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In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
PHP has hundreds of base functions and thousands more from extensions. Prior to PHP version 5.3.0, functions are not first-class functions and can only be referenced by their name, whereas PHP 5.3.0 introduces closures. [35] User-defined functions can be created at any time and without being prototyped. [35]
PHP has a direct module interface called SAPI for different web servers; [273] in case of PHP 5 and Apache 2.0 on Windows, it is provided in form of a DLL file called php5apache2.dll, [274] which is a module that, among other functions, provides an interface between PHP and the web server, implemented in a form that the server understands. This ...
Φ functions are not implemented as machine operations on most machines. A compiler can implement a Φ function by inserting "move" operations at the end of every predecessor block. In the example above, the compiler might insert a move from y 1 to y 3 at the end of the middle-left block and a move from y 2 to y 3 at the end of the middle-right ...
A scalar is an element of a field which is used to define a vector space.In linear algebra, real numbers or generally elements of a field are called scalars and relate to vectors in an associated vector space through the operation of scalar multiplication (defined in the vector space), in which a vector can be multiplied by a scalar in the defined way to produce another vector.
If the time taken for the vector unit to add an array of 64 numbers is 10 times faster than its equivalent scalar counterpart, r = 10. Also, if the total number of operations in a program is 100, out of which only 10 are scalar (after vectorization), then f = 0.9, i.e., 90% of the work is done by the vector unit.
Processors, especially vector processors, are often optimized for array operations. Arrays are useful mostly because the element indices can be computed at run time. Among other things, this feature allows a single iterative statement to process arbitrarily many elements of an array. For that reason, the elements of an array data structure are ...
The set of submodules of a given module M, together with the two binary operations + (the module spanned by the union of the arguments) and ∩, forms a lattice that satisfies the modular law: Given submodules U, N 1, N 2 of M such that N 1 ⊆ N 2, then the following two submodules are equal: (N 1 + U) ∩ N 2 = N 1 + (U ∩ N 2).