A Fast Implementation of Matrix-matrix Product in Double-double Precision on NVIDIA C2050 and Application to Semidefinite Programming

Abstract

We have implemented a fast double-double precision (has approx. 32 decimal significant digits) version of matrix-matrix multiplication routine called "Rgemm" of MPACK (http://mplapack.sourceforge.net/) on NVIDIA C2050 GPU. This routine is a higher precision version of gdgemmh in the BLAS (Basic Linear Algebra Subprograms) library. Our implementation is the fastest to date using NVIDIA C2050 and most efficient on NVIDIA GPUs, we achieved the peak performances of 16.4GFlops for the kernel performance (16.1GFlops with CPU-GPU transfer included), and 26.4GFlops (25.7GFlops with CPU-GPU transfer included) by employing lower accuracy arithmetic. These are 92.3% (90.7%) and 87.1% (84.8%) of the theoretical peak performance of NVIDIA C2050, which is about 150 times faster than the reference implementation on Intel Xeon X3470. Moreover, our implementations can handle arbitrary sizes of matrices by employing gPointer redirectingh technique by Nath et al. We integrated this GPU-accelerated version of Rgemm for double-double precision version of semi definite programming solver called SDPA-DD, and the performance improved at most 14.5 times. This version of Rgemm is available at http://mplapack.sourceforge.net/ since 2011/10/28.