assertions are your friend.
If you pass -DNDEBUG into C-compiler at C-compile-time, the assertions will not be compiled. However, except for your inner-number-crunching loops I'd suggest leaving them on.
once you get an assertion to core dump, assuming you have compiled with debugging on, I believe (haven't actually done it though ...) that you can fire up gdb with the core file and at hopefully get a pretty good idea of the state of things with just up,down, and print.
If things get hairy enough so that the above still doesn't cut it, I think what you want to do is try to make the actual C code that appears in the Inline:: part as small as possible, making it just Interface code to a library. Then make a separate C 'client' for the same library and do all your C debugging in a normal C way. If problems persist then you can be pretty sure its an interface problem.
I'm reinventing this particular wheel slowly at home (The neural net wheel... not the Inline::C wheel). Out of curiosity, how much is done in C and how much in perl? Based on a purely anecdotal analysis (i.e. I've been too lazy to profile it) I think the matrix-vector multiplication and multiplication by the transpose is about the only part that really needs to be done in C.
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