Context. A novel high-performance exact pair-counting toolkit called fast correlation function calculator (FCFC) is presented.Aims. With the rapid growth of modern cosmological datasets, the evaluation of correlation functions with observational and simulation catalogues has become a challenge. High-efficiency pair-counting codes are thus in great demand.Methods. We introduce different data structures and algorithms that can be used for pair-counting problems, and perform comprehensive benchmarks to identify the most efficient algorithms for real-world cosmological applications. We then describe the three levels of parallelisms used by FCFC, SIMD, OpenMP, and MPI, and run extensive tests to investigate the scalabilities. Finally, we compare the efficiency of FCFC with alternative pair-counting codes.Results. The data structures and histogram update algorithms implemented in FCFC are shown to outperform alternative methods. FCFC does not benefit greatly from SIMD because the bottleneck of our histogram update algorithm is mainly cache latency. Nevertheless, the efficiency of FCFC scales well with the numbers of OpenMP threads and MPI processes, even though speedups may be degraded with over a few thousand threads in total. FCFC is found to be faster than most (if not all) other public pair-counting codes for modern cosmological pair-counting applications.