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

Abstract

International audienceNumerical 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 performances. 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 than the implementations of compensated algorithms when the latter exist

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

“…Measurements also confirm the interest of compensated algorithms, exhibiting a better ILP potential than DD algorithms. Finally, we note that the ILP potential is not fully exploited in our experimental environment .…”

“…In this section, we briefly introduce the EFT previously discussed in (we refer to the latter for a more detailed description). EFTs provide lossless transformations of basic floating‐point operations ∘∈{ + , − , × }.…”

“…We will now focus on two methods using these EFTs to double the accuracy: double‐double expansions and compensations. We will then recall why compensated algorithms run faster than double‐double algorithms (we refer to for a complete discussion on these two approaches). Double‐double expansions.…”

“…In this section, we briefly introduce the EFT previously discussed in [11] (we refer to the latter for a more detailed description [26]), and TWOPRODUCT [1] algorithms, which exactly compute in floating-point arithmetic the error term of the sum and the product. Figure 2 defines diagrams for floating-point operations˙and , and for their EFTs.…”

“…Here, PAPI measures the actual mean of 10 6 executions. PERPI ideal measures are presented in [11]. Figure 9(a) shows the cycle and instruction ratios.…”