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