string.Format() on double values gives inaccurate results

Question

I've got this code:

<tbody>
    @foreach (var day in user.WorkDays)
    {
        <tr>
            <th>@day.Date.ToString("MM/dd/yy")</th>
            <td>
                <ul>
                    @foreach (var note in day.Notes)
                    {
                        <li>@note.Text</li>
                    }
                </ul>
            </td>
            <td>@string.Format("{0:0.00}", Math.Truncate(day.Totals.Regular * 100) / 100)</td>
            <td>@string.Format("{0:0.00}", Math.Truncate(day.Totals.Overtime * 100) / 100)</td>
            <td>@string.Format("{0:0.00}", Math.Truncate(day.Totals.Doubletime * 100) / 100)</td>
            <td>@string.Format("{0:0.00}", Math.Truncate(day.Totals.Sick * 100) / 100)</td>
            <td>@string.Format("{0:0.00}", Math.Truncate(day.Totals.Vacation * 100) / 100)</td>
            <td>@string.Format("{0:0.00}", Math.Truncate(day.Totals.Holiday * 100) / 100)</td>
            <td>@string.Format("{0:0.00}", Math.Truncate(day.Totals.Overall * 100) / 100)</td>
        </tr>
    }
</tbody>
<tfoot>
    <tr>
        <th>Totals:</th>
        <th></th>
        <th>@string.Format("{0:0.00}", Math.Truncate(user.Totals.Regular * 100) / 100)</th>
        <th>@string.Format("{0:0.00}", Math.Truncate(user.Totals.Overtime * 100) / 100)</th>
        <th>@string.Format("{0:0.00}", Math.Truncate(user.Totals.Doubletime * 100) / 100)</th>
        <th>@string.Format("{0:0.00}", Math.Truncate(user.Totals.Sick * 100) / 100)</th>
        <th>@string.Format("{0:0.00}", Math.Truncate(user.Totals.Vacation * 100) / 100)</th>
        <th>@string.Format("{0:0.00}", Math.Truncate(user.Totals.Holiday * 100) / 100)</th>
        <th>@string.Format("{0:0.00}", Math.Truncate(user.Totals.Overall * 100) / 100)</th>
    </tr>
</tfoot>

It produces this result:

(Open the image in a new tab to see it full-sized.)

If you look at the values on the right-most column, you'll notice that they do not add up to the 79.98 at the bottom right of the table. I calculated that they add up to 79.93.

Since I know somebody is going to ask, yes, 79.98 is the correct total. It's the values that are supposed to add up to that total that are incorrect.

What am I doing wrong? I've been fiddling around with this for far too long and haven't seen any change.

Edit:

After reading some comments, it's clear that the Math.Truncate() calls are not helping. Here's what I had previously:

<tbody>
    @foreach (var day in user.WorkDays)
    {
        <tr>
            <th>@day.Date.ToString("MM/dd/yy")</th>
            <td>
                <ul>
                    @foreach (var note in day.Notes)
                    {
                        <li>@note.Text</li>
                    }
                </ul>
            </td>
            <td>@day.Totals.Regular.ToString("0.00")</td>
            <td>@day.Totals.Overtime.ToString("0.00")</td>
            <td>@day.Totals.Doubletime.ToString("0.00")</td>
            <td>@day.Totals.Sick.ToString("0.00")</td>
            <td>@day.Totals.Vacation.ToString("0.00")</td>
            <td>@day.Totals.Holiday.ToString("0.00")</td>
            <td>@day.Totals.Overall.ToString("0.00")</td>
        </tr>
    }
</tbody>
<tfoot>
    <tr>
        <th>Totals:</th>
        <th></th>
        <th>@user.Totals.Regular.ToString("0.00")</th>
        <th>@user.Totals.Overtime.ToString("0.00")</th>
        <th>@user.Totals.Doubletime.ToString("0.00")</th>
        <th>@user.Totals.Sick.ToString("0.00")</th>
        <th>@user.Totals.Vacation.ToString("0.00")</th>
        <th>@user.Totals.Holiday.ToString("0.00")</th>
        <th>@user.Totals.Overall.ToString("0.00")</th>
    </tr>
</tfoot>

Now, those values add up to 80 even. Even that's .02 higher than the actual value.

Answer 1

So here's the real question - should the "total" be the total of the original numbers or the truncated numbers. (As a side note, ROUND would reduce the error but not eliminate it.). If the total should be the sum of the original numbers then you can either:

1. Leave the report alone and explain in a footnote that the total may not match exactly due to rounding.
2. Add a row for "rounding error".
3. Allocate the rounding error to one or more of the items (here's a question and argument I had on how to do that)

If the total should be the total of the rounded numbers, then that's easy to do in the report, but it won't match the total of the original numbers (unless you round the original numbers in the source).

Answer 2

You really should read this paper:

David Goldberg. 1991. What every computer scientist should know about floating-point arithmetic. ACM Comput. Surv. 23, 1 (March 1991), 5-48. DOI=10.1145/103162.103163 http://doi.acm.org/10.1145/103162.103163

• http://dl.acm.org/citation.cfm?id=103163
• https://ece.uwaterloo.ca/~dwharder/NumericalAnalysis/02Numerics/Double/paper.pdf
• http://www.validlab.com/goldberg/paper.pdf
• http://www.cs.ucdavis.edu/~bai/ECS231/Goldberg91.pdf

Abstract Floating-point arithmetic is considered as esoteric subject by many people. This is rather surprising, because floating-point is ubiquitous in computer systems: Almost every language has a floating-point datatype; computers from PCs to supercomputers have floating-point accelerators; most compilers will be called upon to compile floating-point algorithms from time to time; and virtually every operating system must respond to floating-point exceptions such as overflow. This paper presents a tutorial on the aspects of floating-point that have a direct impact on designers of computer systems. It begins with background on floating-point representation and rounding error, continues with a discussion of the IEEE floating point standard, and concludes with examples of how computer system builders can better support floating point.

But the problem most likely is that your are either truncating or rounding the values for display and computing the sum of the raw values. Hence the delta.

If you want them to match:

• sum the displayed values
• use decimal instead of double.

Answer 3

The real issue here isn't string.Format(). The issue here is Math.Truncate().

Allow me to demonstrate:

Math.Truncate(4.499999 * 100) / 100 = 4.49
Math.Round(4.499999, 2) = 4.50

Now .01 is a relatively small amount but your way of calculation is what's causing the issue here. Your example has 14 rows. If every row was wrong, your display would be wrong if people were to calculate it themselves (even though your total is correct).