Compute values for rational magnitude powers

[chiphogg]

Since this will only ever be done at compile time (as guaranteed by
using consteval), we can afford to prioritize precision over speed. To
compute an Nth root, we simply do a binary search over representable
floating point numbers, looking for the number whose Nth power most
closely matches the original number.

Fixes #474. We have included a test case reproducing the original
problem exactly. All tests use "within 4 ULPs" as the criterion, which
is (I believe) equivalent to the googletest EXPECT_DOUBLE_EQ
criterion.

[mpusz]

"Formatting CI" fails. Please run pre-commit according to the instructions in https://github.com/mpusz/mp-units/blob/master/CONTRIBUTING.md#unified-code-formatting.

[mpusz]

math.h is not constexpr in libc++. Please maybe use runtime tests for that or provide a compilation condition similar to

mp-units/test/static/math_test.cpp

Line 39 in f5eda4a

#if __cpp_lib_constexpr_cmath || MP_UNITS_COMP_GCC

[mpusz]

It seems that the libc++-18 issues are fixed now, and a few problems have surfaced in our code. I fixed all of them today. Please rebase to master and fix the remaining issues in your code. There are at least two more issues to be fixed:

• https://github.com/mpusz/mp-units/actions/runs/10085773853/job/27887189635?pr=601
• https://github.com/mpusz/mp-units/actions/runs/10085773853/job/27887192303?pr=601

[chiphogg]

Apple clang does not like this linkage:

It's weird, because the undefined symbol is mp_units::detail::expr_multiply<mp_units::derived_unit, mp_units::one, mp_units::detail::type_list_of_unit_less, mp_units::si::metre, mp_units::si::metre>(mp_units::si::metre, mp_units::si::metre), and expr_multiply comes from expression_template.h, which is in mp_units::core. And unit_test_runtime is already linked to mp_units::mp_units, which itself depends on mp_units::core. So as far as I can tell, we should be good!

Maybe the solution is more obvious to you.

[mpusz]

This was also the case for clang-16:
https://github.com/mpusz/mp-units/actions/runs/10154113253/job/28078706674?pr=601

Hopefully, now it will be OK.

[chiphogg]

Really glad I asked for help instead of trying to solve it on my own --- I would never have come up with that!

[mpusz]

Yeah, I had a few issues with clang-16 already 😉

[chiphogg]

I had to manually restart each of 3 failed jobs. The jobs gave no reason for their failure, and all of them passed on retry. In any case, we're at a 100% pass rate right now!

[mpusz]

Thanks @chiphogg!