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Complexity issues in counting, polynomial evaluation and zero finding
In the present thesis, we try to compare the classical boolean complexity with the algebraic complexity, by studying problems related to polynomials. We consider the... -
Proposal for a Standardization of Mathematical Function Implementation in Flo...
Some aspects of what a standard for the implementation of the mathematical functions could be are presented. Firstly, the need for such a standard is motivated. Then... -
A non-local method for robustness analysis of floating point programs
International audience -
Finite Precision Elementary Geometric Constructions
In this paper we propose a new approach for the robust computation of the nearest integer lattice points of some specific geometric constructions (intersection of two... -
An Automatic Correcting Method
Correcting methods intend to improve the accuracy of results computed in finite precision. The CENA method processes an automatic correction of the first-order effect... -
Additive Symmetric: the Non-Negative Case
International audience -
A Revised Presentation of the CENA Method
The CENA method is a new automatic method to correct the first-order effect of floating point rounding errors on the result of a numerical algorithm. A first... -
From Rounding Error Estimation to Automatic Correction with Automatic Differe...
Using automatic differentiation (AD) to estimate the propagation of rounding errors in numerical algorithms is classic. We propose a new application of AD to roundoff... -
Automatic Linear Correction of Rounding Errors
A new automatic method to correct the first-order effect of floating point rounding errors on the result of a numerical algorithm is presented. A correcting term and a... -
Less Hazardous and More Scientific Research for Summation Algorithm Computing...
Manuscrit soumis à Science of Computer Programming -
Contributions to the Formal Verification of Arithmetic Algorithms
The Floating-Point (FP) implementation of a real-valued function is performed with correct rounding if the output is always equal to the rounding of the exact value,... -
Simultaneous floating-point sine and cosine for VLIW integer processors
Accepted for publication in the proceedings of the 23rd IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP 2012). -
Rigorous Polynomial Approximations and Applications
For purposes of evaluation and manipulation, mathematical functions f are commonly replaced by approximation polynomials p. Examples include floating-point... -
Efficient algorithms for verified scientific computing : Numerical linear alg...
Interval arithmetic is a means to compute verified results. However, a naive use of interval arithmetic does not provide accurate enclosures of the exact results.... -
Non-generic floating-point software support for embedded media processing
International audience -
A New Abstract Domain for the Representation of Mathematically Equivalent Exp...
International audience -
MPFR: A Multiple-Precision Binary Floating-Point Library With Correct Rounding
This paper presents a multiple-precision binary floating-point library, written in the ISO C language, and based on the GNU MP library. Its particularity is to extend... -
The Euclidean Division Implemented with a Floating-Point Division and a Floor
We study conditions under which the Euclidean division can be implemented using a floating-point division followed by a floor function. We show that under reasonable... -
Tradeoffs between Accuracy and Efficiency for Optimized and Parallel Interval...
International audience -
A floating-point library for integer processors
This paper presents a C library for the software support of single precision floating-point (FP) arithmetic on processors without FP hardware units such as VLIW or DSP...
