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The DALI team is developing a unified research theme to improve the numerical quality and high performance of calculations. DALI allows the interaction, rare in France within the same team, of experts in micro-architecture and computer arithmetic. On the performance side, our work focuses on exploiting the ever-increasing computational potential of processors: path widening (vector micro-architecture), multiplication of cores (task parallelism), increased instruction parallelism. On the arithmetic side, the numerical quality of scientific computing applications and the operating safety of embedded applications depend crucially on the mastery of finite precision and floating-point arithmetic in particular. It is a question of controlling and certifying calculations (algorithms, codes) but also of optimising the precision of results. Many software applications, both scientific and embedded, need to improve numerical quality without sacrificing speed of execution. Thus, performance improvement and numerical quality come together.

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Logistic map Matrix multiplication Performance evaluation Fixed-point arithmetic Hydrodynamics simulation Arithmétique des corps finis Fuzzy intervals Chaotic map Parallel implementation Differential power analysis Block recombination Abstract interpretation Automated code synthesis Multi-criteria optimization Cryptography Multiplication Floating-point arithmetic Certified numerical accuracy Cosmic radiation Binary floating-point arithmetic Finite field Pseudo-random Polynomial evaluation BLAS Multi-precision FPGA Side channel analysis RSA Arithmétique flottante Compensated algorithms RNS Reproductibilité ECC Error-free transformations Determinism Computer architecture OpenTelemac Midpoint-radius Randomization Accurate summation C software implementation Domain decomposition GPGPU Précision Compensation Performance Code Synthesis Reproducibility Digital Signature GPU Floating-Point Numbers Instruction level parallelism Cryptographie IEEE 754 Binary field Program Transformation VLIW integer processor Parallelism Architecture des ordinateurs Finite element Memory Storage Automated design Graphic Processing Units Numerical Reproducibility Arithmétique des ordinateurs Correct rounding PRBG HPC PerPI Parallel floating-point summation Floating-Point Arithmetic Parallélisme d'instruction Multiplication scalaire Abstract Interpretation Computer arithmetic Efficient Software Implementation Accuracy Modular Exponentiation Kulisch long accumulator Asynchronous iterations Numerical accuracy Binary polynomial multiplication Modular exponentiation Code synthesis Elliptic curve Parallel algorithms Optimized recursive reconstruction Long accumulator Multi- and many-core architectures Elementary functions Horner scheme AMNS Toeplitz matrix Code generation Numerical reproducibility Execution-time performance Karatsuba Error-free transformation Scalar multiplication IEEE754 Standard