[pwang]

Good points, certainly, but just to clarify: Numba is not particularly dependent on Numpy's built-in vectorized and matrix operations. Instead, it's using the datatype information to do JIT type inference over the functions being called with the matrix/array arguments, and building machine code for them. You can call Numba JITted functions from other Numba JITted functions, and the overhead is the same as C functions calling each other.

[emn13]

I've got no numba experience whatsoever, but if you're doing real function calls and memory allocations for simple things like multiplying small matrices, your code will be at least an order of magnitude slower than optimal, even in C. malloc's a big hit, and function calls often are too - not just because of the call itself (and the CPU cache hit that can involve), but no less significantly because they're opaque to the optimizer - and that means that the wrapping function is often optimized much less well.

It's not a fundamental issue, but I haven't seen a JIT do this particularly well, yet. All that inlining makes compiling slower, so to some extent the run-time nature of the JIT is an inherent limitation here.