tp: fold tree values in a streaming pipeline

[LalitMaganti]

Once rows are in tree order, a fold only needs one running value per node.
TreeAccumulateUp consumes child-first rows and adds each completed child into
its parent. TreeAccumulateDown consumes parent-first rows and carries each
parent total into its children.

Both operators append the accumulated value and stream batches without keeping
another copy of the input.

The SqlScan test covers the complete path from SQLite variants through type
validation, node numbering, ordering, and accumulation.

[github-actions]

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[sashwinbalaji]

There are CI failures as test written accoding to the old API

[sashwinbalaji]

how about TreeAccumulateSpec as it's in exec namespace

[sashwinbalaji]

Do we need this to be in .h as we will anywya talk in terms of OperatorState right?

[sashwinbalaji]

ok so I was thinking why we need all the nodes (by_node) as I thought (maybe incorrectly) we wanted DFS post-order and also #7214 said,

Folding up a tree needs every child before its parent, and needs the order
to be a depth first post-order so the fold can carry a stack of the current
path instead of an array indexed by node.

But then I checked the pr again and see in tree_order some early exits which won't necessarily guarantee DFS post order right ?

if (s.child_first) {
  // Already in the requested order, so no reordering is needed.
  s.order.clear();
  return true;
}
if (s.parent_first) {
  for (uint32_t row = 0; row < rows; ++row) {
    s.order[row] = rows - 1 - row;
  }
  return true;
}

Just to make sure, I asked AI to find a possible scenario and it said:

for example, we can have this tree:

      0
     / \
    1   2
    |   |
    3   4

3, 4, 1, 2, 0 has every child before its parent, so we would pass it through, but it is not DFS post-order. A DFS post-order would be 3, 1, 4, 2, 0.

So I guess this is why we need by_node here. Wanted to just make sure this is intentional. And, yes I see the comment on TreeParentFirst saying below so I think we just need to add similar comment for child first also.

// The order is parent first and nothing more: not a pre-order, so a fold
// down keeps a value per node rather than a path. The input columns are node
// numbers, which TreeNumberNodes produces. No column is added.