Add multithreading support?

[MikaelSlevinsky]

In Bogaert's paper, a billion GL nodes takes 11.0 seconds using his C++ implementation and 8 threads with 4 logical cores. Compare this to the 131 seconds for a billion and one GL nodes.

Threading should improve the computational times since all these methods are trivially parallel. Alternatively, this package could end up being a wrapper for low-level codes that have better thread support. For example, Bogaert's code is written in C++, but minor changes could have it rewritten as C.

[dlfivefifty]

Have you done a profiling of the current gausslegendre? Is it Bogaert's method? (A citation should be added to the code.)

For single threads, there is pretty much no reason this kind of code would be faster in C than in Julia. But there seems to be some sillyness in the current implementation, e.g., constants like -65 / 1024 which may be evaluated every loop.

[MikaelSlevinsky]

Note that issue is speculative since threading is still experimental in Julia. In my personal experience, Julia's experimental threading is still about a factor of 30% off from OpenMP paradigms and less flexible too.

As far as I can tell, the current implementation is a transliteration of Bogaert's method (though some terms in the series are pared down, and you're right about the constants that are fed into the macros).

For reference, here is the original C++ that appears to have been released in the public domain and here is a C version.

[AshtonSBradley]

are these threading comments still relevant? Julia's threading is pretty solid now. Anyone done any recent tests of timing?