Fix for #3596: Make fftconvolve threadsafe

[foogod]

First pass at a fix for #3596: For NumPy versions prior to 1.9.0, will make sure that numpy.fft.rfftn / irfftn are only called from one thread at a time. Will fall back to the slower SciPy complex-FFT routines for all other simultaneous threads.

[coveralls]

Coverage remained the same when pulling 972481f on foogod:bugfix-3596 into 7ff4e90 on scipy:master.

[endolith]

Maybe instead of duplicating the ret = ifftn(fftn(in1, fshape) *... code, it should use something like if complex_result or not _rfft_mt_safe:?

[foogod]

The problem with that is that it would force even single-threaded code to use the slower FFT routines, even though they don't need to, so it would make fftconvolve slower in general, with all current versions of NumPy..

The advantage of doing it this way is that it uses the faster RFFT routines whenever possible, only falling back to the complex FFT routines if it actually does encounter multiple threads running at the same time. It should therefore be about the same speed as before for all single-threaded programs.

[endolith]

shouldn't this be followed by ret = ret.real? (purpose is to strip away negligible imaginary parts?) I don't know why irfftn would return anything but real, but it was there in the original...

[foogod]

I'll admit this omission was unintentional, but it turns out that since we're doing an inverse real-FFT transform, the output is already a real array by definition, so that step is redundant anyway (and didn't need to be in the original)..

[endolith]

Yeah I guess that's my fault: 5567c9c It previously existed to strip away negligible imaginary parts from ifftn, but irfftn output should always be real already, so this line isn't needed with irfftn at all.

[endolith]

In other words, I think this is equivalent, but doesn't duplicate the same operation in multiple places?

if complex_result or (not _rfft_mt_safe and not _rfft_lock.acquire(False)):
    ret = ifftn(fftn(in1, fshape) * fftn(in2, fshape))[fslice].copy()
    if not complex_result:
        ret = ret.real

I don't know if the 2 irfftn calls can be similarly combined, though, because of the try and lock, which I don't know much about.

[foogod]

So it took some doing but I think I've figured out a way to consolidate the duplicated code without making things entirely impossible to follow.. let me know what you think of the updated version..

[pv]

Looks good to me

[endolith]

While you're changing things, I don't see any reason for the complex_result = ( line to appear between the s2 = line and the shape = line. I think it would be more readable if it were right before the if not complex_result line. Its arguments aren't changing in between these points

Also there's a completely inconsequential typo in but slower) ScipPy complex-FFT

I don't see any real problems, though. The comments are very helpful

[pv]

Thanks, merged.