I primarily want to address this part of the question, as the underlying issue has been addressed elsewhere, multiple times:
The problem arises firstly from the "isfinite" function: (undefined reference to isfinite). From google search I find that I must include "math.h" and write three lines of code, like:
ifdef __linux__
define _finite(v) (__builtin_isfinite(v))
endif
I started to write "Google led you astray", but I think it's more likely that you seriously misunderstood what it led you to. And perhaps you happened to choose poor results.
The error message indicates that you put those lines in your makefile, but they are wholly inappropriate for that. Don't put them there.
The lines are C preprocessor directives that have been stripped of their leading # characters. You would use them by restoring the # characters ...
#ifdef __linux__
#define _finite(v) (__builtin_isfinite(v))
#endif
... and putting the resulting lines into one or more of your C source files. BUT DON'T! Those lines are unnecessary and at best unhelpful.
You do need to #include <math.h> in each C source file that contains a call to isfinite(), because that is the header that provides a declaration of the function. Since C99, functions must be declared before they are called (and it was good practice well before then).
Other than that, with GCC and many other traditional-style Unix C compilers, you need to explicitly include the math library in your link when you need any of the functions it provides. That would involve adding -lm to your makefile, at the end of the gcc command that builds the final executable. This is covered in gcc will not properly include math.h, and many other duplicates on this site.
