Dynamic Precision for Electron Repulsion Integral Evaluation on Graphical Processing Units (GPUs)

It has recently been demonstrated that novel streaming architectures found in consumer video gaming hardware such as graphical processing units (GPUs) are well-suited to a broad range of computations including electronic structure theory (quantum chemistry). Although recent GPUs have developed robust support for double precision arithmetic, they continue to provide 2-8 x more hardware units for single precision. In order to maximize performance on GPU architectures, we present a technique of dynamically selecting double or single precision evaluation for electron repulsion integrals (ERIs) in Hartree-Fock and density functional self-consistent field (SCF) calculations. We show that precision error can be effectively controlled by evaluating only the largest integrals in double precision. By dynamically scaling the precision cutoff over the course of the SCF procedure, we arrive at a scheme that minimizes the number of double precision integral evaluations for any desired accuracy. This dynamic precision scheme is shown to be effective for an array of molecules ranging in size from 20 to nearly 2000 atoms.