CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications. Many scientific computing applications demand massive numerical computations on parallel architectures such as Graphics Processing Units (GPUs). Usually, either floating-point single or double precision arithmetic is used. Higher precision is generally not available in hardware and software extended precision libraries are much slower and rarely supported on GPUs. We develop CAMPARY: a multiple-precision floating-point arithmetic library using the CUDA programming language for the NVidia GPU platform. In our approach, the precision is extended by representing real numbers as the unevaluated sum of several standard machine precision floating-point numbers. We make use of error-free transforms addition and multiplication algorithms, which are based only on native precision operations, but keep track of all rounding errors. This offers the simplicity of using hardware highly optimized floating-point operations, while also allowing for rigorously proven rounding error bounds. This allows as well for an interval arithmetic. Currently, all basic multiple-precision arithmetic operations are supported. Our target applications are in chaotic dynamical systems or automatic control.
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- Joldes, Mioara; Muller, Jean-Michel; Popescu, Valentina; Tucker, Warwick: CAMPARY: cuda multiple precision arithmetic library and applications (2016)