Efficient Aggregates in Julia

5 March 2013 | Jeff Bezanson

We recently introduced an exciting feature that has been in planning for some time: immutable aggregate types. In fact, we have been planning to do this for so long that this feature is the subject of our issue #13 on GitHub, out of more than 2400 total issues so far.

Essentially, this feature drastically reduces the overhead of user-defined types that represent small number-like values, or that wrap a small number of other objects. Consider an RGB pixel type:

immutable Pixel

Instances of this type can now be packed efficiently into arrays, using exactly 3 bytes per object. In all other respects, these objects continue to act like normal first-class objects. To see how we might use this, here is a function that converts an RGB image in standard 24-bit framebuffer format to grayscale:

function rgb2gray!(img::Array{Pixel})
    for i=1:length(img)
        p = img[i]
        v = uint8(0.30*p.r + 0.59*p.g + 0.11*p.b)
        img[i] = Pixel(v,v,v)

This code will run blazing fast, performing no memory allocation. We have not done thorough benchmarking, but this is in fact likely to be the fastest way to write this function in Julia from now on.

The key to this behavior is the new immutable keyword, which means instances of the type cannot be modified. At first this sounds like a mere restriction — how come I'm not allowed to modify one? — but what it really means is that the object is identified with its contents, rather than its memory address. A mutable object has "behavior"; it changes over time, and there may be many references to the object, all of which can observe those changes. An immutable object, on the other hand, has only a value, and no time-varying behavior. Its location does not matter. It is "just some bits".

Julia has always had some immutable values, in the form of bits types, which are used to represent fixed-bit-width numbers. It is highly intuitive that numbers are immutable. If x equals 2, you might later change the value of x, but it is understood that the value of 2 itself does not change. The immutable keyword generalizes this idea to structured data types with named fields. Julia variables and containers, including arrays, are all still mutable. While a Pixel object itself can't change, a new Pixel can be written over an old one within an array, since the array is mutable.

Let's take a look at the benefits of this feature.

  1. The compiler and GC have a lot of freedom to move and copy these objects around.

This flexibility can be used to store data more efficiently, for example keeping the real and imaginary parts of a complex number in separate registers, or keeping only one part in a register.

  1. Immutable objects are easy to reason about.

Some languages, such as C++ and C#, provide "value types", which have many of the benefits of immutable objects. However, their behavior can be confusing. Consider code like the following:

item = lookup(collection, index)

The question here is whether we have modified the same item that is in the collection, or if we have modified a local copy. In Julia there are only two possibilities: either item is mutable, in which case we modified the one and only copy of it, or it is immutable, in which case modifying it is not allowed.

  1. No-overhead data abstractions become possible.

It is often useful to define a new type that simply wraps a single value, and modifies its behavior in some way. Our favorite modular integer example type fits this description:

immutable ModInt{n} <: Integer
  ModInt(k) = new(mod(k,n))

Since a given ModInt doesn't need to exist at a particular address, it can be passed to functions, stored in arrays, and so on, as efficiently as a single Int, with no wrapping overhead. But, in Julia, the overhead will not always be zero. The ModInt type information will "follow the data around" at compile time to the extent possible, but heap-allocated wrappers will be added as needed at run time. Typically these wrappers will be short-lived; if the final destination of a ModInt is in a ModInt array, for example, the wrapper can be discarded when the value is assigned. But if the value is only used locally inside a function, there will most likely be no wrappers at all.

  1. Abstractions are fully enforced. If a custom constructor is written for an immutable type, then all instances will be created by it.

Since the constructed objects are never modified, the invariants provided by the constructor cannot be violated. At this time, uninitialized arrays are an exception to this rule. New arrays of "plain data" immutable types have unspecified contents, so it is possible to obtain an invalid value from one. This is usually harmless in practice, since arrays must be initialized anyway, and are often created through functions like zeros that do so.

  1. We can automatically type-specialize fields.

Since field values at construction time are final, their types are too, so we learn everything about the type of an immutable object when it is constructed.

There are many potential optimizations here, and we have not implemented all of them yet. But having this feature in place provides another lever to help us improve performance over time.

For now though, we at least have a much simpler implementation of complex numbers, and will be able to take advantage of efficient rational matrices and other similar niceties.

Addendum: Under the hood

For purposes of calling C and writing reflective code, it helps to know a bit about how immutable types are implemented. Before this change, we had types AbstractKind, BitsKind, and CompositeKind, for separating which types are abstract, which are represented by immutable bit strings, and which are mutable aggregates. It was sometimes convenient that the type system reflected these differences, but also a bit unwarranted since all these types participate in the same hierarchy and follow the same subtyping rules.

Now, the type landscape is both simpler and more complex. The three Kinds have been merged into a single kind called DataType. The type of every value in Julia is now either a DataType, or else a tuple type (union types still exist, but of course are always abstract). To find out the details of a DataType's physical representation, you must query its properties. DataTypes have three boolean properties abstract, mutable, and pointerfree, and an integer property size. The CompositeKind properties names and types are still there to describe fields.

The abstract property indicates that the type was declared with the abstract keyword and has no direct instances. mutable indicates, for concrete types, whether instances are mutable. pointerfree means that instances contain "just data" and no references to other Julia values. size gives the size of an instance in bytes.

What used to be BitsKinds are now DataTypes that are immutable, concrete, have no fields, and have non-zero size. The former CompositeKinds are mutable and concrete, and either have fields or are zero size if they have zero fields. Clearly, new combinations are now possible. We have already mentioned immutable types with fields. We could have the equivalent of mutable BitsKinds, but this combination is not exposed in the language, since it is easily emulated using mutable fields. Another new combination is abstract types with fields, which would allow you to declare that all subtypes of some abstract type should have certain fields. That one is definitely useful, and we plan to provide syntax for it.

Typically, the only time you need to worry about these things is when calling native code, when you want to know whether some array or struct has C-compatible data layout. This is handled by the type predicate isbits(T).