Asynchronous Parallel Prefix Computation

• Authors: Rajit Manohar;José A. Tierno
• Venue: IEEE Transactions on Computers
• Year: 1998

The prefix problem is to compute all the products $x_1 \otimes x_2 \otimes \cdots \otimes x_k,$ for 1 驴k驴n, where $\otimes$ is an associative binary operation. We start with an asynchronous circuit to solve this problem with O(log n) latency and O(n log n) circuit size, with $O(n)\ \otimes\!\!-{\rm operations}$ in the circuit. Our contributions are: 1) a modification to the circuit that improves its average-case latency from O(log n) to O(log log n) time, and 2) a further modification that allows the circuit to run at full-throughput, i.e., with constant response time. The construction can be used to obtain a asynchronous adder with O(log n) worst-case latency and O(log log n) average-case latency.