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Arénaire project, scientific objectives and documents

In 2012, Arénaire merges into AriC, Arithmetic and Computing

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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.

Hardware arithmetic operators - digital integrated circuit, ASIC, FPGA, VHDL, low-power consumption, reconfigurable operator, asynchronous circuit
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
Software arithmetic operators - C,specific processors, libm, DSP, VLIW
Fixed and floating-point arithmetic, correct rounding, fused-mac, range reduction, multiprecision
Algebraic, elementary and special functions
Function approximation, analysis of algorithms
Models and properties of computation, validation and proof - C++, Coq, PVS
Correct rounding, interval arithmetic, formal proof
Specification of the arithmetic, program and algorithm analysis
Error bounds, Taylor model, bounding of results
Use and applications of arithmetic operators - C, C++, Maple
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

Activity reports

INRIA activity report 2011 [html] [pdf]
INRIA activity report 2010 [html] [pdf]
INRIA activity report 2009 [html] [pdf]
INRIA activity report 2008 [html] [pdf]
INRIA activity report 2007 [html] [pdf]
INRIA activity report 2006 [html] [pdf]
INRIA activity report 2005 [html] [pdf]
INRIA activity report 2004 [html] [pdf]
INRIA activity report 2003 [html] [pdf]
LIP activity report 2002/2003 (in french) [ps]


Project presentation (in fr., CP INRIA, 30/01/04) [pdf]
Project presentation (in fr., évaluation du LIP, 10/01/06) [pdf]
Project presentation (in fr., J. Vuillemin visit, 7/03/06) [pdf]


Presentation of the team (in french) (30/12/05)
Hardware function evaluation (30/12/05)
Management of numerical errors (30/12/05)