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(Abridged) We have developed a numerical software library for collisionlessN-body simulations named "Phantom-GRAPE" which highly accelerates forcecalculations among particles by use of a new SIMD instruction set extension tothe x86 architecture, AVX, an enhanced version of SSE. In our library, not onlythe Newton's forces, but also central forces with an arbitrary shape f(r),which has a finite cutoff radius r_cut (i.e. f(r)=0 at r>r_cut), can be quicklycomputed. Using an Intel Core i7--2600 processor, we measure the performance ofour library for both the forces. In the case of Newton's forces, we achieve 2 x10^9 interactions per second with 1 processor core, which is 20 times higherthan the performance of an implementation without any explicit use of SIMDinstructions, and 2 times than that with the SSE instructions. With 4 processorcores, we obtain the performance of 8 x 10^9 interactions per second. In thecase of the arbitrarily shaped forces, we can calculate 1 x 10^9 and 4 x 10^9interactions per second with 1 and 4 processor cores, respectively. Theperformance with 1 processor core is 6 times and 2 times higher than those ofthe implementations without any use of SIMD instructions and with the SSEinstructions. These performances depend weakly on the number of particles. Itis good contrast with the fact that the performance of force calculationsaccelerated by GPUs depends strongly on the number of particles. Substantiallyweak dependence of the performance on the number of particles is suitable tocollisionless N-body simulations, since these simulations are usually performedwith sophisticated N-body solvers such as Tree- and TreePM-methods combinedwith an individual timestep scheme. Collisionless N-body simulationsaccelerated with our library have significant advantage over those acceleratedby GPUs, especially on massively parallel environments.

Phantom-GRAPE: numerical software library to accelerate collisionless $N$-body simulation with SIMD instruction set on x86 architecture