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