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