That’s mostly true, but not quite. For instance, suppose you aim to support all of 32/64-bit and little/big-endian. You’ll likely end up factoring straightforward math operations out into standalone functions. Granted, those will probably get inlined, but it may mean your structure is more abstracted than it would be otherwise. Just supporting the options has implications.
That’s not the strongest example. I just meant it to be illustrative of the idea.
The way glibc's source works (for something like math functions) is that essentially every function is implemented in its own file, and various config knobs can provide extra directories to compile and provide function definitions. This can make actually finding the implementation that's going to be used difficult, since a naive search for the function name can turn up like 20 different function definitions, and working out which one is actually in play can be difficult (especially since it's more than just the architecture name).
Math functions aren't going to be strongly impacted by diverse hardware support. In practice, you largely care about 32-bit and 64-bit IEEE 754 types, which means your macros to decompose floating-point types to their constituent sign/exponent/significand fields are already going to be pretty portable even across different endianness (just bitcast to a uint32_t/uint64_t, and all of the shift logic will remain the same). And there's not much reason to vary the implementation except to take advantage of hardware instructions that implement the math functions directly... which are generally better handled by the compiler anyways.
People don't typically implement math functions by pulling bits out of a reinterpreted floating point number. If you rely on the compiler, you get whatever it decides for you, which might be something dumb like float80.
That’s not the strongest example. I just meant it to be illustrative of the idea.