Fast rounding error estimation for compute-intensive operations using standard floating-point arithmetic
Fabienne Jezequel  1, 2@  , Stef Graillat  3  , Daichi Mukunoki  4  , Toshiyuki Imamura  5  , Roman Iakymchuk  1, 6  
1 : LIP6
Sorbonne Université, Centre National de la Recherche Scientifique : UMR7606
2 : Université Panthéon-Assas
université Paris 2, Panthéon-Assas
3 : Université Pierre et Marie Curie - LIP6  (UPMC - LIP6)  -  Site web
Université Pierre et Marie Curie [UPMC] - Paris VI
4 place Jussieu 75252 Paris -  France
4 : RIKEN Center for Computational Science [Kobe]
5 : RIKEN Advanced Institute for Computational Science  (RIKEN AICS)  -  Site web
7-1-26 Minatojima-minimi-machi, Chuo-ku, Kobe, Hyogo 650-0047 -  Japon
6 : Fraunhofer Institute of Industrial Mathematics

Numerical validation enables one to ensure the reliability of
numerical computations that rely on floating-point operations. Discrete
Stochastic Arithmetic (DSA) makes it possible to validate the accuracy
of floating-point computations using random rounding. However, it may
bring a large performance overhead compared with the standard floating-
point operations. In this talk, we show that with perturbed data it is
possible to use standard floating-point arithmetic instead of DSA for the
purpose of numerical validation. For instance, for codes including matrix
multiplications, we can directly utilize the matrix multiplication routine
(GEMM) of level-3 BLAS that is performed with standard floating-point
arithmetic. Consequently, we can achieve a significant performance im-
provement by avoiding the performance overhead of DSA operations as
well as by exploiting the speed of highly-optimized BLAS implementa-
tions. Finally, we demonstrate the performance gain using Intel MKL
routines compared against the DSA version of BLAS routines.

 



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