approximation to the area under a conic section by filling the area with a known number of rectangles of known size and then sum the areas of the rectangles. The narrower the rectangles, the more accurate the approximation. This is a data parallel problem and embarrassingly parallel.
is commutative and associative so we can partition the overall summation in any way we want: a + b + c + d + e + f ( a + b ) + ( c + d ) + ( e + f ) Can partition the overall sum into bits to be done on different processors. This should make things faster.
Instead of doing all the calculations sequentially, partition the problem into a number of chunks. problem subproblem result subproblem subproblem subproblem . . . scatter gather fork join reduce Data parallel map
Use NumPy. • Use C. • Use C++/Boost. • Use D/PyD. • Use Chapel/PyChapel. Offload the whole computation, Leaving Python code as the coordination code. https://github.com/russel/Pi_Quadrature/tree/master/Python http://dlang.org/ http://pyd.readthedocs.org/ http://chapel.cray.com/ http://pychapel.readthedocs.org/
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