Today, GPUs represent an important hardware development platform for many problems in dynamical systems, where massive parallel computations are needed. Besides that, many numerical studies of chaotic dynamical systems require a computing precision higher than common Floating Point (FP) formats. One such application is locating invariant sets for chaotic dynamical systems. In particular, the authors focus on rigorously proving the existence of stable periodic orbits for the Henon map for parameter values close to the classical ones. For that, they present a multiple-precision floating-point arithmetic library in CUDA programming language for the NVIDIA GPU platform.