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This paper considers the construction of canonical representations of datapath circuits by arithmetic transform (AT) and its extensions to express word-level representations of combinational and sequential blocks for hardware verification and component matching. Construction of an overall circuit by composition helps engineers to process a block-level netlist representing a complex circuit and to...
For imprecise circuits, error is unavoidable, so implementations only realize specifications to some extent. Investigation of their difference is necessary. To overcome disadvantages of simulation, intermediate Arithmetic Transform polynomials are used as an analytical apparatus suitable to precision analysis for both the quantization (bit-width) and approximation sources, and a simple algorithm is...
We consider synthesis of arithmetic DSP circuits with finite precision fixed-point operations. The aim is to choose the lowest cost implementation that matches a real-valued specification within the allowed imprecision. Starting from Taylor series or real-valued polynomials, we demonstrate first a method to obtain satisfying implementations that uses intermediate arithmetic transform polynomials as...
This paper addresses the use of Arithmetic Transforms (AT) and its extensions to express word-level quantities and sequential elements. Their applications cover equivalence checking and component matching. Compositional construction of an overall circuit becomes critical. In order to facilitate the compositions, novel algorithms are proposed to get high performance and experiments prove their efficiency.
We develop a new method to compute representations of imprecise datapaths for purpose of equivalence checking and component matching. From a Taylor series, we devise an efficient algorithm to produce arithmetic transform (AT) which is a function representation behind word-level decision diagrams such as BMDs. Also, we introduce an efficient algorithm for verifying the imprecise circuits.
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