关于tidb:读TiDB源码聊设计浅析HTAP的SQL优化器

本文的的源码剖析全副基于 TiDB6.5 来做剖析。

1. 引子

如果让你做一个分布式数据库的优化器，面对以下的 SQL，你会想到什么好的办法去执行他们呢？

• SELECT id, name FROM person WHERE age >= 18 or height > 180 limit 100;：从条件上看，咱们看到条件其实是二选一的：age >= 18 or height > 180。基于这种状况，咱们必定会去抉择有索引的数据，如果都有索引 or 都没有，那么必定抉择扫描行数起码的数据。如果有一些算子在外面的话，则额定须要思考数据的就近准则——有些算子在局部架构下能够充分利用 MPP 的能力，而有些则不行。
• SELECT orders.order_id, customers.customer_name, orders.order_date FROM orders LEFT JOIN customers ON orders.customer_id=customers.customer_id;分布式数据库中的 join，最优的形式就是小表播送到大表数据所在的中央。那么首先咱们得晓得谁是小表，谁是大表。

2. 统计信息收集

依据后面的两个例子，咱们能够发现——如果咱们须要找到 SQL 对应的最佳打算，咱们会须要一些表的元数据，或者说是统计信息。从惯例的角度来说，以下统计信息是必须收集的：

• 表的总行数
• 每列数据的均匀大小
• 每列数据的基数：即 NDV（distinct value）
• 列的 NULL 值个数

如果是事务型的（行式存储），那么还要思考索引均匀长度、值的散布等等。

如果是剖析型的（列式存储），那么还须要思考相干列的最大值、最小值等等。

而统计形式的收集，会有多种形式。次要是思考资源和准确性之间的 Trade off。常见的有：

• TopN：相干数据呈现次数前 n 的值。
• 直方图：用于形容数据分布图的工具。依照数据的值大小进行分桶，并用一些简略的数据来形容每个桶，比方落在桶里的值的个数。
• 2D 直方图：因为直方图无奈反馈列之间的关联，能够用 2D 直方图（联结散布）做到，但空间占用也比拟多。
• Count-Min Sketch：相似哈希表加上计算器的实现。能够用很少的数据来形容整体数据的个性。
• HyperLogLog：一种估算海量数据基数的办法。很多状况下，统计并不需要那么准确。工程方面要在应用资源和准确性里找均衡。因而有人提出用 HLL，这是一种占用资源少，但能给出较为精确的近似后果的算法。

TiDB 收集的统计信息见：https://docs.pingcap.com/zh/tidb/v6.5/statistics#%E7%9B%B4%E6…

3. 代价的评估

一个 SQL 真正的物理执行打算可能是有多个的。在以统计信息为根底之上，咱们还须要退出相应的权重，举个例子：

1. 如果可能在内存中计算实现，就不必去重复发动本地 IO
2. 如果能在本地 IO 中实现，就不要去发动网络申请

等等 …

这在 TiDB 的代码中也有对应的默认值。

DefOptCPUFactor                                = 3.0
DefOptCopCPUFactor                             = 3.0
DefOptTiFlashConcurrencyFactor                 = 24.0
DefOptNetworkFactor                            = 1.0
DefOptScanFactor                               = 1.5
DefOptDescScanFactor                           = 3.0
DefOptSeekFactor                               = 20.0
DefOptMemoryFactor                             = 0.001
DefOptDiskFactor                               = 1.5
DefOptConcurrencyFactor                        = 3.0

var defaultVer2Factors = costVer2Factors{TiDBTemp:      costVer2Factor{"tidb_temp_table_factor", 0.00},
    TiKVScan:      costVer2Factor{"tikv_scan_factor", 40.70},
    TiKVDescScan:  costVer2Factor{"tikv_desc_scan_factor", 61.05},
    TiFlashScan:   costVer2Factor{"tiflash_scan_factor", 11.60},
    TiDBCPU:       costVer2Factor{"tidb_cpu_factor", 49.90},
    TiKVCPU:       costVer2Factor{"tikv_cpu_factor", 49.90},
    TiFlashCPU:    costVer2Factor{"tiflash_cpu_factor", 2.40},
    TiDB2KVNet:    costVer2Factor{"tidb_kv_net_factor", 3.96},
    TiDB2FlashNet: costVer2Factor{"tidb_flash_net_factor", 2.20},
    TiFlashMPPNet: costVer2Factor{"tiflash_mpp_net_factor", 1.00},
    TiDBMem:       costVer2Factor{"tidb_mem_factor", 0.20},
    TiKVMem:       costVer2Factor{"tikv_mem_factor", 0.20},
    TiFlashMem:    costVer2Factor{"tiflash_mem_factor", 0.05},
    TiDBDisk:      costVer2Factor{"tidb_disk_factor", 200.00},
    TiDBRequest:   costVer2Factor{"tidb_request_factor", 6000000.00},
}

4. 执行打算枚举与择优

当咱们能够评估出物理执行打算的代价时，将会枚举所有能够用上物理执行打算，并在其中抉择代价最小的物理执行打算。个别枚举分为两个流派：

1. 自底向上：代表有 System R。
2. 自顶向下：代表有 Cascade。

自底向上没法解决一个问题。当下层对上层的输入后果程序感兴趣时，那就不能只能从底层的视角来寻找部分最优。

举个例子，多表 Join。一开始两个表 Join 可能 HashJoin 代价很低，然而 Join 下一个表时，用 MergeJoin 从整体来看代价更低。从这个 case 来看，自底向上来做打算取优并不适合。

所以有了 Cascade：

1. 搜寻计划是自顶向下的。这意味着它能够防止部分最优而导致全局不优。从 Operator Tree 自顶向下遍历时，能够做一系列变换：

• • Implementation：逻辑算子能够转换成物理算子；例如 Join 转换成 NestLoop 或者 HashJoin 等
  • Exploration：逻辑算子能够做等价变换；例如替换 Inner Join 的两个子节点，即可枚举 Join 程序

图片来自于：Cascades Optimizer——https://zhuanlan.zhihu.com/p/73545345

2. 它是基于 Volcano 模型演进而来的。
3. 用面向对象的形式进行建模，编写规定时不须要关怀搜寻过程。相比传统优化器中面向过程去一条条的编写，确实是很大的改良。

5.TiDB 的实现

大抵的代码调用链为：

-- session/session.go

\-- ExecuteStmt //SQL 执行的入口

|-- executor/compiler.go

\-- Compile // 将 SQL 变成可执行的打算

|--planner/planner/optmize.go

\-- Optimize // 优化的入口

\-- optimize // 这里有两个入口。一种是新的优化器入口，一种是老的优化器入口。依据配置来抉择。最终都会返回最优的物理执行打算。|-- planner/cascades/optmize.go

        \--FindBestPlan 见 5.1
    
        \-- onPhasePreprocessing // 见 5.3

        \-- implGroup

        |--planner/core/optmizer.go // 见 5.4

            \-- DoOptimize

            \-- physicalOptimize

            |--planner/core/find_best_task.go

            \-- findBestTask

            \-- enumeratePhysicalPlans4Task

            \-- compareTaskCost
    
            \-- getTaskPlanCost
    
            |-- planner/core/plan_cost_ver2.go

            \-- getPlanCost

5.1 逻辑优化

外围入口为：

// FindBestPlan is the optimization entrance of the cascades planner. The
// optimization is composed of 3 phases: preprocessing, exploration and implementation.
//
// ------------------------------------------------------------------------------
// Phase 1: Preprocessing
// ------------------------------------------------------------------------------
//
// The target of this phase is to preprocess the plan tree by some heuristic
// rules which should always be beneficial, for example Column Pruning.
//
// ------------------------------------------------------------------------------
// Phase 2: Exploration
// ------------------------------------------------------------------------------
//
// The target of this phase is to explore all the logically equivalent
// expressions by exploring all the equivalent group expressions of each group.
//
// At the very beginning, there is only one group expression in a Group. After
// applying some transformation rules on certain expressions of the Group, all
// the equivalent expressions are found and stored in the Group. This procedure
// can be regarded as searching for a weak connected component in a directed
// graph, where nodes are expressions and directed edges are the transformation
// rules.
//
// ------------------------------------------------------------------------------
// Phase 3: Implementation
// ------------------------------------------------------------------------------
//
// The target of this phase is to search the best physical plan for a Group
// which satisfies a certain required physical property.
//
// In this phase, we need to enumerate all the applicable implementation rules
// for each expression in each group under the required physical property. A
// memo structure is used for a group to reduce the repeated search on the same
// required physical property.
func (opt *Optimizer) FindBestPlan(sctx sessionctx.Context, logical plannercore.LogicalPlan) (p plannercore.PhysicalPlan, cost float64, err error) {logical, err = opt.onPhasePreprocessing(sctx, logical)
    if err != nil {return nil, 0, err}
    rootGroup := memo.Convert2Group(logical)
    err = opt.onPhaseExploration(sctx, rootGroup)
    if err != nil {return nil, 0, err}
    p, cost, err = opt.onPhaseImplementation(sctx, rootGroup)
    if err != nil {return nil, 0, err}
    err = p.ResolveIndices()
    return p, cost, err
}

正文 + 代码很洁净，这里一共做三件事

1. onPhasePreprocessing：正文很切实，说for example Column Pruning，后果外面真的只做了列裁剪。
2. onPhaseExploration：摸索所有逻辑等价存在的可能
3. onPhaseImplementation：依据代价寻找最优的物理执行打算

这块官网的博客写的十分好，我就不反复了：https://cn.pingcap.com/blog/tidb-cascades-planner/

5.2 统计信息收集

这块代码次要集中在 stats.go 里，外面的外围数据结构是 stats_info.go 里的 StatsInfo。调用链大抵为：

|-- planner/cascades/optimizer.go

\--fillGroupStats

|-- planner/core/stats.go

\--DeriveStats

type LogicalPlan interface {
    Plan
    //...... 疏忽一些代码
    // DeriveStats derives statistic info for current plan node given child stats.
    // We need selfSchema, childSchema here because it makes this method can be used in
    // cascades planner, where LogicalPlan might not record its children or schema.
    DeriveStats(childStats []*property.StatsInfo, selfSchema *expression.Schema, childSchema []*expression.Schema, colGroups [][]*expression.Column) (*property.StatsInfo, error)
    //...... 疏忽一些代码
}

有很多构造体实现了这个办法：

3. 收集统计信息次要是 analyze.go#Next 办法中调用的 #analyzeWorker。

5.3 新版本 物理执行打算的抉择

代码入口为：

// implGroup finds the best Implementation which satisfies the required
// physical property for a Group. The best Implementation should have the
// lowest cost among all the applicable Implementations.
//
// g:            the Group to be implemented.
// reqPhysProp: the required physical property.
// costLimit:   the maximum cost of all the Implementations.
func (opt *Optimizer) implGroup(g *memo.Group, reqPhysProp *property.PhysicalProperty, costLimit float64) (memo.Implementation, error) {groupImpl := g.GetImpl(reqPhysProp)
    if groupImpl != nil {if groupImpl.GetCost() <= costLimit {return groupImpl, nil}
        return nil, nil
    }
    // Handle implementation rules for each equivalent GroupExpr.
    var childImpls []memo.Implementation
    err := opt.fillGroupStats(g)
    if err != nil {return nil, err}
    outCount := math.Min(g.Prop.Stats.RowCount, reqPhysProp.ExpectedCnt)
    for elem := g.Equivalents.Front(); elem != nil; elem = elem.Next() {curExpr := elem.Value.(*memo.GroupExpr)
        impls, err := opt.implGroupExpr(curExpr, reqPhysProp)
        if err != nil {return nil, err}
        for _, impl := range impls {childImpls = childImpls[:0]
            for i, childGroup := range curExpr.Children {childImpl, err := opt.implGroup(childGroup, impl.GetPlan().GetChildReqProps(i), impl.GetCostLimit(costLimit, childImpls...))
                if err != nil {return nil, err}
                if childImpl == nil {impl.SetCost(math.MaxFloat64)
                    break
                }
                childImpls = append(childImpls, childImpl)
            }
            if impl.GetCost() == math.MaxFloat64 {continue}
            implCost := impl.CalcCost(outCount, childImpls...)
            if implCost > costLimit {continue}
            if groupImpl == nil || groupImpl.GetCost() > implCost {groupImpl = impl.AttachChildren(childImpls...)
                costLimit = implCost
            }
        }
    }
    // Handle enforcer rules for required physical property.
    for _, rule := range GetEnforcerRules(g, reqPhysProp) {newReqPhysProp := rule.NewProperty(reqPhysProp)
        enforceCost := rule.GetEnforceCost(g)
        childImpl, err := opt.implGroup(g, newReqPhysProp, costLimit-enforceCost)
        if err != nil {return nil, err}
        if childImpl == nil {continue}
        impl := rule.OnEnforce(reqPhysProp, childImpl)
        implCost := enforceCost + childImpl.GetCost()
        impl.SetCost(implCost)
        if groupImpl == nil || groupImpl.GetCost() > implCost {
            groupImpl = impl
            costLimit = implCost
        }
    }
    if groupImpl == nil || groupImpl.GetCost() == math.MaxFloat64 {return nil, nil}
    g.InsertImpl(reqPhysProp, groupImpl)
    return groupImpl, nil
}

这里个函数会找出潜在符合条件的物理执行打算，并一直的搜寻。但它有一个剪枝逻辑——会记录以后最小的 cost，如果一个执行打算自上向下搜寻时，如果超过了这个 cost，则间接返回。这就是在第 3 节提到的自顶向下的优化。

接下来咱们看一下 memo.Implementation 的定义：

package memo

import (plannercore "github.com/pingcap/tidb/planner/core")

// Implementation defines the interface for cost of physical plan.
type Implementation interface {CalcCost(outCount float64, children ...Implementation) float64
    SetCost(cost float64)
    GetCost() float64
    GetPlan() plannercore.PhysicalPlan

    // AttachChildren is used to attach children implementations and returns it self.
    AttachChildren(children ...Implementation) Implementation

    // GetCostLimit gets the costLimit for implementing the next childGroup.
    GetCostLimit(costLimit float64, children ...Implementation) float64
}

其中 CalcCost 办法就是用来计算物理执行打算的代价。一共有这么多构造体实现了它：

5.3.1 代价的评估

咱们以结尾的例子，解说代价的评估。

select 代价计算形式

// CalcCost calculates the cost of the table scan Implementation.
func (impl *TableScanImpl) CalcCost(outCount float64, _ ...memo.Implementation) float64 {ts := impl.plan.(*plannercore.PhysicalTableScan)
    width := impl.tblColHists.GetTableAvgRowSize(impl.plan.SCtx(), impl.tblCols, kv.TiKV, true)
    sessVars := ts.SCtx().GetSessionVars()
    impl.cost = outCount * sessVars.GetScanFactor(ts.Table) * width
    if ts.Desc {impl.cost = outCount * sessVars.GetDescScanFactor(ts.Table) * width
    }
    return impl.cost
}

// GetScanFactor returns the session variable scanFactor
// returns 0 when tbl is a temporary table.
func (s *SessionVars) GetScanFactor(tbl *model.TableInfo) float64 {
    if tbl != nil {
        if tbl.TempTableType != model.TempTableNone {return 0}
    }
    return s.scanFactor 
}


// CalcCost implements Implementation interface.
func (impl *IndexScanImpl) CalcCost(outCount float64, _ ...memo.Implementation) float64 {is := impl.plan.(*plannercore.PhysicalIndexScan)
    sessVars := is.SCtx().GetSessionVars()
    rowSize := impl.tblColHists.GetIndexAvgRowSize(is.SCtx(), is.Schema().Columns, is.Index.Unique)
    cost := outCount * rowSize * sessVars.GetScanFactor(is.Table)
    if is.Desc {cost = outCount * rowSize * sessVars.GetDescScanFactor(is.Table)
    }
    cost += float64(len(is.Ranges)) * sessVars.GetSeekFactor(is.Table)
    impl.cost = cost
    return impl.cost
}

这里咱们以全表扫描表和命中索引的代码为例子。其中默认的 scanFactor 是 1.5。这里能够看到 indexScan 和 tableScan 少了一个因数：width。这个变量代表了所需列的均匀大小。这么看基本上是 indexScan 最优了。

这里的代码笔者认为有点不优雅——当 Desc 时，其实之前的 Cost 是没必要算一遍的，节约 CPU 资源。

join 代价计算形式

// CalcCost implements Implementation CalcCost interface.
func (impl *HashJoinImpl) CalcCost(_ float64, children ...memo.Implementation) float64 {hashJoin := impl.plan.(*plannercore.PhysicalHashJoin)
    // The children here are only used to calculate the cost.
    hashJoin.SetChildren(children[0].GetPlan(), children[1].GetPlan())
    selfCost := hashJoin.GetCost(children[0].GetPlan().StatsCount(), children[1].GetPlan().StatsCount(), false, 0, nil)
    impl.cost = selfCost + children[0].GetCost() + children[1].GetCost()
    return impl.cost
}

// CalcCost implements Implementation CalcCost interface.
func (impl *MergeJoinImpl) CalcCost(_ float64, children ...memo.Implementation) float64 {mergeJoin := impl.plan.(*plannercore.PhysicalMergeJoin)
    // The children here are only used to calculate the cost.
    mergeJoin.SetChildren(children[0].GetPlan(), children[1].GetPlan())
    selfCost := mergeJoin.GetCost(children[0].GetPlan().StatsCount(), children[1].GetPlan().StatsCount(), 0)
    impl.cost = selfCost + children[0].GetCost() + children[1].GetCost()
    return impl.cost
}

具体的计算都在 plan_cost_v1.go 里：

// GetCost computes cost of hash join operator itself.
func (p *PhysicalHashJoin) GetCost(lCnt, rCnt float64, isMPP bool, costFlag uint64, op *physicalOptimizeOp) float64 {
    buildCnt, probeCnt := lCnt, rCnt
    build := p.children[0]
    // Taking the right as the inner for right join or using the outer to build a hash table.
    if (p.InnerChildIdx == 1 && !p.UseOuterToBuild) || (p.InnerChildIdx == 0 && p.UseOuterToBuild) {
        buildCnt, probeCnt = rCnt, lCnt
        build = p.children[1]
    }
    sessVars := p.ctx.GetSessionVars()
    oomUseTmpStorage := variable.EnableTmpStorageOnOOM.Load()
    memQuota := sessVars.MemTracker.GetBytesLimit() // sessVars.MemQuotaQuery && hint
    rowSize := getAvgRowSize(build.statsInfo(), build.Schema().Columns)
    spill := oomUseTmpStorage && memQuota > 0 && rowSize*buildCnt > float64(memQuota) && p.storeTp != kv.TiFlash
    // Cost of building hash table.
    cpuFactor := sessVars.GetCPUFactor()
    diskFactor := sessVars.GetDiskFactor()
    memoryFactor := sessVars.GetMemoryFactor()
    concurrencyFactor := sessVars.GetConcurrencyFactor()

    cpuCost := buildCnt * cpuFactor
    memoryCost := buildCnt * memoryFactor
    diskCost := buildCnt * diskFactor * rowSize
    // Number of matched row pairs regarding the equal join conditions.
    helper := &fullJoinRowCountHelper{sctx:            p.SCtx(),
        cartesian:       false,
        leftProfile:     p.children[0].statsInfo(),
        rightProfile:    p.children[1].statsInfo(),
        leftJoinKeys:    p.LeftJoinKeys,
        rightJoinKeys:   p.RightJoinKeys,
        leftSchema:      p.children[0].Schema(),
        rightSchema:     p.children[1].Schema(),
        leftNAJoinKeys:  p.LeftNAJoinKeys,
        rightNAJoinKeys: p.RightNAJoinKeys,
    }
    numPairs := helper.estimate()
    // For semi-join class, if `OtherConditions` is empty, we already know
    // the join results after querying hash table, otherwise, we have to
    // evaluate those resulted row pairs after querying hash table; if we
    // find one pair satisfying the `OtherConditions`, we then know the
    // join result for this given outer row, otherwise we have to iterate
    // to the end of those pairs; since we have no idea about when we can
    // terminate the iteration, we assume that we need to iterate half of
    // those pairs in average.
    if p.JoinType == SemiJoin || p.JoinType == AntiSemiJoin ||
        p.JoinType == LeftOuterSemiJoin || p.JoinType == AntiLeftOuterSemiJoin {if len(p.OtherConditions) > 0 {numPairs *= 0.5} else {numPairs = 0}
    }
    if hasCostFlag(costFlag, CostFlagUseTrueCardinality) {numPairs = getOperatorActRows(p)
    }
    // Cost of querying hash table is cheap actually, so we just compute the cost of
    // evaluating `OtherConditions` and joining row pairs.
    probeCost := numPairs * cpuFactor
    probeDiskCost := numPairs * diskFactor * rowSize
    // Cost of evaluating outer filter.
    if len(p.LeftConditions)+len(p.RightConditions) > 0 {
        // Input outer count for the above compution should be adjusted by SelectionFactor.
        probeCost *= SelectionFactor
        probeDiskCost *= SelectionFactor
        probeCost += probeCnt * cpuFactor
    }
    diskCost += probeDiskCost
    probeCost /= float64(p.Concurrency)
    // Cost of additional concurrent goroutines.
    cpuCost += probeCost + float64(p.Concurrency+1)*concurrencyFactor
    // Cost of traveling the hash table to resolve missing matched cases when building the hash table from the outer table
    if p.UseOuterToBuild {
        if spill {
            // It runs in sequence when build data is on disk. See handleUnmatchedRowsFromHashTableInDisk
            cpuCost += buildCnt * cpuFactor
        } else {cpuCost += buildCnt * cpuFactor / float64(p.Concurrency)
        }
        diskCost += buildCnt * diskFactor * rowSize
    }

    if spill {memoryCost *= float64(memQuota) / (rowSize * buildCnt)
    } else {diskCost = 0}
    if op != nil {
        setPhysicalHashJoinCostDetail(p, op, spill, buildCnt, probeCnt, cpuFactor, rowSize, numPairs,
            cpuCost, probeCost, memoryCost, diskCost, probeDiskCost,
            diskFactor, memoryFactor, concurrencyFactor,
            memQuota)
    }
    return cpuCost + memoryCost + diskCost
}


// GetCost computes cost of merge join operator itself.
func (p *PhysicalMergeJoin) GetCost(lCnt, rCnt float64, costFlag uint64) float64 {
    outerCnt := lCnt
    innerCnt := rCnt
    innerKeys := p.RightJoinKeys
    innerSchema := p.children[1].Schema()
    innerStats := p.children[1].statsInfo()
    if p.JoinType == RightOuterJoin {
        outerCnt = rCnt
        innerCnt = lCnt
        innerKeys = p.LeftJoinKeys
        innerSchema = p.children[0].Schema()
        innerStats = p.children[0].statsInfo()}
    helper := &fullJoinRowCountHelper{sctx:          p.SCtx(),
        cartesian:     false,
        leftProfile:   p.children[0].statsInfo(),
        rightProfile:  p.children[1].statsInfo(),
        leftJoinKeys:  p.LeftJoinKeys,
        rightJoinKeys: p.RightJoinKeys,
        leftSchema:    p.children[0].Schema(),
        rightSchema:   p.children[1].Schema(),}
    numPairs := helper.estimate()
    if p.JoinType == SemiJoin || p.JoinType == AntiSemiJoin ||
        p.JoinType == LeftOuterSemiJoin || p.JoinType == AntiLeftOuterSemiJoin {if len(p.OtherConditions) > 0 {numPairs *= 0.5} else {numPairs = 0}
    }
    if hasCostFlag(costFlag, CostFlagUseTrueCardinality) {numPairs = getOperatorActRows(p)
    }
    sessVars := p.ctx.GetSessionVars()
    probeCost := numPairs * sessVars.GetCPUFactor()
    // Cost of evaluating outer filters.
    var cpuCost float64
    if len(p.LeftConditions)+len(p.RightConditions) > 0 {
        probeCost *= SelectionFactor
        cpuCost += outerCnt * sessVars.GetCPUFactor()}
    cpuCost += probeCost
    // For merge join, only one group of rows with same join key(not null) are cached,
    // we compute average memory cost using estimated group size.
    NDV, _ := getColsNDVWithMatchedLen(innerKeys, innerSchema, innerStats)
    memoryCost := (innerCnt / NDV) * sessVars.GetMemoryFactor()
    return cpuCost + memoryCost
}

HashJoin 要思考到内存不够的状况，因而在计算到数据不够时，会将对应的数据压入硬盘。但它对数据的程序并无要求，因而能够并发的去做。见：

    // Cost of traveling the hash table to resolve missing matched cases when building the hash table from the outer table
    if p.UseOuterToBuild {
        if spill {
            // It runs in sequence when build data is on disk. See handleUnmatchedRowsFromHashTableInDisk
            cpuCost += buildCnt * cpuFactor
        } else {cpuCost += buildCnt * cpuFactor / float64(p.Concurrency)
        }
        diskCost += buildCnt * diskFactor * rowSize
    }

而 MergeJoin 的代价显然会更小，但可能选则到这个打算也有较高的要求：当两个关联表要 Join 的字段须要按排好的程序读取时，实用 Merge Join 算法。

5.4 老版本 物理执行打算的抉择

5.4.1 代价的评估

这块代码次要是在 plan_cost_ver1.go 和plan_cost_ver2.go。v2 对代价公式进行了更准确的回归校准，调整了局部代价公式，比此前版本的代价公式更加精确。代码上也更为简洁：v2 只暴露出了一个公共办法，外部通过不同的类型做转发。

// GetPlanCost returns the cost of this plan.
func GetPlanCost(p PhysicalPlan, taskType property.TaskType, option *PlanCostOption) (float64, error) {return getPlanCost(p, taskType, option)
}

func getPlanCost(p PhysicalPlan, taskType property.TaskType, option *PlanCostOption) (float64, error) {if p.SCtx().GetSessionVars().CostModelVersion == modelVer2 {planCost, err := p.getPlanCostVer2(taskType, option)
        return planCost.cost, err
    }
    return p.getPlanCostVer1(taskType, option)
}

依据不同的 PhysicalPlan 类型，会找到不同绑定办法：

v1 的局部办法展现：

select 代价计算形式

// getPlanCostVer2 returns the plan-cost of this sub-plan, which is:
// plan-cost = child-cost + filter-cost
func (p *PhysicalSelection) getPlanCostVer2(taskType property.TaskType, option *PlanCostOption) (costVer2, error) {if p.planCostInit && !hasCostFlag(option.CostFlag, CostFlagRecalculate) {return p.planCostVer2, nil}

    inputRows := getCardinality(p.children[0], option.CostFlag)
    cpuFactor := getTaskCPUFactorVer2(p, taskType)

    filterCost := filterCostVer2(option, inputRows, p.Conditions, cpuFactor)

    childCost, err := p.children[0].getPlanCostVer2(taskType, option)
    if err != nil {return zeroCostVer2, err}

    p.planCostVer2 = sumCostVer2(filterCost, childCost)
    p.planCostInit = true
    return p.planCostVer2, nil
}

这部分代码简略易读。代价就是子查问的代价 + 筛选的代价。

那么问题来了，中索引的和不中索引的代价应该是不一样的。这里没有体现进去啊。认真看childCost, err := p.children[0].getPlanCostVer2(taskType, option)，这里是会去获取子物理执行打算的代价。

// getPlanCostVer2 returns the plan-cost of this sub-plan, which is:
func (p *PointGetPlan) getPlanCostVer2(taskType property.TaskType, option *PlanCostOption) (costVer2, error) {if p.planCostInit && !hasCostFlag(option.CostFlag, CostFlagRecalculate) {return p.planCostVer2, nil}

    if p.accessCols == nil { // from fast plan code path
        p.planCostVer2 = zeroCostVer2
        p.planCostInit = true
        return zeroCostVer2, nil
    }
    rowSize := getAvgRowSize(p.stats, p.schema.Columns)
    netFactor := getTaskNetFactorVer2(p, taskType)

    p.planCostVer2 = netCostVer2(option, 1, rowSize, netFactor)
    p.planCostInit = true
    return p.planCostVer2, nil
}

func netCostVer2(option *PlanCostOption, rows, rowSize float64, netFactor costVer2Factor) costVer2 {
    return newCostVer2(option, netFactor,
        rows*rowSize*netFactor.Value,
        func() string { return fmt.Sprintf("net(%v*rowsize(%v)*%v)", rows, rowSize, netFactor) })
}



// getPlanCostVer2 returns the plan-cost of this sub-plan, which is:
// plan-cost = rows * log2(row-size) * scan-factor
// log2(row-size) is from experiments.
func (p *PhysicalTableScan) getPlanCostVer2(taskType property.TaskType, option *PlanCostOption) (costVer2, error) {if p.planCostInit && !hasCostFlag(option.CostFlag, CostFlagRecalculate) {return p.planCostVer2, nil}

    rows := getCardinality(p, option.CostFlag)
    var rowSize float64
    if p.StoreType == kv.TiKV {rowSize = getAvgRowSize(p.stats, p.tblCols) // consider all columns if TiKV
    } else { // TiFlash
        rowSize = getAvgRowSize(p.stats, p.schema.Columns)
    }
    rowSize = math.Max(rowSize, 2.0)
    scanFactor := getTaskScanFactorVer2(p, p.StoreType, taskType)

    p.planCostVer2 = scanCostVer2(option, rows, rowSize, scanFactor)

    // give TiFlash a start-up cost to let the optimizer prefers to use TiKV to process small table scans.
    if p.StoreType == kv.TiFlash {p.planCostVer2 = sumCostVer2(p.planCostVer2, scanCostVer2(option, 10000, rowSize, scanFactor))
    }

    p.planCostInit = true
    return p.planCostVer2, nil
}

func scanCostVer2(option *PlanCostOption, rows, rowSize float64, scanFactor costVer2Factor) costVer2 {
    if rowSize < 1 {rowSize = 1}
    return newCostVer2(option, scanFactor,
        // rows * log(row-size) * scanFactor, log2 from experiments
        rows*math.Log2(rowSize)*scanFactor.Value,
        func() string { return fmt.Sprintf("scan(%v*logrowsize(%v)*%v)", rows, rowSize, scanFactor) })
}

scanFactor 的代价默认是 40.7，netFactor 的代价默认是 3.96。联合代码来看，命中索引的代价更优。

join 代价计算形式

// getPlanCostVer2 returns the plan-cost of this sub-plan, which is:
// plan-cost = build-child-cost + build-filter-cost +
// (probe-cost + probe-filter-cost) / concurrency
// probe-cost = probe-child-cost * build-rows / batchRatio
func (p *PhysicalIndexJoin) getPlanCostVer2(taskType property.TaskType, option *PlanCostOption) (costVer2, error) {return p.getIndexJoinCostVer2(taskType, option, 0)
}

func (p *PhysicalIndexHashJoin) getPlanCostVer2(taskType property.TaskType, option *PlanCostOption) (costVer2, error) {return p.getIndexJoinCostVer2(taskType, option, 1)
}

func (p *PhysicalIndexMergeJoin) getPlanCostVer2(taskType property.TaskType, option *PlanCostOption) (costVer2, error) {return p.getIndexJoinCostVer2(taskType, option, 2)
}

func (p *PhysicalIndexJoin) getIndexJoinCostVer2(taskType property.TaskType, option *PlanCostOption, indexJoinType int) (costVer2, error) {if p.planCostInit && !hasCostFlag(option.CostFlag, CostFlagRecalculate) {return p.planCostVer2, nil}

    build, probe := p.children[1-p.InnerChildIdx], p.children[p.InnerChildIdx]
    buildRows := getCardinality(build, option.CostFlag)
    buildRowSize := getAvgRowSize(build.Stats(), build.Schema().Columns)
    probeRowsOne := getCardinality(probe, option.CostFlag)
    probeRowsTot := probeRowsOne * buildRows
    probeRowSize := getAvgRowSize(probe.Stats(), probe.Schema().Columns)
    buildFilters, probeFilters := p.LeftConditions, p.RightConditions
    probeConcurrency := float64(p.ctx.GetSessionVars().IndexLookupJoinConcurrency())
    cpuFactor := getTaskCPUFactorVer2(p, taskType)
    memFactor := getTaskMemFactorVer2(p, taskType)
    requestFactor := getTaskRequestFactorVer2(p, taskType)

    buildFilterCost := filterCostVer2(option, buildRows, buildFilters, cpuFactor)
    buildChildCost, err := build.getPlanCostVer2(taskType, option)
    if err != nil {return zeroCostVer2, err}
    buildTaskCost := newCostVer2(option, cpuFactor,
        buildRows*10*cpuFactor.Value,
        func() string { return fmt.Sprintf("cpu(%v*10*%v)", buildRows, cpuFactor) })
    startCost := newCostVer2(option, cpuFactor,
        10*3*cpuFactor.Value,
        func() string { return fmt.Sprintf("cpu(10*3*%v)", cpuFactor) })

    probeFilterCost := filterCostVer2(option, probeRowsTot, probeFilters, cpuFactor)
    probeChildCost, err := probe.getPlanCostVer2(taskType, option)
    if err != nil {return zeroCostVer2, err}

    var hashTableCost costVer2
    switch indexJoinType {
    case 1: // IndexHashJoin
        hashTableCost = hashBuildCostVer2(option, buildRows, buildRowSize, float64(len(p.RightJoinKeys)), cpuFactor, memFactor)
    case 2: // IndexMergeJoin
        hashTableCost = newZeroCostVer2(traceCost(option))
    default: // IndexJoin
        hashTableCost = hashBuildCostVer2(option, probeRowsTot, probeRowSize, float64(len(p.LeftJoinKeys)), cpuFactor, memFactor)
    }

    // IndexJoin executes a batch of rows at a time, so the actual cost of this part should be
    //  `innerCostPerBatch * numberOfBatches` instead of `innerCostPerRow * numberOfOuterRow`.
    // Use an empirical value batchRatio to handle this now.
    // TODO: remove this empirical value.
    batchRatio := 6.0
    probeCost := divCostVer2(mulCostVer2(probeChildCost, buildRows), batchRatio)

    // Double Read Cost
    doubleReadCost := newZeroCostVer2(traceCost(option))
    if p.ctx.GetSessionVars().IndexJoinDoubleReadPenaltyCostRate > 0 {batchSize := float64(p.ctx.GetSessionVars().IndexJoinBatchSize)
        taskPerBatch := 1024.0 // TODO: remove this magic number
        doubleReadTasks := buildRows / batchSize * taskPerBatch
        doubleReadCost = doubleReadCostVer2(option, doubleReadTasks, requestFactor)
        doubleReadCost = mulCostVer2(doubleReadCost, p.ctx.GetSessionVars().IndexJoinDoubleReadPenaltyCostRate)
    }

    p.planCostVer2 = sumCostVer2(startCost, buildChildCost, buildFilterCost, buildTaskCost, divCostVer2(sumCostVer2(doubleReadCost, probeCost, probeFilterCost, hashTableCost), probeConcurrency))
    p.planCostInit = true
    return p.planCostVer2, nil
}

关键在于：

    switch indexJoinType {
    case 1: // IndexHashJoin
        hashTableCost = hashBuildCostVer2(option, buildRows, buildRowSize, float64(len(p.RightJoinKeys)), cpuFactor, memFactor)
    case 2: // IndexMergeJoin
        hashTableCost = newZeroCostVer2(traceCost(option))
    default: // IndexJoin
        hashTableCost = hashBuildCostVer2(option, probeRowsTot, probeRowSize, float64(len(p.LeftJoinKeys)), cpuFactor, memFactor)
    }

对应办法：

func hashBuildCostVer2(option *PlanCostOption, buildRows, buildRowSize, nKeys float64, cpuFactor, memFactor costVer2Factor) costVer2 {// TODO: 1) consider types of keys, 2) dedicated factor for build-probe hash table
    hashKeyCost := newCostVer2(option, cpuFactor,
        buildRows*nKeys*cpuFactor.Value,
        func() string { return fmt.Sprintf("hashkey(%v*%v*%v)", buildRows, nKeys, cpuFactor) })
    hashMemCost := newCostVer2(option, memFactor,
        buildRows*buildRowSize*memFactor.Value,
        func() string { return fmt.Sprintf("hashmem(%v*%v*%v)", buildRows, buildRowSize, memFactor) })
    hashBuildCost := newCostVer2(option, cpuFactor,
        buildRows*cpuFactor.Value,
        func() string { return fmt.Sprintf("hashbuild(%v*%v)", buildRows, cpuFactor) })
    return sumCostVer2(hashKeyCost, hashMemCost, hashBuildCost)
}

func newZeroCostVer2(trace bool) (ret costVer2) {
    if trace {ret.trace = &costTrace{make(map[string]float64), ""}
    }
    return
}

简略的看一下代码，咱们能够发现，从大多数的场景来看，依照代价从小到大来排，这几种 Join 是 MergeJoin<HashJoin<IndexJoin。

5.4.2 执行打算枚举与择优

总得来说这块代码较为简单，实质就是枚举所有符合条件的物理执行打算，并挑选出代价最小的执行打算，故不再列举代码。有趣味的同学能够依据以下纲要自行翻阅：

|--planner/core/find_best_task.go

\-- findBestTask

\-- enumeratePhysicalPlans4Task

\-- compareTaskCost

\-- getTaskPlanCost

|-- planner/core/plan_cost_ver2.go

\-- getPlanCost

6. 其余

6.1 参考与援用的文章

• Cascades Optimizer：https://zhuanlan.zhihu.com/p/73545345
• 揭秘 TiDB 新优化器：Cascades Planner 原理解析：https://cn.pingcap.com/blog/tidb-cascades-planner/
• TiDB 文档 - 统计信息简介：https://docs.pingcap.com/zh/tidb/v6.5/statistics#%E7%BB%9F%E8…
• TiDB 文档 - 谬误索引的解决方案：https://docs.pingcap.com/zh/tidb/v6.5/wrong-index-solution#%E…
• The Volcano Optimizer Generator: Extensibility and Efficient Search：https://15721.courses.cs.cmu.edu/spring2019/papers/22-optimiz…
• The Cascades Framework for Query Optimization：https://15721.courses.cs.cmu.edu/spring2018/papers/15-optimiz…

6.2 常识补充：code generation && vectorized execution

数据库引擎执行器中十分闻名的两种优化形式，code generation 和 vectorized execution。

code generation 次要是依据上下文来生成一整段优化过的代码，这与那种嵌套大量 if…else、for 循环、虚办法的代码齐全相同，齐全面向性能思考。

vectorized execution 基于拉模型。相比于一次拉一个 tuple 来说，它的批量拉取缩小了屡次拉取的开销，同时还能够应用到 SIMD。基于这种场景，vectorized execution 的优化更加实用于列式数据库。