The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. With CADNA the numerical quality of any simulation program can be controlled. Furthermore by detecting all the instabilities which may occur at run time, a numerical debugging of the user code can be performed. CADNA provides new numerical types on which round-off errors can be estimated. Sligh...

The CADNA library enables one to estimate round-off error propagation using a probabilistic approach. The CADNA C version enables this estimation in C or C++ programs, while the previous version had been developed for Fortran programs. The CADNA C version has the same features as the previous one: with CADNA the numerical quality of any simulation program can be controlled. Furthermore by detec...

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 ...

An important task in solving second order linear ordinary differential equations by the finite difference is to choose a suitable stepsize h. In this paper, by using the stochastic arithmetic, the CESTAC method and the CADNA library we present a procedure to estimate the optimal stepsize hopt, the stepsize which minimizes the global error consisting of truncation and round-off error. Keywords—o...

Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic. We propose that there is a need to perform regular numerical ‘health checks’ on scientific codes in order to detect the cancerous effect of round-off er...

In this paper, we apply the Newton’s and He’s iteration formulas in order to solve the nonlinear algebraic equations. In this case, we use the stochastic arithmetic and the CESTAC method to validate the results. We show that the He’s iteration formula is more reliable than the Newton’s iteration formula by using the CADNA library.

Numerical validation of computed results in scienti c computation is always an essential problem as well on sequential architecture as on parallel architecture. The probabilistic approach is the only one that allows to estimate the round-o error propagation of the oating point arithmetic on computers. We begin by recalling the basics of the CESTAC method (Contrôle et Estimation STochastique des...

The aim of this paper is to apply the Taylor expansion method solve first and second kinds Volterra integral equations with Abel kernel. This study focuses on two main arithmetics: FPA DSA. In order DSA, we use CESTAC CADNA library. Using method, can find optimal step approximation, error, some numerical instabilities. They are novelties DSA in comparison FPA. error analysis proved. Furthermore...

The polynomial spline collocation method is proposed for solution of Volterra integral equations the first kind with special piecewise continuous kernels. Gausstype quadrature formula used to approximate integrals during discretization projection method. estimate accuracy obtained. Stochastic arithmetics also based on Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) and Cont...

Finite precision computations may affect the stability of algorithms and the accuracy of computed solutions. In this paper we first obtain a relation for computing the number of common significant digits between the exact solution and a computed solution of a one-dimensional initial-value problem obtained by using a single-step or multi-step method. In fact, by using the approximate solutions o...