Automatic Source-to-Source Error Compensation of Floating-Point Programs

Numerical programs with IEEE 754 floating-point computations may suffer from inaccuracies since finite precision arithmetic is an approximation of real arithmetic. Solutions that reduce the loss of accuracy are available as, for instance, compensated algorithms, more precise computation with double-double or similar libraries. Our objective is to automatically improve the numerical quality of a numerical program with the smallest impact on its performance. We define and implement source code transformation to derive automatically compensated programs. We present several experimental results to compare the transformed programs and existing solutions. The transformed programs are as accurate and efficient as the implementations of compensated algorithms when the latter exist.