high performance computing on graphics processing units: hgpu.org

Beal’s Conjecture asserts that if Ax + By = Cz for integers A,B,C > 0 and integers x,y,z > 2, then A, B, and C share a common prime factor. While empirical computational studies by several researchers have established that Beal’s Conjecture holds for all A,B,C,x,y,z < 1000, the truth of the general conjecture remains unresolved. Extending the search for counterexamples to significantly greater values of the conjecture’s six integer parameters is a task ideally suited to the use of an SIMD parallel algorithm implemented on a GPGPU platform. In 2009 researchers developed such an algorithm, implemented in the C programming language with CUDA extensions for execution on the NVidia GeForce 8400GS GPGPU. In the concluding remarks accompanying the report of their results, the researchers suggested that in the future the practical search range for their algorithm might be extended by implementing it as a distributed application across multiple GPGPUs. This thesis project is one of a pair of related thesis projects aimed at developing a heterogeneous NPACI-Rocks/MPI/CUDA distributed multi-GPGPU application for seeking counterexamples to Beal’s Conjecture. In particular, this thesis project comprised the development and testing of the MPI-based communications and task-management layer and MPI/CUDA integration for the application on a commodity cluster host with NVidia GeForce 8400GS GPGPU-enabled compute nodes.