If you provided a human contractor with the specifications for the code you want, the courts have repeatedly made clear you have not provided the creative input from a copyright perspective, and the contractor needs to explicitly assign those rights to you if want to own the copyright on the code.
- Specifiers, who make the specification for the system
- Programmers, who write C code
- Machine encoders, that take that C code and write machine code for a CPU
Would it be that the copyright would then belong to programmers, if no other explicit assignments would be made?
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Thinking about it, probably yes: copyright of the spec belongs to specifies, copyright of the C belong to programmers, and copyright of machine code to machine encoders. Or would it depend on the amount of optimizations the machine encoders would do, i.e. is it creative or not? And then does this relate to the task and copyrightability of C compiler output, where optimizations can sometimes surprise the developer?
So, in your example, the specifiers would own the specification, the programmers the C code, and machine encoders own the machine code.
But the ownership wouldn't be complete. If you sell the machine code, you'd have to pay royalties to all three. If you only sold the C code, only to the specifiers and the programmers.