join_funcs.go

// Copyright 2020 The Cockroach Authors.
//
// Use of this software is governed by the Business Source License
// included in the file licenses/BSL.txt.
//
// As of the Change Date specified in that file, in accordance with
// the Business Source License, use of this software will be governed
// by the Apache License, Version 2.0, included in the file
// licenses/APL.txt.

package xform

import (
	"fmt"

	"github.com/cockroachdb/cockroach/pkg/sql/opt"
	"github.com/cockroachdb/cockroach/pkg/sql/opt/cat"
	"github.com/cockroachdb/cockroach/pkg/sql/opt/invertedidx"
	"github.com/cockroachdb/cockroach/pkg/sql/opt/memo"
	"github.com/cockroachdb/cockroach/pkg/sql/opt/props/physical"
	"github.com/cockroachdb/cockroach/pkg/sql/sem/tree"
	"github.com/cockroachdb/cockroach/pkg/sql/types"
	"github.com/cockroachdb/cockroach/pkg/util"
	"github.com/cockroachdb/errors"
)

// GenerateMergeJoins spawns MergeJoinOps, based on any interesting orderings.
func (c *CustomFuncs) GenerateMergeJoins(
	grp memo.RelExpr,
	originalOp opt.Operator,
	left, right memo.RelExpr,
	on memo.FiltersExpr,
	joinPrivate *memo.JoinPrivate,
) {
	if joinPrivate.Flags.Has(memo.DisallowMergeJoin) {
		return
	}

	leftProps := left.Relational()
	rightProps := right.Relational()

	leftEq, rightEq := memo.ExtractJoinEqualityColumns(
		leftProps.OutputCols, rightProps.OutputCols, on,
	)
	n := len(leftEq)
	if n == 0 {
		return
	}

	// We generate MergeJoin expressions based on interesting orderings from the
	// left side. The CommuteJoin rule will ensure that we actually try both
	// sides.
	orders := DeriveInterestingOrderings(left).Copy()
	orders.RestrictToCols(leftEq.ToSet())

	if !c.NoJoinHints(joinPrivate) || c.e.evalCtx.SessionData.ReorderJoinsLimit == 0 {
		// If we are using a hint, or the join limit is set to zero, the join won't
		// be commuted. Add the orderings from the right side.
		rightOrders := DeriveInterestingOrderings(right).Copy()
		rightOrders.RestrictToCols(leftEq.ToSet())
		orders = append(orders, rightOrders...)

		// If we don't allow hash join, we must do our best to generate a merge
		// join, even if it means sorting both sides. We append an arbitrary
		// ordering, in case the interesting orderings don't result in any merge
		// joins.
		o := make(opt.Ordering, len(leftEq))
		for i := range o {
			o[i] = opt.MakeOrderingColumn(leftEq[i], false /* descending */)
		}
		orders.Add(o)
	}

	if len(orders) == 0 {
		return
	}

	var colToEq util.FastIntMap
	for i := range leftEq {
		colToEq.Set(int(leftEq[i]), i)
		colToEq.Set(int(rightEq[i]), i)
	}

	var remainingFilters memo.FiltersExpr

	for _, o := range orders {
		if len(o) < n {
			// TODO(radu): we have a partial ordering on the equality columns. We
			// should augment it with the other columns (in arbitrary order) in the
			// hope that we can get the full ordering cheaply using a "streaming"
			// sort. This would not useful now since we don't support streaming sorts.
			continue
		}

		if remainingFilters == nil {
			remainingFilters = memo.ExtractRemainingJoinFilters(on, leftEq, rightEq)
		}

		merge := memo.MergeJoinExpr{Left: left, Right: right, On: remainingFilters}
		merge.JoinPrivate = *joinPrivate
		merge.JoinType = originalOp
		merge.LeftEq = make(opt.Ordering, n)
		merge.RightEq = make(opt.Ordering, n)
		merge.LeftOrdering.Columns = make([]physical.OrderingColumnChoice, 0, n)
		merge.RightOrdering.Columns = make([]physical.OrderingColumnChoice, 0, n)
		for i := 0; i < n; i++ {
			eqIdx, _ := colToEq.Get(int(o[i].ID()))
			l, r, descending := leftEq[eqIdx], rightEq[eqIdx], o[i].Descending()
			merge.LeftEq[i] = opt.MakeOrderingColumn(l, descending)
			merge.RightEq[i] = opt.MakeOrderingColumn(r, descending)
			merge.LeftOrdering.AppendCol(l, descending)
			merge.RightOrdering.AppendCol(r, descending)
		}

		// Simplify the orderings with the corresponding FD sets.
		merge.LeftOrdering.Simplify(&leftProps.FuncDeps)
		merge.RightOrdering.Simplify(&rightProps.FuncDeps)

		c.e.mem.AddMergeJoinToGroup(&merge, grp)
	}
}

// GenerateLookupJoins looks at the possible indexes and creates lookup join
// expressions in the current group. A lookup join can be created when the ON
// condition has equality constraints on a prefix of the index columns.
//
// There are two cases:
//
//  1. The index has all the columns we need; this is the simple case, where we
//     generate a LookupJoin expression in the current group:
//
//         Join                       LookupJoin(t@idx))
//         /   \                           |
//        /     \            ->            |
//      Input  Scan(t)                   Input
//
//
//  2. The index is not covering. We have to generate an index join above the
//     lookup join. Note that this index join is also implemented as a
//     LookupJoin, because an IndexJoin can only output columns from one table,
//     whereas we also need to output columns from Input.
//
//         Join                       LookupJoin(t@primary)
//         /   \                           |
//        /     \            ->            |
//      Input  Scan(t)                LookupJoin(t@idx)
//                                         |
//                                         |
//                                       Input
//
//     For example:
//      CREATE TABLE abc (a INT PRIMARY KEY, b INT, c INT)
//      CREATE TABLE xyz (x INT PRIMARY KEY, y INT, z INT, INDEX (y))
//      SELECT * FROM abc JOIN xyz ON a=y
//
//     We want to first join abc with the index on y (which provides columns y, x)
//     and then use a lookup join to retrieve column z. The "index join" (top
//     LookupJoin) will produce columns a,b,c,x,y; the lookup columns are just z
//     (the original index join produced x,y,z).
//
//     Note that the top LookupJoin "sees" column IDs from the table on both
//     "sides" (in this example x,y on the left and z on the right) but there is
//     no overlap.
//
// A lookup join can be created when the ON condition or implicit filters from
// CHECK constraints and computed columns constrain a prefix of the index
// columns to non-ranging constant values. To support this, the constant values
// are cross-joined with the input and used as key columns for the parent lookup
// join.
//
// For example, consider the tables and query below.
//
//   CREATE TABLE abc (a INT PRIMARY KEY, b INT, c INT)
//   CREATE TABLE xyz (
//     x INT PRIMARY KEY,
//     y INT,
//     z INT NOT NULL,
//     CHECK z IN (1, 2, 3),
//     INDEX (z, y)
//   )
//   SELECT a, x FROM abc JOIN xyz ON a=y
//
// GenerateLookupJoins will perform the following transformation.
//
//         Join                       LookupJoin(t@idx)
//         /   \                           |
//        /     \            ->            |
//      Input  Scan(t)                   Join
//                                       /   \
//                                      /     \
//                                    Input  Values(1, 2, 3)
//
// If a column is constrained to a single constant value, inlining normalization
// rules will reduce the cross join into a project.
//
//         Join                       LookupJoin(t@idx)
//         /   \                           |
//        /     \            ->            |
//      Input  Scan(t)                  Project
//                                         |
//                                         |
//                                       Input
//
func (c *CustomFuncs) GenerateLookupJoins(
	grp memo.RelExpr,
	joinType opt.Operator,
	input memo.RelExpr,
	scanPrivate *memo.ScanPrivate,
	on memo.FiltersExpr,
	joinPrivate *memo.JoinPrivate,
) {
	if joinPrivate.Flags.Has(memo.DisallowLookupJoinIntoRight) {
		return
	}
	md := c.e.mem.Metadata()
	inputProps := input.Relational()

	leftEq, rightEq := memo.ExtractJoinEqualityColumns(inputProps.OutputCols, scanPrivate.Cols, on)
	n := len(leftEq)
	if n == 0 {
		return
	}

	// Generate implicit filters from CHECK constraints and computed columns as
	// optional filters to help generate lookup join keys.
	optionalFilters := c.checkConstraintFilters(scanPrivate.Table)
	computedColFilters := c.computedColFilters(scanPrivate.Table, on, optionalFilters)
	optionalFilters = append(optionalFilters, computedColFilters...)

	var pkCols opt.ColList
	var iter scanIndexIter
	iter.Init(c.e.mem, &c.im, scanPrivate, on, rejectInvertedIndexes)
	iter.ForEach(func(index cat.Index, onFilters memo.FiltersExpr, indexCols opt.ColSet, isCovering bool) {
		// Find the longest prefix of index key columns that are constrained by
		// an equality with another column or a constant.
		numIndexKeyCols := index.LaxKeyColumnCount()

		var constFilters memo.FiltersExpr
		allFilters := append(onFilters, optionalFilters...)

		// Check if the first column in the index has an equality constraint, or if
		// it is constrained to a constant value. This check doesn't guarantee that
		// we will find lookup join key columns, but it avoids the unnecessary work
		// in most cases.
		firstIdxCol := scanPrivate.Table.IndexColumnID(index, 0)
		if _, ok := rightEq.Find(firstIdxCol); !ok {
			if _, _, ok := c.findJoinFilterConstants(allFilters, firstIdxCol); !ok {
				return
			}
		}

		lookupJoin := memo.LookupJoinExpr{Input: input}
		lookupJoin.JoinPrivate = *joinPrivate
		lookupJoin.JoinType = joinType
		lookupJoin.Table = scanPrivate.Table
		lookupJoin.Index = index.Ordinal()

		lookupJoin.KeyCols = make(opt.ColList, 0, numIndexKeyCols)
		rightSideCols := make(opt.ColList, 0, numIndexKeyCols)

		// All the lookup conditions must apply to the prefix of the index and so
		// the projected columns created must be created in order.
		for j := 0; j < numIndexKeyCols; j++ {
			idxCol := scanPrivate.Table.IndexColumnID(index, j)
			if eqIdx, ok := rightEq.Find(idxCol); ok {
				lookupJoin.KeyCols = append(lookupJoin.KeyCols, leftEq[eqIdx])
				rightSideCols = append(rightSideCols, idxCol)
				continue
			}

			// Try to find a filter that constrains this column to non-NULL
			// constant values. We cannot use a NULL value because the lookup
			// join implements logic equivalent to simple equality between
			// columns (where NULL never equals anything).
			foundVals, allIdx, ok := c.findJoinFilterConstants(allFilters, idxCol)
			if !ok {
				break
			}

			// We will join these constant values with the input to make
			// equality columns for the lookup join.
			if constFilters == nil {
				constFilters = make(memo.FiltersExpr, 0, numIndexKeyCols-j)
			}

			idxColType := c.e.f.Metadata().ColumnMeta(idxCol).Type
			constColAlias := fmt.Sprintf("lookup_join_const_col_@%d", idxCol)
			join, constColID := c.constructJoinWithConstants(
				lookupJoin.Input,
				foundVals,
				idxColType,
				constColAlias,
			)

			lookupJoin.Input = join
			lookupJoin.KeyCols = append(lookupJoin.KeyCols, constColID)
			rightSideCols = append(rightSideCols, idxCol)
			constFilters = append(constFilters, allFilters[allIdx])
		}

		if len(lookupJoin.KeyCols) == 0 {
			// We couldn't find equality columns which we can lookup.
			return
		}

		tableFDs := memo.MakeTableFuncDep(md, scanPrivate.Table)
		// A lookup join will drop any input row which contains NULLs, so a lax key
		// is sufficient.
		lookupJoin.LookupColsAreTableKey = tableFDs.ColsAreLaxKey(rightSideCols.ToSet())

		// Remove the redundant filters and update the lookup condition.
		lookupJoin.On = memo.ExtractRemainingJoinFilters(onFilters, lookupJoin.KeyCols, rightSideCols)
		lookupJoin.On.RemoveCommonFilters(constFilters)
		lookupJoin.ConstFilters = constFilters

		if isCovering {
			// Case 1 (see function comment).
			lookupJoin.Cols = scanPrivate.Cols.Union(inputProps.OutputCols)
			c.e.mem.AddLookupJoinToGroup(&lookupJoin, grp)
			return
		}

		_, isPartial := index.Predicate()
		if isPartial && (joinType == opt.SemiJoinOp || joinType == opt.AntiJoinOp) {
			// Typically, the index must cover all columns in the scanPrivate in
			// order to generate a lookup join without an additional index join
			// (case 1, see function comment). However, if the index is a
			// partial index, the filters remaining after proving
			// filter-predicate implication may no longer reference some
			// columns. A lookup semi- or anti-join can be generated if the
			// columns in the new filters from the right side of the join are
			// covered by the index. Consider the example:
			//
			//   CREATE TABLE a (a INT)
			//   CREATE TABLE xy (x INT, y INT, INDEX (x) WHERE y > 0)
			//
			//   SELECT a FROM a WHERE EXISTS (SELECT 1 FROM xyz WHERE a = x AND y > 0)
			//
			// The original ON filters of the semi-join are (a = x AND y > 0).
			// The (y > 0) expression in the filter is an exact match to the
			// partial index predicate, so the remaining ON filters are (a = x).
			// Column y is no longer referenced, so a lookup semi-join can be
			// created despite the partial index not covering y.
			//
			// Note that this is a special case that only works for semi- and
			// anti-joins because they never include columns from the right side
			// in their output columns. Other joins include columns from the
			// right side in their output columns, so even if the ON filters no
			// longer reference an un-covered column, they must be fetched (case
			// 2, see function comment).
			filterColsFromRight := scanPrivate.Cols.Intersection(onFilters.OuterCols())
			if filterColsFromRight.SubsetOf(indexCols) {
				lookupJoin.Cols = filterColsFromRight.Union(inputProps.OutputCols)
				c.e.mem.AddLookupJoinToGroup(&lookupJoin, grp)
				return
			}
		}

		// All code that follows is for case 2 (see function comment).

		if scanPrivate.Flags.NoIndexJoin {
			return
		}
		if joinType == opt.SemiJoinOp || joinType == opt.AntiJoinOp {
			// We cannot use a non-covering index for semi and anti join. Note that
			// since the semi/anti join doesn't pass through any columns, "non
			// covering" here means that not all columns in the ON condition are
			// available.
			//
			// TODO(radu): We could create a semi/anti join on top of an inner join if
			// the lookup columns form a key (to guarantee that input rows are not
			// duplicated by the inner join).
			return
		}

		if pkCols == nil {
			pkIndex := md.Table(scanPrivate.Table).Index(cat.PrimaryIndex)
			pkCols = make(opt.ColList, pkIndex.KeyColumnCount())
			for i := range pkCols {
				pkCols[i] = scanPrivate.Table.IndexColumnID(pkIndex, i)
			}
		}

		// The lower LookupJoin must return all PK columns (they are needed as key
		// columns for the index join).
		lookupJoin.Cols = scanPrivate.Cols.Intersection(indexCols)
		for i := range pkCols {
			lookupJoin.Cols.Add(pkCols[i])
		}
		lookupJoin.Cols.UnionWith(inputProps.OutputCols)

		var indexJoin memo.LookupJoinExpr

		// onCols are the columns that the ON condition in the (lower) lookup join
		// can refer to: input columns, or columns available in the index.
		onCols := indexCols.Union(inputProps.OutputCols)
		if c.FiltersBoundBy(lookupJoin.On, onCols) {
			// The ON condition refers only to the columns available in the index.
			//
			// For LeftJoin, both LookupJoins perform a LeftJoin. A null-extended row
			// from the lower LookupJoin will not have any matches in the top
			// LookupJoin (it has NULLs on key columns) and will get null-extended
			// there as well.
			indexJoin.On = memo.TrueFilter
		} else {
			// ON has some conditions that are bound by the columns in the index (at
			// the very least, the equality conditions we used for KeyCols), and some
			// conditions that refer to other columns. We can put the former in the
			// lower LookupJoin and the latter in the index join.
			//
			// This works for InnerJoin but not for LeftJoin because of a
			// technicality: if an input (left) row has matches in the lower
			// LookupJoin but has no matches in the index join, only the columns
			// looked up by the top index join get NULL-extended.
			if joinType == opt.LeftJoinOp {
				// TODO(radu): support LeftJoin, perhaps by looking up all columns and
				// discarding columns that are already available from the lower
				// LookupJoin. This requires a projection to avoid having the same
				// ColumnIDs on both sides of the index join.
				return
			}
			conditions := lookupJoin.On
			lookupJoin.On = c.ExtractBoundConditions(conditions, onCols)
			indexJoin.On = c.ExtractUnboundConditions(conditions, onCols)
		}

		indexJoin.Input = c.e.f.ConstructLookupJoin(
			lookupJoin.Input,
			lookupJoin.On,
			&lookupJoin.LookupJoinPrivate,
		)
		indexJoin.JoinType = joinType
		indexJoin.Table = scanPrivate.Table
		indexJoin.Index = cat.PrimaryIndex
		indexJoin.KeyCols = pkCols
		indexJoin.Cols = scanPrivate.Cols.Union(inputProps.OutputCols)
		indexJoin.LookupColsAreTableKey = true

		// Create the LookupJoin for the index join in the same group.
		c.e.mem.AddLookupJoinToGroup(&indexJoin, grp)
	})
}

// constructContinuationColumnForPairedJoin constructs a continuation column
// ID for the paired-joiners used for left outer/semi/anti joins when the
// first join generates false positives (due to an inverted index or
// non-covering index). The first join will be either a left outer join or
// an inner join.
func (c *CustomFuncs) constructContinuationColumnForPairedJoin() opt.ColumnID {
	return c.e.f.Metadata().AddColumn("continuation", c.BoolType())
}

// GenerateInvertedJoins is similar to GenerateLookupJoins, but instead
// of generating lookup joins with regular indexes, it generates lookup joins
// with inverted indexes. Similar to GenerateLookupJoins, there are two cases
// depending on whether or not the index is covering. See the comment above
// GenerateLookupJoins for details.
func (c *CustomFuncs) GenerateInvertedJoins(
	grp memo.RelExpr,
	joinType opt.Operator,
	input memo.RelExpr,
	scanPrivate *memo.ScanPrivate,
	on memo.FiltersExpr,
	joinPrivate *memo.JoinPrivate,
) {
	if joinPrivate.Flags.Has(memo.DisallowInvertedJoinIntoRight) {
		return
	}

	inputCols := input.Relational().OutputCols
	var pkCols opt.ColList
	var leftEqCols opt.ColList
	var rightEqCols opt.ColList
	var rightSideCols opt.ColList

	var iter scanIndexIter
	iter.Init(c.e.mem, &c.im, scanPrivate, on, rejectNonInvertedIndexes)
	iter.ForEach(func(index cat.Index, on memo.FiltersExpr, indexCols opt.ColSet, isCovering bool) {
		invertedJoin := memo.InvertedJoinExpr{Input: input}
		numPrefixCols := index.NonInvertedPrefixColumnCount()

		// Only calculate the left and right equality columns if there is a
		// multi-column inverted index.
		if numPrefixCols > 0 && leftEqCols == nil {
			inputProps := input.Relational()
			leftEqCols, rightEqCols = memo.ExtractJoinEqualityColumns(inputProps.OutputCols, scanPrivate.Cols, on)
		}

		// The non-inverted prefix columns of a multi-column inverted index must
		// be constrained in order to perform an inverted join. We attempt to
		// constrain each prefix column to non-ranging constant values. These
		// values are joined with the input to create key columns for the
		// InvertedJoin, similar to GenerateLookupJoins.
		// TODO(mgartner): Try to constrain prefix columns with CHECK
		// constraints and computed column expressions.
		var constFilters memo.FiltersExpr
		for i, n := 0, numPrefixCols; i < n; i++ {
			prefixCol := scanPrivate.Table.IndexColumnID(index, i)

			// Check if prefixCol is constrained by an equality constraint.
			if eqIdx, ok := rightEqCols.Find(prefixCol); ok {
				invertedJoin.PrefixKeyCols = append(invertedJoin.PrefixKeyCols, leftEqCols[eqIdx])
				rightSideCols = append(rightSideCols, prefixCol)
				continue
			}

			// Try to constrain prefixCol to constant, non-ranging values.
			foundVals, onIdx, ok := c.findJoinFilterConstants(on, prefixCol)
			if !ok {
				// Cannot constrain prefix column and therefore cannot generate
				// an inverted join.
				return
			}

			// We will join these constant values with the input to make
			// equality columns for the inverted join.
			if constFilters == nil {
				constFilters = make(memo.FiltersExpr, 0, n)
			}

			prefixColType := c.e.f.Metadata().ColumnMeta(prefixCol).Type
			constColAlias := fmt.Sprintf("inverted_join_const_col_@%d", prefixCol)
			join, constColID := c.constructJoinWithConstants(
				invertedJoin.Input,
				foundVals,
				prefixColType,
				constColAlias,
			)

			invertedJoin.Input = join
			invertedJoin.PrefixKeyCols = append(invertedJoin.PrefixKeyCols, constColID)
			constFilters = append(constFilters, on[onIdx])
		}

		// Remove the redundant filters and update the ON condition if there are
		// non-inverted prefix columns that have been constrained.
		if len(rightSideCols) > 0 || len(constFilters) > 0 {
			on = memo.ExtractRemainingJoinFilters(on, invertedJoin.PrefixKeyCols, rightSideCols)
			on.RemoveCommonFilters(constFilters)
			invertedJoin.ConstFilters = constFilters
		}

		// Check whether the filter can constrain the inverted column.
		invertedExpr := invertedidx.TryJoinInvertedIndex(
			c.e.evalCtx.Context, c.e.f, on, scanPrivate.Table, index, inputCols,
		)
		if invertedExpr == nil {
			return
		}

		// All geospatial and JSON inverted joins that are currently supported
		// are not covering, so we must wrap them in an index join.
		// TODO(rytaft): Avoid adding an index join if possible for Array
		// inverted joins.
		if scanPrivate.Flags.NoIndexJoin {
			return
		}

		if pkCols == nil {
			tab := c.e.mem.Metadata().Table(scanPrivate.Table)
			pkIndex := tab.Index(cat.PrimaryIndex)
			pkCols = make(opt.ColList, pkIndex.KeyColumnCount())
			for i := range pkCols {
				pkCols[i] = scanPrivate.Table.IndexColumnID(pkIndex, i)
			}
		}

		// Though the index is marked as containing the column being indexed, it
		// doesn't actually, and it is only valid to extract the primary key
		// columns and non-inverted prefix columns from it.
		indexCols = pkCols.ToSet()
		for i, n := 0, index.NonInvertedPrefixColumnCount(); i < n; i++ {
			prefixCol := scanPrivate.Table.IndexColumnID(index, i)
			indexCols.Add(prefixCol)
		}

		continuationCol := opt.ColumnID(0)
		invertedJoinType := joinType
		// Anti joins are converted to a pair consisting of a left inverted join
		// and anti lookup join.
		if joinType == opt.LeftJoinOp || joinType == opt.AntiJoinOp {
			continuationCol = c.constructContinuationColumnForPairedJoin()
			invertedJoinType = opt.LeftJoinOp
		} else if joinType == opt.SemiJoinOp {
			// Semi joins are converted to a pair consisting of an inner inverted
			// join and semi lookup join.
			continuationCol = c.constructContinuationColumnForPairedJoin()
			invertedJoinType = opt.InnerJoinOp
		}
		invertedJoin.JoinPrivate = *joinPrivate
		invertedJoin.JoinType = invertedJoinType
		invertedJoin.Table = scanPrivate.Table
		invertedJoin.Index = index.Ordinal()
		invertedJoin.InvertedExpr = invertedExpr
		invertedJoin.InvertedCol = scanPrivate.Table.IndexColumnID(index, 0)
		invertedJoin.Cols = indexCols.Union(inputCols)
		if continuationCol != 0 {
			invertedJoin.Cols.Add(continuationCol)
			invertedJoin.IsFirstJoinInPairedJoiner = true
			invertedJoin.ContinuationCol = continuationCol
		}

		var indexJoin memo.LookupJoinExpr

		// ON may have some conditions that are bound by the columns in the index
		// and some conditions that refer to other columns. We can put the former
		// in the InvertedJoin and the latter in the index join.
		invertedJoin.On = c.ExtractBoundConditions(on, invertedJoin.Cols)
		indexJoin.On = c.ExtractUnboundConditions(on, invertedJoin.Cols)

		indexJoin.Input = c.e.f.ConstructInvertedJoin(
			invertedJoin.Input,
			invertedJoin.On,
			&invertedJoin.InvertedJoinPrivate,
		)
		indexJoin.JoinType = joinType
		indexJoin.Table = scanPrivate.Table
		indexJoin.Index = cat.PrimaryIndex
		indexJoin.KeyCols = pkCols
		indexJoin.Cols = scanPrivate.Cols.Union(inputCols)
		indexJoin.LookupColsAreTableKey = true
		if continuationCol != 0 {
			indexJoin.IsSecondJoinInPairedJoiner = true
		}

		// If this is not a semi- or anti-join, create the LookupJoin for the index
		// join in the same group.
		if joinType != opt.SemiJoinOp && joinType != opt.AntiJoinOp {
			c.e.mem.AddLookupJoinToGroup(&indexJoin, grp)
			return
		}

		// Some semi and anti joins require a project on top (see below). Avoid
		// adding that projection if it will be a no-op (i.e., we already have
		// the correct output columns from the lookup join).
		outputCols := indexJoin.Cols.Intersection(indexJoin.Input.Relational().OutputCols)
		if outputCols.SubsetOf(inputCols) {
			c.e.mem.AddLookupJoinToGroup(&indexJoin, grp)
			return
		}

		// For some semi and anti joins, we need to add a project on top to ensure
		// that only the original left-side columns are output. Normally, the
		// LookupJoin would be able to perform the necessary projection for semi
		// and anti joins by intersecting Cols with the OutputCols of its input,
		// but that doesn't work for paired joins since the input to the second
		// join may include more columns than the original input.
		var project memo.ProjectExpr
		project.Input = c.e.f.ConstructLookupJoin(
			indexJoin.Input,
			indexJoin.On,
			&indexJoin.LookupJoinPrivate,
		)
		project.Passthrough = grp.Relational().OutputCols
		c.e.mem.AddProjectToGroup(&project, grp)
	})
}

// findJoinFilterConstants tries to find a filter that is exactly equivalent to
// constraining the given column to a constant value or a set of constant
// values. If successful, the constant values and the index of the constraining
// FiltersItem are returned. Note that the returned constant values do not
// contain NULL.
func (c *CustomFuncs) findJoinFilterConstants(
	filters memo.FiltersExpr, col opt.ColumnID,
) (values tree.Datums, filterIdx int, ok bool) {
	for filterIdx := range filters {
		props := filters[filterIdx].ScalarProps()
		if props.TightConstraints {
			constCol, constVals, ok := props.Constraints.HasSingleColumnConstValues(c.e.evalCtx)
			if !ok || constCol != col {
				continue
			}
			hasNull := false
			for i := range constVals {
				if constVals[i] == tree.DNull {
					hasNull = true
					break
				}
			}
			if !hasNull {
				return constVals, filterIdx, true
			}
		}
	}
	return nil, -1, false
}

// constructJoinWithConstants constructs a cross join that joins every row in
// the input with every value in vals. The cross join will be converted into a
// projection by inlining normalization rules if vals contains only a single
// value. The constructed expression and the column ID of the constant value
// column are returned.
func (c *CustomFuncs) constructJoinWithConstants(
	input memo.RelExpr, vals tree.Datums, typ *types.T, columnAlias string,
) (join memo.RelExpr, constColID opt.ColumnID) {
	constColID = c.e.f.Metadata().AddColumn(columnAlias, typ)
	tupleType := types.MakeTuple([]*types.T{typ})

	constRows := make(memo.ScalarListExpr, len(vals))
	for i := range constRows {
		constRows[i] = c.e.f.ConstructTuple(
			memo.ScalarListExpr{c.e.f.ConstructConst(vals[i], typ)},
			tupleType,
		)
	}

	values := c.e.f.ConstructValues(
		constRows,
		&memo.ValuesPrivate{
			Cols: opt.ColList{constColID},
			ID:   c.e.mem.Metadata().NextUniqueID(),
		},
	)

	// We purposefully do not propagate any join flags into this JoinPrivate. If
	// a LOOKUP join hint was propagated to this cross join, the cost of the
	// cross join would be artificially inflated and the lookup join would not
	// be selected as the optimal plan.
	join = c.e.f.ConstructInnerJoin(input, values, nil /* on */, &memo.JoinPrivate{})
	return join, constColID
}

// ShouldReorderJoins returns whether the optimizer should attempt to find
// a better ordering of inner joins. This is the case if the given expression is
// the first expression of its group, and the join tree rooted at the expression
// has not previously been reordered. This is to avoid duplicate work. In
// addition, a join cannot be reordered if it has join hints.
func (c *CustomFuncs) ShouldReorderJoins(root memo.RelExpr) bool {
	// Only match the first expression of a group to avoid duplicate work.
	if root != root.FirstExpr() {
		return false
	}

	private, ok := root.Private().(*memo.JoinPrivate)
	if !ok {
		panic(errors.AssertionFailedf("operator does not have a join private: %v", root.Op()))
	}

	// Ensure that this join expression was not added to the memo by a previous
	// reordering, as well as that the join does not have hints.
	return !private.WasReordered && c.NoJoinHints(private)
}

// ReorderJoins adds alternate orderings of the given join tree to the memo. The
// first expression of the memo group is used for construction of the join
// graph. For more information, see the comment in join_order_builder.go.
func (c *CustomFuncs) ReorderJoins(grp memo.RelExpr) memo.RelExpr {
	c.e.o.JoinOrderBuilder().Init(c.e.f, c.e.evalCtx)
	c.e.o.JoinOrderBuilder().Reorder(grp.FirstExpr())
	return grp
}

// IsSimpleEquality returns true if all of the filter conditions are equalities
// between simple data types (constants, variables, tuples and NULL).
func (c *CustomFuncs) IsSimpleEquality(filters memo.FiltersExpr) bool {
	for i := range filters {
		eqFilter, ok := filters[i].Condition.(*memo.EqExpr)
		if !ok {
			return false
		}

		left, right := eqFilter.Left, eqFilter.Right
		switch left.Op() {
		case opt.VariableOp, opt.ConstOp, opt.NullOp, opt.TupleOp:
		default:
			return false
		}

		switch right.Op() {
		case opt.VariableOp, opt.ConstOp, opt.NullOp, opt.TupleOp:
		default:
			return false
		}
	}

	return true
}

// ConvertIndexToLookupJoinPrivate constructs a new LookupJoinPrivate using the
// given IndexJoinPrivate with the given output columns.
func (c *CustomFuncs) ConvertIndexToLookupJoinPrivate(
	indexPrivate *memo.IndexJoinPrivate, outCols opt.ColSet,
) *memo.LookupJoinPrivate {
	// Retrieve an ordered list of primary key columns from the lookup table;
	// these will form the lookup key.
	md := c.e.mem.Metadata()
	primaryIndex := md.Table(indexPrivate.Table).Index(cat.PrimaryIndex)
	lookupCols := make(opt.ColList, primaryIndex.KeyColumnCount())
	for i := 0; i < primaryIndex.KeyColumnCount(); i++ {
		lookupCols[i] = indexPrivate.Table.IndexColumnID(primaryIndex, i)
	}

	return &memo.LookupJoinPrivate{
		JoinType:              opt.InnerJoinOp,
		Table:                 indexPrivate.Table,
		Index:                 cat.PrimaryIndex,
		KeyCols:               lookupCols,
		Cols:                  outCols,
		LookupColsAreTableKey: true,
		ConstFilters:          nil,
		JoinPrivate:           memo.JoinPrivate{},
	}
}