A few years ago, I wrote Implementing Dictionary In Swift, which was a crash course on how to create something similar to Swift’s Dictionary type.

Since our dictionary will be backed with an array, we need a way to convert the key that’s given into an integer, and then a way to force that integer into the bounds of our array. These two methods are the hashing function and the modulus operation, respectively. By hashing, we can consistently turn our key (usually a string, but can be any type that is Hashable) into a number, and by taking the modulus with respect to the length of the array, we’ll get a consistent slot in the array to set and retrieve the value.

Because there can be collisions, each “bucket” needs to potentially contain multiple items, so the whole thing was modeled as an array of arrays. This was a less-than-performant shortcut to get code that was working up quickly. In the post, I noted that:

A nice implementation of this Dictionary might use a linked list for the values property of the Placeholder.

Since writing that post, I’ve learned a lot of things, but germane to the discussion here: this is a bad strategy. Linked lists are very good when memory is tightly limited, and you can’t reliably secure a long, unbroken block of memory. As memory in our computers has gotten bigger, CPUs have learned to predict and preload memory in long sequences, so working with continuous blocks of memory is remarkably faster to jumping around the memory space through a discontinuous chain.

So if we don’t want to use an array of arrays, and we don’t want to use an array of linked lists, what else can we do? It turns out that there is a Dictionary storage technique that avoids the problems with both solutions.

If you remember that any array of arrays can be “flattened” into one large array, a solution begins to take shape. If the bucket for a given hash value is taken, instead of storing a second value at the same location, put the new value in the neighboring bucket. Then, when searching for that element, if you see something where it should be, check the neighboring buckets until you find it (or an empty slot).

This technique is called “linear probing”. It was invented in 1954 and is the way that Swift’s Dictionary is actually implemented!

In this post, we’re going to writing a Dictionary that’s backed by linear probing. I’m going to use a test-driven development approach for a few reasons.

First, a key thing in Swift has changed since I wrote the last dictionary blog post. Swift 4.2 changed Swift’s hashing to be non-deterministic. This makes it really hard to write to simple tests in a playground, since any value’s hash changes between runs. We need to tightly control how our hash values are produced so that we can be sure that our Dictionary behaves appropriately as we refactor it.

Second, this algorithm behaves interestingly at the boundaries — that is, as it runs up against the end of the backing array and needs to roll over to the start of the array — and we need to make sure we handle that behavior correctly.

Third, deletion is really, really hard to get right with linear probing, and there are quite a few edge cases that need to be examined closely.

The technique also lends itself to some refactoring and restructuring, and having tests will be a great safety net to ensure that we don’t break old behavior as we make the code cleaner and simpler.

Getting Things Compiling

So, let’s get started. Test-driven development requires that you write a failing test before writing the code that makes it work, so let’s do that here.

func testGettingFromAnEmptyDictionary() {
    var dictionary = ProbingDictionary<String, String>()
    XCTAssertEqual(dictionary["a"], nil)
}

This test doesn’t compile, so we can call that failing. Let’s build the basics of the type and get this test passing.

struct ProbingDictionary<Key: Hashable, Value> {

    subscript(key: Key) -> Value? {
        get {
            return nil
        }
        set {
        }
    }

}

Not a very good dictionary, but at least it compiles and passes the first test.

Getting and Setting a Single Value

Next, let’s get it to be able to set and then get a single value. Test first:

func testSettingAndGettingAValue() {
    var dictionary = ProbingDictionary<String, String>()
    dictionary["a"] = "123"
    XCTAssertEqual(dictionary["a"], "123")
}

(The most hardcore TDD acolytes will change the implementation so that it can store exactly one value, probably in an instance variable, since that’s the bare minimum of code that you need to make this test pass. I think that’s kind of silly, so I will skip that step and jump straight to an implementation that works with multiple values.)

For the implementation, we need a few things already. We need some kind of Placeholder type again, like in the last post. However, instead of being able to store an array of key/value pairs, it’ll just store a key and a value, or nothing:

enum Item {
    case element(Key, Value)
    case empty
}

I also added some helpers for grabbing stuff like the key and value easily:

extension Item {
    var value: Value? {
        if case let .element(_, value) = self {
            return value
        }
        return nil
    }
}

We also need storage for the data in the dictionary:

private var storage: [Item] = Array(repeating: .empty, count: 8)

(8 is the initial size of the dictionary. In a real implementation, you might want to start with a bigger value, but for this example, smaller is easier to understand. We’ll implement resizing soon anyway.)

Next, we need to rewrite the get and set subscript methods. This looks a lot like the version of the dictionary from the last post:

subscript(key: Key) -> Value? {
    get {
        let index = abs(key.hashValue % storage.count)
        return storage[index].value
    }
    set {
        if let newValue = newValue {
            let index = abs(key.hashValue % storage.count)
            storage[index] = .element(key, newValue)
        }
    }
}

The abs ensures that negative values are handled correctly. This simple implementation makes our new test pass, but doesn’t handle collisions, so it’s time to write a test for that.

Handling Collision

We’d like to handle collisions, but we have a problem in setting up a test for them. As I mentioned earlier, Swift’s hashing is non-deterministic as of Swift 4.2, which means that if you run the same code twice, you’ll get two different hash values for the same object. That makes forcing a collision to happen really difficult.

We need a way to ensure that our test is perfectly reproducible and actually tests the thing we’re trying to test, which is a collision that has to occur every time we run this test. There two options here. First, you can set an environment variable called SWIFT_DETERMINISTIC_HASHING and find two values that happen to hash to the same bucket.

However, according to Karoy in the Swift forum thread announcing this new feature,

setting SWIFT_DETERMINISTIC_HASHING does not guarantee that hash values remain stable across different versions of the compiler/stdlib – please do not rely on specific hash values and do not save them across executions.

This means that we might have to update our tests every time the Swift toolchain is updated, and that’s not great. Instead, we can write a small type that can perfectly control what it hashes to. It needs fields for its underlying value and its hash value separately, so that a collision (two values that aren’t equal but have the same hash value) can be forced:

struct Hash: Hashable {

    let value: String

    let hashValue: Int

    init(value: String, hashValue: Int) {
        self.value = value
        self.hashValue = hashValue
    }

    static func == (lhs: Hash, rhs: Hash) -> Bool {
        return lhs.value == rhs.value
    }
}

(This type has a warning telling us not to use hashValue directly. Nothing can really be done about that.) Given this small type, we can now write a test with a forced collision:

func testACollision() {
    var dictionary = ProbingDictionary<Hash, String>()
    dictionary[Hash(value: "a", hashValue: 1)] = "123"
    dictionary[Hash(value: "b", hashValue: 1)] = "abc"
    XCTAssertEqual(dictionary[Hash(value: "a", hashValue: 1)], "123")
    XCTAssertEqual(dictionary[Hash(value: "b", hashValue: 1)], "abc")
}

The first and second items in the Dictionary have different values, but the same hash value, which will cause a collision. Running this test, we can observe the failure. The second item is overwriting the first. To fix this, we need to rewrite our get and set functions again.

Instead of returning the value at the hashed index, we need to check if it contains the right key. If it doesn’t, we need to step to the next value and check if it contains the right key. We keep doing this until we find the right key or hit an .empty element. Here’s an implementation that gets the job done.

get {
    let index = abs(key.hashValue % storage.count)
    return storage[index...]
        .prefix(while: { !$0.isEmpty })
        .first(where: { $0.key == key })?
        .value
}
set {
    if let newValue = newValue {
        let index = abs(key.hashValue % storage.count)
        if let insertionIndex = storage[index...].firstIndex(where: { $0.isEmpty || $0.key == key }) {
            storage[insertionIndex % storage.count] = .element(key, newValue)
        }
    }
}

It can be nice to notice that while the prefix + first(where:) in the get and the firstIndex(where:) look different, they can actually be both written the same. By rewriting the get to use .first(where: { $0.isEmpty || $0.key == key }), you can make the two blocks look the same, which suggests that there might be some shared code we can extract from here. We’ll come back to that soon.

Collisions Near the Rollover Boundary

Now that our test is passing, time to write our next failing test. Careful readers will note that we’re not handling the rollover case correctly. If the probing happens at the boundary where the storage array rolls over it’ll return nil even though there is a value in the dictionary at that spot. Let’s write a test for that.

func testARolloverCollision() {
    var dictionary = ProbingDictionary<Hash, String>()
    dictionary[Hash(value: "a", hashValue: 7)] = "123"
    dictionary[Hash(value: "b", hashValue: 7)] = "abc"
    XCTAssertEqual(dictionary[Hash(value: "a", hashValue: 7)], "123")
    XCTAssertEqual(dictionary[Hash(value: "b", hashValue: 7)], "abc")
}

We happen to know that our dictionary’s original size is 8, so we know to put the colliding elements at index 7 of the storage. However, to make this more robust, you might expose the size of the storage as an internal detail so your tests can rely on it but consumer code can’t. Either way, we have another failing test.

Fixing this one is kind of easy, but also kind of hard. Instead of just checking storage[index...], we need to follow it up with a check storage[..<index] as well. The naive solution for this is just to append the two together with a +.

let rotated = storage[index...] + storage[..<index]

This causes a major performance issue, which we have to address.

By examining the types, we can see what’s going on. rotated is an ArraySlice, which usually represents a view on an array — it stores the original array, a start index and an end index. However, this is not really one slice of an array, but rather two concatenated together, which means that because the internal storage of ArraySlice (the array and the two indices) can’t store the components of two different arrays, it will have to copy and modify one of them. Because ArraySlice is a copy-on-write type, this means that the whole storage array has to be copied into new storage when you execute that + operator. This has the ultimate effect of making every read from the dictionary be an O(n) operation, which is unacceptable. There are a few ways to fix this.

The apple/swift repo has a “Prototypes” folder which contains lots of interest and useful things that aren’t shipped with Swift or its standard library, but are useful nonetheless. Two of these are Concatenated and RotatedCollection. The first allows you to concatenate two collection together without copying, and the second enables you to “rotate” a collection around a pivot, which is exactly what we’re trying to do here. However, because we don’t have this type available to us, I’m going to take a different approach.

We discussed earlier that there’s a shared function we can extract from here, called firstOrEmptyIndex(matchingKey:), which finds the first index that matches our key or is empty. We can use that in both the get (grab the value of that Item, which return nil if it’s empty) and set (overwrite the key-value pair at that index). Let’s take a look at that function. We can add support for our new behavior here, checking all indices before the pivot as well.

func firstOrEmptyIndex(matchingKey key: Key) -> Int {
    let block: (Item) -> Bool = { $0.isEmpty || $0.key == key }
    let initialIndex = abs(key.hashValue % storage.count)
    let index = storage[initialIndex...].firstIndex(where: block)
        ?? storage[..<initialIndex].firstIndex(where: block)
     return index! % storage.count
}

Getting and setting become a lot simpler now:

subscript(key: Key) -> Value? {
    get {
        let index = firstOrEmptyIndex(forKey: key)
        return storage[index].value
    }
    set {
        if let newValue = newValue {
            let insertionIndex = firstOrEmptyIndex(forKey: key)
            storage[insertionIndex] = .element(key, newValue)
        }
    }
}

Tests are now passing. We can now handle rollover collisions.

At this point, I added a few more tests that didn’t require code changes. What if there’s a triple collision? What if there’s two or three objects in the dictionary that don’t collide? What about neighboring non-colliding objects? They all passed without requiring any code changes, so I’ll elide them here.

Resizing

The next feature I want to build is resizing. You might have noticed the force unwrap in that new function we just added. If none of our slots are .empty, we risk a crash. Resizing helps us ensure that there’s always free space in the dictionary. Again, test first! I think the best approach here is to store a large number of items in the dictionary (in this case 1000 items) and then assume that that’s enough items to force a resize.

func testResizing() {
    let letters = "abcdefghijklmnopqrstuvwxyz"
    func randomString() -> String {
        return String((0...10).compactMap({ _ in letters.randomElement() }))
    }
    let values = (1...1000).map({ (randomString(), $0) })
    var dictionary = ProbingDictionary<Hash, String>()
    for (key, hash) in values {
        dictionary[Hash(value: key, hashValue: hash)] = key
    }

    for (key, hash) in values {
        XCTAssertEqual(dictionary[Hash(value: key, hashValue: hash)], key)
    }
}

This test fails, so we know that it tests resizing correctly. Resizing is a pretty straightforward feature, and it’s very similar to how the resizing code in the previous blog post worked:

private mutating func resizeIfNeeded() {
    guard self.storage.filter({ $0.hasElement }).count > storage.count / 2 else { return }
    let originalStorage = self.storage
    self.storage = Array(repeating: .empty, count: originalStorage.count * 2)
    for case let .element(key, value) in originalStorage {
        self[key] = value
    }
}

Copy the storage, create a new storage that’s twice as big, and then copy all the elements into the new storage. I even got to use for case syntax in Swift, which I’ve never used before. If we call this method before trying to set any values, our new test will pass.

Collection Conformance

Let’s implement Collection conformance next. Instead of having a separate test for Collection stuff, we can just add an extra assert at the bottom of each test, asserting how many items should be in the Dictionary by the end of the test.

func testACollision() {
    var dictionary = ProbingDictionary<Hash, String>()
    dictionary[Hash(value: "a", hashValue: 1)] = "123"
    dictionary[Hash(value: "b", hashValue: 1)] = "abc"
    XCTAssertEqual(dictionary[Hash(value: "a", hashValue: 1)], "123")
    XCTAssertEqual(dictionary[Hash(value: "b", hashValue: 1)], "abc")
    XCTAssertEqual(dictionary.count, 2)
}

This is this simplest I could get the conformance to be, code-wise:

extension ProbingDictionary: Collection {
    var startIndex: Int {
        return storage.firstIndex(where: { $0.hasElement }) ?? storage.endIndex
    }

    var endIndex: Int {
        return storage.endIndex
    }

    func index(after i: Int) -> Int {
        return storage[i...].dropFirst().firstIndex(where: { $0.hasElement }) ?? endIndex
    }

    subscript(index: Int) -> (Key, Value) {
        return (storage[index].key!, storage[index].value!)
    }
}

While this works, it doesn’t quite meet the performance characteristics that Collection expects. startIndex should be an O(1) operation, but here it’s O(n), since it has to run through the storage array to find the first non-empty element. A better implementation would store the startIndex (and probably the current count, too) so that those things could be returned in O(1) time. The start index would store the first index in the storage array that is not .empty. Although it would add to the layout of the Dictionary, it’s probably worth it in order to deliver complexity guarantees that consumers would expect.

Now is also a fine time to throw in helpers for keys and values, which users also expect:

extension ProbingDictionary {
    var keys: AnySequence<Key> {
        return AnySequence(storage.lazy.compactMap({ $0.key }))
    }

    var values: AnySequence<Value> {
        return AnySequence(storage.lazy.compactMap({ $0.value }))
    }
}

Deletion

Okay. It’s time to write the code to handle deletion from the dictionary. I won’t lie to you — deletion with linear probing is hard. Think about it: you have to find the index (easy enough), replace it with .empty (fine), and then slide down every other element until the next .empty, unless the element is already in the lowest possible slot, in which case skip it and look for another one you can swap down (yikes!).

As always, test first:

func testDeletion() {
    var dictionary = ProbingDictionary<Hash, String>()
    dictionary[Hash(value: "a", hashValue: 7)] = "123"
    dictionary[Hash(value: "b", hashValue: 4)] = "abc"
    dictionary[Hash(value: "a", hashValue: 7)] = nil

    XCTAssertEqual(dictionary[Hash(value: "a", hashValue: 7)], nil)
    XCTAssertEqual(dictionary[Hash(value: "b", hashValue: 4)], "abc")
    XCTAssertEqual(dictionary.count, 1)
}

(Adding collection conformance is quite nice here, since it lets us check that size of the dictionary is accurate after the deletion.)

Writing this code frankly sucked. There’s no cute code that could dig me out of this one:

var deletionIndex = firstOrEmptyIndex(forKey: key)
repeat {
    let potentialNextIndex = (storage[deletionIndex...] + storage[..<deletionIndex])
        .prefix(while: { !$0.isEmpty })
        .dropFirst()
        .firstIndex(where: { abs($0.key!.hashValue % storage.count) <= deletionIndex })
    storage[deletionIndex] = .empty
    if let nextIndex = potentialNextIndex {
        let nextIndex = nextIndex % storage.count
        storage[deletionIndex] = storage[nextIndex]
        deletionIndex = nextIndex
    }
} while !storage[deletionIndex].isEmpty

Truly the stuff of nightmares. Does it work? I think so. It’s hard to be confident when the algorithm is this complicated. At this point, I added tests to cover the cases I could think of — deletion with neighboring non-colliding elements, deletion with colliding elements, deletion with neighboring elements that both collide and don’t collide, deleting elements that don’t exist, deleting an element and writing back to that same key, and so on. I’m fairly confident at this point that the code works, but I much prefer code that I can understand by reading, rather than code whose working state depends on what failures I can think of and write tests for.

Tombstones

Fortunately, there is a better way to handle deletion. Right now, we only have two cases in our Item enum: either it has an element, or it doesn’t. But if we could add a little bit of information to that, we could make a distinction between slots that have never held an element, and slots that used to hold an element but don’t anymore. We call these tombstones, since they represent a marker for something that lived once, but is now dead. Tombstones help us because when we are doing a set, we can treat tombstones the same as empty elements (because they are writable slots) but when doing a get, we can treat them as a filled slot that doesn’t match our key, so we always pass over them and continue. This simplifies things greatly.

Our “first or empty” function needs to change its signature a bit:

func firstOrEmptyIndex(forKey key: Key, includeTombstones: Bool = false) -> Int

Since we now make a distinction between .tombstone and .empty when reading and writing, each of those two operations will pass a different value for this Bool.

This makes our reading, writing, and deleting code super simple:

subscript(key: Key) -> Value? {
    get {
        let index = firstOrEmptyIndex(forKey: key)
        return storage[index].value
    }
    set {
        resizeIfNeeded()
        if let newValue = newValue {
            let insertionIndex = firstOrEmptyIndex(forKey: key, includeTombstones: true)
            storage[insertionIndex] = .element(key, newValue)
        } else {
            let index = firstOrEmptyIndex(forKey: key)
            if !storage[index].isEmpty {
                storage[index] = .tombstone
            }
        }
    }
}

I like simple, because I can understand simple. All the tests still pass, and thus we know our refactor was successful.

As an aside, I’d like to look at our original Item enum again:

enum Item {
    case element(Key, Value)
    case empty
}

When you first see this type, it can be tempting to try to replace it with (Key, Value)?, since this type holds the same amount of information as the optional tuple. However, not only does a custom enum provide more information to the reader of the code, it also is more easily extended to add the .tombstone case. With the optional tuple, it’s tough to see how the tombstone can be added. Using an enum makes it easy it add that extra case and get to the refactored state.

Linear probing is a super interesting approach for building dictionaries. Given that this post is nearly 3000 words, it’s not an easy technique, but as far as I know, it’s the gold standard for fast, reliable dictionaries. It’s used in Python, Rust, Swift, and many other languages besides. Understanding how it works is key to appreciating the speed and structure of a dictionary.

A few months ago, Aaron Patterson tweeted about some three-year-old uncommitted code:

tfw you work on a patch for 3 years and it’s like 2k lines and then you commit it and hope CI passes

Aaron’s CI build, naturally, didn’t pass.

At this point, Martin Fowler (the Martin Fowler, that Martin Fowler) chimed in:

is this where I get to be the annoying internet pedant and point out that if a patch has been developed for 3 years it’s most certainly not CI?

Why am I dredging up a twitter dunk from 3 months ago? Because this tweet, these 146 characters, have completely upended the way I think about branches, working in teams, and continuous integration in general.

Up until reading that tweet — a tweet! — almost all of the usage of the phrase “continuous integration” in my day-to-day life revolved around setting up some build server (usually but not always something like BitRise, BuddyBuild, Travis, etc) to build my code and run tests before I’m allowed to merge a branch.

But Martin’s tweet made me realize something. Build servers are just a tool used in the service of continuous integration. They don’t represent the philosophy behind it. The name carries the meaning quite well — continuously (as frequently as possible) integrate your work into some shared place, usually the mainline branch.

The implications are manifest. Integrating frequently means:

  1. You don’t have to deal with horrible merges.
  2. Not only do your teammates know what you’re working on at any given time, they can begin using it before you’re finished
  3. If you have to drop your work for months (or, in Aaron’s case, years), the work you’ve done isn’t in limbo, doesn’t go out of date, and can be built on by the rest of your team.
  4. Code review on shorter diffs is more fruitful than code review on longer diffs.
  5. Code review earlier in the process can yield useful discussion on architecture and high-level patterns than code review later in the process, after the feature is fully built.
  6. The fault lines between features form earlier, and any bugs that happen because of the interaction between two features emerge earlier, making them easier to solve and alleviating crunch time before a release — a problem that even the Swift compiler team has run into.

Code that isn’t integrated into your team’s mainline branch should be considered a liability at best, and dead at worst. Your job is to get the small, workable units of code merged in as early as possible.

A problem presents itself, however. You need to build a feature that takes 1,000 lines of code, but you’d like to merge it in in smaller chunks. How can you merge the code in if it’s not finished?

Broadly, the strategy is called “branch by abstraction”. You “branch” your codebase, not using git branches, but rather branches in the code itself. There’s no one way to do branch by abstraction, but many techniques that are all useful in different situations.

The easiest way to do this is to create functions and objects that aren’t actually called from anywhere. For example, making a new feature can involve writing the model objects first and making a PR from just those. Super easy to code review and get out of the way before the meat of your feature is ready.

Of course, the humble if statement is also a great way to apply this technique; use it liberally with feature flags to turn features on and off. (A feature flag doesn’t have to be complicated. A global constant boolean gets you pretty far. Feature flags don’t have to come from a remote source! However, I would recommend against compile-time #if statements, however. Code that doesn’t get compiled might as well be dead.)

Lastly, you can take advantage the language features you have access to. Get creative! I like to use Swift’s typealiases to enable old code to work while I rename a type or refactor some code. The Swift standard library uses this feature to great effect:

public typealias BidirectionalSlice<T> = Slice<T> where T : BidirectionalCollection

BidirectionalSlice used to be its own type, but with conditional conformance, a separate type wasn’t needed any more. However, in order for consumer code to continue compiling, a typealias was added to ease the transition between a world with this discrete type and a world without, all the while never breaking anyone’s code. If you’re interested, this whole file is full of such goodies.

If your team decides to take this approach, then you’re going to have a lot more code reviews in front of you. If there’s a lot of latency in your pull request pipeline, then that latency will begin to block you and your teammates efforts to continuously integrate their changes into the mainline branch.

It’s important to remember that code review is a blocked thread of execution, and, as a reviewer, your job is to unblock your teammates as quickly as possible. Prioritizing code review over almost all other work alleviates the slow code review pipeline, and enables steady integration of your coworkers’s code.

Ultimately, continuous integration isn’t a build server, it’s a mindset. Keep your outstanding branches small and get code into the mainline branch steadily and frequently, and your team will see appreciable yields.

Just a heads up — this blog post has nothing to do with the coordinator pattern.

Those that have been following my blog for a long time might remember an old post, Cache Me If You Can. The idea behind the post was simple: if you just want caching, eschew Core Data in favor of something simple: a file on disk that represents a single NSCoding object. Multiple types of things you want to store? Multiple files on disk.

That concept found its way into the Backchannel SDK, as BAKCache, and has sort of followed me around ever since. It found its way into Swift, learned what a generic was, got renamed ObjectStorage, figured out how to handle user data as well as caches, and now supports Codable instead of NSCoding. You can find that version in this gist.

Recently, I’d found myself reading the object, mutating it, and then writing it back. Once I wrote that code a few times, I started noticing a pattern, and decided to formalize it in a method on the class:

func mutatingObject(defaultValue: T, _ block: @escaping (inout T) -> Void) {
    var object = self.fetchObject() ?? defaultValue
    block(&object)
    self.save(object: object)
}

However, there’s a problem revealed by this method. The class’s design encourages you to create lots of instances of ObjectStorage wherever you need them, and thus allows you to read and write to the same file from lots of different places. What happens when two instances read at the same time, both mutate the object in question, and try to write it back to the file? Even if the read and write were individually perfectly atomic, the second instance to write would overwrite the mutation from the first!

Access to the file needs to be gated somehow, and if one object is in the process of mutating, no other object should be allowed to read until that mutation is complete.

Foundation provides a handy API for this, called NSFileCoordinator, which, along with a protocol called NSFilePresenter, ensures that any time a file is updated on the disk, the NSFilePresenter object can be notified about it, and update itself accordingly. This coordination works across processes, which is impressive, and is what enables features like Xcode prompting you to reopen the Xcode project when there’s a change from a git reset or similar.

NSFileCoordinator is indispensable in a few cases:

  1. Since Mac apps deal with files being edited by multiple apps at once, almost all document-based Mac apps use it. It provides the underpinning for NSDocument.
  2. Extensions on iOS and the Mac are run in different process and may be mutating the same files at the same time.
  3. Syncing with cloud services requires the ability to handle updates to files while they are open, as well as special dispensation for reading files for the purpose of uploading them.

For our use case, we don’t really fall into any of the buckets where NSFileCoordinator is crucial — our files are all in our sandbox so no one else is allowed to touch them, and we don’t have an extension. However, NSFileCoordinator can help with file access coordination within the same process as well, so it can potentially solve our problem.

The documentation for NSFileCoordinator and NSFilePresenter are sadly not great. Here’s the gist: NSFilePresenter is the protocol through which the system informs you about what changes are about to happen to your file and how to react to them. NSFileCoordinator, on the other hand, does two things: first, it “coordinates” access to files at URLs, ensuring that two chunks of code don’t modify the data at some URL at the same time; second, it informs any active presenters (across processes!) about upcoming changes to files. We don’t care much about the latter, but the former is relevant to our work here.

Let’s add coordination to the save(object:) method.

func save(object: T) {

You need to keep track of a mutable error, which reports if another file presenter caused an error while it was trying to prepare for the execution of the block.

    var error: NSError?

Next, you create a file coordinator specific to the operation. You can also pass the NSFilePresenter responsible for this change to the NSFileCoordinator. As far as I can tell, this is only used to exclude the current file presenter from getting updates about the file. Since we don’t need any of the file presenter callbacks, we can just pass nil for this parameter and not worry about it.

    let coordinator = NSFileCoordinator(filePresenter: nil)

This next line includes a lot of detail. Let’s take a look first and then break it down.

    coordinator.coordinate(writingItemAt: storageURL, options: .forReplacing, error: &error, byAccessor: { url in

The method is passed the URL we care about, as well as our mutable error.

The block returns to you a URL that you can use. It asks you to use this URL, since it might not be the same as the URL you pass in.The reading and writing options are very important. They are the biggest determinant of what URL you’ll get in your block. If you pass something like .forUploading as a reading option, it’ll copy the file to a new place (no doubt using APFS’s copy-on-write feature), and point you to that new location so that you can perform your lengthy upload without blocking any other access to the file.

With that heavy line of code past us, the actual content of the block stays largely the same as before:

do {
    let data = try Data(contentsOf: url)
    let decoder = JSONDecoder()
    result = try decoder.decode(T.self, from: data)
} catch {
    if (error as NSError).code != NSFileReadNoSuchFileError {
        print("Error reading the object: \(error)")
    }
}

I replicated the same pattern across the fetch, mutate, and delete functions as well. You can see that version of the code here.

To test, for example, the mutatingObject code, I hit the file with 10,000 accesses, each incrementing an integer in the stored file by 1. I’ll leave out the cruft of the test, but the bulk of it looked like this:

let limit = 10_000
DispatchQueue.concurrentPerform(iterations: limit, execute: { i in
    objectStorage.mutatingObject(defaultValue: IntHolder(value: 0), { holder in
        holder.value += 1
    })
})

XCTAssertEqual(objectStorage.fetchObject()?.value, limit)

This is where I discovered my problem. Without using NSFileCoordinator, the mutatingObject dropped about 70% of writes. With it, even using the reading and writing options correctly, I was still losing a few dozen writes every 10,000. This was a serious issue. An object storage that loses about half a percent of writes still isn’t reliable enough to use in production. (Apple folks, here’s a radar. It includes a test project with a failing test.)

At this point, I started thinking about what I was actually trying to do, and whether NSFileCoordinator was really the right API for the job.

The primary use cases for NSFileCoordinator are dealing with document-like files that can change out from underneath you from other processes, and syncing data to iCloud, where data might change out from underneath you from iCloud. Neither of these are really issues that I have, I just need to coordinate writes in a single process to ensure that no data races occur. The fundamental abstraction of “coordinating” reads and writes is sound, I don’t happen to need most of the complexity of NSFileCoordinator.

I started thinking about how NSFileCoordinator had to be structured under the hood to act the way it does. It must have some kind of locking mechanism around each URL. Reads can be concurrent and writes have to be serial. Other than that, I don’t need much.

Based on that, I built my own simple file coordinator. It keeps track of a global mapping of URLs to dispatch queues.

final class FileCoordinator {
            
    private static var queues: [URL: DispatchQueue] = [:]

To make ensure that access of the global queues variable is thread-safe, I need a queue to access the queues. (I heard you like queues.)

    private static let queueAccessQueue = DispatchQueue(label: "queueAccessQueue")

From there, we need to get a queue for any URL. If the queue doesn’t exist yet in the queue map yet, we can make one and stick it in.

    private func queue(for url: URL) -> DispatchQueue {
        return FileCoordinator.queueAccessQueue.sync { () -> DispatchQueue in
            if let queue = FileCoordinator.queues[url] { return queue }
            let queue = DispatchQueue(label: "queue-for-\(url)", attributes: .concurrent)
            FileCoordinator.queues[url] = queue
            return queue
        }
    }

Lastly, we can implement our public interface, and use the reader-writer pattern to ensure that data is accessed safely.

    func coordinateReading<T>(at url: URL, _ block: (URL) throws -> T) rethrows -> T {
        return try queue(for: url).sync {
            return try block(url)
        }
    }
    
    func coordinateWriting(at url: URL, _ block: (URL) throws -> Void) rethrows {
        try queue(for: url).sync(flags: .barrier) {
            try block(url)
        }
    }
}

There are a few benefits of this over Foundation’s NSFileCoordinator. First, it doesn’t drop any writes. I can hammer on this implementation and it safely updates the file on each iteration. Second, I control it. I can change it if I run into any issues, and it has clear room to grow. Lastly, it takes advantage of some great Swift features, like rethrows and using generics to return an object from the inner block and have it be returned from the outer method call.

There are downsides to this approach, too. It naturally won’t work across processes like Apple’s version can, and it won’t have a lot of the optimizations for the different reading and writing options (even though we could add them).

There’s also lots of room to grow here. For example, if you’re touching a lot of URLs, your queues dictionary would grow boundlessly. There are a few approaches to add a limit to that, but I don’t expect it to touch more than 10 or so URLs, so I think it’s fine without the added complexity for now.

Replacing a system class can be a tough call — Apple’s classes tend to be well-written and handle lots of edge cases gracefully. However, when you find that their implementations aren’t serving you, it can be worth it to examine how complicated replacing it will be. In this case, replacing it wasn’t too much code, my test harness could catch bugs, and not relying on already-written code reduced the complexity rather than increasing it.

Update: An engineer at Apple responded to my Radar. It was a configuration error on my part:

The problem here is that the code is using an (apparently useless) NSFilePresenter when initializing the NSFileCoordinator. File Coordination will actually NOT block again other read/write claims made with the same NSFileCoordinator instance or NSFileCoordinator instances made with the same filePresenter or purposeIdentifier.

You most likely just want to use the default initializer for NSFileCoordinator here, or else manually queue up writes internally.

They continued:

Note: if you don’t care about other processes or in-process code outside of your control (i.e. in a framework), you absolutely should NOT use file coordination as a means of mutual exclusion. The cross-process functionality is definitely the main motivation to use File Coordination, but it comes with a relatively high performance (and cognitive) cost in comparison to in-process means.

Given that my in-process FileCoordinator works well, and the Apple engineer so strenously recommended that I don’t use NSFileCoordinator, I’ll probably just keep using the class I made.

In Dave Abraham’s WWDC talk, Embracing Algorithms, he talks about finding common algorithms and extracting them into the generic (and testable) functions. One thing in this vein that I like to look for is a few collection operations that cluster together that can be combined into a single operation. Often times, when combining these operations, you’ll also find a beneficial optimization that can be drawn out.

The first example of this is a method added in Swift 3:

// when you see:
myArray.filter({ /* some test */ }).first

// you should change it to:
myArray.first(where: { /* some test */ })

The predicate block stays exactly the same and the result is the same, but it’s shorter, more semantic, and more performant, since it’s not allocating a new array and finding every single object in the array that passes the test — just the first.

Another example is the count(where:) function that I helped add to Swift 5:

// when you see:
myArray.filter({ /* some test */ }).count

// you should change it to:
myArray.count(where: { /* some test */ })

Again: shorter, more semantic, and more performant. No arrays allocated, no extra work done.

In a particular project of ours, we had one common pattern where we would do a sort followed by a prefix. This code, for example, needed to find the 20 most recently created images.

return images
    .sorted(by: { $0.createdAt > $1.createdAt })
    .prefix(20)

You could also imagine something like a leaderboard, where you want the top 5 users with the highest scores.

I stared at this code until my eyes began to bleed. Something was fishy about it. I started thinking about the time complexity. If you think of the length of the original array as n, and the number of items you want to end up with as m, you can start to analyze the code. The sort is O(nlogn), and prefixing is a very cheap operation, O(1). (Prefixing can be as slow as O(m), but arrays, which are what we are dealing with here, are random access collections and can prefix in constant time.

Here’s what was bugging me: Getting the single smallest element of a sequence (using min()) requires only a single pass over the all of its contents, or O(n). Getting all of the elements ordered by size is a full sort, or O(nlogn). Getting some number m of them where m is smaller than n should be somewhere in between, and if m is much, much smaller than n, it should be even closer to O(n).

In our case, there are lots of images (n is about 55,000) and the amount we’re actually interested in small (m is 20). There should be something to optimize here. Can we optimize sorting such that will only sort the first m elements?

It turns out that, yes, we can do something along those lines. I call this function smallest(_:by:). It takes both the parameters of the sort and the prefix, which are the number m and the comparator to sort with:

func smallest(_ m: Int, by areInIncreasingOrder: (Element, Element) -> Bool) -> [Element] {

Starting with the first m elements pre-sorted (this should be quick, since m should be much smaller than the length of the sequence):

	var result = self.prefix(m).sorted(by: areInIncreasingOrder)

We loop over all the remaining elements:

		for element in self.dropFirst(m) {

For each element, we need to find the index of the first item that’s larger than it. Given our areInIncreasingOrder function, we can do this by passing the element first, and each element of result second.

        if let insertionIndex = result.index(where: { areInIncreasingOrder(element, $0) }) {

If an index is found, that means that there’s a value bigger than element in our result array, and if we insert our new value at that value’s index, it’ll be correctly sorted:

            result.insert(element, at: insertionIndex)

And remove the last element (which is now out of bounds of our number m):

            result.removeLast()

If the index wasn’t found, we can ignore the value. Lastly, once the for loop is done, we can return the result:

        }
    }

    return result
}

The whole function looks like this:

extension Sequence {
    func smallest(_ m: Int, by areInIncreasingOrder: (Element, Element) -> Bool) -> [Element] {
        var result = self.prefix(m).sorted(by: areInIncreasingOrder)
        	
        for e in self.dropFirst(n) {
            if let insertionIndex = result.index(where: { areInIncreasingOrder(e, $0) }) {
                result.insert(e, at: insertionIndex)
                result.removeLast()
            }
        }
        
        return result
    }
}

If this is reminding of you of your early coursework in computer science classes, that’s good! This algorithm is something like a selection sort. (They aren’t exactly the same, because this pre-sorts some amount, and selection sort is a mutating algorithm and this isn’t.)

The time complexity of this is a bit tougher to analyze, but we can do it. The sort of the initial bit is O(mlogm). The big outer loop is O(n), and each time it loops, it calls index(where:) (O(m)) and insert(_:at:) (O(m) as well). (Insertion is O(m) because it potentially has to slide all the elements down to make space for the new element.) Therefore, the time complexity of this is O(mlogm + n * (m + m)), or O(mlogm + 2nm). Constants fall out, leaving us with O(mlogm + nm).

If m is much, much smaller than n, the m terms become more or less constant, and you end up with O(n). That’s a good improvement over our original O(nlogn)! For our original numbers of 55,000 images, that’s should be a roughly five-fold improvement.

This function that we’ve written is broadly an optimization over prefix + sort, but there are two smaller optimizations that I want to discuss here as well.

There’s one pretty low hanging fruit optimization here. We’re looking for the smallest 20 items in an array of 55,000 elements. Most (almost all!) of the elements we check are not going to be needed for our result array. If we throw in one check to see if the element we’re looking at is larger than the last element in the result array, and if it is, just skip it entirely. There’s no sense searching through the array for its insertion index if the element is larger than the last element of result.

if let last = result.last, areInIncreasingOrder(last, e) { continue }

Testing with this check enabled caused a 99.5% drop in linear searches through the result array, and the whole algorithm increased roughly 10x in speed. I want to credit to Greg Titus for pointing this optimization out to me — I would have missed it entirely.

If you want to go take another step, you can do one more (slightly harder to implement) optimization. This one relies on two facts. First, we’re using index(where:) to find the insertion in the result array; second, the result is always sorted. index(where:) is a linear operation by default, but if we’re searching through an already-sorted list, it can be tempting try and replace the linear search with a binary search. I took a crack at this.

To understand how these optimizations affected the performance of the algorithm, Nate Cook helped me become familiar with Karoy Lorentey’s Attabench tool, benchmarking each of these solutions. Because all of our complexity analysis until this point was theoretical, until we actually profile the code we’re concerned with (and ideally on the devices in question), any conclusions are just educated guesses. For example, sort generally is O(nlogn), but different algorithms handle different kinds of data differently. For example, already sorted data might be slower or faster to sort for a particular algorithm.

Attabench showed me a few things.

Profiling data

(I also threw in a priority queue/heap solution written by Tim Vermuelen, since a few people asked for how that compares.)

First, my guess that searching through the array a single time was faster than fully sorting the array was correct. Especially as the sequence in question gets long, sorting gets worse but our “naive optimization” stays constant. (The Y axis represents the time spent per item, rather than total, meaning that O(n) algorithms should be a flat line.)

Second, the “last check” and the binary search optimizations have almost exactly the same performance characteristics when they are on their own (you can’t actually see the orange and yellow lines because they’re behind the green), as when they’re used together. However, because binary search is hard to write and even harder to get right, you may decide it isn’t worth it to add.

The takeaway here for me is that profiling and optimizing is hard. While complexity analysis can seem a bit academic — “When am I going to use this in my real career?” one asks — understanding the time and space complexity of your algorithms can help you decide which directions to explore. In this case, understanding the time complexity of sorting led us towards a broad idea which bore fruit. Finally, benchmarking and profiling with a wide variety of data leads to the most accurate information about how your code will work in production.

And also, next time you see a sort followed by a prefix, think about replacing it with smallest(_: by:).

Foundation’s URL loading is robust. iOS 7 brought the new URLSession architecture, making it even more robust. However, one thing that it’s never been able to do natively is multipart file uploads.

What is a multipart request?

Multipart encoding is the de facto way of sending large files over the internet. When you select a file as part of a form in a browser, that file is uploaded via a multipart request.

A multipart request mostly looks like a normal request, but it specifies a unique encoding for the HTTP request’s body. Unlike JSON encoding ({ "key": "value" }) or URL string encoding (key=value), multipart encoding does something a little bit different. Because of the body of a request is just a long stream of bytes, the entity parsing the data on the other side needs to be able to determine when one part ends and another begins. Multipart requests solve this problem using a concept of “boundaries”. In the Content-Type header of the request, you define a boundary:

Accept: application/json
Content-Type: multipart/form-data; boundary=khanlou.comNczcJGcxe

The exact content of the boundary is not important, it just needs to be a series of bytes that is not present in the rest of the body (so that it can meaningfully act as a boundary). You can use a UUID if you like.

Each part can be data (say, an image) or metadata (usually text, associated with a name, to form a key-value pair). If it’s an image, it looks something like this:

--<boundary>
Content-Disposition: form-data; name=<name>; filename=<filename.jpg>
Content-Type: image/jpeg

<image data>

And if it’s simple text:

--<boundary>
Content-Disposition: form-data; name=<name>
Content-Type: text/plain

<some text>

After the last part in the request, there’s one more boundary, which includes an extra two hyphens, --<boundary>--. (Also, note that the new lines all have to be CRLF.)

That’s pretty much it. It’s not a particularly complicated spec. In fact, when I was writing my first client-side implementation of multipart encoding, I was a bit scared to read the RFC for multipart/form-data. Once I took a look at it, however, I understood the protocol a lot better. It’s surprisingly readable, and nice to go straight to the source for stuff like this.

That first implementation was in the Backchannel SDK, which is still open source. You can see the BAKUploadAttachmentRequest and the BAKMultipartRequestBuilder, which combine to perform the bulk of the multipart handling code. This particular implementation only handles a single file and no metadata, but it serves as an example of how this request can be constructed. You could modify it to support metadata or multiple files by adding extra “parts”.

However, if you want to upload multiple files, whether your service expects one request with many files or many requests with one file each, you’ll soon run into a problem. If you try to upload too many files at once, your app will crash. Because this version of the code loads the data that will be uploaded into memory, a few dozen full-size images can crash even the most modern phones.

Streaming files off the disk

The typical solution to this is to “stream” the files off the disk. The idea is that the bytes for any given file stay on the disk, until the moment they’re needed, at which point they’re read off the disk and sent straight to the network machinery. Only a small amount of the bytes for the images is in memory at any given time.

I came up with two broad approaches to solving this problem. First, I could write the entire data for the multipart request body to a new file on disk, and use an API like URLSession’s uploadTask(with request: URLRequest, fromFile fileURL: URL) to stream that file to the API. This would work, but it seemed like it should be possible to accomplish this without writing a new file to the disk for each request. There would also be a bit of cleanup to handle after the request has been sent.

The second approach is to build a way to mix data in memory with data on the disk, and present an interface to the network loading architecture that looks like a chunk of data from a single source, rather than many.

If you’re thinking this sounds like a case for class clusters, you’re dead on. Many common Cocoa classes allow you to make a subclass that can act as the super class by implementing a few “primitive” methods. Think -count and -objectAtIndex: on NSArray. Since every other method on NSArray is implemented in terms of those two, you can write optimized NSArray subclasses very easily.

You can create an NSData that doesn’t actually read any data off the disk, but rather creates a pointer directly to the data on disk, so that it never has to load the data into memory to read it. This is called memory mapping, and it’s built on a Unix function called mmap. You can use this feature of NSData by using the .mappedIfSafe or .alwaysMapped reading options. And NSData is a class cluster, so if we could make a ConcatenatedData subclass (that works like FlattenCollection in Swift) that allows you treat many NSData objects as one continuous NSData, we would have everything we need to solve this problem.

However, when we look at the primitive methods of NSData, we see that they are -count and -bytes. -count isn’t a big deal, since we can easily sum up the counts of all the child datas; -bytes, however, poses a problem. -bytes should return a pointer to a single continuous buffer, which we won’t have.

To handle discontinuous data, Foundation gives us NSInputStream. Fortunately, NSInputStream is also a class cluster. We can create a subclass that makes many streams look like one. And with APIs like +inputStreamWithData: and +inputStreamWithURL:, we can easily create input streams that represent the files on the disk and the data in memory (such as our boundaries).

If you look at the major third-party networking libraries, you’ll see that this is how AFNetworking actually works. (Alamofire, the Swift version of AFNetworking, loads everything into memory but writes it to a file on disk if it is too big.)

Putting all the pieces together

You can see my implementation of a serial InputStream here in Objective-C and here in Swift.

Once you have something like SKSerialInputStream, you can combine streams together. Given a way to make the prefix and postfix data for a single part:

extension MultipartComponent {
    var prefixData: Data {
        let string = """
        \(self.boundary)
        Content-Disposition: form-data; name="\(self.name); filename="\(self.filename)"
        """
        return string.data(using: .utf8)
    }
    
    var postfixData: Data {
        return "\r\n".data(using: .utf8)
    }
}

You can compose the metadata for the upload and the dataStream for the file to upload together into one big stream.

extension MultipartComponent {
    var inputStream: NSInputStream {
        
        let streams = [
            NSInputStream(data: prefixData),
            self.fileDataStream,
            NSInputStream(data: postfixData),
        ]
    
        return SKSerialInputStream(inputStreams: streams)
    }
}

Once you can create an input stream for each part, you can join them all together to make an input stream for the whole request, with one extra boundary at the end to signal the end of the request:

extension RequestBuilder {
    var bodyInputStream: NSInputStream {
        let stream = parts
            .map({ $0.inputStream })
            + [NSInputStream(data: "--\(self.boundary)--".data(using: .utf8))]
    
        return SKSerialInputStream(inputStreams: streams)
    }
}

Finally, assigning that to the httpBodyStream of your URL request completes the process:

let urlRequest = URLRequest(url: url)

urlRequest.httpBodyStream = requestBuilder.bodyInputStream;

The httpBodyStream and httpBody fields are exclusive — only one can be set. Setting the input stream invalidates the Data version and vice versa.

The key to streaming file uploads is being able to compose many disparate input streams into one. Something like SKSerialInputStream makes the process a lot more manageable. Even though subclassing NSInputStream can be a bit perilous, as we’ll see, once it’s solved the solution to the problem falls out more or less naturally.

Subclassing notes

The actual process of subclassing NSInputStream wasn’t fun. Broadly put, subclassing NSInputStream is hard. You have to implement 9 methods, 7 of which can have trivial default implementations that the superclass should handle. The documentation only mentions 3 of the 9 methods, and you have to dig to find out that you have to implement 6 more methods from NSStream (the superclass of NSInputStream) including two run loop methods where empty implementations are valid. There also used to be 3 private methods that you had to implement, though they don’t seem to be a concern any longer. Once you’ve implemented these methods, you also have to support several readonly properties as well: streamStatus, streamError, and delegate need to be defined.

Once you get all the details about subclassing right, you get to the challenge of providing an NSInputStream that behaves in a way that other consumers would expect. The state of this class is heavily coupled in non-obvious ways.

There are a few pieces of state, and they all need to act in concert at all times. For example, hasBytesAvailable is defined separately from the other state, but there are still subtle interactions. I found a late-breaking bug where my serial stream would ideally return self.currentIndex != self.inputStreams.count for hasBytesAvailable, but that caused a bug where the stream stayed open forever and would cause a timeout for the request. I patched over this bug by always returning YES, but I never figured out the root of it.

Another piece of state, streamStatus, has many possible values, but the only ones that seem to matter are NSStreamStatusOpen and NSStreamStatusClosed.

The final interesting piece of state is the byte count, returned from the read method. In addition to returning a positive integer for the byte count, a stream can return a byte count of -1, which indicates an error, which then has to be checked by via the streamError property, which must no longer be nil. It can also return a byte count of 0, which, according to the documentation, is another way that to indicate that the end of the stream has been reached.

The documentation doesn’t guide you what combinations of states are valid. If my stream has a streamError, but the status is NSStreamStatusClosed rather than NSStreamStatusError, will that cause a problem? Managing all this state is harder than it needs to be, but it can be done.

I’m still not fully confident that SKSerialStream behaves perfectly in all situations, but it seems to support uploading multipart data via URLSession well. If you use this code and find any issues, please reach out and we can make the class better for everyone.

Update, August 2019: One final note I want to add on this code. I was seeing some small bugs with it, and I spent a few nights debugging. This was pretty painful, so I want to leave this note for readers and of course, future versions of myself. If you give you URLRequest a Content-Length, NSURLSession will use that to determine exactly how many bytes to pull out of your input stream. If the content length is too low, it will truncate your stream precisely at that byte. If the content length is too high, your request will timeout as it waits for bytes that will never come because the stream is exhausted. This, sadly, is not documented anywhere.

Swift 4.2 brings some new changes to how hashing works in Swift. Previously, hashing was fully delegated to the object itself. You would ask an object for its hashValue, and it would respond with the fully cooked integer representing the hash. Now, objects that conform to Hashable describe how to combine their constituent components into a Hasher object that’s passed in as a parameter. This is great for a few reasons.

  • Good hashing algorithms are hard to write. End users of Swift shouldn’t be responsible for knowing the best way to combine their constituent components into a good hash value.
  • Hash values should be different for each execution of the program, to discourage users from storing them in any way and for security reasons. Descriptive hashing allows the seeds of the hashing function to change each time you run the program.
  • It makes more interesting data structures possible, which is what we’re going to focus on in this post.

I’ve written here before about how to use Swift’s Hashable protocol to write a Dictionary from scratch (and it will help to read that post before this one, but isn’t necessary). Today, I want to talk about a different kind of data structure, one that’s probabilistic rather than definite: the Bloom filter. As we build it, we’ll use a few new features in Swift 4.2, including the new hashing model.

Bloom filters are weird. Imagine a data structure where:

  • you can insert values into it
  • you can query it to see if a value is contained in it
  • it can use a tiny amount of storage to a store a huge amount of objects

but:

  • you can’t enumerate the objects in it
  • it sometimes has false positives (but never false negatives)
  • you can’t remove values from them

When would you want something like this? Medium uses them to keep track of the read status of posts. Bing uses them for search indexes. You could use them to build a cache for if a username is valid (in an @-mention, for example) without having to hit the database. They’re particularly useful on the server, where you could have immense scale but not necessarily immense resources.

(If you’ve ever done any graphics work, you might be wondering how this relates to the other bloom filter. The answer is, it doesn’t. That bloom filter is a lowercase b bloom, like a flower. This one is named after a person named Bloom. Total coincidence.)

How do they work?

Putting an object into a Bloom filter is sort of like putting it into a set or a dictionary: you need to calculate a hash value for the object and mod the hash value by the size of your storage array. At that point, instead of storing the value at that position in the index (like you would with a set or a dictionary), you simply flip a bit at that index: change a value from false to true.

Let’s take a simple example to understand how the filter works, and then we’ll crank it up to make it web scale. Imagine a boolean array (sometimes called a bit array) of 8 false values:

| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---------------------------------
|   |   |   |   |   |   |   |   |

This represents our Bloom filter. I’d like to insert the string “soroush” into it. The string hashes to 9192644045266971309, which, when modded by 8, yields 5. I’ll flip the bit at that index.

| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---------------------------------
|   |   |   |   |   | * |   |   |

Next, I’d like to insert the string, “swift”. It yields a hash of 7052914221234348788, which we then mod by 8: flip the bit at index 4.

| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
---------------------------------
|   |   |   |   | * | * |   |   |

To test if the Bloom filter contains the string “soroush”, I hash and mod again, yielding 5 again, which is set to true. “soroush” is indeed in the Bloom filter.

You can’t just test the cases where your thing works though, so let’s write some negative tests. Testing the string “khanlou” yields an index of 2, so we know it’s not in the bloom filter. So far, so good. Next test: the string “hashable” yields an index of 5, which…causes a collision! It returns true even though the value was never inserted into the Bloom filter. This is an example of a Bloom filter giving you a false positive.

Since we want to minimize these false positives, there are two main strategies we can use. First, and the more interesting of the two: instead of hashing the value once, we can hash it twice, or three times, with different hashing functions. As long as they are all well-behaved hashing functions (evenly distributed, consistent, minimal collisions), we can generate multiple indices to flip for each value. Now, when we hash “soroush”, we do it twice, and generate two indices, and flip the bools there. But now, when we go to check if “khanlou” is included in the Bloom filter, one of its hashes will collide with one of the hashes for “soroush”, but the chance that both of its hashes will collide has become smaller. You can scale this number up. I’ll use the 3 hashes in the code below, but you could use more.

Of course, if you use more hashes, each element will take up more space in the bit array. However, we’re using practically nothing right now. Our data array is 8 booleans (or bits) which is 1 byte. This is second tactic for minimizing false positives: scale the bit array up. We can make it pretty big before we even start noticing it. We’ll use a default of 512 bits for the code example below.

Now, even using both of these strategies, you’ll still get collisions, and thus false positives, but you’ll get fewer of them. This is one of the downsides of using Bloom filters, but in the right circumstances, the speed and space savings are a worthwhile tradeoff.

I want to touch on three other things to note before we get into code. First, you can’t resize a Bloom filter. When you mod the hash value, you’re destroying information, and you can’t get that information back unless you keep the original hashes around — defeating the dramatic space savings you can get with this data structure.

Secondly, you can see how it would be impossible to enumerate the elements in a Bloom filter. You don’t have them anymore, just some of their artifacts (in the form of hashes).

Lastly, you can also see how you can’t remove elements from a Bloom filter. If you try to flip the bits back to false, you don’t know who had originally flipped them to true. The value you’re trying to remove, or a different value? You’d start causing false negatives as well as false positives. (This may actually be a worthwhile tradeoff for you!) You could get around this by keeping a count at each index instead of a boolean, which would also have storage implications, but again, could be worthwhile depending on your use case.

So, let’s get to some code. There are some choices that I’ll make here that you might choose to make differently, starting with whether or not to make the object generic. I think it makes sense to have the object have a little more metadata about what it’s supposed to be storing, but if you find that too restrictive, you can change it.

struct BloomFilter<Element: Hashable> {
	// ...
}

We need to store two main things in this type. First, data, which represents our bit array. This will store all the flags that correspond to the hashes:

private var data: [Bool]

Next, we need our different hash functions. Some Bloom filters use actually different methods of computing the hash, but I think it’s easier to use the same algorithm, but mix in one additional randomly generated value.

private let seeds: [Int]

When setting up the Bloom filter, we need to set up both instance variables. Our bit array is going to simply repeat the false value, and our seeds will use Swift 4.2’s new Int.random API to generate the seeds we need.

init(size: Int, hashCount: Int) {
	data = Array(repeating: false, count: size)
	seeds = (0..<hashCount).map({ _ in Int.random(in: 0..<Int.max) })
}

I also included a convenience initializer with some nice defaults.

init() {
	self.init(size: 512, hashCount: 3)
}

There are two main functions we need to write: insert and contains. They both need to take the element and calculate one hash value for each of the seeds. Great fodder for a private helper function. We need to create one hash value for each seed, because our seed values represent the “different” hashing functions.

private func hashes(for element: Element) -> [Int] {
	return seeds.map({ seed -> Int in
		// ...
	})
}

To write the body of this function, we need to create a Hasher (new in Swift 4.2), and pass in the object we want to hash. Mixing in the seed as well ensures that the hashes won’t collide.

private func hashes(for element: Element) -> [Int] {
	return seeds.map({ seed -> Int in
		var hasher = Hasher()
		hasher.combine(element)
		hasher.combine(seed)
		let hashValue = abs(hasher.finalize())
		return hashValue
	})
}

Also, note the absolute value on the hash value. Hashes can come back as negative, which will crash our array access later. This removes one bit of entropy, which is probably fine.

Ideally, you’d be able to initialize the Hasher with a seed, instead of mixing it in. Swift’s Hasher uses a different seed for each launch of the application (unless you set an environment variable which they added for consistent hashing between launch, mostly for testing purposes), meaning you can’t write these values to disk. If we controlled the seed of the Hasher, then we could write these values to disk as well. As this Bloom filter currently stands, it should only be used for in-memory caches.

The hashes(for:) function does a lot of the heavy lifting, and makes our insert method very straightforward:

mutating func insert(_ element: Element) {
	hashes(for: element)
		.forEach({ hash in
			data[hash % data.count] = true
		})
}

Generate all the hashes, mod each one by the length of the data array, and set the bit at that index to true.

contains is likewise simple, and gives us a chance to use another new Swift 4.2 feature, allSatisfy. This new function tells you if all of the objects in the sequence pass some test, represented by a block:

func contains(_ element: Element) -> Bool {
	return hashes(for: element)
		.allSatisfy({ hash in
			data[hash % data.count]
		})
}

Because the result of data[hash % size] is already a boolean, it fits quite nicely into allSatisfy.

You can also add an isEmpty method that checks if all of the values in the data are false.

Bloom filters are one of the weirder data structures. Most of the data structures we deal with are deterministic. When you put an object in a dictionary, you know it’ll be there later. Bloom filters, on the other hand, are probabilistic, sacrificing certainty for space and speed. Bloom filters aren’t something that you’ll use every day, but when you do need them, you’ll be happy to know they exist.

Back in the days before Crusty taught us “protocol-oriented programming”, sharing of implementations happened mostly via inheritance. In an average day of UIKit programming, you might subclass UIView, add some child views, override -layoutSubviews, and repeat. Maybe you’ll override -drawRect. But on weird days, when you need to do weird things, you start to look at those other methods on UIView that you can override.

One of the more eccentric corners of UIKit is the touch handling subsystem. This primarily includes the two methods -pointInside:withEvent: and -hitTest:withEvent:.

-pointInside: tells the caller if a given point is inside a given view. -hitTest: uses -pointInside: to tell the caller which subview (if any) would be the receiver for a touch at a given point. It’s this latter method that I’m interested in today.

Apple gives you barely enough documentation to figure out how to reimplement this method. Until you learn to reimplement it, you can’t change how it works. Let’s check out the documentation and try to write the function.

override func hitTest(_ point: CGPoint, with event: UIEvent?) -> UIView? {
	// ...
}

First, let’s start with a bit from the second paragraph:

This method ignores view objects that are hidden, that have disabled user interactions, or have an alpha level less than 0.01.

Let’s put some quick guard statements up front to handle these preconditions.

override func hitTest(_ point: CGPoint, with event: UIEvent?) -> UIView? {

	guard isUserInteractionEnabled else { return nil }
	
	guard !isHidden else { return nil }
	
	guard alpha >= 0.01 else { return nil }
			
	// ...

Easy enough. What’s next?

This method traverses the view hierarchy by calling the -pointInside:withEvent: method of each subview to determine which subview should receive a touch event.

While a literal reading of the documentation makes it sound like -pointInside: is called on each of the subviews inside a for loop, this isn’t quite correct.

Thanks to a reader dropping breakpoints in -hitTest: and -pointInside:, we know -pointInside: is called on self (with the other guards), rather than on each of the subviews. So we can add this line of code to the other guards:

guard self.point(inside: point, with: event) else { return nil }

-pointInside: is another override point for UIView. Its default implementation checks if the point that is passed in is contained within the bounds of the view. If a view returns true for the -pointInside: call, that means the touch event was contained within its bounds.

With that minor discrepency out of the way, we can continue with the documentation:

If -pointInside:withEvent: returns YES, then the subview’s hierarchy is similarly traversed until the frontmost view containing the specified point is found.

So, from this, we know we need to iterate over the view tree. This means looping over all the views, and calling -hitTest: on each of those to find the proper child. In this way, the method is recursive.

To iterate the view hierarchy, we’re going to need a loop. However, one of the more counterintuitive things about this method is we need to iterate the views in reverse. Views that are toward the end of the subviews array are higher in Z axis, and so they should be checked out first. (I wouldn’t quite have picked up on this point without this blog post.)

// ...
for subview in subviews.reversed() {

}
// ...

The point that we are passed is defined relative to the coordinate system of this view, not the subview that we’re interested in. Fortunately UIKit gives us a handy function to convert points from our reference to the reference frame of any other view.

// ...
for subview in subviews.reversed() {
	let convertedPoint = subview.convert(point, from: self)
	// ...
}
// ...

Once we have a converted point, we can simply ask each subview what view it thinks is at that point. Remember, if the point lies outside that view (i.e., -pointInside: returns false), the -hitTest will return nil, and we’ll check the next subview in the hierarchy.

// ...
let convertedPoint = subview.convert(point, from: self)
if let candidate = subview.hitTest(convertedPoint, with: event) {
	return candidate
}
//...

Once we have our loop in place, the last thing we need to do is return self. If the view is tappable (which all of our guard statements assert), but none of our subviews want to take this touch, that means that the current view, self, is the correct target for the touch.

Here’s the whole algorithm:

override func hitTest(_ point: CGPoint, with event: UIEvent?) -> UIView? {
	
	guard isUserInteractionEnabled else { return nil }
	
	guard !isHidden else { return nil }
	
	guard alpha >= 0.01 else { return nil }
	
	guard self.point(inside: point, with: event) else { return nil }	
	
	for subview in subviews.reversed() {
		let convertedPoint = subview.convert(point, from: self)
		if let candidate = subview.hitTest(convertedPoint, with: event) {
			return candidate
		}
	}
	return self
}

Now that we have a reference implementation, we can begin to modify it to enable specific behaviors.

I’ve discussed one of those behaviors on this blog before, in Changing the size of a paging scroll view, I talked about the “old and busted” way to create this effect. Essentially, you’d

  1. turn off clipsToBounds.
  2. put an invisible view over the scrollable area.
  3. override -hitTest: on the invisible view to pass all touches through to the scrollview.

The -hitTest: method was the cornerstone of this technique. Because hit testing in UIKit is delegated to each view, each view gets to decide which view receives its touches. This enables you to override the default implementation (which does something expected and normal) and replace it with whatever you want, even returning a view that’s not a direct child of the original view. Pretty wild.

Let’s take a look at a different example. If you’ve played with this year’s version of Beacon, you might have noticed that the physics for the swipe-to-delete behavior on events feel a little different from the built-in stuff that the rest of the OS uses. This is because we couldn’t quite get the appearance we wanted with the system approach, and we had to reimplement the feature.

As you can imagine, rewriting the physics of swiping and bouncing is needlessly complicated, so we used a UIScrollView with pagingEnabled set to true to get as much of the mechanics of the bouncing for free. Using a technique similar to an older post on this blog, we set a custom page size by making our scroll view bounds smaller and moving the panGestureRecognizer to an overlay view on top of the event cell.

However, while the overlay correctly passes touch events through to the scroll view, there are other events that the overlay incorrectly intercepts. The cell contains buttons, like the “join event” button and the “delete event” button that need to be able to receive touches. There are a few custom implementations of the -hitTest: method that would work for this situation; one such implementation is to explicitly check the two button subviews:

override func hitTest(_ point: CGPoint, with event: UIEvent?) -> UIView? {

	guard isUserInteractionEnabled else { return nil }
	
	guard !isHidden else { return nil }
	
	guard alpha >= 0.01 else { return nil }

	guard self.point(inside: point, with: event) else { return nil }

	if joinButton.point(inside: convert(point, to: joinButton), with: event) {
		return joinButton
	}
	
	if isDeleteButtonOpen && deleteButton.point(inside: convert(point, to: deleteButton), with: event) {
		return deleteButton
	}
	return super.hitTest(point, with: event)
}

This correctly forwards the right tap events to the right buttons without breaking the scrolling behavior that reveals the delete button. (You could try ignoring just the deletionOverlay, but then it won’t correctly forward scroll events.)

-hitTest: is an override point for views that is rarely used, but when needed, can provide behaviors that are hard to build using other tools. Knowing how to implement it yourself gives you the ability to replace it at will. You can use the technique to make tap targets bigger, remove certain subviews from touch handling without removing them from the visible hierarchy, or use one view as a sink for touches that will affect a different view. All things are possible!

Martin Fowler’s seminal 1999 book Refactoring includes a chapter with Kent Beck on “code smells”. Code smells, they say, are “certain structures in the code that suggest (sometimes they scream for) the possibility of refactoring”. One of the code smells they talk about is the Data Clump.

Often you’ll see the same three or four data items together in lots of places: fields in a couple of classes, parameters in many method signatures. Bunches of data that hang around together really ought to be made into their own object.

They give a quick test for a data clump: if you delete one of the data values, would the others make sense?

This is a good test, and in today’s article, I’d like to propose another useful way to detect data clumps. To be honest, I thought I’d read this elsewhere, but I’ve done some deep googling and scouring of the original texts, and I can’t find any reference to it anywhere. If you do find a good reference to this thought technology, please be sure to reach out. Update: I found it. In Sandi Metz’s 2014 RailsConf talk, All the Little Things, she discusses this at ~22:30.

If two or more instance variables (or parameters in a parameter list, etc) have a similar prefix or suffix, they’re probably a data clump. They should be associated with each other more closely than being placed next to each other.

Three distinct examples of this stick out to me.

The second app I ever made, Fireside, was a podcast player, and (among its many mistakes) it had the following in its Podcast model:

@property (nonatomic, copy) NSString *filePath;
@property (nonatomic, assign) BOOL isDownloaded;
@property (nonatomic, assign) BOOL fullyDownloaded;
@property (nonatomic, strong) NSDate *expirationDate;

@property (nonatomic, copy) NSString *streamedCopyFilePath;
@property (nonatomic, assign) BOOL streamedCopyIsDownloaded;
@property (nonatomic, assign) BOOL streamedCopyFullyDownloaded;
@property (nonatomic, strong) NSDate *streamedCopyExpirationDate;

(Pardon the Objective-C, this code is from 2011.)

In the fullness of time, it’s so obvious that this is a bad model. These four properties, filePath, isDownloaded, isFullyDownloaded, and expirationDate, should live on a new class, maybe called DownloadDetails, which would also serve as a nice home for any logic around this data, such as if the download is past its expiration date.

(If you’re wondering why there are two boolean values for the downloaded state, fullyDownloaded represents if the podcast is downloaded from the first byte to the end, and isDownloaded represents if the podcast has been downloaded from any point, such as a point the user has scrubbed to, to the end. These days, I’d probably make it an enum with three states: not downloaded, downloaded, and fully downloaded, but that’s another post.)

The matching prefixes on the properties are the clue here that concepts are duplicated. Seeing them now, they’re begging for refactoring.

Another classic example of similar prefixes can be found in the view layer. Raise your hand if you’ve done this one:

let headerContainer = UIView()

let headerBackgroundImage = UIImageView()

let headerAvatarImage = UIImageView()

let headerTitle = UILabel()

let headerDescription = UILabel()

If you’re making a bunch of views that all have the same prefix, chances are they represent a logical unit. In this case, they even have a common superview, the headerContainer. Are you really sure you’re not going to reuse these 5 views and their layout? Make the HeaderView class, don’t be lazy. (H/t to Rosa McGee for this example, and John Sundell for a blog post in a similar vein.)

The last example I want to look at happened recently, and was the impetus for this blog post. The original code wasn’t the worst code, but it was sprinkled into 600 lines of unrelated singleton code:

private var sequenceStartTime: Date?
private var sequencePauseTime: Date?

// 150 lines of other stuff

func startSequenceTimer() {		
	self.sequenceStartTime = Date()
}

func pauseSequenceTimer() {		
	self.sequencePauseTime = Date()
}

// 50 lines of unrelated responsibilities 

func resumeSequenceTimer() {		
	let pauseEndTime = Date()		
	let duration = pauseEndTime.timeIntervalSince1970 - sequencePauseTime.timeIntervalSince1970
	self.sequenceStartTime = Date().addingTimeInterval(duration)
}

// 100 more lines of just whatever

func calculateDuration() {
	let sequenceEndTime = Date()
	let duration: Double		
	if let startTime = sequenceStartTime {
		duration = Double(sequenceEndTime.timeIntervalSince1970 - sequenceStartTimetimeIntervalSince1970) / 1_000
	} else {
		duration = 0.0
	}
	return duration
}

This is clearly its own responsibility, and the start and end time variables are the first clue into that. This singleton doesn’t care about how to pause the timer or calculate the current running duration, it just needs to be able to pause a timer. This eventually became its own type and the two instance variables became the central identity of the type:

struct Milliseconds {
	let rawValue: Int
}

protocol Clock {
	func now() -> Milliseconds
}

class Stopwatch {
 
	let clock: Clock
	
	private var startTime: Milliseconds?
	 
	private var pauseTime: Milliseconds?

	// ...
	
}

The Clock protocol also enables the type to be tested, which wasn’t possible before. (H/t to Olivier Halligon showing me how to test this class.) The tests also enabled me to fix a few bugs in the original code. (If you’re wondering what kinds of bugs, look at the original code: what happens if you’ve currently paused and you try to check the duration?)

Extracting data clumps is a great way to find hidden classes and responsibilities within your code, and a great way to locate their hiding spots is to look at the language you use to define the variables. If there is a relationship between the language of the two properties, perhaps there is a deeper relationship is waiting to be drawn out as well. Expressing those relationships explicitly can lead to cleaner, more testable, and more reusable code.

A lot of what I do for my clients is code review. Code review is one of the better ways we know of to catch bugs early. I’ve been doing more code review in my day-to-day, and I’ve started to notice patterns arising out of the mire — little things that I see and can flag for deeper attention. One of these little smells is the case of the missing else branch.

Let’s say we’re trying to enable a button when a UITextField has more than 8 characters:

@objc func textChanged(_ sender: UITextField) {
	if (sender.text ?? "").count >= 8 {
		submitButton.isEnabled = true
	}
}

There’s a bug here. UIKit warriors have probably seen this particular bug many times and solved it an equal number of times. But because our programming tools are stuck in the Dark Ages, we can’t see the bug, so let’s spin up a little virtual machine in our brains. We’ll need to keep track of the text of the sender, the user’s keyboard entry, and the enabled state of the submitButton.

What happens when if the user types their 8 characters and then deletes one? The button becomes enabled, but stays enabled when they delete a character.

The bug is hard to spot, but, if the title of the blog post doesn’t give it away, easy to fix.

@objc func textChanged(_ sender: UITextField) {
	if (sender.text ?? "").count >= 8 {
		submitButton.isEnabled = true
	} else {
		submitButton.isEnabled = false
	}
}

Now, when the user types in their 8 characters and deletes one, the submit button is correctly disabled. Leaving out the else branch meant that a path of code wasn’t fully handled. Swift lets us elide the else branch, which it conceals its true nature: the code path was empty.

Let’s look at another example. This time, we do have an else branch:

if let location = venue.location {
	cell.addressLabel?.text = location.address
} else {
	cell.addressLabel?.isHidden = true
}

At first glance, the code seems sensible. If there’s no address, hide the addressLabel. That probably causes some side effect in layout, maybe moving some neighboring views around.

But similar to the last example, there’s a bug. Let’s spin up another virtual machine to model all this state. This particular code has an issue on reuse. What happens if the cell is used for a venue without an address, then used for a venue with an address?

The addressLabel is hidden and never unhidden.

Like the last snippet, we could solve this by adding another line of code, this time to our if branch rather than our else branch. However, I think the code is served better by assigning the isHidden property to a computed boolean, instead of manually branching on that boolean with an if/else. Here’s what that looks like:

if let location = venue.location {
	cell.addressLabel?.text = location.address
}
cell.addressLabel?.isHidden = venue.location == nil

We can even take this a step further and remove the branching entirely, since text accepts an optional String:

cell.addressLabel?.text = venue.location?.address
cell.addressLabel?.isHidden = venue.location == nil

Much simpler, with zero branching.

It should be said that the first snippet can be written in this terse style as well. This is how I prefer to write it:

@objc func textChanged(_ sender: UITextField) {
	submitButton.isEnabled = (sender.text ?? "").count >= 8
}

What’s interesting about this class of bug is that some languages simply don’t let you write code like this. For example, Haskell has an if..then..else construct, and the else branch is required. This Haskell won’t compile without the last line:

if a
  then b
  else c

Haskell’s if..then..else is an expression, so it has a result (either b or c in this case) and that result has a type. Without an else branch, what would that result evaluate to? It’s an impossible question to answer, so Haskell makes it invalid at a code level as well. (A functional way to think about this: side effects aren’t allowed in Haskell. In the same way a Void-returning function must perform a side effect (or do nothing), an if with no else must also perform a side effect.)

You can approximate this behavior in Swift by returning something — you have to include an else branch. For example, this code won’t compile. How could it?

func addressLength() -> Int {
	if let address = self.address {
		return address.count
	}
} // Missing return in a function expected to return 'Int'

If you think about the myriad ways Swift gives you to handle branching — stuff like guard, assigning a boolean, ternaries, and of course, our friendly neighborhood if statement — the if statement is the only that lets the user leave out one of the branches. Even switch requires you to either exhaustively handle all cases or include a default case. From that perspective, leaving the else out is almost syntactic sugar. In some ways, it’s comparable to using a exclamation point to force unwrap. You can do it, but you’re leaving code paths unwritten.

Writing an if with no else isn’t wrong per se, it’s just a smell. When you see it, give it a second pass and really make sure that if it were there, the else branch would actually have no code in it.

There’s quite a bit of conversation on Swift Evolution about the potential future of Sequence and Collection hierarchy. There’s a number of problems that the community is trying to solve and a variety of approaches that have been presented to solve them. Several of these approaches include the ability to create infinite collections, and every time anyone brings this up, someone invariably asks how they would work. Nothing in the type system prevents us from making an infinite collection — it’s purely a semantic constraint — meaning that while we can write infinite collections in Swift today, we’re not supposed to. It violates the assumptions that other people’s code will make about our object. In this post, I’ll take an infinite sequence and demonstrate how we could turn it into an infinite collection.

The Fibonacci numbers are a great example of an infinite sequence. For a quick refresher, each element in that sequence is the sum of the previous two numbers.

Swift has pretty good facility for defining new sequences quickly. Two useful functions are sequence(state:next:) and sequence(first:next). Here, we’ll use the state version:

let fib = sequence(state: (0, 1), next: { state -> Int? in
    let next = state.0 + state.1
    state = (state.1, next)
    return next
})

Calling fib.prefix(10) will give you the first 10 Fibonacci numbers.

Note that this is an infinite sequence! If you try to map over this sequence (which the type system fully allows!), your program will just spin infinitely until it runs out of integers or the heat death of the universe, whichever comes first.

To convert this into an infinite collection, we need to think about a few things. First, how will we represent an index to a value? For an array, this is a number that probably represents a memory offset. For a string, this might represents a byte offset that that character starts at. It needs to be some value that lets us retrieve the value at that index at constant time, or O(1).

One of the interesting things about iterators is that their current state represents the data that you need to get to the next value in constant time. So any deterministic sequence can be represented as a collection, by using its iterator’s state as an index. Our state before is (Int, Int), so we can start off by using that type for our Index. These are the four methods we need to define a Collection:

struct FibonacciCollection: Collection {

	typealias Index = (Int, Int)
	
	var startIndex: Index {
		return (0, 1)
	}
	
	func index(after previous: Index) -> Index {
		return (previous.1, previous.0 + previous.1)
	}
	
	var endIndex: Index {
		fatalError("This collection has no endIndex, because it is infinite")
	}
	
	subscript(index: Index) -> Int {
		return index.0 + index.1
	}
}

We can use (Int, Int) (our state from the fibonacci numbers when they were a sequence) as the index, and use (0, 1) as our starting value (just like our sequence).

But there are a few problems with this approach. To iterate over an arbitrary collection, you can imagine constructing a big while loop:

var index = collection.startIndex
while index < endIndex {
	let value = collection[index]
	// use `value` somehow
	index = collection.index(after: index)
}

(This isn’t how we’d use our collection, since we know it’s infinite, but this is how normal collections work.) Two things stand out. First, we need the Index type to be Comparable — so we can’t use a tuple — and we need endIndex to be defined so that we can check against it — so we can’t fatalError (ding!).

So we need a new index type: something that’s Comparable and something that’s unreachable. The unreachable value should compute to being “greater” than all the reachable values (since it goes at the “end” of the collection). Our first attack is to model this as a struct of two integers, to solve the comparability problem:

struct FibIndex {
	let first: Int
	let second: Int
}

extension FibIndex: Comparable {
	static func == (lhs: FibIndex, rhs: FibIndex) -> Bool {
		return lhs.first == rhs.first && lhs.second == rhs.second
	}
	
	static func < (lhs: FibIndex, rhs: FibIndex) -> Bool {
		return lhs.first < rhs.first
	}
}

This solves the comparability problem, but not the unreachability problem. We need a way to represent one more value, a value that’s separate from all the others. Let’s start over, but with an enum this time:

enum FibIndex {
	case reachable(Int, Int)
	case unreachable
}

This could solve both of our problems. Unfortunately, it makes writing == and < pretty messy:

extension FibIndex: Comparable {
	static func == (lhs: FibIndex, rhs: FibIndex) -> Bool {
		switch (lhs, rhs) {
		case (.unreachable, .unreachable):
			return true
		case let (.reachable(l1, l2), .reachable(r1, r2)):
			return l1 == r1 && l2 == r2
		case (.reachable, .unreachable):
			return false
		case (.unreachable, .reachable):
			return false
		}
	}
	
	static func < (lhs: FibIndex, rhs: FibIndex) -> Bool {
		switch (lhs, rhs) {
		case (.unreachable, .unreachable):
			return false
		case let (.reachable(l1, l2), .reachable(r1, r2)):
			return l1 < r1
		case (.reachable, .unreachable):
			return true
		case (.unreachable, .reachable):
			return false
		}
	}
}

(There are some ways to clean this up with better pattern matching, but I’m going with the explicitness of the full patterns here.)

Let’s add some helpers:

extension FibIndex {
	var sum: Int {
		switch self {
		case .unreachable:
			fatalError("Can't get the sum at an unreachable index")
		case let .reachable(first, second): 
			return first + second
		}
	}
	
	var next: FibIndex {
		switch self {
		case .unreachable:
			fatalError("Can't get the next value of an unreachable index")
		case let .reachable(first, second): 
			return .reachable(second, first + second)
		}
	}
}

And now we can complete our FibonacciCollection:

struct FibonacciCollection: Collection {

	typealias Index = FibIndex
	
	var startIndex: Index {
		return .reachable(0, 1)
	}
	
	func index(after previous: Index) -> Index {
		return previous.next
	}
	
	var endIndex: Index {
		return .unreachable
	}
	
	subscript(index: Index) -> Int {
		return index.sum
	}
}

This is pretty good! We get all of the methods from the Sequence and Collection protocols for free. Unfortunately, this is still an infinite collection, and just like the infinite sequence, we can’t map over it, or we’ll risk looping forever. There are new things on the Collection protocol that we also can’t do — like get the count of this collection. That will also spin forever.

There is one more tweak I’d like to show here, which is extracting the Fibonacci-specific parts of this and making a generic InfiniteCollectionIndex. To do this, we’d keep our basic enum’s structure, but instead of the .reachable case having type (Int, Int), we’d need to put a generic placeholder there. How would that look?

Let’s call the inner index type WrappedIndex. We need to make sure that the wrapped Index is comparable:

enum InfiniteCollectionIndex<WrappedIndex: Comparable>: Comparable {
	case reachable(WrappedIndex)
	case unreachable
}

The Equatable and Comparable implementation stay mostly the same, but instead of comparing integers, they just forward to WrappedIndex:

extension InfiniteCollectionIndex: Comparable {
	static func == (lhs: InfiniteCollectionIndex, rhs: InfiniteCollectionIndex) -> Bool {
		switch (lhs, rhs) {
		case (.unreachable, .unreachable):
		    return true
		case let (.reachable(left), .reachable(right)):
		    return left == right
		case (.reachable, .unreachable):
		    return false
		case (.unreachable, .reachable):
		    return false
		}
	}
	
	static func < (lhs: InfiniteCollectionIndex, rhs: InfiniteCollectionIndex) -> Bool {
		switch (lhs, rhs) {
		case (.unreachable, .unreachable):
			return false
		case let (.reachable(left), .reachable(right)):
			return left < right
		case (.reachable, .unreachable):
			return true
		case (.unreachable, .reachable):
			return false
		}
	}
}

And one more helper, because there will be a lot of situations where we want to assume that that the .unreachable value is, well, unreachable:

extension InfiniteCollectionIndex {
	func assumingReachable<T>(_ block: (WrappedIndex) -> T) -> T {
		switch self {
		case .unreachable:
			fatalError("You can't operate on an unreachable index")
		case let .reachable(wrapped):
			return block(wrapped)
		}
	}
	
	func makeNextReachableIndex(_ block: (WrappedIndex) -> WrappedIndex) -> InfiniteCollectionIndex {
		return .reachable(assumingReachable(block))
	}
}

This function takes a block that assumes that the value is .reachable, and returns whatever that block returns. If the value is .unreachable, it crashes.

We can now use the struct form of FibIndex from above:

struct FibIndex {
	let first: Int
	let second: Int
}

extension FibIndex: Comparable {
	static func == (lhs: FibIndex, rhs: FibIndex) -> Bool {
		return lhs.first == rhs.first && lhs.second == rhs.second
	}
	
	static func < (lhs: FibIndex, rhs: FibIndex) -> Bool {
		return lhs.first < rhs.first
	}
}

I won’t go into too much of the details here, but this allows us to define simple Comparable index types, and make them into infinite indexes easily:

struct FibonacciCollection: Collection {

	typealias Index = InfiniteCollectionIndex<FibIndex>
	
	var startIndex: Index {
		return .reachable(FibIndex(first: 0, second: 1))
	}
	
	func index(after previous: Index) -> Index {
		return previous.makeNextReachableIndex({
			FibIndex(first: $0.second, second: $0.first + $0.second)
		})
	}
	
	var endIndex: Index {
		return .unreachable
	}
	
	subscript(index: Index) -> Int {
		return index.assumingReachable({ $0.first + $0.second })
	}
}

It’s not clear which way the tides will ultimately shift with Swift’s Collection model, but if and when infinite collections become legal in Swift, this technique will help you define them easily.