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Incomputer programming,rank with no further specifications is usually a synonym for (or refers to) "number of dimensions";[1] thus, a two-dimensional array has ranktwo, a three-dimensional array has rankthree and so on.Strictly, no formal definition can be provided which applies to everyprogramming language, since each of them has its own concepts,semantics 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.
In the case ofAPL the notion applies to every operand; anddyads ("binary functions") have aleft rank and aright rank.
The box below instead shows howrank of a type andrank of an array expression could be defined (in a semi-formal style) for C++ and illustrates a simple way to calculate them at compile time.
#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<typenameT>structrank{staticconststd::size_tvalue=0;};template<typenameT,std::size_tN>structrank<T[N]>{staticconststd::size_tvalue=1+rank<T>::value;};template<typenameT>constexprautorank_v=rank<T>::value;/* Rank of an expression * * Let the rank of an expression be the rank of its type */template<typenameT>usingunqualified_t=std::remove_cv_t<std::remove_reference_t<T>>;template<typenameT>autorankof(T&&expr){returnrank_v<unqualified_t<T>>;}
Given the code above the rank of a type T can be calculated at compile time by
rank<T>::value
or the shorter form
rank_v<T>
Calculating the rank of an expression can be done using
rankof(expr)
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