Abstract
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 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 algorithms, which are based only on native precision operations, but keep track of all rounding errors that occur when performing a sequence of additions and multiplications. This offers the simplicity of using hardware highly optimized floating-point operations, while also allowing for rigorously proven rounding error bounds. This also allows for easy implementation of 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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Notes
- 1.
A FMA (Fused Multiply-Add) operator evaluates an expression of the form \(xy+t\) with one final rounding only.
- 2.
Certified algorithms are available in multi_prec_certified.h file.
- 3.
“Quick-and-dirty” algorithms are available in multi_prec.h file.
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Joldes, M., Muller, JM., Popescu, V., Tucker, W. (2016). CAMPARY: Cuda Multiple Precision Arithmetic Library and Applications. In: Greuel, GM., Koch, T., Paule, P., Sommese, A. (eds) Mathematical Software – ICMS 2016. ICMS 2016. Lecture Notes in Computer Science(), vol 9725. Springer, Cham. https://doi.org/10.1007/978-3-319-42432-3_29
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