# February 23, 11

**Update: I’ve finally (nearly two years later) created a dedicated GitHub repo for this.**

Inspired by this Stack Overflow question, I started thinking about possible ways of implementing the `IList<T>`

interface in a lock-free *concurrent* data structure, with the following notes:

- I highly doubt a lock-free
`Insert`

or`RemoveAt`

implementation is possible. I could be wrong, of course; but I don’t think so. So I would implement those explicitly (and throw a`NotSupportedException`

). - I would want guaranteed O(1) random access, at least. (Otherwise, the whole point of implementing
`IList<T>`

seems kind of questionable.)

OK, so, **how do we do it**?

Before I even describe my idea (still a work in progress), I should disclose the fact that, to my simultaneous disappointment and delight, it appears I managed to come up with a concept on my own that is *remarkably* similar to what researchers at Texas A&M University, including Bjarne Stroustrup, designed and published.

Here’s the basic idea. Clearly utilizing a single array that is resized on certain Add operations would be problematic: allocating a new array and copying all elements to it in a lock-free way would be, at least I have to speculate, quite costly (imagine multiple concurrent threads all copying elements concurrently—seems very wasteful). So I considered using a *linked list* of arrays, where when an Add call requires additional storage, a new array could be allocated and appended to the linked list. But once you introduce a linked list, random access in O(1) becomes, well, less possible.

I was *thinking* you probably couldn’t do it with a simple array of arrays (e.g., a `List<T[]>`

) simply because then you’d eventually run into the problem of having to resize the “outer” array eventually. But then it dawned on me: **assuming Count is bounded at int.MaxValue, we could actually use a **

*fixed-size*array of arrays.

If each array is twice the size of the previous one, this means we’d only need an array big enough to reach a total capacity of `int.MaxValue`

, which ends up being a measly 32 (quite reasonable for a concurrent data structure, if you ask me)!

This is assuming the first array has a `Length`

of 1. How do I figure? Believe it or not, I didn’t have to do any fancy math. The answer is actually quite simple when you visualize array sizes as binary numbers.

That is, if the first array’s `Length`

is 1, then its size is:

00000000000000000000000000000001

Then, if the second array’s `Length`

is 2 (twice the previous), then its size is:

00000000000000000000000000000010

And, of course, 1 + 2 = 3, or:

00000000000000000000000000000011

Now, if the next array’s `Length`

is 4 (again, twice the previous), then that’s:

00000000000000000000000000000100

And 4 + 3 (the capacity of the previous two arrays) = 7, or:

00000000000000000000000000000111

See a pattern?

So the first six elements (just for illustration) of this “outer” array would look like this:

The beauty of this design is that it facilitates O(1) random access, when you consider the following: the starting “index” of each array is the sum of the lengths of all previous arrays, which is in turn the sum of a **geometric sequence**:

Determining *which array* a particular index falls into, then, requires simply rearranging the above formula to solve for *n*:

With an *a _{1}* of 1 and an

*r*of 2, this translates to the following code:

int GetArrayIndex(int index) { double n = Math.Log(index + 1, 2); return (int)Math.Truncate(n); }

Pretty simple, right?

Believe it or not, the main issue I’ve encountered so far is **having an accurate O(1) Count operation**. To understand why, consider this implementation of

`Add`

:public void Add(T element) { int index = Interlocked.Increment(ref m_index) - 1; int arrayIndex = GetArrayIndex(index); if (arrayIndex > 0) { index -= ((int)Math.Pow(2, arrayIndex) - 1); } if (m_array[arrayIndex] == null) { int previousArrayLength = m_array[arrayIndex - 1].Length; Interlocked.CompareExchange(ref m_array[arrayIndex], new T[previousArrayLength * 2], null); } m_array[arrayIndex][index] = element; Interlocked.Increment(ref m_count); }

Notice anything fishy? The call to `Interlocked.Increment(ref m_index)`

happens *before* `element`

is inserted into the array, which means using `m_index`

as `Count`

will result in “false positives,” by which I mean values *higher* than the actual number of elements inserted. However, the “workaround” in the above implementation—maintaining a separate `m_count`

field and calling `Interlocked.Increment(ref m_count)`

at the end of the `Add`

method—also has a flaw: if two `Add`

operations take place concurrently, `m_count`

may be incremented after the *higher* index **first**, resulting in the following problem:

for (int i = 0; i < list.Count; ++i) { // This element may not have been set yet! T element = list[i]; }

This is something I haven’t worked out 100% yet. The structure designed by Stroustrup et al. resolves this issue by utilizing a `Descriptor`

object which describes the most recent operation performed on the array and is updated with a single *CAS* (compare-and-swap) instruction. What I don’t like about this is that it means *every* call to Add allocates a new object. A small one, yes, but an object nonetheless.

Personally, I like the idea of a `ConcurrentList<T>`

class that allows thread-safe appends, O(1) random acccess, and does not produce (much) garbage. What I have so far seems to meet these requirements, while exhibiting some “iffy” behavior surrounding the Count property.

And honestly, I’m wondering if that’s OK; maybe we can just embrace eventual consistency and say this implementation is efficient and just has a “fuzzy” Count.

Anyway, like I said, it’s still a work in progress. But once I’ve gotten it to a state that I like (with unit tests, etc.), I will push it to my GitHub repo!

Try not to get too excited ;)