bpo-45548: Have Modules/Setup only try to compile _math once by brettcannon · Pull Request #29177 · python/cpython
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I don't think that will work with *shared** mode.
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You're right.
/usr/bin/ld: Modules/cmathmodule.o: relocation R_X86_64_32 against `.data' can not be used when making a shared object; recompile with -fPIC`
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Your idea of making the functions static might actually be necessary to solve this. Not sure how _math.h influences anything as I haven't looked to see if it's included anywhere else.
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The relocation R_X86_64_32 against `.data' issue is a different problem. You are trying to use an .o file from a static build in a shared module. You must make clean every time you modify Modules/Setup. ccache helps a lot here.