Arénaire project, scientific objectives and documents

Our general goal is to improve arithmetic operators. Among various hardware and software constraints, we focus on reliability, accuracy, speed and energy efficiency of the arithmetic computations. The project is working in four main directions.

Number systems: integers, fixed point, floating point, (semi-)logarithmic, modular representation, finite field

Basic operations: addition, multiplication, operations involving constants, FIR filters, DSP operators

Algebraic functions (division, square root, power) and elementary functions (sine, cosine, exponential...)

Dedicated arithmetic operators for cryptography, digital signal processing and image processing

Fixed and floating-point arithmetic, correct rounding, fused-mac, range reduction, multiprecision

Algebraic, elementary and special functions

Standardization

Function approximation, analysis of algorithms

Correct rounding, interval arithmetic, formal proof

Specification of the arithmetic, program and algorithm analysis

Error bounds, Taylor model, bounding of results

Approximate / interval / exact computation

Specific arithmetic library development and test : multiprecision intervals, finite fields, integers and rational numbers

Numerical analysis for intervals, automatic precision choice

Computer algebra, binary versus algebraic complexity of algorithms, exact linear algebra, polynomial matrices