Previous rejected attempt: PR #594.

cc @mdickinson

The Windows build looks broken:

Run .\python.bat -m test.pythoninfo
Running Release|x64 interpreter...
##[error]Process completed with exit code 1.

Thanks for reviewing.

Also added unit tests as suggested (in addition to the existing test coverage). I briefly disabled the branch with clz (8e3ce66) to get a CI run with the fallback implementation. The current fallback is identical to the original (except for inlining).

Using gcc 10 -O3 -flto, I get the following machine code in test_bit_length():

# input = rax
# if (x != 0)
test   rax,rax
je     0x7fffeaa99978 <test_bit_length+504>

# return (int)sizeof(unsigned long) * 8 - __builtin_clzl(x);
# return 0x40 - bsr(rax) ^ 0x3f
bsr    rax,rax
mov    ecx,0x40
xor    rax,0x3f
mov    r9d,ecx
sub    r9d,eax
# result = r9d

x86 BSR (Bit Scan Reverse) instruction is used as expected.

@mdickinson: Do you want to review this PR as well?

I'd very much like to take a look, but am short on available time. Can you give me until the weekend? If I've failed to review by the start of next week, go ahead and merge.

@mdickinson: this PR can wait one week :-)

Thanks @niklasf, I merged your PR.

I removed "(mostly theoretical)" from your commit message:

* Pick a (mostly theoretical) fallback implementation suitable for
  inlining.

We support other C compilers, like XLC.