You might be able to accelerate the CRC calculation with very little effort; I've dealt with this recently, here is my experience:

A *lot* of implementations you'll find online are obsolete (e.g. the one found in the boost-library) and use the 1byte-at-a-time (256 LUT entries) or even 1 nibble-at ...

Not sure if you evaluated this, but CRlibm provides correctly (=> deterministically) rounded math functions (all the C99 ones).

If you're using the LuaJIT implementation (just-in-time compiled Lua, significantly faster than the lua.org implementation), at least the basic floating point operations ...