This discussion is majorly lacking a hugely important point:
Calling convention in x64 always uses the RCX, RDX, R8, R9 registers for passing the first 4 arguments (anything up to 64 bit values or pointers), while additionally to those 4 registers, RAX, R10 and R11 are considered volatile. The return value is in the RAX or possibly for a 128-bit return value would be in the RAX:RDX.
This is opposed to x86 where the prior scheme is closest to fastcall which used the ECX and EDX for argument passing before resorting to the stack with additionally the EAX volatile. However in cdecl (caller clean-up stack) calling convention, arguments are all passed on the stack, EAX, ECX and EDX are considered volatile, and the return value in EAX or EAX:EDX. syscall is the same except without the 3 registers being considered volatile. stdcall is also almost the same except the callee cleans up the stack.
If mixing C with external asm, it would be extremely wise to be familiar with all these details.
For more details which are too lengthly to include, refer to:
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https://en.wikipedia.org/wiki/X86_calling_conventions
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