Tuesday, January 31, 2012

DAX Query Plan, Part 2, Operator Properties

Last time we learned that DAX Query Plans are tree structures formatted as indented text with each text line representing a single operator node in a tree. A text line begins with an operator name followed by a colon and then properties of the operator. Today we study the operator properties. You will see that for the four types of operators, ScaLogOp, RelLogOp, LookupPhyOp, and IterPhyOp, each type has a fixed set of common properties, and an individual operator may contain extra properties to provide supplemental information. We’ll focus on the semantics of the common properties in this post.

List of Columns
In a DAX Query Plan, a list of columns is shown as a list of comma-delimited column numbers in a pair of parentheses plus a list of comma-delimited fully-qualified column names in another pair of parentheses, see Figure 1. In a degenerate case, two pairs of empty parentheses, ()(), represent an empty list. Note that some properties, like LookupCols and IterCols, are not shown in the plan when they contain no columns, but other properties, like DependOnCols and RequiredCols, are always shown even when their list of columns is empty.

Column numbers are helpful when you need to disambiguate two separate references to the same column. When you execute Query 1 against the tabular AdventureWorks database, the logical plan, shown in Figure 2, assigns different numbers to column ‘Date’[Month]: number 1 refers to the column in the outer table scan and number 2 refers to the column in the inner table scan. Column numbers are not chosen to be globally unique, but rather unique within a local context.
// Query 1
define measure 'Internet Sales'[Total Sales Amount] = Sum([Sales Amount])
      values('Date'[Month]),           -- outer scan
      calculate([Total Sales Amount],
            All('Date'[Month]),        -- inner scan
            'Date'[Month]              -- refer to inner scan
            earlier('Date'[Month])     -- refer to outer scan
    'Date'[Calendar Year] = 2003

Common Properties of Logical Plan Nodes

Here are the properties common to all scalar logical operators (ScaLogOp):

·         DependOnCols
Marks columns from the left-side of a tree on which the current logical operator depends. The current operator may return a different value for each distinct combination of values of DependOnCols. Some table scanning functions, e.g. AddColumns and Filter, create a row context using its left child subtree and then evaluate the value of its right child subtree in this context. This creates a dependency of the right child subtree on some columns from the left child subtree. DependOnCols captures this correlation between the two sides of a tree. Figure 3 shows an example where a ScaLogOp subtree on the right depends on some columns from two RelLogOp subtrees on the left. At the bottom level of a tree, DependOnCols are established by either an explicit reference to a column on the left or by a leaf table scan that joins directly or indirectly (through SetFilter arguments of Calculate function) to columns on the left. DependOnCols are then propagated up through intermediate parent nodes to the root node of the right subtree. Since DAX automatic cross-table filtering rules can be tricky sometimes, beginners can use this property to help them figure out whether their measures have the correct dependencies on external row contexts.

·         Data type
One of the six data types DAX supports. Values returned by the operator must be either of this data type or be the BLANK value.

·         DominantValue
Captures the sparsity of a scalar logical operator. When DominantValue is NONE, the operator is dense, otherwise, it is sparse. When a scalar subtree is sparse, DAX Formula Engine may pick a physical plan that can be orders of magnitudes faster than a na├»ve physical plan. For example, if the predicate child operator of a Filter operator has a DominantValue of FALSE, DAX Formula Engine can construct an iterator physical plan for the predicate subtree that automatically skips large chunks of rows which would otherwise return FALSE and be thrown away any way by the Filter operator.  For users coming from MDX background, this reminds them of the huge performance difference between block mode vs. cell-by-cell mode. The technique to derive the sparsity of a scalar subtree is very sophisticated and beyond the scope of this post. It’s enough to know that a sparse scalar operator is the key to great performance in many common query patterns.

Here are properties common to all relational logical operators (RelLogOp):
·         DependOnCols
Identical to the same named property of ScaLogOp. The current operator may return a different table for each distinct combination of values of DependOnCols.
·         Range of column numbers
Although a relation may contain many columns in its heading, DAX Formula Engine is smart enough to derive the minimal subset of columns, see RequiredCols property, which are needed to answer a query. To save space, DAX Query Plan does not list all columns in the relation header, instead, it assigns continuous column numbers to all columns in the relation header and only shows <beginning column name>-<ending column name> as a part of the plan. Note that this property may be missing when a relation has no column at all.
·         RequiredCols
This is the union of DependOnCols and the subset of columns from the relation header which are needed to answer a query. For example, when you examine the logical plan, shown in Figure 4, which corresponds to Query 2, you can see that only one column, [Sales Amount], among 129 columns is a required column. In case you are wondering why ‘Internet Sales’ table has 129 columns, you can find the answer in one of my earlier posts.
// Query 2
define measure 'Internet Sales'[Total Sales Amount] = Sum([Sales Amount])
evaluate row("x", [Total Sales Amount])

Common Properties of Physical Plan Nodes
In a physical plan tree, an iterator operator supplies rows of column values to other nodes. When those rows are fed to a lookup operator, it can return a scalar value from each input row. When the rows are fed to another iterator operator, it can output any number of rows of its own columns for each input row. Therefore, both iterators and lookups share the same input property, LookupCols, but they produce different outputs. Let’s use the physical plan tree, shown in Figure 5, captured from Query 1 to illustrate the common properties of physical operators.
Here are the properties common to all lookup physical operators (LookupPhyOp):
·         LookupCols
Columns supplied by an iterator whose values are used to calculate a scalar value. In Figure 5, lookup operators 1 and 2 read their input values from iterator 3; their output values are later on used by their parent operator, LessThanOrEqualTo, to calculate a Boolean value.
·         Data type
One of the six data types DAX supports. Values returned by the operator must be either of this data type or be the BLANK value.
Here are the properties common to all iterator physical operators (IterPhyOp):
·         LookupCols
Identical to the same named property of LookupPhyOp. In Figure 5, iterator 5, which doesn’t have the LookupCols property, hence a pure iterator, supplies column 2 to iterator 4 as its LookupCols property which in turn produces output column 1.
·         IterCols
Columns output by the iterator.
It is interesting to learn that a DAX iterator can be a pure iterator, when it only has the IterCols property, or a table-valued function as in T-SQL Apply operator when it has both LookupCols and IterCols properties, or a pure row checker when it only has the LookupCols property. In the last case, the iterator serves the purpose of removing unwanted rows from other iterators.
For many DAX operators, common properties are all they offer. But some DAX operators output additional properties to provide more information about themselves. I am not going to go into details about all those operator-specific properties today because it would drag this blog on far too long. I’ll only describe the proprietary properties of one physical operator Spool_IterOnly and postpone the discussion of private properties of other operators in future blogs when we get to study individual operators.
Special Properties of Physical Operator Spool_IterOnly<>
Spool_IterOnly is a pure iterator that draws its rows from an in-memory spool which is built through some other means. DAX Formula Engine builds different flavors of in-memory spools, therefore Spool_IterOnly along with several other physical operators built from spools put the name of the spool in a pair of angle brackets <> as a part of their names. This is partly caused by the fact that spools are not first class citizens in query plan trees as of SQL Server 2012. As a result, some spool specific properties are added directly to physical operators built on top of the spool. Below is one line I extracted from Figure 5 with Spool_IterOnly specific properties highlighted in bold face. They tell us that there are 12 records in the spool and there are 240 key columns (most of which are compressed to 0 bit hence record size is not as wide as it seems) and no value columns.
Spool_IterOnly<Spool>: IterPhyOp IterCols(1)('Date'[Month]) #Records=12 #KeyCols=240 #ValueCols=0
Today we studied properties of operator nodes in DAX Query Plan trees. We have learned that some properties are common to all operators of one type and some properties are specific to a particular operator. While I described in details those common properties, I just cited one example of operator specific properties. Now that we have covered the basics of DAX Query Plans, we will be able to explore ways to take advantage of them to investigate performance issues in future posts. When we run into a specific operator of importance, I’ll explain its associated properties at that time.