My Modulus Obsession

A modulus (modulo or mod) is the remainder of a division operation. PowerShell, like many other languages, includes a modulus operator ( % ) that returns the remainder of division between any 2 numbers. The immediate and somewhat obvious use case for the modulus operator is to test if a number is even or odd.

Simple Examples:

4 % 2 Returns: 0, and means 4 is evenly divisible.
5 % 2 Returns: 1, which is of course the remainder and means 5 is odd and not evenly divisible.

This simple function can be very useful. In one of my Exchange environments databases were distributed in an even/odd pattern across even/odd numbered servers respectively.  For example, DB001’s activation preference 1 is ExchSrv1 and preference 2 is ExchSrv2, while DB002 was the opposite.  With simple knowledge of this distribution matrix, the modulus operator enables me to quickly determine which DBs should be active on a given server.

Get-MailboxDatabase -Server ExchSrv1 |
Where-Object{ $_.Name.SubString(2) % 2 -eq 1 }

This would return all odd numbered DBs with copies on ExchSrv1, and because I know my configuration, I know these should normally be active on the same server.  This is particularly useful when putting a server back in service, I can simply add the Move-ActiveDatabase command as below:

Get-MailboxDatabase -Server ExchSrv1 | 
Where-Object{ $_.Name.SubString(2) % 2 -eq 1 } |
Move-ActiveMailboxDatabase -ActivateOnServer ExchSrv1

To return even numbered DBs all I’d need to do is compare to 0 instead of 1, so if I were working on server 2, ExchSrv2:

Get-MailboxDatabase -Server ExchSrv2 | 
Where-Object{ $_.Name.SubString(2) % 2 -eq 0 } |
Move-ActiveMailboxDatabase -ActivateOnServer ExchSrv2

PowerShell’s type conversion engine can shorten the evaluations in the above Where clauses.  This is because a Boolean 0 is False & a Boolean 1 (or anything non-zero) is True.

[Boolean]4 % 2 Returns: False
[Boolean]5 % 2 Returns: True

So technically the above examples can be shortened like below:

Get-MailboxDatabase -Server ExchSrv1 | 
Where-Object{ $_.Name.SubString(2) % 2 } |
Move-ActiveMailboxDatabase -ActivateOnServer ExchSrv1

To get even numbered DBs you’d have to negate the modulus return with either ! or -not :

Get-MailboxDatabase -Server ExchSrv2 | 
Where-Object{ !($_.Name.SubString(2) % 2) } |
Move-ActiveMailboxDatabase -ActivateOnServer ExchSrv2

Given the Boolean conversions I find it helpful to think of these expressions as something like an .IsOdd() test method. However, I find the shortened format to be a little confusing, so I prefer the more explicit approach.

So far these are relatively straight forward uses for the modulus operator.  However, this simple operation can be used in clever ways to solve other types of problems. One use case is the distribution of one set of values across another usually larger set.

As a realistic example, let’s say I have a group of students I need to assign to classrooms.

$Rooms = 101, 102, 103, 104

# Establish test objects:
$Students = @(
    'Mike', 'Chris',   'Jessica', 'Matt'
    'Jenn', 'Josh',    'Amanda',  'Dan'
    'Jim',  'Rob',     'John',    'Joseph'
    'Ryan', 'Brandon', 'Jason',   'Justin'
) | 
Select-Object @{Name = 'Name'; Expression = { $_ }},
    @{Name = 'Room'; Expression = { 0 }}

# Assign students to rooms:
For($i = 0; $i -lt $Students.Count; ++$i)
{
    $Students[$i].Room = $Rooms[$i % $Rooms.Count]
}

$Students

Return:

Name    Room
----    ----
Mike     101
Chris    102
Jessica  103
Matt     104
Jenn     101
Josh     102
Amanda   103
Dan      104
Jim      101
Rob      102
...

The first few lines merely establish the test data. What stands out, is the compact and easy to understand loop that’s assigning students to rooms. By calculating the remainder of $i divided by the number of elements in the $Rooms array, the loop assigns rooms to the students in a rolling pattern. When the end of the $Rooms array is reached it starts again at the beginning. This works without a nested loop, tracking or flag variables.

Here’s how it works:

1st iteration $i is 0, 0 % 3 returns  index 0 is selected from the $Locations array.
2nd iteration $i is 11 % 3 returns 1, index 1 is selected.
3rd iteration $i is 22 % 3 returns 2, index 2 is selected.

This will continue until $i exceeds $Rooms.Count:

4th iteration $i is 33 % 3 returns 0, index 0 is selected.
5th iteration $i is 44 % 3 returns 1, index 1 is selected.

The first 3 iterations are straight forward, but things get interesting as the value of $i meets then exceeds $Rooms.Count. Since the modulus calculation is based on whole number division, the size of the numbers are irrelevant, and the remainder always maps to the “next” index in the other array.  Whenever $i is equivalent to or an even multiple of $Rooms.Count the remainder will be zero effectively wrapping around to the beginning of the $Rooms array and completing an instance of the pattern.

Another real world example is the allocation of mailboxes to databases for an Exchange migration. This is a little more complicated because we also have to account for mailbox size. Otherwise, arbitrary assignments will result in poor distribution of data. An initial step in solving this problem is to sort the mailboxes in size order.  However, sorting alone, would result in a lopsided data distribution where, assuming a descending sort, DBs earlier in the collection will contain disproportionately more data.

Here’s how I’ve solved this problem in the past without using the modulus operator:

$AllDBs =
@(
    "DB001","DB002","DB003","DB004","DB005","DB006","DB007","DB008"
    "DB009","DB010","DB011","DB012","DB013","DB014","DB015","DB016"
    "DB017","DB018","DB019","DB020","DB021","DB022","DB023","DB024"
    "DB025","DB026","DB027","DB028","DB029","DB030","DB031","DB032"
    "DB033","DB034","DB035","DB036","DB037","DB038","DB039","DB040"
    "DB041","DB042","DB043","DB044","DB045","DB046","DB047","DB048"
)

$Direction = 1
$Index     = 0

For($i = 0; $i -lt $Mailboxes.Count; ++$i)
{
    $Mailboxes[$i].DestinationDB = $AllDBs[$Index]
    If($Direction -eq 1) {
        $Index++
    }
    ElseIf($Direction -eq 0) {
        $Index--
    }

    # Alternate direction and adjust $index.
    If($Index -eq $AllDBs.Count) {
        $Direction = 0
        $Index--
    }
    ElseIf($Index -eq -1) {
        $Direction = 1
        $Index++
    }
}

This code certainly gets the job done. It was a little difficult to develop, but it’s relatively literal to understand.  For brevity’s sake the creation of $Mailboxes isn’t shown but it’s a collection of [PSCustomObjects] representing user mailboxes, with an added yet empty DestinationDB property. $Index is manually incremented or decremented within the loop and controls which DB is assigned from the $AllDBs collection.

When $Index exceeds the $AllDBs.Count the flag variable $Direction is flipped and $Index starts decrementing instead of incrementing. This causes DBs to be assigned from both directions climbing up and down the $AllDBs array and resulting a smoother data distribution.

There’s nothing wrong with the above example, however leveraging the modulus operator I can accomplish the same thing with much less code:

For($i = 0; $i -lt $Mailboxes.Count; ++$i)
{
    $Modulus = $i % $AllDBs.Count

    $Mailboxes[$i].DestinationDB = $AllDBs[$Modulus]

    If( $Modulus -eq $AllDBs.Count -1 ) {
        [Array]::Reverse($AllDBs)
    }
}

Note: Didn’t bother restating the $AllDBs array above.

With an understanding of how the modulus based pattern works, I’ve written code that’s easy to read, efficient and, of course, nice to look at. There’s only 1 conditional statement to execute per iteration. Compare that to the previous code where depending on $Index & $Direction there were 2 – 4 conditionals executing per iteration. Furthermore, 1 – 2 incrementation operations have been replaced with just the 1 modulus calculation to assign the $Modulus variable. Granted, that might be offset by the reversal of the $AllDBs array, but in this case I’ll chance it, given how many lines I’ve saved. In closing, beautiful patterns like this are why I have a little bit of a modulus obsession.