Using loop transformations for precision tuning in iterative programs

Many floating-point formats are available, providing all different levels of precision. By mixing several of these formats in the same program, it is possible to achieve good performance while maintaining an acceptable level of output accuracy. Therefore various tools have been designed to adapt the precision of computations in floating-point programs for performance and accuracy purposes. However most of them do not consider the iterative nature of these programs. This article presents a tool that enables to adapt the precision of floating-point computations in iterative routines, at the iteration level. This tool is based on multiple-precision computations to evaluate the impact of some format adaptations on the output accuracy, and it uses the delta-debugging to isolate the most relevant instruction set to be tuned. The originality of our approach is that it relies on static loop transformations to duplicate loop body instructions, and thus to increase the number of possible instructions that can be targeted. These transformations include especially the loop splitting and unrolling, which enable to allocate different precisions for different iterations, and thus to improve the tuning process. We show the advantages of this approach on a representative set of iterative programs.