Obtain more code coverage

[ckormanyos]

This PR obtains more code coverage. But it is for later in 1.90 (not for today's 1.89).

[codecov]

Codecov Report

❌ Patch coverage is 99.89259% with 1 line in your changes missing coverage. Please review.
✅ Project coverage is 96.2%. Comparing base (55bf069) to head (5b53322).
⚠️ Report is 65 commits behind head on develop.

Files with missing lines	Patch %	Lines
include/boost/multiprecision/cpp_dec_float.hpp	99.7%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff            @@
##           develop    #711     +/-   ##
=========================================
+ Coverage     94.7%   96.2%   +1.5%     
=========================================
  Files          296     297      +1     
  Lines        30881   31177    +296     
=========================================
+ Hits         29233   29967    +734     
+ Misses        1648    1210    -438     

Files with missing lines	Coverage Δ
example/exercise_threading_log_agm.cpp	100.0% <100.0%> (ø)
include/boost/multiprecision/complex_adaptor.hpp	92.3% <100.0%> (+2.8%)	⬆️
include/boost/multiprecision/cpp_bin_float.hpp	93.9% <ø> (+2.7%)	⬆️
include/boost/multiprecision/cpp_double_fp.hpp	100.0% <100.0%> (ø)
...nclude/boost/multiprecision/detail/default_ops.hpp	93.5% <ø> (+2.5%)	⬆️
...oost/multiprecision/detail/functions/constants.hpp	99.2% <100.0%> (ø)
...lude/boost/multiprecision/detail/functions/pow.hpp	99.4% <100.0%> (+4.7%)	⬆️
...ude/boost/multiprecision/detail/functions/trig.hpp	97.5% <ø> (+0.8%)	⬆️
test/git_issue_167.cpp	100.0% <100.0%> (+50.0%)	⬆️
test/git_issue_464.cpp	100.0% <100.0%> (ø)
... and 17 more

... and 4 files with indirect coverage changes

---

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[ckormanyos]

Ok so I worked on coverage, mostly with focus on cpp_dec_float. That file is pretty well covered now, but missing 8 interesting lines. I'll let this one sit for a while.

I would like to improve the line coverage of the tests and then we can discuss which headers need more dedicated edge tests.

Let's just leave this as a draft until the action on 1.90 wraps up.

[ckormanyos]

In cpp_dec_float going to nearly $99\%$ coverage was straightforward. Sure it needed a few hundred lines of dedicated test code.

I only found 1 bug, but harmless, in the area of negative infinity ($-\infty$). There were several areas having redundant or unclear lines. I cleared up (or subjectively think I cleared up) a bunch of these sequences. Nothing really critical was found, and this shows how well this thing was tested to begin with. I'm really impressed with the test-suite.

[ckormanyos]

OK this one is green again and ready for review.

I'm pretty satisfied with these results. Project coverage is at a solid $96.2\%$, with cpp_double_fp_backend.hpp fully covered and cpp_dec_float missing fewer than $5$ lines.

A few bug fixes were done along the way. In future work, I'd like to see how to hit some of the missing lines in cpp_int.hpp and cpp_bin_float.hpp. I took a few tries at this but only had modest success.

When stressing cpp_bin_float, I ran across #726, which seems like an actual (still non-solved) bug.

There is also a hefty TODO list (for myself) at #703. So after concluding this more_coverage PR, I'll move on to #703 and possibly #726.

Cc: @jzmaddock and @mborland

[jzmaddock]

Thanks Chris for this, looks good other than my few comments on the header changes.

[jzmaddock]

When erf(cpp_bin_float(-0.0)) is called, the generic implementation does not catch the negative zero. It simply goes to the Taylor series and returns zero.

Good catch!

My gut says something like:

if(fabs(z) < tools::root_epsilon<T>())
   return invert ? 1 : 2 * z / constants::root_pi<T>();

Which should make that zone more efficient as well as fixing the signed zero issue? Note: just typed in off the top of my head!!

[ckormanyos]

Removed the constexpr-ness efforts, as these will be handled in a future, separate branch. The most modern, mostly passing commit having the bulk of the constexpr-ness efforts is ac1b954.