> It's my understanding that SSE registers require the use of a special API and standard floating point operations do not use them.

No, SSE registers are used by most compilers that do floating point these days. They support all the usual IEEE float math operations and a host of bit twiddling operations as well as vector operations. The vector operations do still require using compiler intrinsics in C++, although some autovectorization does occur in gcc, icc, and llvm.