specfun CI tests for cpp_double_fp_backend

[ckormanyos]

The purpose of this issue is to get the specfun GHA CI tests running for the cpp_double_fp_backend<> template type.

Instantiate at first for double and see how that goes. If more needed, such as __float128, we will decide as we go.

Cc: @sinandredemption and @cosurgi

[ckormanyos]

I will take the first try at this.

[ckormanyos]

We have now specfun running (but failing as expected) on develop in CI for cpp_double_fp< 8-byte-double >.
At the moment 11 files fail.
See detailed comments in #138

Cc: @sinandredemption and @cosurgi

[ckormanyos]

Correction: See #138

[ckormanyos]

We keep moving forward, now with only 5 files failing specfun in CI for cpp_double_fp< 8 -byte-double >.

See also #142

Work continues on edge cases which should eventually get all of specfun passinf for this data type.

Cc: @sinandredemption

[ckormanyos]

Hi Fahad (@sinandredemption) in order to provide very clear and easy-to-understand instances of failing test cases, I have prepared the first of two in a series of failing test case studies.

These can be found in #143 and #144

Cc: @cosurgi

[ckormanyos]

We are now down to two and only two meaningful files with failing test cases in specfun.
See the comments in #146

Cc: @sinandredemption and @cosurgi

[ckormanyos]

... down to two and only two meaningful files with failing test cases in specfun.

In particular, see the build log for #146.

[ckormanyos]

See also comments and build logs from #147

[ckormanyos]

I just posted in the wrong thread for these specfun tests.

See #136

Cc: @sinandredemption

[ckormanyos]

See also #150

[ckormanyos]

Still getting closer to passing all of specfun. See detailed comments from #154, repeated here.

Remaining specfun issues include:

• gamma_inv (several issues ALL around extremely small/subnormal values),
• one single exception thrown in elliptic_3,
• several issues (still) in cyl_bessel_k.

Cc: @sinandredemption and @cosurgi

[ckormanyos]

one single exception thrown in elliptic_3

This has been correected in #155. The read of overly large strings (that will be infinite) did not properly regard the result sign of ${\pm}{\infty}$, and they were all positive. Now the sign is correctly retained.

Also the square root of infinity was improperly given in the eval_sqrt function as NaN, but it should also be infinity.

[ckormanyos]

OK with #157 cyl_bessel_k is finished.

The only specfun with remaining test failures is igamma_inv, which will be handled specifically in a separate issue.