PerfML Part 2: Self-Tuning with a Tally Table

In PerfML Part 1 we covered a some new algorithms for creating a self-tuning function. In Part 2 we’ll turbo charge our algorithm with parallelism and a tally table.

Before You Begin

This is the second article about PerfML, where I introduced some new concepts, as well as some less common ones which will be referenced heavily in this article, such as the dynamic algorithm (completely unrelated to dynamic programming). If you haven’t read Part 1, I suggest you do so before continuing as you will get much more out of this article. I use delimitedsplit8k, fnTally and make_parallel so grab a copy of each if you are playing along at home.


In Part 1 of this series you were introduced to the self-tuning function and PerfML, the science of creating fast, deterministic, elegant self-tuning routines such as functions and stored procedures. We reviewed the difference between exact and approximation algorithms and how they can be combined to return a deterministic result. I also introduced a new type of parameter: the gap parameter (G)which can be used to add gaps to a sequence the purpose of creating an approximation algorithm. We then created a string search routine which leveraged an exact, brute force algorithm to find a specific sequence in a string. Then we transformed the function to leverage an approximation algorithm using our gap parameter which allowed us to introduce a margin of error, or range of possible valid values, while reducing the cost of the algorithm by a factor of G while preserving the ability to return an exact result when G=1. Lastly, we reviewed how to reduce the search area of our exact algorithm by first using an approximation to identify a much smaller range of possible valid answers.

Today I’ll define and teach you how to use a tuning parameter, the most important component of PerfML. A tuning parameter can be defined as:

A parameter that allows you to dynamically tune a deterministic function’s algorithm while guaranteeing the same deterministic return value.

The gap parameter (introduced in Part 1), is a form of tuning parameter. The tuning parameter is the core component of PerfML, tuning parameters are where your intelligence lives. For any given input there can be only one tuning parameter value which does the least amount of work, that value will be perform the best – both in speed and resource usage (memory, IO). Determining the best value for your tuning parameter is the most important (and daunting) task you will perform while developing self-tuning functions; master this and your algorithms will figure out how to mater themselves. Choosing the best tuning parameter value can be done as part of a pre-processing task, at runtime or a combination of both. This will all make more sense when you see the code examples.

Sequential to Set-Based with fnTally

In part 1 we created a self-tuning function leveraging a self-referencing recursive scalar UDF. The goal was not to develop the most performant function but rather to understand the algorithms and other new concepts which are vital to PerfML; iterative programming and basic recursion are easier to understand. Functions are a vital component of any major programming language and avoiding loops, and other iterative, RBAR-style logic is vital to writing fast clean code in most declarative programming languages. For this series I’m using Microsoft SQL server which means we’ll be using fnTally by SQL MVP Jeff Moden to replace our loop logic fromPart 1. There are many advantages to a tally table of a loop, these are the ones I consider most important:

  1. Speed
  2. Functional Purity
  3. Ability to measure performance
  4. Parallel execution
1.    Speed

First, a lazy sequence (CTE tally table in this case) will perform faster than a loop, cursor, iterative recursion (using recursion for counting) and any other iterative methods used for solving common programming problems. fnTally counts to one billion in 90 seconds on my laptop. Second, the fastest kind of T-SQL function in SQL Server is the Inline Table Valued Function (iTVF). With iTVFs, however, data structures are immutable so there is no way to perform your typical loop (do, while, etc.) This leaves you two options in SQL: recursion  or a tally table. Recursion is slow, tally tables are fast and virtually I/O free (readless). Because of the immutable data structures, the functional purity of an iTVF and  speed of a quality tally table or tally table function, the SQL optimizer a full range of options including the ability to multi-thread execution, that is, leverage parallelism.  

2.    Functional Purity

fnTally is an iTVF, which is SQL Server’s version of a pure function . Pure functions are generally side-effect free, don’t experience memory leaks and allow for very clean, concise and reusable code. Note the Advantages of pure functions section of this Microsoft article: Functional programming vs. imperative programming and the benefits on SQL iTVFs in Paul White’s article about APPLY.

The primary reason to implement functional transformations as pure functions is that pure functions are composable: that is, self-contained and stateless. These characteristics bring a number of benefits, including the following:

  1. Increased readability and maintainability. This is because each function is designed to accomplish a specific task given its arguments. The function doesn’t rely on any external state.
  2. Easier reiterative development. Because the code is easier to refactor, changes to design are often easier to implement. For example, suppose you write a complicated transformation, and then realize that some code is repeated several times in the transformation. If you refactor through a pure method, you can call your pure method at will without worrying about side effects.
  3. Easier testing and debugging. Because pure functions can more easily be tested in isolation, you can write test code that calls the pure function with typical values, valid edge cases, and invalid edge cases.

Starting with fast and clean pure functions for our self-tuning algorithms will keep your functions blazing while being easier to debug.

3.    Measuring Performance

It is very difficult to accurately measure scalar UDF performance (except when leveraging SQL Server 2019 scalar UDF inlining.) Key performance metric collection tasks such as measuring I/O, accurate run times and even extracting a usable execution plan are impossible when writing non-inline (impure) T-SQL scalar UDFs. The opposite is true with an inline table valued function (iTVF); fnTally is an iTVF and will be used later in this article for the logic used to replace our recursive scalar logic from Part 1 (dbo.stringSearchV1) .Below is a portion  of the execution plan from dbo.stringSearch (truncated for brevity) which leverages fnTally.

Our iTVF that generated the plan above uses the same “exact approximation” logic we used in our scalar UDF from the previous article. In this plan, because I’m familiar with my logic I can see that approximation algorithm retrieves 32,064 rows from my fnTally, which grows to 42,064 during the merge join. The exact algorithm then requires another 18,144 rows from fnTally which grows to 26,613 during the second merge join. The number of iterations for the scalar UDF is a mystery; all we know for sure as you will see, is that the fnTally version is profoundly faster.

4.    Parallel Execution

T-SQL scalar UDFs (as well as multi-statement table values functions) cannot utilize a parallel execution plan unless they can leverage SQL Server 2019 scalar UDF inlining, and still parallel execution is not possible with inlined scalar UDFs that are self-referencing (in my experience). iTVFs that leverage fnTally, on the other hand, can be processed asynchronously and are often substantially faster as you will see momentarily.

Most of my functions which leverage a tally table or correctly developed tally table function, such as dbo.fnTally, run much faster when leveraging a parallel execution plan. Sometimes a parallel plan yields no performance benefit at all which, then, is a liability – you have multiple CPUs doing the job of one instead doing something more productive. Sometimes parallel plans are slower than serial, that’s an even bigger bummer. Sometimes it’s system/instance level settings (e.g. cost threshold for parallelism) and sometimes even your set-based code is bad (set-based != bullet proof.) Sometimes the optimizer just gets it wrong. Either way, if you need a parallel execution plan you have two options, Trace Flag 8649 and make_parallel by Adam Machanic. Trace Flag 8649 is not documented and therefore not safe for production. make_parallel is a simple T-SQL function which, in short, freaks the optimizer out and causes it to choose parallel execution if it’s available. make_parallel adds a lot of bloat to the execution plan so: in Dev I use the trace flag, in Production I use make_parallel when I have determined that doing so is the best option.

Function Logic

We are going to build the same function from part 1, dbo.stringsearchV1, using fnTally for our iterative logic. These are the parameters we’ll use:

  @G BIGINT       = 5,   -- gap param
  @C VARCHAR(100) = 'X', -- search character
  @L BIGINT       = 1,   -- min length
  @H BIGINT       = 22,  -- max length
  @S VARCHAR(MAX) = '999999999-XXXXXXXXXXXXXX-999999999'; -- sample search string

fnTally takes two parameters: @ZeroOrOne, which determines is the first row will be zero or one; we will set this to 0. @MaxN will be the highest integer returned, for @MaxN I came up with this formula: (@H-@L+1)/@G+SIGN((@H-@L+1)%@G); it will determine the correct number of rows with the @G-sized gaps in the.

Avoiding the descending sort

SQL sorts generally have a complexity of N log N, which is worse than linear. This means that the more rows we sort, the cost to sort each row increases. For row counts in the 10’s of thousands, this is not a big deal but it becomes a problem when we get into the 100’s of thousands and beyond.

The recursive solution from Part 1 did not require a sort to determine the “longest” allowable string. For our fnTally version we will be seeking the longest value which does requires us to use an ORDER BY N DESC clause. To circumvent this problem we can return N is descending order using Jeff Moden’s formula: @MaxN-N+1, mentioned in the fnTally documentation. This only works, however, when we are seeking an exact result (@G=1) and, therefore, no gaps in the sequence.

To return the numbers beginning with @H, decrementing by @G until @L we’ll use: IIF(t.N<gap.N, @H-@G*t.N, @L). If the final number is less than @L, @L is returned for the final iteration. So far we have:

  [N ASC]  = t.N,                          -- fnTally "N" (0-base row number)
  [N DESC] = IIF(t.N<gap.N, @H-@G*t.N, @L) -- Gap reduced sequence from @H to @L
FROM        (VALUES((@H-@L+1)/@G+SIGN((@H-@L+1)%@G))) AS gap(N) -- number of rows
CROSS APPLY dbo.fnTally(0,gap.N)                      AS t;     -- fnTally call

With this logic, setting @G=2 would return (truncated) [22 20 … 6 4 2 1] for “[N DESC]”; @G=5 returns [22 17 12 7 2 1], @G=6 returns [22 16 10 4 1], and so on. For the L column (the lower-bound value) we’re using [N Desc] from earlier. For H, the upper-bound, we’ll leverage LAG: f.N+ISNULL(LAG(f.N,1) OVER (ORDER BY t.N)-f.N,1)-1.

  L = IIF(t.N<gap.N, @H-@G*t.N, @L), -- Gap reduced sequence from @H to @L
  H = f.N+ISNULL(LAG(f.N,1) OVER (ORDER BY t.N)-f.N,1)-1
FROM        (VALUES((@H-@L+1)/@G+SIGN((@H-@L+1)%@G))) AS gap(N) -- how many rows
CROSS APPLY dbo.fnTally(0, gap.N)                     AS t
CROSS APPLY (VALUES(IIF(t.N<gap.N, @H-@G*t.N, @L)))   AS f(N);
Retrieving matched values

Then add a subquery that searches the string (@S) for an L-sized series of @C in the input string (@S), and exclude rows where there is no match:

WHERE        p.Idx > 0

Finally, we wrap our logic into a subquery, add our TOP (1) clause, ordered by N. Note that I am using the aliased of “RN” for “Row Number”; I use RN as my sort-key, and “N” for my tally table N column. We’ll wrap all this up in an iTVF and create a VARCHAR(8000) and VARCHAR(MAX) version of our new stringsearch function. The only difference between the two functions is the data type for @S. The final tally table (lazy sequence) logic for the our two set-based approximation function are:


  @C CHAR(1),
  @S VARCHAR(8000),
/* Created on 20201004 by Alan Burstein. */
  L   = f2.L,  -- Lower Boundary
  H   = f2.H,  -- Upper Boundary
  Idx = p.Idx -- ItemIndex (position of the item match)
  SELECT t.N, f.N, f.N+ISNULL(LAG(f.N,1) OVER (ORDER BY t.N)-f.N,1)-1
  FROM        (VALUES((@H-@L+1)/@G+SIGN((@H-@L+1)%@G))) AS gap(N) -- how many rows
  CROSS APPLY dbo.fnTally(0, gap.N)                     AS t
  CROSS APPLY (VALUES(IIF(t.N<gap.N, @H-@G*t.N, @L)))   AS f(N)
) AS f2(RN,L,H)
WHERE        p.Idx > 0
ORDER BY     f2.RN;


  @C CHAR(1),
/* Created on 20201004 by Alan Burstein. */
  L   = f2.L, -- Lower Boundary
  H   = f2.H, -- Upper Boundary
  Idx = p.Idx -- ItemIndex (position of the item match)
  SELECT t.N, f.N, f.N+ISNULL(LAG(f.N,1) OVER (ORDER BY t.N)-f.N,1)-1
  FROM        (VALUES((@H-@L+1)/@G+SIGN((@H-@L+1)%@G))) AS gap(N) -- how many rows
  CROSS APPLY dbo.fnTally(0, gap.N)                     AS t
  CROSS APPLY (VALUES(IIF(t.N<gap.N, @H-@G*t.N, @L)))   AS f(N)
) AS f2(RN,L,H)
WHERE        p.Idx > 0
ORDER BY     f2.RN;

The 8K version is slightly faster when dealing with smaller strings with a smaller range of acceptable values. As the strings and range of acceptable values grow, the Max version becomes faster.

The Tuning Procedure

The tuning procedure (see the attached DDL as a text file below) is a T-SQL stored procedure I spun up quickly to test different design patterns using values for @G. This will help us find the optimal parameter for a specific predictable input. The procedure accepts the following parameters:

The procedure accepts all the parameters required for dbo.stringsearch. @I is for the number of test iterations the stored procedure should perform. @mode is for selecting on of 10 different design patterns to test. The parameter, @gaps is a comma-delimited list of different gap parameters (@G) for our function to accept. @puff and @C build sample strings of NEWIDs with the search pattern stuffed in the middle. Setting @mode=1, @I=5, @gaps = ‘1,2,5,10’ will test a specific design pattern using dbo.stringsearch 5 times for each value in @gaps. There are 4 gap values so for this example that would be a total of 20 tests.

The proc has examples with a performance test for each design pattern; executed with serial and parallel execution plans. Again, in Development environments I use the trace_flag 8649 because it’s easier to read the execution plan. I use make_parallel in Production because it performs the same and is safe to use in Production.

Below is the example output from a test I ran against a large set of rows five times (@I=5) for seven parameters between 5 and 35 (@gaps=’5,10,15,20,25,30,35′). The Gap column is the value of @G, Total is the total run time, min and max represent the slowest and fastest runs respectively. TAvg is a rolling average of the total time.

Gap   Total  Min    Max    TAvg
----- ------ ------ ------ ------
25    69294  13140  14437  69294
20    69546  12804  14603  69420
30	  71460  13096  14950  70100
35	  74830  13514  15990  71282
15    75196  13790  16413  72065
10    94631  17383  20097  75826
5     165316 30423  34530  88610

In this above example, with the example data used, @G=20 had the fastest run at 12.8 seconds, but it appears that 25 is the optimal value based on the total run time.

In the real world we would replace our sample data table, ##strings, with a sampling of real data you are developing a self-tuning functions for. For example, once I used to write ETL packages that collected social media metrics from search and social media companies. The source data from each company came in as a text file where we would extract key metrics. The content of each file, and the input strings within, was looked very different for each company but, for each the text was predictable. The optimal use case for self-tuning function for string parsing here would be to determine the best gap parameter value for each companies source data. For this we could build a tuning procedure for each company and store the best parameter value for later use.

Design Patterns Tested

We have two versions of our function, one for 8K strings and one for VARCHAR(MAX). The performance is nearly identical for both functions except that the 8K version is faster with shorter strings (e.g. less than a 1000 characters). Note these parameters, the queries, my comments and the results.

Test Parameters and sample data

Executing this code will create the sample data table (##strings) leaving it intact for further analysis.

  @rows BIGINT        = 2000,
  @puff BIGINT        = 5,
  @gaps VARCHAR(8000) = '5,10,15,20,25,30,35', -- Gap parameters to test
  @C    VARCHAR(100)  = 'X',
  @L    BIGINT        = 1,
  @H    BIGINT        = 1000,
  @max  BIGINT        = 1100,
  @I    BIGINT        = 1,
  @out  BIGINT        = 1; -- general performance details of test run

  EXEC dbo.usp_stringsearch_test1 @rows, @puff, @G, @C, @L, @H, @max, 15, @out, @I, 0;

Please test away and let me know what you find.

Design Patterns

With our sample table in place we can test a few different design patterns; there are three: our exact algorithm, a dynamic algorithm (approximation > exact) and a dynamic algorithm with two approximation reductions (approximation > approximation > exact).

--==== 1. EXACT algorithm
  s.stringId, s.string,             -- ##strings attributes
  Boundaries = CONCAT(f.L,'-',f.H), -- The Upper and lower bounds (exact because @G=1))
  ItemIndex  = f.Idx
FROM        ##strings                             AS s
CROSS APPLY dbo.stringSearch(@C,s.String,@L,@H,1) AS f -- @G=1 means EXACT
WHERE       f.L >= @L;

--==== 2. DYNAMIC algorithm: approximation to exact reduction
  SELECT      @X = f.L
  FROM        ##strings                                 AS s
  CROSS APPLY dbo.stringSearch(@C,s.String,@L,@H,@G)    AS f0
  CROSS APPLY dbo.stringSearch(@C,s.String,f0.L,f0.H,1) AS f
  WHERE       f.L >= @L

--==== 3. DYNAMIC algorithm with two reductions: Approx to Approx to Exact
DECLARE @G2 BIGINT = @G/3+1; -- Simple reduction: split by 1/3rd then add 1 (min=2)

SELECT      @X = f.L
FROM        ##strings                                       AS s
CROSS APPLY dbo.stringSearch(@C, s.String, @L, @H, @G)      AS f0
CROSS APPLY dbo.stringSearch(@C, s.String, f0.L, f0.H, @G2) AS f1
CROSS APPLY dbo.stringSearch(@C, s.String, f1.L,
                              IIF(f1.L+2<=@H,f1.L+2,@H), 1) AS f
WHERE       f.L >= @L;

The first will be the slowest because it’s running in serial mode. The second is much faster because, again, parallel plans turbo charge the performance when combining fnTally and a pure dynamic alogrithm. The Third example, the two-reduction solution is slower for short strings but the fastest (by far) as strings and search patterns get longer. When I already know a query is going to be slow I’ll often set @I low (1 or 2) just to confirm while saving time.

Performance Test

Using the parameters posted above let’s execute dbo.usp_stringsearch_test1 to as shown below.

--==== 8K - Dynamic with 1 reduction - SERIAL
  EXEC dbo.usp_stringsearch_test1 @rows, @puff, @gaps, @C, @L, @H, @max, 5,  @out, @I, 1;

--==== VARCHAR MAX - Dynamic with 1 reduction(#6) & 1 string reduction(#7) - PARALLEL
 SELECT @puff *= 10/*500*/, @I=5, @H=2000, @max=2000;
  EXEC dbo.usp_stringsearch_test1 @rows, @puff, @gaps, @C, @L, @H, @max, 6,  @out, @I, 1;
  EXEC dbo.usp_stringsearch_test1 @rows, @puff, @gaps, @C, @L, @H, @max, 7,  @out, @I, 1;

--==== 8K & VARCHAR MAX - Dynamic with 2X reductions (@G2=@G/2+1) - PARARLLEL
 SELECT @gaps = '100,250,500,800,1000,2000', @I=10;
  EXEC dbo.usp_stringsearch_test1 @rows, @puff, @gaps, @C, @L, @H, @max, 8,  @out, @I, 1;
  EXEC dbo.usp_stringsearch_test1 @rows, @puff, @gaps, @C, @L, @H, @max, 10, @out, @I, 1;

You can see from the results below that:

  1. Parallelism makes a huge difference
  2. The two reduction solution is the fastest
  3. The 8K and VARCHAR(MAX) versions perform almost identically
  4. With the one-reduction solutions the tuning parameter can be way too high or way too low, the two-reduction solution seems to perform better with the highest possible value for @G.

Note that, for modes 8 & 10 (the two-reduction test), I chose different (higher) values for the gap:


In Part 1 we learned how to develop a self-tuning function using a dynamic algorithm. Today we created a much faster version of our function leveraging fnTally. Things get even nasty faster when we add make_parallel. Another victory for set-based SQL and the tally table. In part 3 we’ll use these concepts to do something much cooler. Thanks for reading!

Author: Alan Burstein

SQL Performance Ninja with 20+ years of writing high-performing, elegant SQL code. Expert at developing super fast NLP algorithms

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