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