Fight for every byte it takes: Storing raw numbers

I write databases for a living, which means that I’m thinking a lot about persistence. Here is a fun challenge that we went through recently. We have the need to store a list of keys and values and then lookup a value by key. Pretty standard stuff. The keys and values are both 64 bits integers. In other words, what I would like to have is:

Dictionary<long,long> lookup;

That would be perfect, except that I’ve to persist the data, which means that I have to work with raw bytes. It’s easiest to think about it if we have some code in front of us. Here is the interface that I need to implement:

As you can see, we have a byte buffer (8KB in size) and we want to add or lookup values from the buffer. All the data resides in the buffer, nothing is external. And we cannot unpack it in memory, because this is used for lookups, so this needs to be really fast.

The keys we are storing are file offsets, so they correlate quite nicely to the overall size of the file. Meaning that you’ll have a lot of small values, but also large ones. Given a key, we need to be able to look its value quickly, since we may run this lookup billions of times.

Given that I have 8KB of data, I can do the following, just treat the buffer as a sorted array, which means that I get a pretty easy way to search for a particular value and a simple way to actually store things.

Theoretically, given an 8KB page, and 16 bytes per each (key, value) entry, we can store up to 512 entries per page. But it turns out that this is just a theory. We also need to keep track of the number of items that we have, and that takes some space. Just a couple of bytes, but it means that we don’t have those bytes available. A page can now contain up to 511 entries, and even at full capacity, we have 14 bytes wasted (2 for the number of entries, and the rest are unused).

Here is what this looks like in code:

As you can see, we are creating two arrays, the keys are growing from the bottom of the page and the values are growing from the top. The idea is that I can utilize the BinarySearch() method to quickly find the index of a key (or where it ought) to go. From there, I can look at the corresponding values array to get the actual value. The fact that they are growing separately (and toward each other) means that I don’t need to move as much memory if I’m getting values out of order.

For now, I want to set up the playground in which we’ll operate. The type of data that you write into such a system is important. I decided to use the following code to generate the test set:

The idea is that we’ll generate a random set of numbers, in the given distribution. Most of the values are in the range of 8MB to 512GB, representing a pretty good scenario overall, I think.

And with that, we just need to figure out what metrics we want to use for this purpose. My goal is to push as many values as I can into the buffer, while maintaining the ability to get a value by its key as fast as possible.

The current approach, for example, does a binary search on a sorted array plus an extra lookup to the companion values array. You really can’t beat this, if you allow to store arbitrary keys. Here is my test bench:

This will insert key/value pairs into the page until it is full. Note that we allow duplicates (we’ll just update the value), so we need to keep track of the number of entries inserted, not just the number of insertions.  We also validate the structure at any step of the way, to ensure that we always get the right behavior.

This code runs as expected and we can put 511 values into the page before it gives up. This approach works, it is simple to reason about and has very few flaws. It is also quite wasteful in terms of information density. I would like to do better than 511 entries / pager. Is it possible to drop below 16 bytes per entry?

Give it some thought, I’m going to present several ways of doing just that in my next post…