  We present a new implementation of the numerical integration of the
classical, gravitational, N-body problem based on a high order Hermite's
integration scheme with block time steps, with a direct evaluation of the
particle-particle forces. The main innovation of this code (called HiGPUs) is
its full parallelization, exploiting both OpenMP and MPI in the use of the
multicore Central Processing Units as well as either Compute Unified Device
Architecture (CUDA) or OpenCL for the hosted Graphic Processing Units. We
tested both performance and accuracy of the code using up to 256 GPUs in the
supercomputer IBM iDataPlex DX360M3 Linux Infiniband Cluster provided by the
italian supercomputing consortium CINECA, for values of N up to 8 millions. We
were able to follow the evolution of a system of 8 million bodies for few
crossing times, task previously unreached by direct summation codes. The code
is freely available to the scientific community.
