Gravitational octree code performance evaluation on Volta GPU

In this study, the gravitational octree code originally optimized for the Fermi, Kepler, and Maxwell GPU architectures is adapted to the Volta architecture. The Volta architecture introduces independent thread scheduling requiring either the insertion of the explicit synchronizations at appropriate locations or the enforcement of the same implicit synchronizations as do the Pascal or earlier architectures by specifying \texttt{-gencode arch=compute\_60,code=sm\_70}. The performance measurements on Tesla V100, the current flagship GPU by NVIDIA, revealed that the $N$-body simulations of the Andromeda galaxy model with $2^{23} = 8388608$ particles took $3.8 \times 10^{-2}$~s or $3.3 \times 10^{-2}$~s per step for each case. Tesla V100 achieves a 1.4 to 2.2-fold acceleration in comparison with Tesla P100, the flagship GPU in the previous generation. The observed speed-up of 2.2 is greater than 1.5, which is the ratio of the theoretical peak performance of the two GPUs. The independence of the units for integer operations from those for floating-point number operations enables the overlapped execution of integer and floating-point number operations. It hides the execution time of the integer operations leading to the speed-up rate above the theoretical peak performance ratio. Tesla V100 can execute $N$-body simulation with up to $25 \times 2^{20} = 26214400$ particles, and it took $2.0 \times 10^{-1}$~s per step. It corresponds to $3.5$~TFlop/s, which is 22\% of the single-precision theoretical peak performance.