In 2012, Arénaire merges into AriC, **Ari**thmetic and **C**omputing

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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
- Standardization
- 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]
## Slides |
## Posters |