IEEE Transactions on Computers
A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations
IEEE Transactions on Computers
Proofs of Correctness and Properties of Integer Adder Circuits
IEEE Transactions on Computers
Hi-index | 0.98 |
The paper presents an algebraic analysis for the correctness of prefix-based adders. In contrast to using higher-order functions and rewriting systems previously, we harness first-order recursive equations for correctness proof. A new carry operator is defined in terms of a semi-group with the set of binary bits. Both sequential and parallel addition algorithms are formalized and analyzed. The formal analysis on some special prefix adder circuits demonstrates the effectiveness of our algebraic approach. This study lays an underpinning for further understanding on computer arithmetic systems.