CADNA_C: A version of CADNA for use with C or C++ programs

Lamotte, Jean Luc; Chesneaux, Jean‐Marie; Jézéquel, Fabienne

doi:10.1016/j.cpc.2010.07.006

Cited by 15 publications

(7 citation statements)

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“…The CADNA 2 software [3,7,12,17] is a library which implements DSA in any code written in C, C++ or Fortran. It has been successfully used for the numerical validation of academic and industrial simulation codes in various domains such as astrophysics [15], atomic physics [24], chemistry, climate science [2,13], fluid dynamics, geophysics [14].…”

Section: The Cadna Softwarementioning

confidence: 99%

Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic

Graillat

Jézéquel

Picot

et al. 2019

Journal of Computational Science

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The type length chosen for floating-point numbers (e.g. 32 bits or 64 bits) may have an impact on the execution time, especially on SIMD (Single Instruction Multiple Data) units. Furthermore optimizing the types used in a numerical simulation causes a reduction of the data volume that is possibly transferred. In this paper we present PROMISE, a tool that makes it possible to optimize the numerical types in a program by taking into account the requested accuracy on the computed results. With PROMISE the numerical quality of results is verified using DSA (Discrete Stochastic Arithmetic) that enables one to estimate roundoff errors. The search for a suitable type configuration is performed with a reasonable complexity thanks to the delta debugging algorithm. The PROMISE tool has been successfully tested on programs implementing several numerical algorithms including linear system solving and also on an industrial code that solves the neutron transport equations.

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Section: The Cadna Softwarementioning

confidence: 99%

Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic

Graillat

Jézéquel

Picot

et al. 2019

Journal of Computational Science

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“…DSA enables to estimate the impact of rounding errors on any result of a scientific code and also to check that no anomaly occurred during the run, especially in branching statements. The CADNA software [10,[28][29][30][31] is a library which implements DSA in any code written in C++ or in Fortran and allows to use new numerical types: the stochastic types. The library contains the definition of all arithmetic operations and order relations for the stochastic types.…”

Section: Discrete Stochastic Arithmeticmentioning

confidence: 99%

Stochastic Arithmetic in Multiprecision

et al. 2011

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Floating-point arithmetic precision is limited in length the IEEE single (respectively double) precision format is 32-bit (respectively 64-bit) long. Extended precision formats can be up to 128-bit long. However some problems require a longer floating-point format, because of round-off errors. Such problems are usually solved in arbitrary precision, but round-off errors still occur and must be controlled. Interval arithmetic has been implemented in arbitrary precision, for instance in the MPFI library. Interval arithmetic provides guaranteed results, but it is not well suited for the validation of huge applications. The CADNA library estimates round-off error propagation using stochastic arithmetic. CADNA has enabled the numerical validation of real-life applications, but it can be used in single precision or in double precision only. In this paper, we present a library called SAM (Stochastic Arithmetic in Multiprecision). It is a multiprecision extension of the classic CADNA library. In SAM (as in CADNA), the arithmetic and relational operators are overloaded in order to be able to deal with stochastic numbers. As a consequence, the use of SAM in a scientific code needs only few modifications. This new library SAM makes it possible to dynamically control the numerical methods used and more particularly to determine the optimal number of iterations in an iterative process. We present some applications of SAM in the numerical validation of chaotic systems modeled by the logistic map.

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“…This principle was introduced in [38] and it was extended to various quadrature rules in [42][43][44] and others [45,46]. The CADNA library should be done on the LINUX operating system and its codes should be written using C, C++ or ADA codes [40,[47][48][49]. The CESTAC method is based on the DSA and instead of applying the absolute error to show the precision of method, a termination criterion is applied based on two successive approximations [50][51][52][53].…”

Section: Introductionmentioning

confidence: 99%

Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

Noeiaghdam

Dreglea

et al. 2020

Symmetry

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This paper studies the second kind linear Volterra integral equations (IEs) with a discontinuous kernel obtained from the load leveling and energy system problems. For solving this problem, we propose the homotopy perturbation method (HPM). We then discuss the convergence theorem and the error analysis of the formulation to validate the accuracy of the obtained solutions. In this study, the Controle et Estimation Stochastique des Arrondis de Calculs method (CESTAC) and the Control of Accuracy and Debugging for Numerical Applications (CADNA) library are used to control the rounding error estimation. We also take advantage of the discrete stochastic arithmetic (DSA) to find the optimal iteration, optimal error and optimal approximation of the HPM. The comparative graphs between exact and approximate solutions show the accuracy and efficiency of the method.

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CADNA_C: A version of CADNA for use with C or C++ programs

Cited by 15 publications

References 0 publications

Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic

Auto-tuning for floating-point precision with Discrete Stochastic Arithmetic

Stochastic Arithmetic in Multiprecision

Error Estimation of the Homotopy Perturbation Method to Solve Second Kind Volterra Integral Equations with Piecewise Smooth Kernels: Application of the CADNA Library

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