Parallel Computation of Normalized Legendre Polynomials Using Graphics Processors

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 687)


To carry out some calculations in physics and Earth sciences, for example, to determine spherical harmonics in geodesy or angular momentum in quantum mechanics, it is necessary to compute normalized Legendre polynomials. We consider the solution to this problem on modern graphics processing units, whose massively parallel architectures allow to perform calculations for many arguments, orders and degrees of polynomials simultaneously. For higher degrees of a polynomial, computations are characterized by a considerable spread in numerical values and lead to overflow and/or underflow problems. In order to avoid such problems, support for extended-range arithmetic has been implemented.


Normalized Legendre polynomials Extended-range arithmetic GPU CUDA 



This work was supported by the Russian Foundation for Basic Research, project No. 16-37-60003 mol_a_dk.


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Copyright information

© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Department of Electronic Computing MachinesVyatka State UniversityKirovRussia

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