Avoiding and Curing Numerical Problems

The basic geometry routines of any Monte Carlo are subjected to a particularly virulent form of Murphy's Law. Not only will every possible (and impossible) situation arrive, but also it is guaranteed to happen at the point of maximun inconvenience - i.e. about 10 hours into the ``definitive'' run. Points will be in two or more regions simulataneously or in no region at all. Tracks will travel in the planes of any flat surface and strike any intersection between two surfaces with a pinpoint accuracy that would be the envy of any tactical force commander. In order to combat these problems we have to try both prevention and cure. Prevention is dealt with by the following:-

• Using, as the basic design, an embedded geometry. If each boundary is only ever dealt with by one piece of code then it may be wrong, but it should at least be consistent!

• The EXTRACT switch GE_DEBUG. Switching this on means that for each call to GE_NEXT, after finding the boundary, GE_REGION is called to check on the region on either side of the boundary. This checks consistency between GE_NEXT and GE_NEAR. This debug code will also pick up a number of other problems.

To help cure problems we need to be able to reproduce bugs when they crop up. Keeping a short history of previous calls to the geometry interface routines that can be dumped when an error occurs will help here.