Media processing applications typically involve numerical blocks that exhibit regular floating-point computation patterns. For processors whose architecture supports only integer arithmetic, these patterns can be profitably turned into custom operators, coming in addition to the five basic ones (+, -, X, / and √), but achieving better performance by treating more operations. This thesis addresses the design of such custom operators as well as the techniques developed in the compiler to select them in application codes. We have designed optimized implementations for a set of custom operators which includes squaring, scaling, adding two nonnegative terms, fused multiply-add, fused square-add (x*x+z, with z>=0), two-dimensional dot products (DP2), sums of two squares, as well as simultaneous addition/subtraction and sine/cosine. With novel algorithms targeting high instruction-level parallelism and detailed here for squaring, scaling, DP2, and sin/cos, we achieve speedups of up to 4.2x for individual custom operators even when subnormal numbers are fully supported. Furthermore, we introduce the optimizations developed in the ST231 C/C++ compiler for selecting such operators. Most of the selections are achieved at high level, using syntactic criteria. However, for fused square-add, we also enhance the framework of integer range analysis to support floating-point variables in order to prove the required positivity condition z>= 0. Finally, we provide quantitative evidence of the benefits to support this selection of custom operations: on DSP kernels and benchmarks, our approach allows us to be up to 1.59x faster compared to the sole usage of basic ones.

Les applications multimédia se composent généralement de blocs numériques exhibant des schémas de calcul flottant réguliers. Sur les processeurs sans support architectural pour l'arithmétique flottante, ils peuvent être profitablement transformés en opérateurs dédiés, s'ajoutant aux 5 opérateurs élémentaires (+, -, X, / et √) : en traitant plus d'opérations simultanément, ils permettent d'obtenir de meilleures performances. Cette thèse porte sur la conception de tels opérateurs, et les techniques de compilation mises en œuvre pour les sélectionner. Nous avons réalisé des implémentations optimisées pour un ensemble d'opérateurs dédiés : élévation au carré, mise à l'échelle, fused multiply-add, produit scalaire en dimension deux (DP2), addition/soustraction simultané et sinus/cosinus simultanés. En proposant de nouveaux algorithmes cherchant à maximiser le parallélisme d'instructions et détaillés ici, nous obtenons des accélérations d'un facteur allant jusqu'à 4.2 par appel. Nous détaillons également les changements apportés dans le compilateur pour effectuer la sélection. La plupart des opérateurs sont sélectionnés au niveau syntaxique. Cependant, pour certains opérateurs, nous avons dû améliorer l'analyse d'intervalles entiers pour prendre en compte les variables de type flottant, afin de prouver certaines conditions de positivité requises à leur sélection. Enfin, nous apportons la preuve en pratique de la pertinence de cette approche : sur des noyaux typiques du traitement du signal et sur certaines applications, nous mesurons une amélioration de performance allant jusqu'à 1.59x en comparaison avec la performance obtenue avec les seuls opérateurs élémentaires. / Media processing applications typically involve numerical blocks that exhibit regular floating-point computation patterns. For processors whose architecture supports only integer arithmetic, these patterns can be profitably turned into custom operators, coming in addition to the five basic ones (+, -, X, / and √), but achieving better performance by treating more operations. This thesis addresses the design of such custom operators as well as the techniques developed in the compiler to select them in application codes. We have designed optimized implementations for a set of custom operators which includes squaring, scaling, adding two nonnegative terms, fused multiply-add, fused square-add (x*x+z, with z>=0), two-dimensional dot products (DP2), sums of two squares, as well as simultaneous addition/subtraction and sine/cosine. With novel algorithms targeting high instruction-level parallelism and detailed here for squaring, scaling, DP2, and sin/cos, we achieve speedups of up to 4.2x for individual custom operators even when subnormal numbers are fully supported. Furthermore, we introduce the optimizations developed in the ST231 C/C++ compiler for selecting such operators. Most of the selections are achieved at high level, using syntactic criteria. However, for fused square-add, we also enhance the framework of integer range analysis to support floating-point variables in order to prove the required positivity condition z>= 0. Finally, we provide quantitative evidence of the benefits to support this selection of custom operations: on DSP kernels and benchmarks, our approach allows us to be up to 1.59x faster compared to the sole usage of basic ones.