statistics: compute and store column order correlation with handle

executor/analyze.go

@@ -254,7 +254,6 @@ type AnalyzeColumnsExec struct {
 	pkInfo          *model.ColumnInfo
 	concurrency     int
 	priority        int
-	keepOrder       bool
 	analyzePB       *tipb.AnalyzeReq
 	resultHandler   *tableResultHandler
 	maxNumBuckets   uint64
@@ -268,7 +267,7 @@ func (e *AnalyzeColumnsExec) open() error {
 		ranges = ranger.FullIntRange(false)
 	}
 	e.resultHandler = &tableResultHandler{}
-	firstPartRanges, secondPartRanges := splitRanges(ranges, e.keepOrder)
+	firstPartRanges, secondPartRanges := splitRanges(ranges, true)
 	firstResult, err := e.buildResp(firstPartRanges)
 	if err != nil {
 		return errors.Trace(err)
@@ -289,9 +288,11 @@ func (e *AnalyzeColumnsExec) open() error {
 
 func (e *AnalyzeColumnsExec) buildResp(ranges []*ranger.Range) (distsql.SelectResult, error) {
 	var builder distsql.RequestBuilder
+	// Always set KeepOrder of the request to be true, in order to compute
+	// correct `correlation` of columns.
 	kvReq, err := builder.SetTableRanges(e.physicalTableID, ranges, nil).
 		SetAnalyzeRequest(e.analyzePB).
-		SetKeepOrder(e.keepOrder).
+		SetKeepOrder(true).
 		SetConcurrency(e.concurrency).
 		Build()
 	if err != nil {
@@ -363,7 +364,8 @@ func (e *AnalyzeColumnsExec) buildStats() (hists []*statistics.Histogram, cms []
 	}
 	for i, col := range e.colsInfo {
 		for j, s := range collectors[i].Samples {
-			collectors[i].Samples[j], err = tablecodec.DecodeColumnValue(s.GetBytes(), &col.FieldType, timeZone)
+			collectors[i].Samples[j].Ordinal = j
+			collectors[i].Samples[j].Value, err = tablecodec.DecodeColumnValue(s.Value.GetBytes(), &col.FieldType, timeZone)
 			if err != nil {
 				return nil, nil, errors.Trace(err)
 			}

executor/analyze_test.go

@@ -54,7 +54,7 @@ PARTITION BY RANGE ( a ) (
 	for _, def := range pi.Definitions {
 		statsTbl := handle.GetPartitionStats(table.Meta(), def.ID)
 		c.Assert(statsTbl.Pseudo, IsFalse)
-		c.Assert(len(statsTbl.Columns), Equals, 2)
+		c.Assert(len(statsTbl.Columns), Equals, 3)
 		c.Assert(len(statsTbl.Indices), Equals, 1)
 		for _, col := range statsTbl.Columns {
 			c.Assert(col.Len(), Greater, 0)
@@ -80,7 +80,7 @@ PARTITION BY RANGE ( a ) (
 		statsTbl := handle.GetPartitionStats(table.Meta(), def.ID)
 		if i == 0 {
 			c.Assert(statsTbl.Pseudo, IsFalse)
-			c.Assert(len(statsTbl.Columns), Equals, 2)
+			c.Assert(len(statsTbl.Columns), Equals, 3)
 			c.Assert(len(statsTbl.Indices), Equals, 1)
 		} else {
 			c.Assert(statsTbl.Pseudo, IsTrue)

executor/builder.go

@@ -1360,9 +1360,7 @@ func (b *executorBuilder) buildAnalyzeIndexPushdown(task plannercore.AnalyzeInde
 
 func (b *executorBuilder) buildAnalyzeColumnsPushdown(task plannercore.AnalyzeColumnsTask, maxNumBuckets uint64) *AnalyzeColumnsExec {
 	cols := task.ColsInfo
-	keepOrder := false
 	if task.PKInfo != nil {
-		keepOrder = true
 		cols = append([]*model.ColumnInfo{task.PKInfo}, cols...)
 	}
 
@@ -1373,7 +1371,6 @@ func (b *executorBuilder) buildAnalyzeColumnsPushdown(task plannercore.AnalyzeCo
 		colsInfo:        task.ColsInfo,
 		pkInfo:          task.PKInfo,
 		concurrency:     b.ctx.GetSessionVars().DistSQLScanConcurrency,
-		keepOrder:       keepOrder,
 		analyzePB: &tipb.AnalyzeReq{
 			Tp:             tipb.AnalyzeType_TypeColumn,
 			StartTs:        math.MaxUint64,

executor/show_stats.go

@@ -100,6 +100,7 @@ func (e *ShowExec) histogramToRow(dbName, tblName, partitionName, colName string
 		hist.NDV,
 		hist.NullCount,
 		avgColSize,
+		hist.Correlation,
 	})
 }
 

executor/show_stats_test.go

@@ -90,14 +90,16 @@ func (s *testSuite1) TestShowPartitionStats(c *C) {
 	c.Assert(result.Rows()[0][2], Equals, "p0")
 
 	result = tk.MustQuery("show stats_histograms").Sort()
-	c.Assert(len(result.Rows()), Equals, 2)
+	c.Assert(len(result.Rows()), Equals, 3)
 	c.Assert(result.Rows()[0][2], Equals, "p0")
 	c.Assert(result.Rows()[0][3], Equals, "a")
 	c.Assert(result.Rows()[1][2], Equals, "p0")
-	c.Assert(result.Rows()[1][3], Equals, "idx")
+	c.Assert(result.Rows()[1][3], Equals, "b")
+	c.Assert(result.Rows()[2][2], Equals, "p0")
+	c.Assert(result.Rows()[2][3], Equals, "idx")
 
 	result = tk.MustQuery("show stats_buckets").Sort()
-	result.Check(testkit.Rows("test t p0 a 0 0 1 1 1 1", "test t p0 idx 1 0 1 1 1 1"))
+	result.Check(testkit.Rows("test t p0 a 0 0 1 1 1 1", "test t p0 b 0 0 1 1 1 1", "test t p0 idx 1 0 1 1 1 1"))
 
 	result = tk.MustQuery("show stats_healthy")
 	result.Check(testkit.Rows("test t p0 100"))

planner/core/cbo_test.go

@@ -483,7 +483,7 @@ func (s *testAnalyzeSuite) TestAnalyze(c *C) {
 	}{
 		{
 			sql:  "analyze table t3",
-			best: "Analyze{Index(a),Table(b)}",
+			best: "Analyze{Index(a),Table(a, b)}",
 		},
 		// Test analyze full table.
 		{
@@ -708,10 +708,10 @@ func (s *testAnalyzeSuite) TestCorrelatedEstimation(c *C) {
 			"  ├─TableReader_12 10.00 root data:TableScan_11",
 			"  │ └─TableScan_11 10.00 cop table:t, range:[-inf,+inf], keep order:false",
 			"  └─MaxOneRow_13 1.00 root ",
-			"    └─Projection_14 0.00 root concat(cast(t1.a), \",\", cast(t1.b))",
-			"      └─IndexLookUp_21 0.00 root ",
+			"    └─Projection_14 0.10 root concat(cast(t1.a), \",\", cast(t1.b))",
+			"      └─IndexLookUp_21 0.10 root ",
 			"        ├─IndexScan_18 1.00 cop table:t1, index:c, range: decided by [eq(t1.c, test.t.c)], keep order:false",
-			"        └─Selection_20 0.00 cop eq(t1.a, test.t.a)",
+			"        └─Selection_20 0.10 cop eq(t1.a, test.t.a)",
 			"          └─TableScan_19 1.00 cop table:t, keep order:false",
 		))
 }

planner/core/planbuilder.go

@@ -645,36 +645,23 @@ func (b *PlanBuilder) buildCheckIndexSchema(tn *ast.TableName, indexName string)
 // getColsInfo returns the info of index columns, normal columns and primary key.
 func getColsInfo(tn *ast.TableName) (indicesInfo []*model.IndexInfo, colsInfo []*model.ColumnInfo, pkCol *model.ColumnInfo) {
 	tbl := tn.TableInfo
-	// idxNames contains all the normal columns that can be analyzed more effectively, because those columns occur as index
-	// columns or primary key columns with integer type.
-	var idxNames []string
 	if tbl.PKIsHandle {
 		for _, col := range tbl.Columns {
 			if mysql.HasPriKeyFlag(col.Flag) {
-				idxNames = append(idxNames, col.Name.L)
 				pkCol = col
 			}
 		}
 	}
 	for _, idx := range tn.TableInfo.Indices {
 		if idx.State == model.StatePublic {
 			indicesInfo = append(indicesInfo, idx)
-			if len(idx.Columns) == 1 {
-				idxNames = append(idxNames, idx.Columns[0].Name.L)
-			}
 		}
 	}
 	for _, col := range tbl.Columns {
-		isIndexCol := false
-		for _, idx := range idxNames {
-			if idx == col.Name.L {
-				isIndexCol = true
-				break
-			}
-		}
-		if !isIndexCol {
-			colsInfo = append(colsInfo, col)
+		if col == pkCol {
+			continue
 		}
+		colsInfo = append(colsInfo, col)
 	}
 	return
 }
@@ -1782,9 +1769,9 @@ func buildShowSchema(s *ast.ShowStmt, isView bool) (schema *expression.Schema) {
 		names = []string{"Db_name", "Table_name", "Partition_name", "Update_time", "Modify_count", "Row_count"}
 		ftypes = []byte{mysql.TypeVarchar, mysql.TypeVarchar, mysql.TypeVarchar, mysql.TypeDatetime, mysql.TypeLonglong, mysql.TypeLonglong}
 	case ast.ShowStatsHistograms:
-		names = []string{"Db_name", "Table_name", "Partition_name", "Column_name", "Is_index", "Update_time", "Distinct_count", "Null_count", "Avg_col_size"}
+		names = []string{"Db_name", "Table_name", "Partition_name", "Column_name", "Is_index", "Update_time", "Distinct_count", "Null_count", "Avg_col_size", "Correlation"}
 		ftypes = []byte{mysql.TypeVarchar, mysql.TypeVarchar, mysql.TypeVarchar, mysql.TypeVarchar, mysql.TypeTiny, mysql.TypeDatetime,
-			mysql.TypeLonglong, mysql.TypeLonglong, mysql.TypeDouble}
+			mysql.TypeLonglong, mysql.TypeLonglong, mysql.TypeDouble, mysql.TypeDouble}
 	case ast.ShowStatsBuckets:
 		names = []string{"Db_name", "Table_name", "Partition_name", "Column_name", "Is_index", "Bucket_id", "Count",
 			"Repeats", "Lower_Bound", "Upper_Bound"}

session/bootstrap.go

@@ -168,6 +168,7 @@ const (
 		cm_sketch blob,
 		stats_ver bigint(64) NOT NULL DEFAULT 0,
 		flag bigint(64) NOT NULL DEFAULT 0,
+		correlation double NOT NULL DEFAULT 0,
 		unique index tbl(table_id, is_index, hist_id)
 	);`
 
@@ -286,6 +287,7 @@ const (
 	version24 = 24
 	version25 = 25
 	version26 = 26
+	version27 = 27
 )
 
 func checkBootstrapped(s Session) (bool, error) {
@@ -448,6 +450,10 @@ func upgrade(s Session) {
 		upgradeToVer26(s)
 	}
 
+	if ver < version27 {
+		upgradeToVer27(s)
+	}
+
 	updateBootstrapVer(s)
 	_, err = s.Execute(context.Background(), "COMMIT")
 
@@ -719,6 +725,10 @@ func upgradeToVer26(s Session) {
 	mustExecute(s, "UPDATE HIGH_PRIORITY mysql.user SET Create_role_priv='Y',Drop_role_priv='Y'")
 }
 
+func upgradeToVer27(s Session) {
+	doReentrantDDL(s, "ALTER TABLE mysql.stats_histograms ADD COLUMN `correlation` double NOT NULL DEFAULT 0", infoschema.ErrColumnExists)
+}
+
 // updateBootstrapVer updates bootstrap version variable in mysql.TiDB table.
 func updateBootstrapVer(s Session) {
 	// Update bootstrap version.

statistics/bootstrap.go

@@ -120,6 +120,7 @@ func (h *Handle) initStatsHistograms4Chunk(is infoschema.InfoSchema, tables stat
 				continue
 			}
 			hist := NewHistogram(id, ndv, nullCount, version, &colInfo.FieldType, 0, totColSize)
+			hist.Correlation = row.GetFloat64(9)
 			table.Columns[hist.ID] = &Column{
 				Histogram:  *hist,
 				PhysicalID: table.PhysicalID,
@@ -134,7 +135,7 @@ func (h *Handle) initStatsHistograms4Chunk(is infoschema.InfoSchema, tables stat
 func (h *Handle) initStatsHistograms(is infoschema.InfoSchema, tables statsCache) error {
 	h.mu.Lock()
 	defer h.mu.Unlock()
-	sql := "select HIGH_PRIORITY table_id, is_index, hist_id, distinct_count, version, null_count, cm_sketch, tot_col_size, stats_ver from mysql.stats_histograms"
+	sql := "select HIGH_PRIORITY table_id, is_index, hist_id, distinct_count, version, null_count, cm_sketch, tot_col_size, stats_ver, correlation from mysql.stats_histograms"
 	rc, err := h.mu.ctx.(sqlexec.SQLExecutor).Execute(context.TODO(), sql)
 	if len(rc) > 0 {
 		defer terror.Call(rc[0].Close)

statistics/builder.go

@@ -105,9 +105,9 @@ func BuildColumn(ctx sessionctx.Context, numBuckets, id int64, collector *Sample
 	}
 	sc := ctx.GetSessionVars().StmtCtx
 	samples := collector.Samples
-	err := types.SortDatums(sc, samples)
+	err := SortSampleItems(sc, samples)
 	if err != nil {
-		return nil, errors.Trace(err)
+		return nil, err
 	}
 	hg := NewHistogram(id, ndv, collector.NullCount, 0, tp, int(numBuckets), collector.TotalSize)
 
@@ -124,9 +124,11 @@ func BuildColumn(ctx sessionctx.Context, numBuckets, id int64, collector *Sample
 	}
 	bucketIdx := 0
 	var lastCount int64
-	hg.AppendBucket(&samples[0], &samples[0], int64(sampleFactor), int64(ndvFactor))
+	var corrXYSum float64
+	hg.AppendBucket(&samples[0].Value, &samples[0].Value, int64(sampleFactor), int64(ndvFactor))
 	for i := int64(1); i < sampleNum; i++ {
-		cmp, err := hg.GetUpper(bucketIdx).CompareDatum(sc, &samples[i])
+		corrXYSum += float64(i) * float64(samples[i].Ordinal)
+		cmp, err := hg.GetUpper(bucketIdx).CompareDatum(sc, &samples[i].Value)
 		if err != nil {
 			return nil, errors.Trace(err)
 		}
@@ -143,14 +145,32 @@ func BuildColumn(ctx sessionctx.Context, numBuckets, id int64, collector *Sample
 			}
 		} else if totalCount-float64(lastCount) <= valuesPerBucket {
 			// The bucket still have room to store a new item, update the bucket.
-			hg.updateLastBucket(&samples[i], int64(totalCount), int64(ndvFactor))
+			hg.updateLastBucket(&samples[i].Value, int64(totalCount), int64(ndvFactor))
 		} else {
 			lastCount = hg.Buckets[bucketIdx].Count
 			// The bucket is full, store the item in the next bucket.
 			bucketIdx++
-			hg.AppendBucket(&samples[i], &samples[i], int64(totalCount), int64(ndvFactor))
+			hg.AppendBucket(&samples[i].Value, &samples[i].Value, int64(totalCount), int64(ndvFactor))
 		}
 	}
+	// Compute column order correlation with handle.
+	if sampleNum == 1 {
+		hg.Correlation = 1
+		return hg, nil
+	}
+	// X means the ordinal of the item in original sequence, Y means the oridnal of the item in the
+	// sorted sequence, we know that X and Y value sets are both:
+	// 0, 1, ..., sampleNum-1
+	// we can simply compute sum(X) = sum(Y) =
+	//    (sampleNum-1)*sampleNum / 2
+	// and sum(X^2) = sum(Y^2) =
+	//    (sampleNum-1)*sampleNum*(2*sampleNum-1) / 6
+	// The formula for computing correlation is borrowed from PostgreSQL.
+	// Note that (itemsCount*corrX2Sum - corrXSum*corrXSum) would never be zero when sampleNum is larger than 1.
+	itemsCount := float64(sampleNum)
+	corrXSum := (itemsCount - 1) * itemsCount / 2.0
+	corrX2Sum := (itemsCount - 1) * itemsCount * (2*itemsCount - 1) / 6.0
+	hg.Correlation = (itemsCount*corrXYSum - corrXSum*corrXSum) / (itemsCount*corrX2Sum - corrXSum*corrXSum)
 	return hg, nil
 }
 

statistics/fmsketch_test.go

@@ -23,7 +23,7 @@ import (
 func (s *testStatisticsSuite) TestSketch(c *C) {
 	sc := &stmtctx.StatementContext{TimeZone: time.Local}
 	maxSize := 1000
-	sampleSketch, ndv, err := buildFMSketch(sc, s.samples, maxSize)
+	sampleSketch, ndv, err := buildFMSketch(sc, extractSampleItemsDatums(s.samples), maxSize)
 	c.Check(err, IsNil)
 	c.Check(ndv, Equals, int64(6232))
 
@@ -51,7 +51,7 @@ func (s *testStatisticsSuite) TestSketch(c *C) {
 func (s *testStatisticsSuite) TestSketchProtoConversion(c *C) {
 	sc := &stmtctx.StatementContext{TimeZone: time.Local}
 	maxSize := 1000
-	sampleSketch, ndv, err := buildFMSketch(sc, s.samples, maxSize)
+	sampleSketch, ndv, err := buildFMSketch(sc, extractSampleItemsDatums(s.samples), maxSize)
 	c.Check(err, IsNil)
 	c.Check(ndv, Equals, int64(6232))
 

statistics/handle_test.go

@@ -437,3 +437,68 @@ func newStoreWithBootstrap(statsLease time.Duration) (kv.Storage, *domain.Domain
 	do.SetStatsUpdating(true)
 	return store, do, errors.Trace(err)
 }
+
+func (s *testStatsSuite) TestCorrelation(c *C) {
+	defer cleanEnv(c, s.store, s.do)
+	testKit := testkit.NewTestKit(c, s.store)
+	testKit.MustExec("use test")
+	testKit.MustExec("create table t(c1 int primary key, c2 int)")
+	testKit.MustExec("insert into t values(1,1),(3,12),(4,20),(2,7),(5,21)")
+	testKit.MustExec("analyze table t")
+	result := testKit.MustQuery("show stats_histograms where Table_name = 't'").Sort()
+	c.Assert(len(result.Rows()), Equals, 2)
+	c.Assert(result.Rows()[0][9], Equals, "0")
+	c.Assert(result.Rows()[1][9], Equals, "1")
+	testKit.MustExec("insert into t values(8,18)")
+	testKit.MustExec("analyze table t")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't'").Sort()
+	c.Assert(len(result.Rows()), Equals, 2)
+	c.Assert(result.Rows()[0][9], Equals, "0")
+	c.Assert(result.Rows()[1][9], Equals, "0.828571")
+
+	testKit.MustExec("truncate table t")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't'").Sort()
+	c.Assert(len(result.Rows()), Equals, 0)
+	testKit.MustExec("insert into t values(1,21),(3,12),(4,7),(2,20),(5,1)")
+	testKit.MustExec("analyze table t")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't'").Sort()
+	c.Assert(len(result.Rows()), Equals, 2)
+	c.Assert(result.Rows()[0][9], Equals, "0")
+	c.Assert(result.Rows()[1][9], Equals, "-1")
+	testKit.MustExec("insert into t values(8,4)")
+	testKit.MustExec("analyze table t")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't'").Sort()
+	c.Assert(len(result.Rows()), Equals, 2)
+	c.Assert(result.Rows()[0][9], Equals, "0")
+	c.Assert(result.Rows()[1][9], Equals, "-0.942857")
+
+	testKit.MustExec("drop table t")
+	testKit.MustExec("create table t(c1 int, c2 int)")
+	testKit.MustExec("insert into t values(1,1),(2,7),(3,12),(4,20),(5,21),(8,18)")
+	testKit.MustExec("analyze table t")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't'").Sort()
+	c.Assert(len(result.Rows()), Equals, 2)
+	c.Assert(result.Rows()[0][9], Equals, "1")
+	c.Assert(result.Rows()[1][9], Equals, "0.828571")
+
+	testKit.MustExec("truncate table t")
+	testKit.MustExec("insert into t values(1,1),(2,7),(3,12),(8,18),(4,20),(5,21)")
+	testKit.MustExec("analyze table t")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't'").Sort()
+	c.Assert(len(result.Rows()), Equals, 2)
+	c.Assert(result.Rows()[0][9], Equals, "0.828571")
+	c.Assert(result.Rows()[1][9], Equals, "1")
+
+	testKit.MustExec("drop table t")
+	testKit.MustExec("create table t(c1 int primary key, c2 int, c3 int, key idx_c2(c2))")
+	testKit.MustExec("insert into t values(1,1,1),(2,2,2),(3,3,3)")
+	testKit.MustExec("analyze table t")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't' and Is_index = 0").Sort()
+	c.Assert(len(result.Rows()), Equals, 3)
+	c.Assert(result.Rows()[0][9], Equals, "0")
+	c.Assert(result.Rows()[1][9], Equals, "1")
+	c.Assert(result.Rows()[2][9], Equals, "1")
+	result = testKit.MustQuery("show stats_histograms where Table_name = 't' and Is_index = 1").Sort()
+	c.Assert(len(result.Rows()), Equals, 1)
+	c.Assert(result.Rows()[0][9], Equals, "0")
+}