I need a fast and accurate method to calculate 3d spherical volume integrals.
I have pre-calculated data of high precision that just needs a few trivial manipulations before each integration step - in other words function calls are mostly just array look ups and multiplication and so are relatively cheap.
The data is evenly spaced in spherical polar coordinates: 4 samples per degree for theta and phi, 500 radial samples.
I need good precision, but I also need to perform several million such integrals, so speed is an important concern.
What algorithm is most suitable for this problem?
Bonus points for a link to an implementation in C++!