array-element-type returns a type specifier for the set of objects that can be stored in the array. This set may be larger than the set requested when the array was created; for example, the result of

could be (mod 5), (mod 8), fixnum, t, or any other type of which (mod 5) is a subtype. See subtypep.

This returns the number of dimensions (axes) of array. This will be a non-negative integer. See array-rank-limit.

The length of dimension number axis-number of the array is returned. array may be any kind of array, and axis-number should be a non-negative integer less than the rank of array. If the array is a vector with a fill pointer, array-dimension returns the total size of the vector, including inactive elements, not the size indicated by the fill pointer. (The function length will return the size indicated by the fill pointer.)

array-dimensions returns a list whose elements are the dimensions of array.

array-total-size returns the total number of elements in the array, calculated as the product of all the dimensions.

Note that the total size of a zero-dimensional array is 1. The total size of a one-dimensional array is calculated without regard for any fill pointer.

This predicate checks whether the subscripts are all legal subscripts for array. The predicate is true if they are all legal; otherwise it is false. The subscripts must be integers. The number of subscripts supplied must equal the rank of the array. Like aref, array-in-bounds-p ignores fill pointers.

This function takes an array and valid subscripts for the array and returns a single non-negative integer less than the total size of the array that identifies the accessed element in the row-major ordering of the elements. The number of subscripts supplied must equal the rank of the array. Each subscript must be a non-negative integer less than the corresponding array dimension. Like aref, array-row-major-index ignores fill pointers.

A possible definition of array-row-major-index, with no error checking, would be

For a one-dimensional array, the result of array-row-major-index always equals the supplied subscript.

This allows any array element to be accessed as if the containing array were one-dimensional. The index must be a non-negative integer less than the total size of the array. It indexes into the array as if its elements were arranged one-dimensionally in row-major order. It may be understood in terms of aref as follows:

In other words, one may treat an array as one-dimensional by creating a new one-dimensional array that is displaced to the old one and then accessing the new array. Alternatively, aref may be understood in terms of row-major-aref:

That is, a multidimensional array access is equivalent to a row-major access using an equivalent row-major index.

Like aref, row-major-aref completely ignores fill pointers. A call to row-major-setf is suitable for use as a place for setf.

This operation makes it easier to write code that efficiently processes arrays of any rank. Suppose, for example, that one wishes to set every element of an array tennis-scores to zero. One might write

Unfortunately, this incurs the overhead of creating a displaced array, and fill cannot be applied to multidimensional arrays. Another approach would be to handle each possible rank separately:

It is easy to get tired of writing such code. Furthermore, this approach is undesirable because some implementations of Common Lisp will in fact correctly support arrays of rank greater than 7 (though no implementation is required to do so). A recursively nested loop does the job, but it is still pretty hairy:

Whether this code is particularly efficient depends on many implementation parameters, such as how &rest arguments are handled and how cleverly calls to apply are compiled. How much easier it is to use row-major-aref!

Surely this code is sweeter than the honeycomb.

This predicate is true if the argument (which must be an array) is adjustable, and otherwise is false.

This returns two values. The first value is the array displaced to and the second is the displacement. If array is not a displaced array then array-displacement returns the values nil and 0.