GH-48123 [C++][Float16] Reimplement arrow::WithinUlp and Enable it for float16

[andishgar]

Rationale for this change

Refer to this comment. Additionally, this change enables arrow::WithinUlp for float16.

What changes are included in this PR?

Re-implement arrow::WithinUlp and enable it for float16, including relevant tests for corner cases around powers of two and Float16.

Are these changes tested?

Yes, I ran the relevant unit tests.

Are there any user-facing changes?

No.

• GitHub Issue: [C++][Float16] Enhance Arrow’s comparison logic to produce more meaningful Float16 comparison results #48123

[github-actions]

⚠️ GitHub issue #48123 has been automatically assigned in GitHub to PR creator.

[pitrou]

This is neat, thank you. A couple comments below, but looks good on the principle.

[andishgar]

@pitrou Thank you for the review. I’ve checked all the comments and will apply your suggestions in the coming days.

[pitrou]

LGTM, thank you @andishgar ! I've just pushed a very minor change and will merge if CI is ok.

[pitrou]

@github-actions crossbow submit -g cpp

[github-actions]

Revision: 0597736

Submitted crossbow builds: ursacomputing/crossbow @ actions-aeed0cd233

Task	Status
example-cpp-minimal-build-static
example-cpp-minimal-build-static-system-dependency
example-cpp-tutorial
test-build-cpp-fuzz
test-conda-cpp
test-conda-cpp-valgrind
test-cuda-cpp-ubuntu-22.04-cuda-11.7.1
test-cuda-cpp-ubuntu-24.04-cuda-13.0.2
test-debian-12-cpp-amd64
test-debian-12-cpp-i386
test-fedora-42-cpp
test-ubuntu-22.04-cpp
test-ubuntu-22.04-cpp-20
test-ubuntu-22.04-cpp-bundled
test-ubuntu-22.04-cpp-emscripten
test-ubuntu-22.04-cpp-no-threading
test-ubuntu-24.04-cpp
test-ubuntu-24.04-cpp-bundled-offline
test-ubuntu-24.04-cpp-gcc-13-bundled
test-ubuntu-24.04-cpp-gcc-14
test-ubuntu-24.04-cpp-minimal-with-formats
test-ubuntu-24.04-cpp-thread-sanitizer

[conbench-apache-arrow]

After merging your PR, Conbench analyzed the 3 benchmarking runs that have been run so far on merge-commit f40d62e.

There were no benchmark performance regressions. 🎉

The full Conbench report has more details. It also includes information about 16 possible false positives for unstable benchmarks that are known to sometimes produce them.