Flows of energy

by Marijn Haverbeke (license)

CodeMirror's document representation

Monday, September 10, 2012 javascript codemirror cm-internals

This post is part of an ongoing series of articles that aim to document the internals of the CodeMirror code editor. I will use the cm-internals tag to distinguish these posts—if you intend to hack on CodeMirror, it might be worthwhile to see what else is there.

The problem

The initial implementation of CodeMirror 2 represented the document as a flat array of line objects. This worked quite well—splicing arrays will require the part of the array after the splice to be moved, but this is basically just a simple memmove of a bunch of pointers, so it is cheap even for huge documents.

However, in version 2.17 (November 2011), I added support for line wrapping and code folding. Once lines start taking up a non-constant amount of vertical space, looking up a line by vertical position (which is needed when someone clicks the document, and to determine the visible part of the document during scrolling) can only be done with a linear scan through the whole array, summing up line heights as you go. One of the design goals of CodeMirror is to make editing responsive even in huge document. So this is not an acceptable solution.

Considerations

Operations that an effective document representation must be supported are looking up lines by line number, looking up lines by vertical position (for example, when figuring out where in a document a mouse click happened, or which lines are visible given a vertical scroll position), the reverse of those two operations (going to a line number or vertical offset given a line object). Furthermore, inserting and deleting lines, as well as updating the height of a line, should be cheap operations.

Anyone with a single computer science course under their belt will recognize this as a problem that calls for some sort of tree representation.

A regular binary tree would work. But the kind of update operations that we should be worried about are big ones—pasting a huge chunk of text, or selecting a few thousand lines and and then pressing delete. All balanced binary trees that I'm familiar with define only single-element insertion and deletion operations, which would have to be repeated a huge amount of times in the case of such mass updates.

We'd also prefer to keep tree depth to a minimum, because we'll be traversing this tree to find a line node or to update a line's parent nodes a lot—conversion between line numbers and line objects are rampant, because both describe essential properties of a line. (The number can not be stored in the line object, because that would require every single line object to be updated whenever someone presses enter near the top of the document.)

Representation

The new representation is based on a B-tree. These have the wide branching factor (and thus shallow depth) that we need, and lend themselves very well to bulk updates (more on that later).

The leaves of the tree contain arrays of line objects, with a fixed minimum and maximum size, and the non-leaf nodes simply hold arrays of child nodes. Each node stores both the amount of lines that live inside of them and the vertical space taken up by these lines. This allows the tree to be indexed both by line number and by vertical position, and all access has logarithmic complexity in relation to the document size.

Because both of these index keys (line number and vertical position) increase monotonically, a single tree can be indexed by both of them. This is great, it gives us the height index almost 'for free', with no additional data structure and only a very small amount of extra logic (maintaining the heights on updates).

Below is an illustration of what a tree might look like. This is a document of 50 lines, where the root node contains two children—one is branching chunk containing a number of leaf chunks, and the other is itself a leaf chunk. The first leaf has been written out, it contains seven lines, of which two are folded (taking up no height), and one is wrapped (taking up more height than a regular, unwrapped line).

root (the document) (size: 50, height: 470)
 ├─ chunk1 (size: 35, height: 300)
 │  ├─ leaf1 (size: 7, height: 70)
 │  │  ├─ line1 (height: 10)
 │  │  ├─ line2 (height: 10)
 │  │  ├─ line3 (wrapped, height: 30)
 │  │  ├─ line4 (height: 10)
 │  │  ├─ line5 (folded, height: 0)
 │  │  ├─ line6 (folded, height: 0)
 │  │  └─ line7 (height: 10)
 │  ├─ leaf2 (size: 10, height: 110) 
 │  │  └─ ...
 │  └─ ...
 └─ leaf3 (size: 15, height: 170)
    └─ ...

The size of the root node indicates the amount of lines that the document contains (and its height indicates the height of the whole document).

If we wanted to find line 12, we'd descend the root node, looking at its child chunk. The first child has size 35, so that's the one that contains line 12. Inside of this chunk, the first child is only of size 7, so we skip that, keeping in mind that we've seen seven lines, and the offset that remains is 12-7=5. The second chunk has size 10, which is more than 5, so we look inside that chunk. It is a leaf chunk, which means that its content is flat, and we can simply grab the line number five from inside of it.

For an interactive visualization of this tree, see this demo on the CodeMirror website.

Updates

The interface for deleting and inserting line objects in a tree is defined in terms of ranges of lines, rather than individual lines. To insert a range of size N at position P, we walk down the tree to find the leaf that contains position P. We then insert the whole range into the leaf. If this makes the leaf too big (there's a fixed maximum size defined for leaves), one or more new leaves will be split off from it, and inserted into its parent. If this, subsequently, makes the parent (non-leaf) chunk too big, that one is also split, and so on. If the root node needs to be split, a new root is created to hold the resulting chunks.

The beauty of B-trees is that this simple and cheap algorithm automatically balances the tree—when a branch grows, instead of growing downwards, its surplus population percolates upwards, towards the root, and causes the tree to grow from the root when it needs to. This is a not a perfectly optimal balance, as in some other kinds of trees, but it is definitely good enough for an editor implementation.

To delete a range of lines, the deletion simply recursively enters the branches that contains parts of the deleted range, and, in the leaf chunks, remove the relevant lines (updating size and height in the process). When a chunk becomes empty, it is simply removed completely, and when a branch chunk's size drops below a certain threshold, it is replaced by a flat leaf chunk. Again, this doesn't result in a perfect balance, but is wonderfully simply. In fact it doesn't even completely protect against pathological cases—there are editing patterns that can result in a seriously unbalanced tree. But those, since the unbalancing happens during deletion, can still only be as deep as the original tree (created by insertion, which has better balancing characteristics) was, and thus can't reach dangerous depths.

Intensive linking

All line objects and tree nodes (except the root) have parent pointers to the node above them. This allows for very fast height updating—when a line changes, find the height delta, and simply walk its parent pointers adding this delta to their height—and finding the line numbers of a given line object.

Maintaining these links, and breaking them when lines are dropped from the document, is somewhat awkward, but having such logic in place turned out to be useful for other purposes as well. It allows CodeMirror to fire an event when a line is dropped from the document, gives an easy way to check whether a line is still live (it is when it has a parent pointer), and makes it more immediately obvious when a data structure is not being maintained consistently (the code will quickly try to follow a null pointer).