Time and energy modeling of a high-performance multi-threaded Cholesky factorization

We present accurate time and energy piece-wise models of high-performance multi-threaded implementations for the general matrix multiplication, triangular system solve with multiple right-hand sides, and symmetric rank-k update. Furthermore, these are then assembled to provide accurate models of the Cholesky factorization built on top of these Level-3 BLAS operations. Our models consider the costs, in terms of time and energy, of the floating-point operations involved in the routines as well as the overhead due to data movements across the levels of the memory hierarchy. The accuracy of the multi-threaded models is tested on an Intel Xeon E5-2620 processor, reporting relative errors for the Cholesky factorization that are, respectively, around 2.4 and 2.9 % on average for time and energy.This work was supported by the CICYT projects TIN2014-53495-R and CICYT-TIN 2012-32180 of the MINECO and FEDER, the EU FET Project FP7 318793 “EXA2GREEN”, and the FPU program of MECD