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Statically sized arrays for Julia

StaticArrays provides a framework for implementing statically sized arrays in Julia, using the abstract type StaticArray{Size,T,N} <: AbstractArray{T,N}. Subtypes of StaticArray will provide fast implementations of common array and linear algebra operations. Note that here "statically sized" means that the size can be determined from the type, and "static" does not necessarily imply immutable.

The package also provides some concrete static array types: SVector, SMatrix and SArray, which may be used as-is (or else embedded in your own type). Mutable versions MVector, MMatrix and MArray are also exported, as well as SizedArray for annotating standard Arrays with static size information. Further, the abstract FieldVector can be used to make fast static vectors out of any uniform Julia "struct".

When a program uses many small ($\lesssim 100$ elements) fixed-sized arrays (whose size is known by the compiler, i.e. "statically," when the performance-critical code is compiled), then using Static Arrays can have several performance advantages:

1. Completely unrolling to loop-free code. e.g. v3 = v1 + v2 is just implemented as 3 scalar additions, with no loop overhead at all, if these are all SVector{3, Float64}. The unrolled loops can also sometimes trigger SIMD optimizations.
2. Avoiding heap (or even stack) allocations of temporary arrays. This is related to point (1) — working with static arrays as local variables is as if you had just written out all of the scalar operations by hand on all the components.
3. Being stored "inline" in other data structures. e.g. a length-$N$ array Vector{SVector{3, Float64}}, such as [v1, v2, v3] from the SVectors in the previous example, is stored as $3N$ consecutive Float64 values. This is much more efficient to access than a Vector{Vector{Float64}}, which is essentially an array of pointers to Vector{Float64} arrays, and is often faster and more convenient than a $3 \times N$ Matrix{Float64} (e.g. because the length 3 is stored in the type you get the benefits of (1) and (2) when accessing vectors in the array, and no "slicing" or "views" are needed). (There is also HybridArrays.jl for matrices with a static number of rows.)

You probably don't want to use Static Arrays if:

1. The size of the array is not static. For example, if it is changing too rapidly at runtime to make it worthwhile to recompile (and/or dynamically dispatch) the code every time the size changes. (Such as when you have a collection of vectors of many different lengths.)
2. The size of the array is large ($\gg 100$ elements) You (1) don't want to unroll vector operations of long lengths because the code size explodes; (2) they need to be heap-allocated because you can't store them in registers or perhaps even on the stack; and (3) you can already get many of the benefits of "inline" storage in arrays by storing them as the columns of a Matrix, whereas you wouldn't want to store a large array inline in an arbitrary struct.
3. Working with the array is not performance critical — static arrays are a little less convenient to work with than an ordinary Array (because the size of the former is a constant encoded in the type), and it may not be worth the inconvenience for cases where performance is not paramount.

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