Controlling Computation Granularity through Fusion in Improving Floating-Point Numbers

Abstract

Improving Floating-Point Numbers (IFN) is a numerical computation library for Haskell. It allows the user to directly specify the accuracy of the result, making accurate computation easy. The library's computation process is based on adaptive control of accuracies, which propagates the demands for more accurate values from an expression to its appropriate subexpressions. However, despite its unique features, programs utilizing the IFN library often encounter efficiency issues regarding memory consumption and execution time due to its fine granularity of computations. This paper presents the computational granularity control mechanism through fusion transformation to resolve these problems and proposes two fusion strategies, the maximal fusion and chain fusion. We have successfully implemented a fusion system that automatically applies these strategies through program transformation. Its effectiveness was confirmed through numerical computation programs.