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Interval-based analysis and word-length optimization of non-linear systems with control-flow structures
Last modified: 2016-09-05
Abstract
The techniques based on extensions of interval computations allow fast and accurate analysis of the behavior of complex systems. Some of the most recent works in this area have presented procedures to evaluate systems with smooth non-linearities. We take this approach a step further by introducing a methodology that combines Multi-Element Generalized Polynomial Chaos (ME-gPC) and Statistical Modified Affine Arithmetic (MAA). This methodology allows modeling systems with highly non-linear operators and/or control-flow structures. It has been implemented in our modular and automated analysis framework, HOPLITE, so that it can be used to estimate the dynamic range, quantization noise and sensitivity of systems containing the aforementioned control-flow blocks. With this approach we have obtained in case studies with non-linear operators a deviation of only 0.04% with respect to the simulation-based reference values, which proves the accuracy of our approach.
Keywords
Interval Computation, Polynomial Chaos, Affine Arithmetic, Digital Signal Processing, Fixed-Point, Quantization, FPGA Implementation
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