## 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 TABLE TestNumbers (
SomeField INT
);

And fill it with some amount of values

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

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

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

## History

- November 18
^{th}, 2012: Tip created.