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selectivity.go
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selectivity.go
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// Copyright 2017 PingCAP, Inc.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS IS" BASIS,
// See the License for the specific language governing permissions and
// limitations under the License.
package statistics
import (
"math"
"github.com/juju/errors"
"github.com/pingcap/tidb/ast"
"github.com/pingcap/tidb/expression"
"github.com/pingcap/tidb/mysql"
"github.com/pingcap/tidb/sessionctx"
"github.com/pingcap/tidb/util/ranger"
)
// If one condition can't be calculated, we will assume that the selectivity of this condition is 0.8.
const selectionFactor = 0.8
// exprSet is used for calculating selectivity.
type exprSet struct {
tp int
ID int64
// mask is a bit pattern whose ith bit will indicate whether the ith expression is covered by this index/column.
mask int64
// ranges contains all the ranges we got.
ranges []*ranger.NewRange
}
// The type of the exprSet.
const (
indexType = iota
pkType
colType
)
const unknownColumnID = math.MinInt64
// getConstantColumnID receives two expressions and if one of them is column and another is constant, it returns the
// ID of the column.
func getConstantColumnID(e []expression.Expression) int64 {
if len(e) != 2 {
return unknownColumnID
}
col, ok1 := e[0].(*expression.Column)
_, ok2 := e[1].(*expression.Constant)
if ok1 && ok2 {
return col.ID
}
col, ok1 = e[1].(*expression.Column)
_, ok2 = e[0].(*expression.Constant)
if ok1 && ok2 {
return col.ID
}
return unknownColumnID
}
func pseudoSelectivity(t *Table, exprs []expression.Expression) float64 {
minFactor := selectionFactor
uniqueCol := make(map[string]bool)
for _, expr := range exprs {
fun, ok := expr.(*expression.ScalarFunction)
if !ok {
continue
}
colID := getConstantColumnID(fun.GetArgs())
if colID == unknownColumnID {
continue
}
switch fun.FuncName.L {
case ast.EQ, ast.NullEQ, ast.In:
minFactor = math.Min(minFactor, 1.0/pseudoEqualRate)
col, ok := t.Columns[colID]
if !ok {
continue
}
if mysql.HasUniKeyFlag(col.Info.Flag) {
uniqueCol[col.Info.Name.L] = true
}
if mysql.HasPriKeyFlag(col.Info.Flag) {
if t.PKIsHandle {
return 1.0 / float64(t.Count)
}
uniqueCol[col.Info.Name.L] = true
}
case ast.GE, ast.GT, ast.LE, ast.LT:
minFactor = math.Min(minFactor, 1.0/pseudoLessRate)
// FIXME: To resolve the between case.
}
}
if len(uniqueCol) == 0 {
return minFactor
}
// use the unique key info
for _, idx := range t.Indices {
if !idx.Info.Unique {
continue
}
unique := true
for _, col := range idx.Info.Columns {
if !uniqueCol[col.Name.L] {
unique = false
break
}
}
if unique {
return 1.0 / float64(t.Count)
}
}
return minFactor
}
// Selectivity is a function calculate the selectivity of the expressions.
// The definition of selectivity is (row count after filter / row count before filter).
// And exprs must be CNF now, in other words, `exprs[0] and exprs[1] and ... and exprs[len - 1]` should be held when you call this.
// TODO: support expressions that the top layer is a DNF.
// Currently the time complexity is o(n^2).
func (t *Table) Selectivity(ctx sessionctx.Context, exprs []expression.Expression) (float64, error) {
// If table's count is zero or conditions are empty, we should return 100% selectivity.
if t.Count == 0 || len(exprs) == 0 {
return 1, nil
}
// TODO: If len(exprs) is bigger than 63, we could use bitset structure to replace the int64.
// This will simplify some code and speed up if we use this rather than a boolean slice.
if t.Pseudo || len(exprs) > 63 || (len(t.Columns) == 0 && len(t.Indices) == 0) {
return pseudoSelectivity(t, exprs), nil
}
var sets []*exprSet
sc := ctx.GetSessionVars().StmtCtx
extractedCols := make([]*expression.Column, 0, len(t.Columns))
extractedCols = expression.ExtractColumnsFromExpressions(extractedCols, exprs, nil)
for _, colInfo := range t.Columns {
col := expression.ColInfo2Col(extractedCols, colInfo.Info)
// This column should have histogram.
if col != nil && !t.ColumnIsInvalid(ctx.GetSessionVars().StmtCtx, col.ID) {
maskCovered, ranges, err := getMaskAndRanges(ctx, exprs, ranger.ColumnRangeType, nil, col)
if err != nil {
return 0, errors.Trace(err)
}
sets = append(sets, &exprSet{tp: colType, ID: col.ID, mask: maskCovered, ranges: ranges})
if mysql.HasPriKeyFlag(colInfo.Info.Flag) {
sets[len(sets)-1].tp = pkType
}
}
}
for _, idxInfo := range t.Indices {
idxCols, lengths := expression.IndexInfo2Cols(extractedCols, idxInfo.Info)
// This index should have histogram.
if len(idxCols) > 0 && idxInfo.Histogram.Len() > 0 {
maskCovered, ranges, err := getMaskAndRanges(ctx, exprs, ranger.IndexRangeType, lengths, idxCols...)
if err != nil {
return 0, errors.Trace(err)
}
sets = append(sets, &exprSet{tp: indexType, ID: idxInfo.ID, mask: maskCovered, ranges: ranges})
}
}
sets = getUsableSetsByGreedy(sets)
ret := 1.0
// Initialize the mask with the full set.
mask := (int64(1) << uint(len(exprs))) - 1
for _, set := range sets {
mask ^= set.mask
var (
rowCount float64
err error
)
switch set.tp {
case pkType, colType:
rowCount, err = t.GetRowCountByColumnRanges(sc, set.ID, set.ranges)
case indexType:
rowCount, err = t.GetRowCountByIndexRanges(sc, set.ID, set.ranges)
}
if err != nil {
return 0, errors.Trace(err)
}
ret *= rowCount / float64(t.Count)
}
// If there's still conditions which cannot be calculated, we will multiply a selectionFactor.
if mask > 0 {
ret *= selectionFactor
}
return ret, nil
}
func getMaskAndRanges(ctx sessionctx.Context, exprs []expression.Expression, rangeType ranger.RangeType,
lengths []int, cols ...*expression.Column) (mask int64, ranges []*ranger.NewRange, err error) {
sc := ctx.GetSessionVars().StmtCtx
var accessConds []expression.Expression
switch rangeType {
case ranger.ColumnRangeType:
accessConds = ranger.ExtractAccessConditionsForColumn(exprs, cols[0].ColName)
ranges, err = ranger.BuildColumnRange(accessConds, sc, cols[0].RetType)
case ranger.IndexRangeType:
ranges, accessConds, err = ranger.DetachSimpleCondAndBuildRangeForIndex(ctx, exprs, cols, lengths)
default:
panic("should never be here")
}
if err != nil {
return 0, nil, errors.Trace(err)
}
for i := range exprs {
for j := range accessConds {
if exprs[i].Equal(ctx, accessConds[j]) {
mask |= 1 << uint64(i)
break
}
}
}
return mask, ranges, nil
}
// getUsableSetsByGreedy will select the indices and pk used for calculate selectivity by greedy algorithm.
func getUsableSetsByGreedy(sets []*exprSet) (newBlocks []*exprSet) {
mask := int64(math.MaxInt64)
for {
// Choose the index that covers most.
bestID, bestCount, bestTp := -1, 0, colType
for i, set := range sets {
set.mask &= mask
bits := popCount(set.mask)
if (bestTp == colType && set.tp < colType) || bestCount < bits {
bestID, bestCount, bestTp = i, bits, set.tp
}
}
if bestCount == 0 {
break
} else {
// update the mask, remove the bit that sets[bestID].mask has.
mask &^= sets[bestID].mask
newBlocks = append(newBlocks, sets[bestID])
// remove the chosen one
sets = append(sets[:bestID], sets[bestID+1:]...)
}
}
return
}
// popCount is the digit sum of the binary representation of the number x.
func popCount(x int64) int {
ret := 0
// x -= x & -x, remove the lowest bit of the x.
// e.g. result will be 2 if x is 3.
for ; x > 0; x -= x & -x {
ret++
}
return ret
}