When Microsoft Access Math Doesn't Add Up
by
Luke Chung, President
of FMS
All rights reserved.
Originally published in Smart Access October 1997 by
Pinnacle Publishing, Inc.; Revised April 2006,
July 2013, December 2014.
All versions of Microsoft Access (and Excel, VBA, Visual Basic 6, C++,
and C# and VB.NET in Visual Studio .NET) share quirks that can result in inaccurate mathematical
calculations in both code and queries. Understanding these issues will
help you avoid unnecessary headaches when the numbers you generate don’t
match the mathematically correct values.
You'd think that today, software programs like Microsoft Access would
handle mathematical calculations properly. For the most part Access,
VBA, VB, and .NET do, but there are several areas where they generate
unexpected results. In most cases, the discrepancies are minor; however,
if you are trying to determine if two values are identical, looking for
small differences between values, or performing multiple calculations,
these errors can diverge significantly from the correct answer. I first
encountered these problems while writing FMS' statistical analysis
program,
Total Access
Statistics. I quickly discovered problems in calculations that used
Taylor Series and other iterative calculations as well as in code that
attempted to trap for division by zero. A little research revealed more
than "rounding error."
Rounding errors aren't uncommon in programs because computers store
and perform mathematical calculations using binary representations of
decimal numbers. This causes rounding errors in inexact calculations
such as division. One can certainly excuse computers for accuracy
problems in the 15th significant digit. That’s expected. What I didn’t
expect, however, is much larger and more obvious errors that must be
corrected for using code.
Subtraction Problems
Subtraction is an area where you shouldn't face rounding problems. By
definition, the result of subtraction can't have more decimal places
than either of the initial numbers. If binary math results in an
inaccurate number, MS Access VBA should round the results accordingly.
Unfortunately, this doesn't happen in many cases.
A simple example reveals the problem. Examine the difference between
100.8 and 100.7. You would expect the solution to be 0.1, but look what
happens when you try this in the debug window:
? 100.8  100.7
9.99999999999943E02
The error is in the 14th most significant digit.
The error worsens if the numbers are larger:
? 10000.8  10000.7
9.99999999985448E02
The error is now in the 11th digit. Now you may wonder why an error
in the 11th digit would be a problem. In most cases it probably isn’t.
However, this error is significant enough to cause unexpected results.
Clearly, you can’t have something like this:
Const X = 100.8
Const Y = 100.7
If X  Y = .1 Then ...
A general rule when working with real number calculations, is to
avoid directly comparing two double (or single) numbers to see if they
are equal. Due to rounding problems, you'd expect differences in the
15th digit. Therefore, you would normally use a function such as the
following to test for identity of two double numbers:
Function IsEqual(dblValue1 As Double, dblValue2 As Double) As Integer
Const dblSmall = .000000000000001
If Abs(dblValue1  dblValue2) <= dblSmall Then
IsEqual = True
Else
IsEqual = False
End If
End Function
By calculating the absolute difference between two values, you can
consider the two values equivalent if the difference is less than a
tiny, nonzero number (in this case 10^{15}).
However, this fails if Access introduces larger differences.
For instance, you might use this function to compare the difference
between 100.8 and 100.7 to 0.1:
IsEqual(100.8100.7, .1)
Unexpectedly, the result is False in Access, which is troublesome. To
get around this, you need to increase the dblSmall value in the
IsEqual( ) function. Unfortunately, the value can be increased so much
that two numbers that aren't really equal return True.
Not being able to determine if two numbers are equal is especially
problematic for division. Here’s a simple function that tries to prevent
division by zero:
Function CalcDivision(dblNumerator As Double, dblDenominator As Double) As Double
If IsEqual(dblDenominator, 0) Then
' Should be undefined.
CalcDivision = 0
Else
CalcDivision = dblNumerator / dblDenominator
End If
End Function
To witness this problem, type the following into the debug window:
? CalcDivision(10, 100.8  100.7)
100.000000000006
While it isn't completely accurate, it’s reasonably close with the
error in the last digit. But look what happens when division by
closetozero occurs:
? CalcDivision(10, 100.8  100.7  .1)
1.757502293608E+15
The CalcDivision function should have trapped 100.8100.70.1 as
zero. Instead, it used the small error as the divisor and created a huge
resulting answer (10 to the 15^{th}
power!).
These problems stem from VBA’s subtraction inaccuracies for
numbers with decimals. Fortunately, there's a way to work around this
problem by using the builtin convert decimal function: CDec.
Function FMS_Subtract(dblValue1 As Double, dblValue2 As Double) As Double
FMS_Subtract = CDec(dblValue1)  CDec(dblValue2)
End Function
With this function, you’ll get the correct result:
? FMS_Subtract(100.8, 100.7)
.1
Applying this to the earlier division, you’ll find that division by
zero is properly trapped:
Sub TestDivision()
' Perform: CalcDivision(10, 100.8100.7.1) which returned
' 1.757502293608E+15 due to subtraction inaccuracies
Dim dblDiff As Double
' Rather than setting dblDiff to 100.8100.7.1 use the FMS_Subtract function for subtraction
dblDiff = FMS_Subtract(100.8, 100.7)
dblDiff = FMS_Subtract(dblDiff, .1)
Debug.Print (CalcDivision(10, dblDiff))
End Sub
Certainly, you don’t want to call a special function every time you
want to perform subtraction. This is needed only when you're calculating
the difference between two numbers that include decimals, and need to
compare the result with another number or want to use it as a divisor.
Type Casting Problems with Rounding
Another common numeric problem is associated with expressions passed
to functions. Before VBA introduced the Round function, the following
was a common function used to round
numbers to the nearest decimal place. Numbers on the border, *.5, should
be rounded up, but are, in fact, always rounded down (note that this is
different from the Banker's Rounding behavior of the VBA Round command):
Function RoundBad(dblNumber As Double, intDecimals As Integer) As Double
Dim dblFactor As Double
dblFactor = 10 ^ intDecimals
RoundBad = Int(dblNumber * dblFactor + .5) / dblFactor
End Function
Running this function generates these results:
? RoundBad(100.06, 1) ' Correctly returns 100.1
? RoundBad(100.04, 1) ' Correctly returns 100.0
? RoundBad(100.05, 1) ' Incorrectly returns 100.0 instead of 100.1
The problem stems from the way the Int( ) function processes the
expression. It actually rounds the number before applying
the Integer conversion. Let’s isolate the problem from the debug window.
As expected, this correctly evaluates to 1001:
? 100.05 * 10 + .5
1001
However, using the same expression inside the Int( ) function gives
the wrong result:
? Int(100.05 * 10 + .5)
1000
Therefore, it is imperative that you avoid passing expressions
involving real numbers to Access/VBA functions. If the expression is
assigned to a variable and then passed to the Int( ) function, it
usually works fine. However, there are times when that also fails and
adding a null string to is fixes the problem. Here’s the correct way to
perform rounding:
Function FMS_Round(dblNumber As Double, intDecimals As Integer) As Double
Dim dblFactor As Double
Dim dblTemp As Double
dblFactor = 10 ^ intDecimals
dblTemp = dblNumber * dblFactor + .5
FMS_Round = Int(CDec(dblTemp)) / dblFactor
End Function
With the simple addition of the CDec conversion, FMS_Round( ) returns
the correct result:
? FMS_Round(100.05, 1) ' Correctly returns 100.1
Conclusion
It's sad, but even in this day and age, you can’t assume math is
accurate. The problems discussed in this article impact not only module
code but also calculations performed in queries, and exists in Microsoft
Excel, C++, Visual Basic 6, and VB.NET and C# in Visual Studio .NET. While some of these
issues can be considered minor rounding errors, I hope I have shown you
that this isn't always the case. Not paying attention to these errors
could cause you huge problems in applications that require these types
of calculations to be accurate. By recognizing where and how such
problems occur, you can take steps to handle or avoid them.
Luke Chung is the
president and founder of FMS, Inc., the world's leading Access
development firm. He has actively participated in designing all of the
FMS products, including solutions for SQL Server, VB, and .NET. He also
wrote major portions of
Total Access Analyzer,
Total Access Analyzer,
Total Access Emailer,
Total Access
Statistics,
Total Visual
CodeTools, and
Total Visual
SourceBook.
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provided "as is" without warranty of any kind.
