Array Programming Languages
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Array Programming Languages
In computer science, array programming refers to solutions which allow the application of operations to an entire set of values at once. Such solutions are commonly used in scientific and engineering settings. Modern programming languages that support array programming (also known as vector or multidimensional languages) have been engineered specifically to generalize operations on scalars to apply transparently to vectors, matrices, and higher-dimensional arrays. These include APL, J, Fortran 90, MATLAB, Analytica, lists), Octave, R, Cilk Plus, Julia, Perl Data Language (PDL). In these languages, an operation that operates on entire arrays can be called a ''vectorized'' operation, regardless of whether it is executed on a vector processor, which implements vector instructions. Array programming primitives concisely express broad ideas about data manipulation. The level of concision can be dramatic in certain cases: it is not uncommon to find array programming language on ...
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Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical disciplines (including the design and implementation of Computer architecture, hardware and Computer programming, software). Computer science is generally considered an area of research, academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing Vulnerability (computing), security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Progr ...
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Vector Processor
In computing, a vector processor or array processor is a central processing unit (CPU) that implements an instruction set where its instructions are designed to operate efficiently and effectively on large one-dimensional arrays of data called ''vectors''. This is in contrast to scalar processors, whose instructions operate on single data items only, and in contrast to some of those same scalar processors having additional single instruction, multiple data (SIMD) or SWAR Arithmetic Units. Vector processors can greatly improve performance on certain workloads, notably numerical simulation and similar tasks. Vector processing techniques also operate in video-game console hardware and in graphics accelerators. Vector machines appeared in the early 1970s and dominated supercomputer design through the 1970s into the 1990s, notably the various Cray platforms. The rapid fall in the price-to-performance ratio of conventional microprocessor designs led to a decline in vector supercom ...
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3DNow!
3DNow! is a deprecated extension to the x86 instruction set developed by Advanced Micro Devices (AMD). It adds single instruction multiple data (SIMD) instructions to the base x86 instruction set, enabling it to perform vector processing of floating-point vector-operations using Vector registers, which improves the performance of many graphic-intensive applications. The first microprocessor to implement 3DNow was the AMD K6-2, which was introduced in 1998. When the application was appropriate, this raised the speed by about 2–4 times. However, the instruction set never gained much popularity, and AMD announced on August 2010 that support for 3DNow would be dropped in future AMD processors, except for two instructions (the PREFETCH and PREFETCHW instructions). The two instructions are also available in Bay-Trail Intel processors. History 3DNow was developed at a time when 3D graphics were becoming mainstream in PC multimedia and games. Realtime display of 3D graphics depended ...
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SSSE3
Supplemental Streaming SIMD Extensions 3 (SSSE3 or SSE3S) is a SIMD instruction set created by Intel and is the fourth iteration of the SSE technology. History SSSE3 was first introduced with Intel processors based on the Core microarchitecture on June 26, 2006 with the "Woodcrest" Xeons. SSSE3 has been referred to by the codenames Tejas New Instructions (TNI) or Merom New Instructions (MNI) for the first processor designs intended to support it. Functionality SSSE3 contains 16 new discrete instructions. Each instruction can act on 64-bit MMX or 128-bit XMM registers. Therefore, Intel's materials refer to 32 new instructions. They include: * Twelve instructions that perform horizontal addition or subtraction operations. * Six instructions that evaluate absolute values. * Two instructions that perform multiply-and-add operations and speed up the evaluation of dot products. * Two instructions that accelerate packed integer multiply operations and produce integer values with ...
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MMX (instruction Set)
MMX is a ''single instruction, multiple data'' (SIMD) instruction set architecture designed by Intel, introduced on January 8, 1997 with its Pentium P5 (microarchitecture) based line of microprocessors, named "Pentium with MMX Technology". It developed out of a similar unit introduced on the Intel i860, and earlier the Intel i750 video pixel processor. MMX is a processor supplementary capability that is supported on IA-32 processors by Intel and other vendors . The New York Times described the initial push, including Super Bowl advertisements, as focused on "a new generation of glitzy multimedia products, including videophones and 3-D video games." MMX has subsequently been extended by several programs by Intel and others: 3DNow!, Streaming SIMD Extensions (SSE), and ongoing revisions of Advanced Vector Extensions (AVX). Overview Naming MMX is officially a meaningless initialism trademarked by Intel; unofficially, the initials have been variously explained as standing for * ...
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Intel
Intel Corporation is an American multinational corporation and technology company headquartered in Santa Clara, California. It is the world's largest semiconductor chip manufacturer by revenue, and is one of the developers of the x86 series of instruction sets, the instruction sets found in most personal computers (PCs). Incorporated in Delaware, Intel ranked No. 45 in the 2020 ''Fortune'' 500 list of the largest United States corporations by total revenue for nearly a decade, from 2007 to 2016 fiscal years. Intel supplies microprocessors for computer system manufacturers such as Acer, Lenovo, HP, and Dell. Intel also manufactures motherboard chipsets, network interface controllers and integrated circuits, flash memory, graphics chips, embedded processors and other devices related to communications and computing. Intel (''int''egrated and ''el''ectronics) was founded on July 18, 1968, by semiconductor pioneers Gordon Moore (of Moore's law) and Robert Noyce ( ...
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Implicit Parallelization
In computer science, implicit parallelism is a characteristic of a programming language that allows a compiler or interpreter to automatically exploit the parallelism inherent to the computations expressed by some of the language's constructs. A pure implicitly parallel language does not need special directives, operators or functions to enable parallel execution, as opposed to explicit parallelism. Programming languages with implicit parallelism include Axum, BMDFM, HPF, Id, LabVIEW, MATLAB M-code, NESL, SaC, SISAL, ZPL, and pH. Example If a particular problem involves performing the same operation on a group of numbers (such as taking the sine or logarithm of each in turn), a language that provides implicit parallelism might allow the programmer to write the instruction thus: numbers = 1 2 3 4 5 6 7 result = sin(numbers); The compiler or interpreter can calculate the sine of each element independently, spreading the effort across multiple processors if available. ...
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Reduce (higher-order Function)
In functional programming, fold (also termed reduce, accumulate, aggregate, compress, or inject) refers to a family of higher-order functions that analyze a recursive data structure and through use of a given combining operation, recombine the results of recursively processing its constituent parts, building up a return value. Typically, a fold is presented with a combining function, a top node of a data structure, and possibly some default values to be used under certain conditions. The fold then proceeds to combine elements of the data structure's hierarchy, using the function in a systematic way. Folds are in a sense dual to unfolds, which take a ''seed'' value and apply a function corecursively to decide how to progressively construct a corecursive data structure, whereas a fold recursively breaks that structure down, replacing it with the results of applying a combining function at each node on its terminal values and the recursive results (catamorphism, versus anamorphism of ...
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Matrix Multiplication
In mathematics, particularly in linear algebra, matrix multiplication is a binary operation that produces a matrix from two matrices. For matrix multiplication, the number of columns in the first matrix must be equal to the number of rows in the second matrix. The resulting matrix, known as the matrix product, has the number of rows of the first and the number of columns of the second matrix. The product of matrices and is denoted as . Matrix multiplication was first described by the French mathematician Jacques Philippe Marie Binet in 1812, to represent the composition of linear maps that are represented by matrices. Matrix multiplication is thus a basic tool of linear algebra, and as such has numerous applications in many areas of mathematics, as well as in applied mathematics, statistics, physics, economics, and engineering. Computing matrix products is a central operation in all computational applications of linear algebra. Notation This article will use the following notati ...
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Cross Product
In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here E), and is denoted by the symbol \times. Given two linearly independent vectors and , the cross product, (read "a cross b"), is a vector that is perpendicular to both and , and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are ''not'' linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendic ...
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Tensor
In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensors. There are many types of tensors, including scalars and vectors (which are the simplest tensors), dual vectors, multilinear maps between vector spaces, and even some operations such as the dot product. Tensors are defined independent of any basis, although they are often referred to by their components in a basis related to a particular coordinate system. Tensors have become important in physics because they provide a concise mathematical framework for formulating and solving physics problems in areas such as mechanics (stress, elasticity, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity, magnetic susceptibility, ...), general relativity ( stress–energy tensor, cur ...
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Function Rank
Function or functionality may refer to: Computing * Function key, a type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriented programming * Function (computer programming), or subroutine, a sequence of instructions within a larger computer program Music * Function (music), a relationship of a chord to a tonal centre * Function (musician) (born 1973), David Charles Sumner, American techno DJ and producer * "Function" (song), a 2012 song by American rapper E-40 featuring YG, Iamsu! & Problem * "Function", song by Dana Kletter from '' Boneyard Beach'' 1995 Other uses * Function (biology), the effect of an activity or process * Function (engineering), a specific action that a system can perform * Function (language), a way of achieving an aim using language * Function (mathematics), a relation that associates an input to a single output * Function (sociology) ...
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