Clock Math – A System for Solving SLEs Exactly

Jakub Hladik, Robert Lorencz, Ivan Simecek
Department of Computer Systems, Faculty of Information Technology, Czech Technical University in Prague, Czech republic
Acta Polytechnica 53(2), 70-74, 2013


   title={Clock Math-a System for Solving SLEs Exactly},

   author={Hlad{‘i}k, Jakub and L{‘o}rencz, R{‘o}bert and {v{S}}ime{v{c}}ek, Ivan},

   journal={Acta Polytechnica},





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In this paper, we present a GPU-accelerated hybrid system that solves ill-conditioned systems of linear equations exactly. Exactly means without rounding errors due to using integer arithmetics. First, we scale floating-point numbers up to integers, then we solve dozens of SLEs within different modular arithmetics and then we assemble sub-solutions back using the Chinese remainder theorem. This approach effectively bypasses current CPU floating-point limitations. The system is capable of solving Hilbert’s matrix without losing a single bit of precision, and with a significant speedup compared to existing CPU solvers.
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