Automatic source-to-source error compensation of floating-point programs: code synthesis to optimize accuracy and time

摘要

Numerical programs with IEEE 754 floating-point computations may suffer from inaccuracies because finiternprecision arithmetic is an approximation of real arithmetic. Solutions that reduce the loss of accuracy arernavailable, such as compensated algorithms or double-double precision floating-point arithmetic. Our goalrnis to automatically improve the numerical quality of a numerical program with the smallest impact onrnits performance. We define and implement source code transformations in order to derive automaticallyrncompensated programs. We present several experimental results to compare the transformed programs andrnexisting solutions. The transformed programs are as accurate and efficient as the implementations of compensatedrnalgorithms when the latter exist. Furthermore, we propose some transformation strategies allowingrnus to partially improve the accuracy of programs and to tune the impact on execution time. Trade-offsrnbetween accuracy and performance are assured by code synthesis. Experimental results show that userdefinedrntrade-offs are achievable in a reasonable amount of time, with the help of the tools we present in thernpaper.