Using M_PI with C89 standard

A conforming standard library file math.h is not only not required to, but actually must not define M_PI by default. In this context 'by default' means that M_PI must only get defined through compiler-specific tricks, most often undefined behavior through the use of reserved identifiers.

Just define the constant yourself (you can use the name M_PI freely, but should you want to be able to compile the code with a non-conforming compiler, you must first check that M_PI is not already defined). For convention's sake, do not define M_PI as anything other than (the approximation of) pi.

I would go for

#ifndef M_PI
#    define M_PI 3.14159265358979323846
#endif

M_PI is not required by the C standard, it's just a common extension, so if you want to be standard you shouldn't rely on it. However, you can easily define your own #define for it, last time I checked it was a universal constant so there's not much space for confusion. :)

I fail to see what the problem is here; there is no incompatability between -std=c89 and _USE_MATH_DEFINES, one defines what language the compiler will compile, the other defines what parts of math.h get enabled.

Those parts that are enabled are not defined as part of the ISO C standard library, but that is not the same thing as not being standard C language, language and library are separate entities in C. It is no less C89 compliant than it would be if you had defined your own macros in your own header.

I would however suggest that you define the macro on the command-line rather than in the code:

-std=c89 -D_USE_MATH_DEFINES

If you ever encounter a math.h implementation that does not define M_PI, then that is easily fixed without code modification by similarly using command line defined macros:

-std=c89 -DM_PI=3.14159265358979323846