Introduction to algorithms
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Parallelizing complex scans and reductions
PLDI '94 Proceedings of the ACM SIGPLAN 1994 conference on Programming language design and implementation
Journal of the ACM (JACM)
Introduction to VLSI Systems
Overview of Hydra: A Concurrent Language for Synchronous Digital Circuit Design
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
Formalization of a parameterized parallel adder within the coq theorem prover
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Formal proof for a general architecture of hybrid prefix/carry-select adders
ICA3PP'10 Proceedings of the 10th international conference on Algorithms and Architectures for Parallel Processing - Volume Part I
Synchronous digital circuits as functional programs
ACM Computing Surveys (CSUR)
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Using Haskell as a digital circuit description language, we transform a ripple carry adder that requires $O(n)$ time to add two $n$-bit words into a parallel carry lookahead adder that requires $O(\log n)$ time. The ripple carry adder uses a scan function to calculate carry bits, but this scan cannot be parallelized directly since it is applied to a non-associative function. Several techniques are applied in order to introduce parallelism, including partial evaluation and symbolic function representation. The derivation given here constitutes a semi-formal correctness proof, and it also brings out explicitly each of the ideas underlying the algorithm.