[LuciferYang]

What changes are proposed in this pull request?

VeloxIntermediateData maps regr_r2's Velox intermediate row to Spark's buffer attributes with Corr's order, because RegrR2 extends PearsonCorrelation. Velox's regr_r2 has a different layout, (c2, count, m2X, meanX, meanY, m2Y) with X being the second argument, and Spark's RegrR2(y, x) passes its arguments to PearsonCorrelation(y, x), so Spark's xAvg and xMk describe y. Plans that run one regr_r2 phase in Velox and another in vanilla Spark returned wrong results. When every phase runs in Velox, the two directions of the mapping cancel out.

This adds a RegrR2 order, ck, n, yMk, yAvg, xAvg, xMk, matched before the PearsonCorrelation case. The intermediate types are the same for both functions, so the type mapping is unchanged.

The Bolt backend has the same mapping in BoltIntermediateData. It is left for a follow-up because no CI job runs the Bolt tests.

How was this patch tested?

Added two tests to VeloxAggregateFunctionsSuite. Both fail without this change, and both check that the plan has a Velox aggregation and a vanilla Spark aggregation computing regr_r2.

• Velox partial, vanilla final: histogram_numeric(distinct z, 3) is not offloaded, so the last two of the four aggregations Spark plans for a single DISTINCT run in vanilla Spark and merge the buffer Velox produced.
• Vanilla partial, Velox final: the partial aggregation is forced to fall back. This test only compares groups where x and y both vary. For a constant x or y, Velox's final regr_r2 result matches Spark only from SPARK-55969 on, so it differs from every Spark version Gluten builds against except 4.2, whichever mapping is used.

Was this patch authored or co-authored using generative AI tooling?

Yes. Generated-by: Claude Opus.

Related issue: #13340.

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[jackylee-ch]

This PR currently has merge conflicts with main. Could you merge the latest main and resolve them?

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[LuciferYang]

Thanks, merged the latest main and resolved the conflict. It was only the aggregate import line in VeloxAggregateFunctionsSuite, which #13350 also changed.

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[LuciferYang]

@jackylee-ch The conflict is resolved. Could you take another look?