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ARROW-10304: [C++][Compute] Optimize variance kernel for integers - #8466

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ARROW-10304: [C++][Compute] Optimize variance kernel for integers#8466
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cyb70289:variance-integer

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@cyb70289cyb70289 commented Oct 15, 2020•
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Improve variance kernel performance for integers by leveraging
textbook one pass algorithm and integer arithmetic.

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https://issues.apache.org/jira/browse/ARROW-10304

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cyb70289 commented Oct 15, 2020•
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NOTE: Benchmark PR #8407 is not merged yet. Need to manually pull that PR to evaluation performance.

Tested on Xeon Gold 5218, clang-9.

 benchmark baseline contender change %
7 VarianceKernelInt32/1048576/0 1.805 GiB/sec 6.896 GiB/sec 282.033 'null_percent': 0.0
8 VarianceKernelInt32/1048576/10000 1.751 GiB/sec 5.113 GiB/sec 191.898 'null_percent': 0.01
16 VarianceKernelInt32/1048576/100 1.139 GiB/sec 2.748 GiB/sec 141.206 'null_percent': 1.0
18 VarianceKernelInt32/1048576/10 862.260 MiB/sec 1.547 GiB/sec 83.714 'null_percent': 10.0
1 VarianceKernelInt32/1048576/2 457.956 MiB/sec 769.333 MiB/sec 67.993 'null_percent': 50.0
9 VarianceKernelInt64/1048576/0 3.596 GiB/sec 4.949 GiB/sec 37.601 'null_percent': 0.0
5 VarianceKernelInt64/1048576/10000 3.484 GiB/sec 4.627 GiB/sec 32.832 'null_percent': 0.01
22 VarianceKernelInt64/1048576/100 2.285 GiB/sec 2.787 GiB/sec 21.955 'null_percent': 1.0
3 VarianceKernelFloat/1048576/2 397.394 MiB/sec 454.485 MiB/sec 14.366 'null_percent': 50.0
10 VarianceKernelFloat/1048576/10 790.793 MiB/sec 854.667 MiB/sec 8.077 'null_percent': 10.0
0 VarianceKernelInt64/1048576/1 1.220 TiB/sec 1.261 TiB/sec 3.353 null_percent': 100.0
14 VarianceKernelInt32/1048576/1 1.222 TiB/sec 1.254 TiB/sec 2.647 null_percent': 100.0
21 VarianceKernelDouble/1048576/1 1.206 TiB/sec 1.235 TiB/sec 2.379 null_percent': 100.0
17 VarianceKernelFloat/1048576/1 1.180 TiB/sec 1.206 TiB/sec 2.208 null_percent': 100.0
4 VarianceKernelDouble/1048576/10000 3.485 GiB/sec 3.475 GiB/sec -0.277 'null_percent': 0.01
23 VarianceKernelDouble/1048576/0 3.595 GiB/sec 3.575 GiB/sec -0.557 'null_percent': 0.0
2 VarianceKernelFloat/1048576/100 1.133 GiB/sec 1.126 GiB/sec -0.632 'null_percent': 1.0
13 VarianceKernelFloat/1048576/0 1.804 GiB/sec 1.792 GiB/sec -0.643 'null_percent': 0.0
20 VarianceKernelFloat/1048576/10000 1.750 GiB/sec 1.739 GiB/sec -0.677 'null_percent': 0.01
11 VarianceKernelDouble/1048576/100 2.287 GiB/sec 2.262 GiB/sec -1.092 'null_percent': 1.0
19 VarianceKernelDouble/1048576/2 866.210 MiB/sec 836.046 MiB/sec -3.482 'null_percent': 50.0
6 VarianceKernelDouble/1048576/10 1.658 GiB/sec 1.597 GiB/sec -3.672 'null_percent': 10.0
15 VarianceKernelInt64/1048576/10 1.687 GiB/sec 1.564 GiB/sec -7.304 'null_percent': 10.0
12 VarianceKernelInt64/1048576/2 914.036 MiB/sec 789.209 MiB/sec -13.657 'null_percent': 50.0

@cyb70289
cyb70289 marked this pull request as draft October 15, 2020 05:48
@cyb70289

cyb70289 commented Oct 15, 2020•
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Turn to draft. Will add 64bit integers optimization.

@cyb70289

cyb70289 commented Oct 16, 2020

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Added int64 optimization. Updated benchmark result. Ready for review.
Big improvement for int32. Moderate improvement for int64 with few null values.
Some drop for int64 with many null values.

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cyb70289 marked this pull request as ready for review October 16, 2020 07:01
pitrou
pitrou reviewed Oct 19, 2020
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Comment threadcpp/src/arrow/compute/kernels/aggregate_var_std.cc Outdated
@cyb70289@kszucs
ARROW-10304: [C++][Compute] Optimize variance kernel for integers
ce6ea45
Improve variance kernel performance for integers by leveraging
textbook one pass algorithm and integer arithmetic.
@pitrou

pitrou commented Oct 21, 2020

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Results on an AMD Zen 2 CPU:

VarianceKernelInt32/1048576/10000 140 us 140 us 5030 bytes_per_second=6.98658G/s null_percent=0.01 size=1048.58k
VarianceKernelInt32/1048576/100 216 us 216 us 3267 bytes_per_second=4.5294G/s null_percent=1 size=1048.58k
VarianceKernelInt32/1048576/10 397 us 397 us 1763 bytes_per_second=2.45765G/s null_percent=10 size=1048.58k
VarianceKernelInt32/1048576/2 974 us 974 us 718 bytes_per_second=1026.87M/s null_percent=50 size=1048.58k
VarianceKernelInt32/1048576/1 0.816 us 0.816 us 844145 bytes_per_second=1.1684T/s null_percent=100 size=1048.58k
VarianceKernelInt32/1048576/0 130 us 130 us 5414 bytes_per_second=7.51569G/s null_percent=0 size=1048.58k
VarianceKernelInt64/1048576/10000 135 us 135 us 5174 bytes_per_second=7.22877G/s null_percent=0.01 size=1048.58k
VarianceKernelInt64/1048576/100 260 us 260 us 2682 bytes_per_second=3.7503G/s null_percent=1 size=1048.58k
VarianceKernelInt64/1048576/10 440 us 440 us 1591 bytes_per_second=2.21931G/s null_percent=10 size=1048.58k
VarianceKernelInt64/1048576/2 884 us 884 us 783 bytes_per_second=1.10507G/s null_percent=50 size=1048.58k
VarianceKernelInt64/1048576/1 0.821 us 0.821 us 840316 bytes_per_second=1.16182T/s null_percent=100 size=1048.58k
VarianceKernelInt64/1048576/0 123 us 123 us 5620 bytes_per_second=7.94262G/s null_percent=0 size=1048.58k
VarianceKernelFloat/1048576/10000 366 us 366 us 1909 bytes_per_second=2.66576G/s null_percent=0.01 size=1048.58k
VarianceKernelFloat/1048576/100 751 us 751 us 909 bytes_per_second=1.3003G/s null_percent=1 size=1048.58k
VarianceKernelFloat/1048576/10 1097 us 1097 us 637 bytes_per_second=911.712M/s null_percent=10 size=1048.58k
VarianceKernelFloat/1048576/2 1803 us 1802 us 387 bytes_per_second=554.854M/s null_percent=50 size=1048.58k
VarianceKernelFloat/1048576/1 0.817 us 0.817 us 838993 bytes_per_second=1.1679T/s null_percent=100 size=1048.58k
VarianceKernelFloat/1048576/0 346 us 346 us 2021 bytes_per_second=2.82409G/s null_percent=0 size=1048.58k
VarianceKernelDouble/1048576/10000 184 us 184 us 3751 bytes_per_second=5.30153G/s null_percent=0.01 size=1048.58k
VarianceKernelDouble/1048576/100 372 us 372 us 1869 bytes_per_second=2.62218G/s null_percent=1 size=1048.58k
VarianceKernelDouble/1048576/10 549 us 549 us 1249 bytes_per_second=1.77993G/s null_percent=10 size=1048.58k
VarianceKernelDouble/1048576/2 909 us 909 us 741 bytes_per_second=1099.92M/s null_percent=50 size=1048.58k
VarianceKernelDouble/1048576/1 0.831 us 0.831 us 831173 bytes_per_second=1.14779T/s null_percent=100 size=1048.58k
VarianceKernelDouble/1048576/0 174 us 174 us 4050 bytes_per_second=5.62431G/s null_percent=0 size=1048.58k

I'm curious why Int64 would be faster than Double. Aren't they using the same algorithm? (and Int64 goes through an additional int-to-float conversion for each value)

@cyb70289

cyb70289 commented Oct 22, 2020•
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I'm curious why Int64 would be faster than Double. Aren't they using the same algorithm? (and Int64 goes through an additional int-to-float conversion for each value)

There's no int-to-float conversion in Int64 summation loop (sum to Int128). It's faster than double summation.
https://quick-bench.com/q/-P9E6tgtXqnVBpVmmN6piaZHeUA

@pitrou

pitrou commented Oct 22, 2020

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Ah, I hadn't noticed the SumType.

pitrou
pitrou approved these changes Oct 22, 2020
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+1

@cyb70289
cyb70289 deleted the variance-integer branch October 22, 2020 08:59
@asfimportasfimport mentioned this pull request Oct 22, 2020
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