12551

Towards fast and certified multiple-precision libraries

Valentina Popescu
Universite Paul Sabatier
Universite Paul Sabatier, 2014

@phdthesis{popescu2014towards,

   title={Towards fast and certified multiple-precision libraries},

   author={Popescu, Valentina},

   year={2014}

}

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Many numerical problems require higher precision than the conventional floating-point (single, double) formats. One solution is to use multiple precision libraries such as GNU MPFR, which allow the manipulation of very high precision numbers. But their generality (they are able to handle numbers with millions of digits), is a quite heavy alternative when medium precision (hundreds of digits) and high performance computing is needed. Our objective is to design a multiple precision arithmetic library targeted for problems where a precision of a few hundred bits is sufficient, and which is tuned for highly parallel architectures such as Graphics Processing Units (GPUs). In this work we present algorithms and implementations of arithmetic operations and an application to long-term iteration of the so-called Henon map chaotic dynamical system.
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