  To improve the efficiency of Gaussian integral evaluation on modern
accelerated architectures FLOP-efficient Obara-Saika-based recursive evaluation
schemes are optimized for the memory footprint. For the 3-center 2-particle
integrals that are key for the evaluation of Coulomb and other 2-particle
interactions in the density-fitting approximation the use of multi-quantal
recurrences (in which multiple quanta are created or transferred at once) is
shown to produce significant memory savings. Other innovation include
leveraging register memory for reduced memory footprint and direct compile-time
generation of optimized kernels (instead of custom code generation) with
compile-time features of modern C++/CUDA. Performance of conventional and
CUDA-based implementations of the proposed schemes is illustrated for both the
individual batches of integrals involving up to Gaussians with low and high
angular momenta (up to $L=6$) and contraction degrees, as well as for the
density-fitting-based evaluation of the Coulomb potential. The computer
implementation is available in the open-source LibintX library.
