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Improving throughput of networks of radix-2 on-line arithmetic modules for small precision applications Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/pv63g353h

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  • On-line arithmetic modules were proposed as a way to explore parallelism in arithmetic operations at digit level. Using always serial operators that receive inputs and compute the outputs from most-significant to least-significant digits, online arithmetic makes it possible to overlap all arithmetic operations and have a pipelined structure. On-line division is one of the slowest operations among the basic arithmetic operations and naturally becomes a bottleneck in networks of on-line modules that use it. A higher radix divider has a good potential to attain higher throughput than radix-2 dividers and therefore improve the overall throughput of networks where division is needed. The improvement in throughput when using radix 4 is not straightforward since several components of the divider become more complex than in the radix-2 case. Previously proposed radix-4 designs were based on operand prescaling to simplify the selection function and reduce the critical path delay, at the cost of more complexity in the algorithm conditions and operations, plus a variable on-line delay, which is a very unattractive feature when small precision values are used (usually the case for DSP). These designs include several phases for pre-scaling and actual division. In this thesis a design approach based on overlapped replication that results in a radix-4 on-line division module with low algorithm complexity, single division phase, less restrictions to the input values, and a small and fixed on-line delay is presented. On-line arithmetic modules have an intrinsic on-line delay that impacts the maximum throughput of networks using these modules. The problem is particularly serious for small precision calculation or deep-pipelined networks. This work presents a solution to the problem. Results of an actual implementation of the solution for some basic arithmetic operators are shown and demonstrate the benefits of the proposed approach. The developed modules are also tested within the framework of an image processing application.
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