Check if a number is a power of 2 with Sql Server 2012

• Download PowersOf2.zip - 457 B

Introduction

Sometimes there's a need to get rows from a table where a numeric field contains values for example a powers of 2. The satisfying rows would contain numbers such as 1, 2, 4, 8, 16 and so forth.  

With previous versions of Sql Server this could be done for example with a user defined function. Since Sql Server 2012 contains a new version for LOG function where the base can be defined separately, such query can be simplified.

So how...  

First let's create a small test table which will contain test numbers 

-- Create the test table
CREATE TABLE TestNumbers (
   SomeField INT
);  

And fill it with some amount of values 

-- Add some numbers
DECLARE @counter AS INT = 1;
BEGIN
   WHILE @counter < 100 BEGIN
      INSERT INTO TestNumbers VALUES (@counter);
	  SET @counter = @counter + 1;
   END;
END;   

Now, the idea is to check if the return value of the LOG function with base of 2 contains an integer without any decimals. If this is true, the number is a power of 2. 

First, lets have a look at the values   

-- Test the logarithm function
SELECT SomeField                    AS OriginalValue,
       LOG(SomeField, 2)            AS Logarithm,
       ROUND( LOG(SomeField, 2), 0) AS RoundedLogarithm
FROM TestNumbers;    

The query above should return results like the following

OriginalValue   Logarithm          RoundedLogarithm
-------------   ----------------   ----------------
1               0                  0
2               1                  1
3               1,58496250072116   2
4               2                  2
5               2,32192809488736   2
6               2,58496250072116   3
7               2,8073549220576    3
8               3                  3
9               3,16992500144231   3
10              3,32192809488736   3
11              3,4594316186373    3
12              3,58496250072116   4
13              3,70043971814109   4
14              3,8073549220576    4
15              3,90689059560852   4
16              4                  4
17              4,08746284125034   4
...  

As you can see the values of the logarithm and the rounded logarithm are exactly the same only when the original number is a power of 2 

So let's convert this to a condition 

-- Get powers of 2
SELECT SomeField AS OriginalValue
FROM   TestNumbers
WHERE  LOG(SomeField, 2) = ROUND( LOG(SomeField, 2), 0);  

The query above now returns the rows where the logarithmic and the rounded values match exactly so the result is 

OriginalValue
-------------
1
2
4
8
16
32
64  

The scripts used in the tip are included in the download.  

Points of Interest  

Note that if there's a value of 0 present in the database, that would result to a floating point error. So you may need to either exclude zeroes or change them to some other value in the query, which ever suits better for the situation.  

References  

• LOG 
• ROUND   

History 

• November 18^th, 2012: Tip created.