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Alexander Kuznetsov

Set based calculation of products of several numbers.

You can use SUM to calculate the sum of several numbers, but you cannot directly use set-based logic to calculate a product. Yet there is a very simple trick – you can use EXP(SUM(LOG(…))) and get a product of several numbers without a loop. The trick was originally posted on newsgroups by Tom Cooper.

For example, suppose that you have to allow for multiple discounts at a time. Consider the following UDF that mocks some complex logic that determines price discounts based on customer and date:

CREATE FUNCTION dbo.GetDiscounts(@CustomerID INT, @AsOfDate DATETIME)




SELECT 0.1 AS Discount, 'Easter Sale' AS Reason


SELECT 0.1 AS Discount, 'Preferred Customer' AS Reason



Currently any customer is eligible for two discounts, 0.1 each. The total discount after applying them both is 0.19. Of course you can write a cursor or a loop to calculate it. However, the following script calculates total discount using set-based logic, without writing a loop:

SELECT 1-EXP(SUM(LOG(1-Discount))) AS TotalDiscount FROM dbo.GetDiscounts(1, '20090320');





(1 row(s) affected)

Published Tuesday, March 17, 2009 6:01 PM by Alexander Kuznetsov



Eric J. Peters said:

Beautiful!  I have a very high appreciation for the old-school/slide-rule mathematical tricks that should be well understood by programmers.

However, it takes a pretty niche problem to need a product of more than a very small number of elements.  But in the virtually all cases, isn't the code-maintainability of a simple loop going to outweigh the costs of actually running the loop?

What's the real gain here?  Considering the cost of the EXP/LOG functions, is there a real gain here?

March 17, 2009 6:57 PM

Alexander Kuznetsov said:


I am considering to have a persisted computed column for LOG(1-Discount) to speed it up. I need to frequently run up to 50 multiplications, will do benchmarks soon. I really like the simplicity of the code - no loop can be shorter or simpler than one line expression:


March 17, 2009 9:54 PM

Hugo Kornelis said:

Hi Alex,

The trick is nice, but you need to be sure that the input will not contain 0 (zero) or negative numbers, otherwise you'll get an error.

Itzik Ben-Gan presents two alternative versions in "Inside Microsoft SQL Server 2005: T-SQL Querying". One is readable, the other one is short.

The readable one (though the formatting will probably be lost):




   CASE WHEN COUNT(CASE WHEN val < 0 THEN 1 END) % 2 = 0

     THEN 1 ELSE -1

   END * EXP(SUM(LOG(NULLIF(ABS(val), 0))))


The short one:


Note that "val" is the value to be multiplied, and that any errors are probably my fault (manually copying lots of nested parentheses from a book is hardly ever a good idea).

Best, Hugo

March 18, 2009 5:00 AM

Alexander Kuznetsov said:

Hi Hugo,

Thank you for sharing a general approach.

For a more specific case of discounts, all numbers are positive and not null, which is enforced by constraints. This allows for much simpler code.

March 18, 2009 8:54 AM

Joe Celko said:

Just for documentation, this method first appeared in SQL FOR SMARTIES Section 21.6 PRD() Function.  

March 22, 2009 9:26 AM

Archivist said:

Joe, not sure about it. The first time this trick appeared in your books was SQL For Smarties Second Edition which was published around 1999. I can still find references to a newgroup post from Isaac Blank in 1997 and I'm pretty sure someone came up with this simple equivalence before.

March 22, 2009 2:16 PM

Madhivanan said:

March 26, 2009 7:31 AM

cinahcaM madA said:


There is a bug in the "short one" posted by Hugo. If your data set is all 0s, it returns NULL rather than 0. If there are any non-0 values and more than one 0, you'll get strange results. These issues do not happen with the longer version, so use that.






values (0),(0),(0)

) x (val)





values (1),(0),(0),(0)

) x (val)


September 7, 2009 4:33 PM

cinahcaM madA said:

And in case anyone cares, Itzik has a fix for the second issue on his corrections page, and I've come up with the following version, a modification of his, that also fixes the first issue:


   COALESCE(EXP(SUM(LOG(ABS(NULLIF(val,0)))))*(1-SUM(1-SIGN(val))%4)*MIN(ABS(SIGN(val))), ABS(SIGN(SUM(val))))



   values (0), (0)

) x (val)

September 7, 2009 5:21 PM

Alexander Kuznetsov said:


This is a nice correction, thanks!

September 7, 2009 8:56 PM
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About Alexander Kuznetsov

Alex Kuznetsov has been working with object oriented languages, mostly C# and C++, as well as with databases for more than a decade. He has worked with Sybase, SQL Server, Oracle and DB2. He regularly blogs on, mostly about database unit testing, defensive programming, and query optimization. Alex has written a book entitled "Defensive Database Programming with Transact-SQL" and several articles on and Currently he works as an agile developer.

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