Row- and column-major order

In computing, row-major order and column-major order are methods for storing <a href="/facts/Multidimensional_array/gHJJ3XPw">multidimensional arrays</a> in linear storage such as <a href="/facts/Random_access_memory/DuD4bxh6">random access memory</a>.
The difference between the orders lies in which elements of an array are contiguous in memory. In row-major order, the consecutive elements of a row reside next to each other, whereas the same holds true for consecutive elements of a column in column-major order. While the terms allude to the rows and columns of a two-dimensional array, i.e. a <a href="/facts/Matrix_(mathematics)/qa8FI4ko">matrix</a>, the orders can be generalized to arrays of any dimension by noting that the terms row-major and column-major are equivalent to <a href="/facts/Lexicographic_order/xQANy8Br">lexicographic and colexicographic orders</a>, respectively. It is also worth noting that matrices, being commonly represented as collections of row or column vectors, using this approach are effectively stored as consecutive vectors or consecutive vector components. Such ways of storing data are referred to as <a href="/facts/AoS_and_SoA/3K9b2l8h">AoS and SoA</a> respectively.
Data layout is critical for correctly passing arrays between programs written in different programming languages. It is also important for performance when traversing an array because modern CPUs process sequential data more efficiently than nonsequential data. This is primarily due to <a href="/facts/CPU_cache/x8BYFcdv">CPU caching</a> which exploits spatial <a href="/facts/Locality_of_reference/fYFKDv5q">locality of reference</a>. In addition, contiguous access makes it possible to use <a href="/facts/Single_instruction,_multiple_data/gQHWQSpo">SIMD</a> instructions that operate on vectors of data. In some media such as <a href="/facts/Magnetic-tape_data_storage/qJUpJnk9">magnetic-tape data storage</a>, accessing sequentially is <a href="/facts/Order_of_magnitude/cWzRP2dM">orders of magnitude</a> faster than nonsequential access.

Row- and column-major order open-in-new

Row- and column-major order