An abstract interpretation framework for the round-off error analysis of floating-point programs

MA Feliú, M Moscato, CA Muñoz - International Conference on …, 2018 - Springer
… methods such as interval arithmetic, affine arithmetic, Bernstein and Taylor models, etc. … in
PRECiSA other abstract domains such as affine arithmetic and a compositional version of the …

Challenges in verifying and optimizing fixed-point arithmetic-intensive designs

Y Pang, O Sarbishei, K Radecka… - 2010 IEEE International …, 2010 - ieeexplore.ieee.org
… The affine arithmetic model (AA) is a derivation of IA, in which the quantities of interest are
represented as linear combinations (affine forms) of certain primitive variables standing for …

Research and design of AES security processor model based on FPGA

P Wang, Y Zhang, J Yang - Procedia computer science, 2018 - Elsevier
… This design using finite field multiplication inverse and affine arithmetic is constructed as
follows the S box module diagram, as shown in Fig. 2, the box also applies to inverse S box S …

Feature-based displacement mapping

XC Wang, J Maillot, E Fiume, V Ng-Thow-Hing… - … Workshop on Rendering …, 2000 - Springer
… Heidrich and Seidel, for example, employ affine arithmetic to ray trace procedural displacement
maps without adding geometry [8]. Pharr and Hanrahan use memory coherence and …

Numerical Analysis of Nonlinear Parameter-Dependent Systems with Continuation Methods

MG Spetzler - 2017 - digital.lib.washington.edu
… The method is based on a reliable computing technique called affine arithmetic, which is
also discussed in the chapter. Some concluding remarks are provided in Chapter 7. …

A risk management procedure for island partitioning of automated radial distribution networks with distributed generators

ZN Popovic, SD Knezevic… - IEEE Transactions on …, 2020 - ieeexplore.ieee.org
… By applying the affine arithmetic [38], the result is z = [5.5, 13] whereas the interval RDM …
in the results obtained by the classical interval arithmetic and affine arithmetic operations. …

Self‐consumption and storage as a way to facilitate the integration of renewable energy in low voltage distribution networks

FM Camilo, R Castro, ME Almeida… - IET Generation …, 2016 - Wiley Online Library
… [37] proposes a complex affine arithmetic-based unbalanced three-phase forward-backward
sweep (FBS) power flow method to deal with the uncertainties of wind and solar DGAQ. The …

Optimization Operation of Multi-energy Complementary System based on Interval Model

L Yuan - 2019 IEEE Innovative Smart Grid Technologies-Asia …, 2019 - ieeexplore.ieee.org
Affine arithmetic can make the uncertain variables (described as affine number) and the
rest of the affine number in the operation process, keep the first order of the relationship …

[HTML][HTML] Constrained global optimization for wine blending

P Vismara, R Coletta, G Trombettoni - Constraints, 2016 - Springer
… Like HC4, Affine arithmetic [13, 19] works with the expression tree of each function. … way,
for each mathematical operator, affine arithmetic combines the affine forms of the children/…

[HTML][HTML] A subinterval decomposition analysis method for uncertain structures with large uncertainty parameters

CM Fu, LX Cao, JC Tang, XY Long - Computers & Structures, 2018 - Elsevier
A simple and efficient subinterval decomposition analysis method is proposed to evaluate
the lower and upper bounds of structural responses with large uncertain parameters. The …