A generalization of the binary GCD algorithm
ISSAC '93 Proceedings of the 1993 international symposium on Symbolic and algebraic computation
Auto-configurable array for GCD computation
FPL '97 Proceedings of the 7th International Workshop on Field-Programmable Logic and Applications
Functional-Based Synthesis of Systolic Online Multipliers
SYNASC '05 Proceedings of the Seventh International Symposium on Symbolic and Numeric Algorithms for Scientific Computing
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We synthesise a systolic pass-through array for the computation of the greatest common divisor (GCD) of multiple precision integers. The synthesis method uses the conceptual similarity between the inductive structure of a systolic array (a head processor followed by an identical tail array) and the inductive decomposition of the argument by a functional program. By formal analysis, we identify the structure of the functions which can be realized by pass-through arrays. Then, by equational rewriting, we transform the expression of the list function which must be realized into an expression having the required structure. The resulting expression reveals the scalar function which must be implemented by each individual processor.