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Rank (computer programming)
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<p>In <a href="/facts/Computer_programming/QmSsFnu0">computer programming</a>, rank with no further specifications is usually a synonym for (or refers to) "number of dimensions"; thus, a two-dimensional array has rank <i>two</i>, a three-dimensional array has rank <i>three</i> and so on. Strictly, no formal definition can be provided which applies to every <a href="/facts/Programming_language/cWTYbgWa">programming language</a>, since each of them has its own concepts, <a href="/facts/Formal_semantics_of_programming_languages/JEP1zyBv">semantics</a> and terminology; the term may not even be applicable or, to the contrary, applied with a very specific meaning in the context of a given language. </p><p>In the case of <a href="/facts/APL_programming_language/E2sb98gC">APL</a> the notion applies to every operand; and <a href="/facts/Binary_function/lAtbyPRG">dyads</a> ("binary functions") have a <i>left rank</i> and a <i>right rank</i>. </p><p>The box below instead shows how <i>rank of a type</i> and <i>rank of an array expression</i> could be defined (in a semi-formal style) for C++ and illustrates a simple way to calculate them at compile time. </p> #include <type_traits> #include <cstddef> /* Rank of a type * ------------- * * Let the rank of a type T be the number of its dimensions if * it is an array; zero otherwise (which is the usual convention) */ template <typename T> struct rank { static const std::size_t value = 0; }; template<typename T, std::size_t N> struct rank<T[N]> { static const std::size_t value = 1 + rank<T>::value; }; template <typename T> constexpr auto rank_v = rank<T>::value; /* Rank of an expression * * Let the rank of an expression be the rank of its type */ template <typename T> using unqualified_t = std::remove_cv_t<std::remove_reference_t<T>>; template <typename T> auto rankof(T&& expr) { return rank_v<unqualified_t<T>>; } <p>Given the code above the rank of a type T can be calculated at compile time by </p> rank<T>::value <p>or the shorter form </p> rank_v<T> <p>Calculating the rank of an expression can be done using </p> rankof(expr)