REF: Use moments accumulator from libalgos to compute variance

[Alvaro-Kothe]

• xref REF: Reductions #53261 (Replace xxxx with the GitHub issue number)
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.
• I have reviewed and followed all the contribution guidelines
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Use the moments accumulator functions introduced in #64366 to compute variance, standard error and standard error of the mean.

Not applying these changes to nanvar because had a big performance impact on several cases, mainly for integer types.

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Benchmarks

Details

Change	Before [3ba8677] <refactor/combine-var-impl~2>	After [23b6f0f] <refactor/combine-var-impl>	Ratio	Benchmark (Parameter)
+	69.6±9μs	81.1±0.6μs	1.17	groupby.GroupByMethods.time_dtype_as_field('float', 'std', 'direct', 1, 'cython')
+	70.9±7μs	81.0±0.1μs	1.14	groupby.GroupByMethods.time_dtype_as_field('float', 'sem', 'direct', 1, 'cython')
+	13.6±0.7ms	15.4±0.08ms	1.14	series_methods.NanOps.time_func('sem', 1000000, 'boolean')
-	53.3±0.7μs	48.4±0.3μs	0.91	series_methods.NanOps.time_func('std', 1000, 'float64')
-	40.6±0.5μs	36.9±0.4μs	0.91	series_methods.NanOps.time_func('std', 1000, 'int8')
-	5.75±0.01ms	5.20±0.5ms	0.9	rolling.Methods.time_method('DataFrame', ('rolling', {'window': 10}), 'float', 'sem')
-	4.40±0.03ms	3.90±0.4ms	0.89	rolling.Methods.time_method('DataFrame', ('expanding', {}), 'int', 'sem')
-	2.73±0ms	2.44±0.3ms	0.89	rolling.Methods.time_method('DataFrame', ('rolling', {'window': 10}), 'float', 'std')
-	140±0.7ms	121±0.6ms	0.86	groupby.GroupByCythonAggEaDtypes.time_frame_agg('Int64', 'var')
-	99.8±1ms	79.8±0.5ms	0.8	groupby.GroupByCythonAggEaDtypes.time_frame_agg('Int32', 'var')
-	92.7±1ms	72.0±0.6ms	0.78	groupby.GroupByCythonAggEaDtypes.time_frame_agg('Float64', 'var')

[jbrockmendel]

possibly also #51332? #61677?

[Alvaro-Kothe]

I checked the reproduction from #51332. The results are exact when not using bottleneck. But due to bottleneck, I think it cannot be closed.

#61677 may be closed due to #63048.

[jbrockmendel]

@Alvaro-Kothe is this worth spending more time reviewing, or is it superceded by the SIMD PR?

[Alvaro-Kothe]

is this worth spending more time reviewing, or is it superceded by the SIMD PR?

This isn't superseded by the SIMD PR (#64905). But I think it's best to put this on a hold for now, because the SIMD code can be used for nanvar.