Considerations for storing Excel cell value in code

You may hate Excel, but you may find a discussion of how Excel stores cell values interesting.

So I have a spreadsheet library. The biggest concern at the initial stage was how to store all the spreadsheet data efficiently. I hear people talking about millions of cells, so I’m scared. If my program stores a spreadsheet cell using 10 bytes (for example), a million cells would take up 10 million bytes in memory.

Let’s start by looking at all the different types of information you can type into a spreadsheet cell. You have:

  • booleans: TRUE or FALSE
  • numbers
  • text
  • rich text (different styled text within the entire text itself)
  • dates and times

For us programmers, “numbers” can be separated into floating point or integer types. An Excel user won’t see a difference.

So how does Excel actually store those values? I’m going to focus only on Open XML because I’m not interested in BIFF files…

  • booleans: TRUE stored as text “1” and FALSE stored as text “0”
  • numbers: stored as text
  • text: duh
  • rich text: stored in a separate shared strings list, with the index to that list stored as text here.
  • dates and times: stored as number that’s in text form

You will see everything is basically stored as text. That’s because the underlying XML files are text files. There’s a property (XML attribute) that differentiates the data, such as boolean, number, string, inline string, shared string.

So why are dates stored as a number? It’s easier to do date calculations with 41449 than “24 June 2013”. So how is this number obtained? See here.

So if you’ve been looking closely enough, Excel’s optimisation tactic is to store everything as numeric text as far as possible. So I want to follow that.

Before doing so however, I went to read what other people are doing AKA open source spreadsheet libraries. In code, they use an object to store the cell value. As in System.Object, the mother of all data types in .NET.

So you have an integer? Dump it into the object variable. Floating point? Dump into object. String of characters? Dump.

How do you read it out? Boxing and unboxing. You remember it’s a floating point value and cast it back from an object to a double variable type.

So what did I do? I have a double variable and a string variable, and I store the cell value in one or the other based on the input.

The “all in object” way has variable (no pun intended) memory size, based on the contents. Sort of. I’m not an expert in this.

My way has a fixed memory size for double’s. Each double takes up 8 bytes (for sure?). A string variable takes up variable size, but because the optimisation tactic is to store data as a number, I can assign the data to the double variable and set the string variable to null. This means the string variable size is sort of fixed too.

So this is what I do. If it’s a number, I store it in the double variable and set the string variable to null. If it’s text, I convert it to a number by using shared strings (out of scope for discussion here) and store the index into the double variable and set the string variable to null. The only cases where the string variable is actually used is if I store the text there, or if I want to store the actual number there (because “1.23456789” may not be stored exactly as that in a double variable. Go read on how floating points are implemented for details), which are rare.

According to Jon Skeet, strings take up 20 + (n/2)*4 bytes (where n is the number of characters). But a null string takes up 8 bytes (it’s either 4 or 8 bytes. I’ll assume the worse scenario).

This means for the most part, each cell has a double variable that takes up 8 bytes and a null string that takes up 8 bytes. A cell value of 10 or 3.14 or 12345678.9 takes up 16 bytes regardless.

Since 16 bytes is less than 20 + (n/2)*4 bytes, I save more memory in most cases. I also have less boxing and unboxing operations, which make things go faster.

Collision detection in merging Excel cells

You can merge cells in Excel. “Duh!” you say. So how does Excel ensure that the cells you want to merge don’t overlap any existing merged cells? How do you check programmatically that the cells you want to merge won’t overlap any existing merged cells?

Well, that was the problem I faced while writing my spreadsheet library software (check out SpreadsheetLight here!). The inkling of an idea was formed when I visited StackOverflow. Can’t remember what I was there for, but the answer page wasn’t about Excel or spreadsheets. It was about collision detection.

Yes, the type of collision detection used in games so you don’t walk through walls and stuff.

And thus I learnt a new mathematical theorem: the separating axis theorem (or hyperplane separation theorem). From what I understand, given two N-dimensional thingies, if you can find one (N-1)-dimensional hyperplane that separates those two thingies, then those two thingies are separate (or not overlapping).

Yes, “thingies” is a technical term.

For example, given two 3D objects, if you can find one 2D plane that separates them, then the 3D objects are not overlapping. Another example is when you’re given two 2D objects, and if you can find one line (which is 1D) that separates them, then the 2D objects are not overlapping.

There are some conditions to be fulfilled, such as the objects being convex and disjoint and whatever. (yes I’m a mathematician…) I’ll leave it to you to do your own reading.

But for our purposes, how do we check if that rectangle of Excel cells we want to merge won’t overlap with any existing merged cells? We have these conditions that make our lives easier:

  • The merged cells are rectangular
  • The 4 end points (top-left, top-right, bottom-left, bottom-right) of a merged cell are in whole numbers
  • The (merged) cells map strictly to a 2D rectangular grid

Since the merged cells are rectangular, they’re also convex (I’m not going to explain why, just trust me). Since the 4 end points are in whole numbers, line boundaries can be easily calculated (it’s easy to check if something is <7 or >=8 for example). And since they map strictly to a 2D rectangular grid, the separating axis is a line. And even better, you can always find a subset of solutions of those separating axes that are either horizontal or vertical.

Ok, diagrams are in order.

Collision detection in merged cells

So in our case, as long as you can find one horizontal line or one vertical line that separates the 2 merged cells we’re checking, then the 2 merged cells are separate.

Let’s try an example. Excel uses cell references that are in the A1 format, which means row 3 column 4 becomes “D3”. The column index uses alphabets and is in base-26. Read more here.

We’re going to simplify that. Let’s say our existing set of merged cells only has one entry. This merged cell has the top-left corner at row 1 column 1, and the bottom-right corner at row 3 column 4. Suppose we want to check if this merge cell overlaps: top-left corner at row 7 column 8, bottom-right corner at row 10 column 10.

The horizontal line of 5 fits the bill, or the line y=5 if you want to be mathematical about it (but y goes from negative to positive downwards instead of the usual Cartesian y). Or y=6. Or even y=7 (note that the line can “touch” one of the merged cells, but not both. This is where the “whole number” condition comes in).

The vertical lines x=5, x=6 or x=8 also fit the bill.

Thus, our 2 merged cells don’t overlap.

So what’s the programmatic way to check? You’d be surprised at the simplicity. To make it easier, the variables with “StartRowIndex” mean the top row of the merged cell, “EndRowIndex” mean the bottom row of the merged cell. And “StartColumnIndex” mean the left-most column of the merged cell, and “EndColumnIndex” mean the right-most column of the merged cell.

if (!(iEndRowIndex < mc.StartRowIndex || iStartRowIndex > mc.EndRowIndex || iEndColumnIndex < mc.StartColumnIndex || iStartColumnIndex > mc.EndColumnIndex))
    // there's an overlap!

So the merge cell we want to check has top-left corner at (iStartRowIndex, iStartColumnIndex) and bottom-right corner at (iEndRowIndex, iEndColumnIndex).

The variable “mc” refers to a custom class I use to represent merged cells. Obviously, you’d run that condition in a loop through all your existing merged cells. If you can’t find an overlap after running through that loop, then the merge cell you’re checking is good to go.

Let’s run through the individual conditions.

  • (iEndRowIndex < mc.StartRowIndex) means our merged cell is completely above the existing merged cell
  • (iStartRowIndex > mc.EndRowIndex) means our merged cell is completely below the existing merged cell
  • (iEndColumnIndex < mc.StartColumnIndex) means our merged cell is completely to the left of the existing merged cell
  • (iStartColumnIndex > mc.EndColumnIndex) means our merged cell is completely to the right of the existing merged cell

The first 2 conditions check for the existence of a horizontal separating axis. The next 2 conditions check for the existence of a vertical separating axis.

Note the negation of the entire boolean condition. Those 4 conditions check for existence of solutions. Negation means checking for overlaps.

Note also that we use strictly greater than or strictly less than checks. If the merge cells share a row or column, then they overlap, right?

Did you know my first draft of writing the code had me checking 6 different conditions? Each condition had its own if statements. This one just had one. I’m so lucky to have learnt the separating axis theorem. I was checking if a point was above, within or below the merge cell, then I had to check if the point was to the left, within or to the right of the merge cell, and … urgh, it was horrible…