AoS and SoA

In

Structure of arrays (SoA) is a layout separating elements of a

For example, to store N points in 3D space using a structure of arrays:

struct pointlist3D {
    float x[N];
    float y[N];
    float z[N];
};
struct pointlist3D points;
float get_point_x(int i) { return points.x[i]; }

Array of structures (AoS) is the opposite (and more conventional) layout, in which data for different fields is interleaved. This is often more intuitive, and supported directly by most

For example, to store N points in 3D space using an array of structures:

struct point3D {
    float x;
    float y;
    float z;
};
struct point3D points[N];
float get_point_x(int i) { return points[i].x; }

Array of structures of arrays (AoSoA) or tiled array of structs is a hybrid approach between the previous layouts, in which data for different fields is interleaved using tiles or blocks with size equal to the SIMD vector size. This is often less intuitive, but can achieve the memory throughput of the SoA approach, while being more friendly to the cache locality and load port architectures of modern processors.^[2] In particular, memory requests in modern processors have to be fulfilled in fixed width (e.g., size of a cacheline^[3]). The tiled storage of AoSoA aligns the memory access pattern to the requests' fixed width, leading to fewer access operations to complete a memory request and thus increasing the efficiency.^[4]

For example, to store N points in 3D space using an array of structures of arrays with a SIMD register width of 8 floats (or 8×32 = 256 bits):

struct point3Dx8 {
    float x[8];
    float y[8];
    float z[8];
};
struct point3Dx8 points[(N+7)/8];
float get_point_x(int i) { return points[i/8].x[i%8]; }

A different width may be needed depending on the actual SIMD register width. The interior arrays may be replaced with SIMD types such as float32x8 for languages with such support.

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It is possible to split some subset of a structure (rather than each individual field) into a

Some

AoS vs. SoA presents a choice when considering 3D or 4D vector data on machines with four-lane SIMD hardware. SIMD ISAs are usually designed for homogeneous data, however some provide a dot product instruction^[5] and additional permutes, making the AoS case easier to handle.

Although most

Software support

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Most languages support the AoS format more naturally by combining

abstract data types

.

SoA is mostly found in languages, libraries, or metaprogramming tools used to support a data-oriented design. Examples include:

• "Data frames," as implemented in R, Python's Pandas package, and Julia's DataFrames.jl package, are interfaces to access SoA like AoS.
• The Julia package StructArrays.jl allows for accessing SoA as AoS to combine the performance of SoA with the intuitiveness of AoS.
• Code generators for the C language, including Datadraw and the
  X Macro
  technique.

Automated creation of AoSoA is more complex. An example of AoSoA in metaprogramming is found in LANL's Cabana library written in C++; it assumes a vector width of 16 lanes by default.^[8]