First-principles simulations of high-Z metallic systems using the Qbox code on the BlueGene/L supercomputer demonstrate unprecedented performance and scaling for a quantum simulation code. Specifically designed to take advantage of massively-parallel systems like BlueGene/L, Qbox demonstrates excellent parallel efficiency and peak performance. A sustained peak performance of 207.3 TFlop/s was measured on 65,536 nodes, corresponding to 56.5% of the theoretical full machine peak using all 128k CPUs.

We demonstrate that the Qbox code supports unprecedented large-scale First-Principles Molecular Dynamics (FPMD) applications on the BlueGene/L supercomputer. Qbox is an FPMD implementation specifically designed for large-scale parallel platforms such as BlueGene/L. Strong scaling tests for a Materials Science application show an 86% scaling efficiency between 1024 and 32,768 CPUs. Measurements of performance by means of hardware counters show that 36% of the peak FPU performance can be attained.

This paper targets automatic performance tuning of numerical kernels in the presence of multilayered memory hierarchies and single-instruction, multiple-data (SIMD) parallelism. The studied SIMD instruction set extensions include Intel's SSE family, AMD's 3DNow!, Motorola's AltiVec, and IBM's BlueGene/L SIMD instructions. FFTW, ATLAS, and SPIRAL demonstrate that near-optimal performance of numerical kernels across a variety of modern computers featuring deep memory hierarchies can be achieved only by means of automatic performance tuning. These software packages generate and optimize ANSI C code and feed it into the target machine's general-purpose C compiler to maintain portability. The scalar C code produced by performance tuning systems poses a severe challenge for vectorizing compilers. The particular code structure hampers automatic vectorization and, thus, inhibits satisfactory performance on processors featuring short vector extensions. This paper describes special-purpose compiler technology that supports automatic performance tuning on machines with vector instructions. The work described includes: 1) symbolic vectorization of digital signal processing transforms; 2) straight-line code vectorization for numerical kernels; and 3) compiler back ends for straight-line code with vector instructions. Methods from all three areas were combined with FFTW, SPIRAL, and ATLAS to optimize both for memory hierarchy and vector instructions. Experiments show that the presented methods lead to substantial speedups (up to 1.8 for two-way and 3.3 for four-way vector extensions) over the best scalar C codes generated by the original systems as well as roughly matching the performance of hand-tuned vendor libraries.

This paper introduces an SIMD vectorization for FFTW-the "fastest Fourier transform in the west" proposed by Frigo and Johnson (see Proceedings of the ACM SIGPLAN '99 , p.169-180, 1999). The new method leads to an architecture independent short vector SIMD FFT vectorization that utilizes the architecture adaptivity of FFTW. It is based on special FFT kernels (up to size 64 and more) that are utilized by FFTW to compute the whole transform. This vectorization supports all features of complex transforms in FFTW (arbitrary size, dimension and stride of the data vector; in-place and out-of-place transforms) and is fully transparent to the user. It is suitable for arbitrary vector sizes of the underlying hardware.