Robert F. Enenkel

Custom math functions for molecular dynamics

While developing the protein folding application for the IBM Blue Gene®/L supercomputer, some frequently executed computational kernels were encountered. These were significantly more complex than the linear algebra kernels that are normally provided as tuned libraries with modern machines. Using regular library functions for these would have resulted in an application that exploited only 5-10% of the potential floating-point throughput of the machine. This paper is a tour of the functions encountered; they have been expressed in C++ (and could be expressed in other languages such as Fortran or C). With the help of a good optimizing compiler, floating-point efficiency is much closer to 100%. The protein folding application was initially run by the life science researchers on IBM POWER3™ machines while the computer science researchers were designing and bringing up the Blue Gene/L hardware. Some of the work discussed resulted in enhanced compiler optimizations, which now improve the performance of floating-point-intensive applications compiled by the IBM VisualAge® series of compilers for POWER3, POWER4™, POWER4+™, and POWER5™. The implementations are offered in the hope that they may help in other implementations of molecular dynamics or in other fields of endeavor, and in the hope that others may adapt the ideas presented here to deliver additional mathematical functions at high throughput.

High-performance computing with sparsity and structure: challenges and directions for single-core and multicore hardware

Computations involving sparse and structured matrices arise frequently in problems in operations research, science and engineering. Exploiting this structure has been a major contributor to the efficient application of past and current computing platforms, and will continue to play an important role for next-generation systems.