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Surface intersection using affine arithmetic
1996We describe a variant of a domain decomposition method proposed by Gleicher and Kass for intersecting and trimming parametric surfaces. Instead of using interval arithmetic to guide the decomposition, the variant described here uses affine arithmetic, a tool recently proposed for range analysis.
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Phase stability analysis using a modified affine arithmetic
Computers & Chemical Engineering, 2013Abstract Phase stability analysis is a crucial step in the determination of multiphase equilibrium. This analysis by the tangent plane distance (TPD) minimization is a well-known technique, as well as the difficulties in providing guarantees that the global minimum has been found. On this regard, interval methods are powerful tools since they provide
P. B. Staudt +2 more
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Finite-precision error modeling using affine arithmetic
2013 IEEE International Conference on Acoustics, Speech and Signal Processing, 2013This paper introduces a new approach for finite-precision error modeling based on affine arithmetic. The paper demonstrates that there is a common hazard in affine arithmetic-based error modeling methods described in the literature. The hazard is linked to early substitution of the signal terms that emerge in operations such as multiplication and ...
Shervin Vakili +2 more
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Floating-point error analysis based on affine arithmetic
2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)., 2003During the development of floating-point signal processing systems, an efficient error analysis method is needed to guarantee the output quality. We present a novel approach to floating-point error bound analysis based on affine arithmetic. The proposed method not only provides a tighter bound than the conventional approach, but also is applicable to ...
Claire Fang Fang +2 more
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Approximating parametric curves with strip trees using affine arithmetic
Proceedings. XV Brazilian Symposium on Computer Graphics and Image Processing, 2003Abstract We show how to use affine arithmetic to represent a parametric curve with a strip tree. The required bounding rectangles for pieces of the curve are computed by exploiting the linear correlation information given by affine arithmetic. As an application, we show how to compute approximate distance fields for parametric curves.
Luiz Henrique de Figueiredo +2 more
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Circuit simulations with uncertainties using affine arithmetic and piecewise affine statemodels
2008 9th International Conference on Solid-State and Integrated-Circuit Technology, 2008Especially in the field of safety critical applications the impact of process variations on the behavior of integrated circuits can not be neglected. Usually, simulation is costly due to the need for multiple simulation runs with different technology parameter settings.
M. Freisfeld, M. Olbrich, E. Barke
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Proceedings of the 42nd annual conference on Design automation - DAC '05, 2005
MiniBit, our automated approach for optimizing bit-widths of fixed-point designs is based on static analysis via affine arithmetic. We describe methods to minimize both the integer and fraction parts of fixed-point signals with the aim of minimizing circuit area. Our range analysis technique identifies the number of integer bits required. For precision
Dong-U Lee +3 more
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MiniBit, our automated approach for optimizing bit-widths of fixed-point designs is based on static analysis via affine arithmetic. We describe methods to minimize both the integer and fraction parts of fixed-point signals with the aim of minimizing circuit area. Our range analysis technique identifies the number of integer bits required. For precision
Dong-U Lee +3 more
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Functional and Affine Completeness and Arithmetical Varieties
1993Our understanding of affine complete and functionally complete algebras and varieties of affine complete algebras is closely related to our understanding of arithmetical algebras and varieties. Because of this we first survey basic results about arithmetical algebras and varieties, emphasizing finite algebras and finitely generated varieties.
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Reachability Analysis of Procedural Programs with Affine Integer Arithmetic
2006We present a tool for reachability analysis of procedural programs whose statements consist of affine equations and inequations. We use finite automata for representing the possibly infinite sets of stack configurations and memory valuations.
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