Also I am not sure which one in common use behaves exactly as you say. On ia32 it's usually all stack. (Though I think Microsoft uses ECX for the c++ this pointer.) On amd64 it's common to use registers for the first few integers. (Say, 4 of them.)
Further, within a non-exported function it's fair game to break ABIs/calling conventions.
The specification that you're both trying to find is called the "System V Application Binary Interface, AMD64 Architecture Processor Supplement" and is found here: http://www.x86-64.org/documentation/abi.pdf
There are similar variations for other architectures. Microsoft does something different, I don't know where their spec lives.
If this sounds far fetched, consider for example that it's common to experience a lot of pain trying to link code compiled with GCC against code compiled with the ms compiler or vice-versa. Same language, CPU, OS. Differing abi.