I want to use pure C to read and write to the serial port of my computer from an arduino uno.
Why? C++ is a superset of C, so all the stuff that the HardwareSerial class is doing is ultimately based on C. Peek at the libraries if you really need to re-invent the wheel.
Don't expect your C implementation to be any faster. By the time the compiler gets done, the C++/C distinction is gone.