Fix idct for complex-valued bigfloat vectors

[daanhb]

The BigFloat implementation of idct was not correct for complex-valued vectors it seems, only when they happened to be of complex type but real-valued.
I changed the implementation to one that seems to work and added a few tests for this case.

I also had to change the threshold for another test involving BigFloat fft's, otherwise the test would fail in my setup.

[daanhb]

Also, I don't think the implementation is correct for matrices, so I've restricted the arguments to be vectors.

[dlfivefifty]

It fails in Julia v0.6.

@MikaelSlevinsky any complaints if we drop v0.6 support?

[MikaelSlevinsky]

It's probably near time to drop support for 0.6, but it also seems arbitrary to drop it for a test that could be changed to complex.(big.(rand(...)),...) (to get random complex big floats), rather than a major refactor.

[MikaelSlevinsky]

Thanks for the fix, btw!

[codecov-io]

Codecov Report

Merging #59 into master will decrease coverage by 31.76%.
The diff coverage is 75%.

@@            Coverage Diff             @@
##           master     #59       +/-   ##
==========================================
- Coverage   84.47%   52.7%   -31.77%     
==========================================
  Files          33      33               
  Lines        3181    3157       -24     
==========================================
- Hits         2687    1664     -1023     
- Misses        494    1493      +999

Impacted Files	Coverage Δ
src/fftBigFloat.jl	71.27% <75%> (-23.57%)	⬇️
src/ChebyshevUltrasphericalPlan.jl	45% <0%> (-55%)	⬇️
src/SphericalHarmonics/Butterfly.jl	36.59% <0%> (-53.75%)	⬇️
src/ChebyshevJacobiPlan.jl	46.39% <0%> (-53.61%)	⬇️
src/recurrence.jl	43.51% <0%> (-47.64%)	⬇️
src/SphericalHarmonics/synthesisanalysis.jl	52.65% <0%> (-43.62%)	⬇️
src/SphericalHarmonics/vectorfield.jl	42.48% <0%> (-41.64%)	⬇️
src/cheb2jac.jl	58.82% <0%> (-41.18%)	⬇️
src/SphericalHarmonics/thinplan.jl	49.67% <0%> (-40.65%)	⬇️
src/cheb2ultra.jl	59.45% <0%> (-40.55%)	⬇️
... and 20 more

---

Continue to review full report at Codecov.

Legend - Click here to learn more
Δ = absolute <relative> (impact), ø = not affected, ? = missing data
Powered by Codecov. Last update 53ec4b0...a1d97ae. Read the comment docs.

[daanhb]

I changed it to c = big.(rand(100)) + im*big.(rand(100)), in order to create a non-zero imaginary part (since that is where the error was). I agree this is not something to drop 0.6 for. However, the 0.6 tests still fail on my system with a "function range does not accept keyword arguments" error in another FFT test, which I did not change.

[MikaelSlevinsky]

I think it's because positional arguments to range are in perhaps newer versions of Compat.jl

[daanhb]

That was it, I hadn't used 0.6 for a while!