优化器直方图
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@@ -1,8 +1,8 @@
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module ChuSQL.Core.Engine.Algebra.Cost (tableMetaOf, probeCost, pointRows, rangeRows, indexCheaper) where
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module ChuSQL.Core.Engine.Algebra.Cost (tableMetaOf, probeCost, pointRows, rangeRows, selectivityOf, indexCheaper) where
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import ChuSQL.Core.Model
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-- 统计与成本估算：行数、列级不同值数与索引探路页数。
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-- 统计与成本估算：行数、不同值数、列直方图与索引探路页数。
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-- | 表统计，拿不到就是 Nothing
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tableMetaOf :: Database -> String -> Maybe TableMeta
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@@ -20,9 +20,42 @@ pointRows m col = case [d | (c, d, _) <- metaDistinct m, c == col, d > 1] of
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where
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rows = max 0 (metaRowCount m)
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-- | 范围扫描的估算命中行数：没有直方图，按四分之一算
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rangeRows :: TableMeta -> Int
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rangeRows m = max 0 (metaRowCount m) `div` 4
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-- | 范围扫描的估算命中行数：有直方图按桶算，没有按四分之一
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rangeRows :: TableMeta -> String -> Maybe (Value, Bool) -> Maybe (Value, Bool) -> Int
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rangeRows m col lo hi = case histogramFor m col of
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Just h -> estimateRows h lo hi
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Nothing -> max 0 (metaRowCount m) `div` 4
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-- | 直方图估算区间命中行数：按桶算交集占比
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estimateRows :: Histogram -> Maybe (Value, Bool) -> Maybe (Value, Bool) -> Int
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estimateRows h lo hi = max 0 (min total (round (sum (zipWith overlap [0 ..] (histBuckets h)))))
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where
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total = sum (histBuckets h)
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width = if histHigh h > histLow h then (histHigh h - histLow h) / fromIntegral (length (histBuckets h)) else 0
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lower = maybe (-1 / 0) id (boundOf lo)
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upper = maybe (1 / 0) id (boundOf hi)
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overlap i count
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| width <= 0 = if lower <= histLow h && histLow h <= upper then fromIntegral count else 0
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| otherwise = fromIntegral count * hit / width
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where
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start = histLow h + width * fromIntegral i
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hit = max 0 (min (start + width) upper - max start lower)
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-- | 区间选择率：直方图命中的比例；没有直方图给 Nothing
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selectivityOf :: TableMeta -> String -> Maybe (Value, Bool) -> Maybe (Value, Bool) -> Maybe Double
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selectivityOf m col lo hi = case histogramFor m col of
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Nothing -> Nothing
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Just h
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| total <= 0 -> Nothing
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| otherwise -> Just (fromIntegral (estimateRows h lo hi) / fromIntegral total)
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where
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total = sum (histBuckets h)
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-- | 边界值转成参与估值的小数；非数值给 Nothing
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boundOf :: Maybe (Value, Bool) -> Maybe Double
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boundOf (Just (VInt n, _)) = Just (fromIntegral n)
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boundOf (Just (VFloat d, _)) = Just d
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boundOf _ = Nothing
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-- | 有索引且探路加命中比全表扫便宜
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indexCheaper :: TableMeta -> String -> Int -> Bool
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@@ -1,6 +1,6 @@
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module ChuSQL.Core.Engine.Algebra.JoinOrder (reorderJoins) where
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import ChuSQL.Core.Engine.Algebra.Cost (pointRows, rangeRows, tableMetaOf)
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import ChuSQL.Core.Engine.Algebra.Cost (pointRows, rangeRows, selectivityOf, tableMetaOf)
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import ChuSQL.Core.Engine.Algebra.Expr (colsInExpr, hasDivision)
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import ChuSQL.Core.Engine.Algebra.Op (RelOp (..), relOpCols)
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import ChuSQL.Core.Engine.Syntax.AST (Expr (..), JoinKind (..))
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@@ -45,7 +45,7 @@ leafRows :: Database -> RelOp -> Maybe Int
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leafRows db op = case op of
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Scan _ t _ -> rowCountOf db t
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Lookup _ t c _ -> pointRows <$> tableMetaOf db t <*> pure c
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Range _ t _ _ _ -> rangeRows <$> tableMetaOf db t
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Range _ t c lo hi -> (\m -> rangeRows m c lo hi) <$> tableMetaOf db t
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Filter p x -> scaleRows db p x <$> leafRows db x
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Project _ x -> leafRows db x
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_ -> Nothing
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@@ -54,12 +54,20 @@ leafRows db op = case op of
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rowCountOf :: Database -> String -> Maybe Int
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rowCountOf db t = metaRowCount <$> tableMetaOf db t
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-- | 过滤之后的大致行数：等值看不同值数，其他按四分之一
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-- | 行数估算：等值看不同值数，区间看直方图，其余四分之一
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scaleRows :: Database -> Expr -> RelOp -> Int -> Int
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scaleRows db p x rows = case p of
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Eq (Col k) _ -> case distinctOf db x k of
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Just d | d > 1 -> max 1 (rows `div` d)
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_ -> quarter
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Gt (Col k) (LitInt v) -> pick k (Just (VInt v, False)) Nothing
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Gt (Col k) (LitStr v) -> pick k (Just (VStr v, False)) Nothing
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GtE (Col k) (LitInt v) -> pick k (Just (VInt v, True)) Nothing
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GtE (Col k) (LitStr v) -> pick k (Just (VStr v, True)) Nothing
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Lt (Col k) (LitInt v) -> pick k Nothing (Just (VInt v, False))
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Lt (Col k) (LitStr v) -> pick k Nothing (Just (VStr v, False))
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LtE (Col k) (LitInt v) -> pick k Nothing (Just (VInt v, True))
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LtE (Col k) (LitStr v) -> pick k Nothing (Just (VStr v, True))
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Gt _ _ -> quarter
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Lt _ _ -> quarter
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GtE _ _ -> quarter
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@@ -70,6 +78,11 @@ scaleRows db p x rows = case p of
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_ -> quarter
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where
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quarter = max 1 (rows `div` 4)
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pick k lo hi = case leafSource x of
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Just (alias, t)
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| Just m <- tableMetaOf db t
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, Just s <- selectivityOf m (unqualify alias k) lo hi -> max 1 (round (fromIntegral rows * s))
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_ -> quarter
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-- | 叶子对应的别名与表名
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leafSource :: RelOp -> Maybe (Maybe String, String)
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@@ -159,10 +159,10 @@ worthLookup db t col = case tableMetaOf db t of
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Just m -> indexCheaper m col (pointRows m col)
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-- | 范围扫描值不值得改写；没有统计就按老规矩改
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worthRange :: Database -> String -> String -> Bool
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worthRange db t col = case tableMetaOf db t of
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worthRange :: Database -> String -> String -> Maybe (Value, Bool) -> Maybe (Value, Bool) -> Bool
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worthRange db t col lo hi = case tableMetaOf db t of
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Nothing -> True
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Just m -> indexCheaper m col (rangeRows m)
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Just m -> indexCheaper m col (rangeRows m col lo hi)
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-- | 单节点重写
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rewriteNode :: Database -> RelOp -> RelOp
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@@ -171,45 +171,53 @@ rewriteNode db (Filter (Eq (Col k) (LitInt v)) (Scan mAlias t Nothing))
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rewriteNode db (Filter (Eq (Col k) (LitStr v)) (Scan mAlias t Nothing))
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| worthLookup db t (unqualify mAlias k) = Lookup mAlias t (unqualify mAlias k) (VStr v)
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rewriteNode db (Filter (And (Gt (Col k1) (LitInt lo)) (Lt (Col k2) (LitInt hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VInt lo, False)) (Just (VInt hi, False)) =
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Range mAlias t (unqualify mAlias k1) (Just (VInt lo, False)) (Just (VInt hi, False))
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rewriteNode db (Filter (And (Gt (Col k1) (LitStr lo)) (Lt (Col k2) (LitStr hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VStr lo, False)) (Just (VStr hi, False)) =
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Range mAlias t (unqualify mAlias k1) (Just (VStr lo, False)) (Just (VStr hi, False))
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rewriteNode db (Filter (Gt (Col k) (LitInt v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) (Just (VInt v, False)) Nothing
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| worthRange db t (unqualify mAlias k) (Just (VInt v, False)) Nothing =
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Range mAlias t (unqualify mAlias k) (Just (VInt v, False)) Nothing
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rewriteNode db (Filter (Gt (Col k) (LitStr v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) (Just (VStr v, False)) Nothing
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| worthRange db t (unqualify mAlias k) (Just (VStr v, False)) Nothing =
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Range mAlias t (unqualify mAlias k) (Just (VStr v, False)) Nothing
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rewriteNode db (Filter (Lt (Col k) (LitInt v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) Nothing (Just (VInt v, False))
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| worthRange db t (unqualify mAlias k) Nothing (Just (VInt v, False)) =
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Range mAlias t (unqualify mAlias k) Nothing (Just (VInt v, False))
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rewriteNode db (Filter (Lt (Col k) (LitStr v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) Nothing (Just (VStr v, False))
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| worthRange db t (unqualify mAlias k) Nothing (Just (VStr v, False)) =
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Range mAlias t (unqualify mAlias k) Nothing (Just (VStr v, False))
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rewriteNode db (Filter (And (GtE (Col k1) (LitInt lo)) (LtE (Col k2) (LitInt hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VInt lo, True)) (Just (VInt hi, True)) =
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Range mAlias t (unqualify mAlias k1) (Just (VInt lo, True)) (Just (VInt hi, True))
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rewriteNode db (Filter (And (GtE (Col k1) (LitInt lo)) (Lt (Col k2) (LitInt hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VInt lo, True)) (Just (VInt hi, False)) =
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Range mAlias t (unqualify mAlias k1) (Just (VInt lo, True)) (Just (VInt hi, False))
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rewriteNode db (Filter (And (Gt (Col k1) (LitInt lo)) (LtE (Col k2) (LitInt hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VInt lo, False)) (Just (VInt hi, True)) =
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Range mAlias t (unqualify mAlias k1) (Just (VInt lo, False)) (Just (VInt hi, True))
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rewriteNode db (Filter (And (GtE (Col k1) (LitStr lo)) (LtE (Col k2) (LitStr hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VStr lo, True)) (Just (VStr hi, True)) =
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Range mAlias t (unqualify mAlias k1) (Just (VStr lo, True)) (Just (VStr hi, True))
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rewriteNode db (Filter (And (GtE (Col k1) (LitStr lo)) (Lt (Col k2) (LitStr hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VStr lo, True)) (Just (VStr hi, False)) =
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Range mAlias t (unqualify mAlias k1) (Just (VStr lo, True)) (Just (VStr hi, False))
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rewriteNode db (Filter (And (Gt (Col k1) (LitStr lo)) (LtE (Col k2) (LitStr hi))) (Scan mAlias t Nothing))
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| k1 == k2 && worthRange db t (unqualify mAlias k1) =
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| k1 == k2 && worthRange db t (unqualify mAlias k1) (Just (VStr lo, False)) (Just (VStr hi, True)) =
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Range mAlias t (unqualify mAlias k1) (Just (VStr lo, False)) (Just (VStr hi, True))
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rewriteNode db (Filter (GtE (Col k) (LitInt v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) (Just (VInt v, True)) Nothing
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| worthRange db t (unqualify mAlias k) (Just (VInt v, True)) Nothing =
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Range mAlias t (unqualify mAlias k) (Just (VInt v, True)) Nothing
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rewriteNode db (Filter (GtE (Col k) (LitStr v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) (Just (VStr v, True)) Nothing
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| worthRange db t (unqualify mAlias k) (Just (VStr v, True)) Nothing =
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Range mAlias t (unqualify mAlias k) (Just (VStr v, True)) Nothing
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rewriteNode db (Filter (LtE (Col k) (LitInt v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) Nothing (Just (VInt v, True))
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| worthRange db t (unqualify mAlias k) Nothing (Just (VInt v, True)) =
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Range mAlias t (unqualify mAlias k) Nothing (Just (VInt v, True))
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rewriteNode db (Filter (LtE (Col k) (LitStr v)) (Scan mAlias t Nothing))
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| worthRange db t (unqualify mAlias k) = Range mAlias t (unqualify mAlias k) Nothing (Just (VStr v, True))
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| worthRange db t (unqualify mAlias k) Nothing (Just (VStr v, True)) =
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Range mAlias t (unqualify mAlias k) Nothing (Just (VStr v, True))
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rewriteNode db (Filter p (Join kind l r c))
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| not (hasDivision p || planHasDivision (Join kind l r c)) =
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case kind of
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@@ -401,7 +401,7 @@ instance MonadStorage IPCStorage where
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-- | 线上表信息转引擎侧统计
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metaOf :: TableInfo -> TableMeta
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metaOf info = TableMeta (tiRows info) (tiStats info) (tiIndexes info)
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metaOf info = TableMeta (tiRows info) (tiStats info) (tiHistograms info) (tiIndexes info)
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-- | 没设库名就照单全收；设了库名只收这个库的表，键名去掉库名前缀
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visibleTables :: Maybe String -> TableInfo -> [(String, Table)]
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@@ -2,6 +2,7 @@
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module Main where
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import ChuSQL.Core.Engine.Algebra.Cost (rangeRows, selectivityOf)
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import ChuSQL.Core.Engine.Algebra.Eval (evalRelOp, evalRelOpM)
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import ChuSQL.Core.Engine.Algebra.Expr (colsInExpr, evalExpr)
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import ChuSQL.Core.Engine.Algebra.Op (RelOp (..), renderPlan)
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@@ -71,7 +72,7 @@ chainA =
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{ tableName = "a"
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, tableCols = [("id", TInt), ("name", TStr)]
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, tableRows = [[("id", VInt n), ("name", VStr ("a" ++ show n))] | n <- [1 .. 6]]
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, tableMeta = Just (TableMeta 6 [("id", 6, False)] ["id"])
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, tableMeta = Just (TableMeta 6 [("id", 6, False)] [] ["id"])
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}
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-- | 连接链测试表 b：4 行，a_id 各不相同
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@@ -81,7 +82,7 @@ chainB =
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{ tableName = "b"
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, tableCols = [("id", TInt), ("a_id", TInt)]
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, tableRows = [[("id", VInt n), ("a_id", VInt n)] | n <- [1 .. 4]]
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, tableMeta = Just (TableMeta 4 [("id", 4, False), ("a_id", 4, False)] ["id"])
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, tableMeta = Just (TableMeta 4 [("id", 4, False), ("a_id", 4, False)] [] ["id"])
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}
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-- | 连接链测试表 c：2 行，b_id 各不相同
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@@ -91,7 +92,7 @@ chainC =
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{ tableName = "c"
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, tableCols = [("id", TInt), ("b_id", TInt)]
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, tableRows = [[("id", VInt n), ("b_id", VInt n)] | n <- [1, 2]]
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, tableMeta = Just (TableMeta 2 [("id", 2, False), ("b_id", 2, False)] ["id"])
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, tableMeta = Just (TableMeta 2 [("id", 2, False), ("b_id", 2, False)] [] ["id"])
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}
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-- | 三张表组成的连接链测试库
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@@ -551,7 +552,7 @@ main = hspec $ do
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executeOperator OpNe [VInt 1, VFloat 1.0] `shouldBe` Right (VBool False)
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it "rewrites >= and <= into an inclusive index range" $ do
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let stat rows distinct indexes = TableMeta rows [(c, d, False) | (c, d) <- distinct] indexes
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let stat rows distinct indexes = TableMeta rows [(c, d, False) | (c, d) <- distinct] [] indexes
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dbWith m = [("users", Table "users" [("id", TInt), ("name", TStr)] [] (Just m))]
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indexed = dbWith (stat 10000 [("id", 10000)] ["id"])
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low = Filter (GtE (Col "id") (LitInt 2)) (Scan Nothing "users" Nothing)
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@@ -1509,6 +1510,44 @@ main = hspec $ do
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[ [("name", VStr "Carol")]
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]
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describe "ChuSQL.Core.Engine.Algebra.Cost (直方图)" $ do
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it "builds a 16-bucket histogram from the numeric values" $ do
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let hist = histogramOf [VInt n | n <- [0 .. 99]]
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fmap histLow hist `shouldBe` Just 0
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fmap histHigh hist `shouldBe` Just 99
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fmap (length . histBuckets) hist `shouldBe` Just 16
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fmap (sum . histBuckets) hist `shouldBe` Just 100
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-- 非数值与 NULL 不参与；只有一个值都落第 0 桶
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histogramOf [VStr "a", VNull] `shouldBe` Nothing
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histogramOf [VInt 5, VNull, VStr "a"] `shouldBe` Just (Histogram 5 5 (1 : replicate 15 0))
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it "estimates a range from the histogram buckets" $ do
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let hist = Histogram 0 1600 (replicate 16 100)
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meta = TableMeta 1600 [] [("id", hist)] ["id"]
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plain = TableMeta 1600 [] [] []
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rangeRows meta "id" (Just (VInt 0, True)) (Just (VInt 100, True)) `shouldBe` 100
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rangeRows meta "id" Nothing Nothing `shouldBe` 1600
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selectivityOf meta "id" (Just (VInt 0, True)) (Just (VInt 100, True)) `shouldBe` Just 0.0625
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-- 没有直方图退回四分之一
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rangeRows plain "id" Nothing Nothing `shouldBe` 400
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selectivityOf plain "id" Nothing Nothing `shouldBe` Nothing
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it "uses the histogram to reject a range that would scan most rows" $ do
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let buckets = replicate 8 63 ++ replicate 8 62
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withHist = TableMeta 1000 [("id", 1000, False)] [("id", Histogram 0 1600 buckets)] ["id"]
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plain = TableMeta 1000 [("id", 1000, False)] [] ["id"]
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dbWith m = [("users", Table "users" [("id", TInt), ("name", TStr)] [] (Just m))]
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narrow = Filter (And (GtE (Col "id") (LitInt 10)) (LtE (Col "id") (LitInt 20))) (Scan Nothing "users" Nothing)
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wide = Filter (Gt (Col "id") (LitInt 0)) (Scan Nothing "users" Nothing)
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-- 直方图说这个窄范围只命中十几行：改写
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optimize (dbWith withHist) narrow
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`shouldBe` Range Nothing "users" "id" (Just (VInt 10, True)) (Just (VInt 20, True))
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-- 直方图说这条范围覆盖全表：索引不比全表扫便宜，不改写
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optimize (dbWith withHist) wide `shouldBe` wide
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-- 没有直方图按四分之一算，仍然改写
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optimize (dbWith plain) wide
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`shouldBe` Range Nothing "users" "id" (Just (VInt 0, False)) Nothing
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describe "ChuSQL.Core.Engine.Algebra.Optimize" $ do
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it "keeps single-table WHERE results identical" $ do
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sameResultAsUnoptimized "SELECT name FROM users WHERE age > 18"
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@@ -1559,7 +1598,7 @@ main = hspec $ do
|
||||
`shouldBe` Right (Just (LitBool False))
|
||||
|
||||
it "picks the index only when the statistics make it cheaper" $ do
|
||||
let stat rows distinct indexes = TableMeta rows [(c, d, False) | (c, d) <- distinct] indexes
|
||||
let stat rows distinct indexes = TableMeta rows [(c, d, False) | (c, d) <- distinct] [] indexes
|
||||
dbWith m = [("users", Table "users" [("id", TInt), ("name", TStr)] [] (Just m))]
|
||||
unknown = [("users", Table "users" [("id", TInt), ("name", TStr)] [] Nothing)]
|
||||
point = Filter (Eq (Col "id") (LitInt 1)) (Scan Nothing "users" Nothing)
|
||||
@@ -2689,7 +2728,7 @@ rowShards width rows
|
||||
|
||||
-- | 声明 1000 行的大表
|
||||
bigTable :: Table
|
||||
bigTable = users {tableName = "big", tableMeta = Just (TableMeta 1000 [("id", 1000, False)] ["id"])}
|
||||
bigTable = users {tableName = "big", tableMeta = Just (TableMeta 1000 [("id", 1000, False)] [] ["id"])}
|
||||
|
||||
-- | 只装大表的库
|
||||
bigDB :: Database
|
||||
|
||||
Reference in new issue
Block a user