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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 (
"github.com/pingcap/errors"
"github.com/pingcap/tidb/sessionctx"
"github.com/pingcap/tidb/sessionctx/stmtctx"
"github.com/pingcap/tidb/types"
)
// SortedBuilder is used to build histograms for PK and index.
type SortedBuilder struct {
sc *stmtctx.StatementContext
numBuckets int64
valuesPerBucket int64
lastNumber int64
bucketIdx int64
Count int64
hist *Histogram
}
// NewSortedBuilder creates a new SortedBuilder.
func NewSortedBuilder(sc *stmtctx.StatementContext, numBuckets, id int64, tp *types.FieldType) *SortedBuilder {
return &SortedBuilder{
sc: sc,
numBuckets: numBuckets,
valuesPerBucket: 1,
hist: NewHistogram(id, 0, 0, 0, tp, int(numBuckets), 0),
}
}
// Hist returns the histogram built by SortedBuilder.
func (b *SortedBuilder) Hist() *Histogram {
return b.hist
}
// Iterate updates the histogram incrementally.
func (b *SortedBuilder) Iterate(data types.Datum) error {
b.Count++
if b.Count == 1 {
b.hist.AppendBucket(&data, &data, 1, 1)
b.hist.NDV = 1
return nil
}
cmp, err := b.hist.GetUpper(int(b.bucketIdx)).CompareDatum(b.sc, &data)
if err != nil {
return errors.Trace(err)
}
if cmp == 0 {
// The new item has the same value as current bucket value, to ensure that
// a same value only stored in a single bucket, we do not increase bucketIdx even if it exceeds
// valuesPerBucket.
b.hist.Buckets[b.bucketIdx].Count++
b.hist.Buckets[b.bucketIdx].Repeat++
} else if b.hist.Buckets[b.bucketIdx].Count+1-b.lastNumber <= b.valuesPerBucket {
// The bucket still have room to store a new item, update the bucket.
b.hist.updateLastBucket(&data, b.hist.Buckets[b.bucketIdx].Count+1, 1)
b.hist.NDV++
} else {
// All buckets are full, we should merge buckets.
if b.bucketIdx+1 == b.numBuckets {
b.hist.mergeBuckets(int(b.bucketIdx))
b.valuesPerBucket *= 2
b.bucketIdx = b.bucketIdx / 2
if b.bucketIdx == 0 {
b.lastNumber = 0
} else {
b.lastNumber = b.hist.Buckets[b.bucketIdx-1].Count
}
}
// We may merge buckets, so we should check it again.
if b.hist.Buckets[b.bucketIdx].Count+1-b.lastNumber <= b.valuesPerBucket {
b.hist.updateLastBucket(&data, b.hist.Buckets[b.bucketIdx].Count+1, 1)
} else {
b.lastNumber = b.hist.Buckets[b.bucketIdx].Count
b.bucketIdx++
b.hist.AppendBucket(&data, &data, b.lastNumber+1, 1)
}
b.hist.NDV++
}
return nil
}
// BuildColumnHist build a histogram for a column.
// numBuckets: number of buckets for the histogram.
// id: the id of the table.
// collector: the collector of samples.
// tp: the FieldType for the column.
// count: represents the row count for the column.
// ndv: represents the number of distinct values for the column.
// nullCount: represents the number of null values for the column.
func BuildColumnHist(ctx sessionctx.Context, numBuckets, id int64, collector *SampleCollector, tp *types.FieldType, count int64, ndv int64, nullCount int64) (*Histogram, error) {
if ndv > count {
ndv = count
}
if count == 0 || len(collector.Samples) == 0 {
return NewHistogram(id, ndv, nullCount, 0, tp, 0, collector.TotalSize), nil
}
sc := ctx.GetSessionVars().StmtCtx
samples := collector.Samples
err := SortSampleItems(sc, samples)
if err != nil {
return nil, err
}
hg := NewHistogram(id, ndv, nullCount, 0, tp, int(numBuckets), collector.TotalSize)
sampleNum := int64(len(samples))
// As we use samples to build the histogram, the bucket number and repeat should multiply a factor.
sampleFactor := float64(count) / float64(len(samples))
// Since bucket count is increased by sampleFactor, so the actual max values per bucket is
// floor(valuesPerBucket/sampleFactor)*sampleFactor, which may less than valuesPerBucket,
// thus we need to add a sampleFactor to avoid building too many buckets.
valuesPerBucket := float64(count)/float64(numBuckets) + sampleFactor
ndvFactor := float64(count) / float64(hg.NDV)
if ndvFactor > sampleFactor {
ndvFactor = sampleFactor
}
bucketIdx := 0
var lastCount int64
var corrXYSum float64
hg.AppendBucket(&samples[0].Value, &samples[0].Value, int64(sampleFactor), int64(ndvFactor))
for i := int64(1); i < sampleNum; 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)
}
totalCount := float64(i+1) * sampleFactor
if cmp == 0 {
// The new item has the same value as current bucket value, to ensure that
// a same value only stored in a single bucket, we do not increase bucketIdx even if it exceeds
// valuesPerBucket.
hg.Buckets[bucketIdx].Count = int64(totalCount)
if float64(hg.Buckets[bucketIdx].Repeat) == ndvFactor {
hg.Buckets[bucketIdx].Repeat = int64(2 * sampleFactor)
} else {
hg.Buckets[bucketIdx].Repeat += int64(sampleFactor)
}
} else if totalCount-float64(lastCount) <= valuesPerBucket {
// The bucket still have room to store a new item, update the bucket.
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].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
// We use "Pearson correlation coefficient" to compute the order correlation of columns,
// the formula is based on https://en.wikipedia.org/wiki/Pearson_correlation_coefficient.
// 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
}
// BuildColumn builds histogram from samples for column.
func BuildColumn(ctx sessionctx.Context, numBuckets, id int64, collector *SampleCollector, tp *types.FieldType) (*Histogram, error) {
return BuildColumnHist(ctx, numBuckets, id, collector, tp, collector.Count, collector.FMSketch.NDV(), collector.NullCount)
}