SHF: Small:Transforming Linear Algebra Libraries

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Ever since the first FORmula TRANslator, compilers have purported totake an algorithm, formulated in human terms, and compile it to anefficient executable. Practice clearly does not live up to thisideal, as programming languages force execution-oriented designdecisions on the programmer, and compiler imperfections necessitatefurther manual optimizations. While the ordinary programmer canignore this problem by using libraries, the library developer cannot.The problem appears more desperate now than ever, since it is notknown what form future architectures will take, combined with a trendtowards pushing complexity away from the architecture (for example tolower power consumption) and onto the program and compiler.The FLAME project already allows linear algebra libraries to bedeveloped and coded at a high level of abstraction that bettercaptures the underlying algorithms. It has already been shown thatthese technique greatly simplify the porting of libraries to differentplatforms ranging from conventional sequential computers to exoticmultiGPU accelerators. However, the APIs for coding at a high levelof abstraction incur a considerable performance penalty for operationsthat in each step perform relatively little computation (e.g., level-2BLAS operations and ``unblocked'' algorithms). As a result, anontrivial part of libflame, the library that has resulted from theproject, still requires coding at a low level.The project will develop a source-to-source translator will takealgorithms expressed at a high level of abstraction and will transformthese into a range of representations, including high-performancelow-level code. This will overcome the final legitimate objection tothe FLAME methodology since coding at a high level of abstraction willno longer carry a performance penalty. The approach will begeneralized so that code transformations that an expert applies byhand in order to target different platforms will be made mechanical.Together, these represent a major departure from traditionalapproaches to library development.