  We present an algorithm named "Chamomile Scheme". The scheme is fully
optimized for calculating gravitational interactions on the latest programmable
Graphics Processing Unit (GPU), NVIDIA GeForce8800GTX, which has (a) small but
fast shared memories (16 K Bytes * 16) with no broadcasting mechanism and (b)
floating point arithmetic hardware of 500 Gflop/s but only for single
precision. Based on this scheme, we have developed a library for gravitational
N-body simulations, "CUNBODY-1", whose measured performance reaches to 173
Gflop/s for 2048 particles and 256 Gflop/s for 131072 particles.
