Asserting the Precision of Floating-Point Computations: a Simple Abstract Interpreter1

Asserting the Precision of Floating-Point Computations: A Simple Abstract Interpreter

Floating-Point Format Inference in Mixed-Precision

In this article, we address the problem of determining the minimal precision on the inputs and on the intermediary results of a program containing floating-point computations in order to ensure a desired accuracy on the outputs. The first originality of our approach is to combine a forward and a backward static analysis, done by abstract interpretation. The backward analysis computes the minima...

Refining Abstract Interpretation-based Approximations with Constraint Solvers

Programs with floating-point computations are tricky to develop because floating-point arithmetic differs from real arithmetic and has many counterintuitive properties. A classical approach to verify such programs consists in estimating the precision of floating-point computations with respect to the same sequence of operations in an idealized semantics of real numbers. Tools like Fluctuat—base...

FPGA Based Quadruple Precision Floating Point Arithmetic for Scientific Computations

In this project we explore the capability and flexibility of FPGA solutions in a sense to accelerate scientific computing applications which require very high precision arithmetic, based on IEEE 754 standard 128-bit floating-point number representations. Field Programmable Gate Arrays (FPGA) is increasingly being used to design high end computationally intense microprocessors capable of handlin...

Utilisation de solveurs de contraintes pour réduire les approximations produites par interprétation abstraite

Programs with floating-point computations are tricky to develop because floating-point arithmetic differs from real arithmetic and has many counterintuitive properties. A classical approach to verify such programs consists in estimating the precision of floatingpoint computations with respect to the same sequence of operations in an idealized semantics of real numbers. Tools like Fluctuat—based...