Optimize dseries.rolling.mean()

[densmirn]

Previous implementation results:

name	nthreads	type	size	median
Series.rolling.mean	1	Python	10000000	0.6860003471374512
Series.rolling.mean	1	SDC	10000000	5.223999977111816

Optimized implementation results:

name	nthreads	type	size	median
Series.rolling.mean	1	Python	10000000	0.6230072975158691
Series.rolling.mean	1	SDC	10000000	0.10899996757507324

The optimized implementation executes faster up to ~45 times than previous one and faster up to ~5 times than Python. There is no scalability due to prange isn't used at all because variable nfinite (number of finite values) is common for all threads.

[densmirn]

Current performance:

name	nthreads	type	size	median
Series.rolling.mean	1	Python	200000	1.298
Series.rolling.mean	1	SDC	200000	1.019
Series.rolling.mean	4	Python	200000	1.418
Series.rolling.mean	4	SDC	200000	0.469

Python 1 / SDC 4 = 2.77
The scalability was enabled.

[densmirn]

Current performance:

name	nthreads	type	size	median
Series.rolling.mean	1	Python	800000	4.135
Series.rolling.mean	1	SDC	800000	0.84
Series.rolling.mean	4	Python	800000	4.009
Series.rolling.mean	4	SDC	800000	0.279

Python 1 / SDC 1 = 4.923
Python 1 / SDC 4 = 14.821
The scalability was enabled.

[AlexanderKalistratov]

Probably we can introduce new function something like get_result. Which for mean would be:

def get_mean(nfinite, result):
    if nfinite:
        return result/nfinite
    return numpy.nan

And then, call it inside result_or_nan:

@sdc_register_jitable
def result_or_nan(get, nfinite, minp, result):
    """Get result taking into account min periods."""
    if nfinite < minp:
        return numpy.nan

    return get(nfinite, result)

For mean we can do recalculations on put/pop stage, but for more complex functions (std, var) it is not that easy.

Hope, it wouldn't ruin our performance

[densmirn]

The latest patch set recommended by @AlexanderKalistratov actually improved performance:

name	nthreads	type	size	median
Series.rolling.mean	1	Python	800000	4.836
Series.rolling.mean	1	SDC	800000	0.496
Series.rolling.mean	4	Python	800000	4.648
Series.rolling.mean	4	SDC	800000	0.256

Python 1 / SDC 1 = 9.75
SDC 1 / SDC 4 = 1.938