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Cyclic Shift
In combinatorial mathematics, a circular shift is the operation of rearranging the entries in a tuple, either by moving the final entry to the first position, while shifting all other entries to the next position, or by performing the inverse operation. A circular shift is a special kind of cyclic permutation, which in turn is a special kind of permutation. Formally, a circular shift is a permutation σ of the ''n'' entries in the tuple such that either :\sigma(i)\equiv (i+1) modulo ''n'', for all entries ''i'' = 1, ..., ''n'' or :\sigma(i)\equiv (i-1) modulo ''n'', for all entries ''i'' = 1, ..., ''n''. The result of repeatedly applying circular shifts to a given tuple are also called the circular shifts of the tuple. For example, repeatedly applying circular shifts to the four-tuple (''a'', ''b'', ''c'', ''d'') successively gives * (''d'', ''a'', ''b'', ''c''), * (''c'', ''d'', ''a'', ''b''), * (''b'', ''c'', ''d'', ''a''), * (''a'', ''b'', ''c'', ''d'') (the original four-tupl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Permutation Matrix
In mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say , represents a permutation of elements and, when used to multiply another matrix, say , results in permuting the rows (when pre-multiplying, to form ) or columns (when post-multiplying, to form ) of the matrix . Definition Given a permutation of ''m'' elements, :\pi : \lbrace 1, \ldots, m \rbrace \to \lbrace 1, \ldots, m \rbrace represented in two-line form by :\begin 1 & 2 & \cdots & m \\ \pi(1) & \pi(2) & \cdots & \pi(m) \end, there are two natural ways to associate the permutation with a permutation matrix; namely, starting with the ''m'' × ''m'' identity matrix, , either permute the columns or permute the rows, according to . Both methods of defining permutation matrices appear in the literature and the properties expressed in one representation can be easily converted to th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cryptography
Cryptography, or cryptology (from grc, , translit=kryptós "hidden, secret"; and ''graphein'', "to write", or ''-logia'', "study", respectively), is the practice and study of techniques for secure communication in the presence of adversarial behavior. More generally, cryptography is about constructing and analyzing protocols that prevent third parties or the public from reading private messages. Modern cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing, physics, and others. Core concepts related to information security ( data confidentiality, data integrity, authentication, and non-repudiation) are also central to cryptography. Practical applications of cryptography include electronic commerce, chip-based payment cards, digital currencies, computer passwords, and military communications. Cryptography prior to the modern age was effectively synonymo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
String (computer Science)
In computer programming, a string is traditionally a sequence of characters, either as a literal constant or as some kind of variable. The latter may allow its elements to be mutated and the length changed, or it may be fixed (after creation). A string is generally considered as a data type and is often implemented as an array data structure of bytes (or words) that stores a sequence of elements, typically characters, using some character encoding. ''String'' may also denote more general arrays or other sequence (or list) data types and structures. Depending on the programming language and precise data type used, a variable declared to be a string may either cause storage in memory to be statically allocated for a predetermined maximum length or employ dynamic allocation to allow it to hold a variable number of elements. When a string appears literally in source code, it is known as a string literal or an anonymous string. In formal languages, which are used in mathematical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Block Code
In coding theory, block codes are a large and important family of error-correcting codes that encode data in blocks. There is a vast number of examples for block codes, many of which have a wide range of practical applications. The abstract definition of block codes is conceptually useful because it allows coding theorists, mathematicians, and computer scientists to study the limitations of ''all'' block codes in a unified way. Such limitations often take the form of ''bounds'' that relate different parameters of the block code to each other, such as its rate and its ability to detect and correct errors. Examples of block codes are Reed–Solomon codes, Hamming codes, Hadamard codes, Expander codes, Golay codes, and Reed–Muller codes. These examples also belong to the class of linear codes, and hence they are called linear block codes. More particularly, these codes are known as algebraic block codes, or cyclic block codes, because they can be generated using boolean polynomi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclic Code
In coding theory, a cyclic code is a block code, where the circular shifts of each codeword gives another word that belongs to the code. They are error-correcting codes that have algebraic properties that are convenient for efficient error detection and correction. Definition Let \mathcal be a linear code over a finite field (also called '' Galois field'') GF(q) of block length n. \mathcal is called a cyclic code if, for every codeword c=(c_1,\ldots,c_n) from \mathcal, the word (c_n,c_1,\ldots,c_) in GF(q)^n obtained by a cyclic right shift of components is again a codeword. Because one cyclic right shift is equal to n-1 cyclic left shifts, a cyclic code may also be defined via cyclic left shifts. Therefore the linear code \mathcal is cyclic precisely when it is invariant under all cyclic shifts. Cyclic codes have some additional structural constraint on the codes. They are based on Galois fields and because of their structural properties they are very useful for error control ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotate Right
Rotation, or spin, is the circular movement of an object around a '' central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional object has an infinite number of possible central axes and rotational directions. If the rotation axis passes internally through the body's own center of mass, then the body is said to be ''autorotating'' or ''spinning'', and the surface intersection of the axis can be called a ''pole''. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called ''revolving'' or ''orbiting'', typically when it is produced by gravity, and the ends of the rotation axis can be called the ''orbital poles''. Mathematics Mathematically, a rotation is a rigid body movement which, unlike a translation, keeps a point fixed. This definition applies to rotations within both two and three dimensions (in a plane and in space, r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotate Left
Rotation, or spin, is the circular movement of an object around a ''axis of rotation, central axis''. A two-dimensional rotating object has only one possible central axis and can rotate in either a clockwise or counterclockwise direction. A three-dimensional object has an infinite number of possible central axes and rotational directions. If the rotation axis passes internally through the body's own center of mass, then the body is said to be ''autorotating'' or ''Angular momentum, spinning'', and the surface intersection of the axis can be called a ''geographical pole, pole''. A rotation around a completely external axis, e.g. the planet Earth around the Sun, is called ''revolving'' or ''orbiting'', typically when it is produced by gravity, and the ends of the rotation axis can be called the ''orbital poles''. Mathematics Mathematics, Mathematically, a rotation is a rigid body movement which, unlike a translation (geometry), translation, keeps a point fixed. This defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Undefined Behaviour
In computer programming, undefined behavior (UB) is the result of executing a program whose behavior is prescribed to be unpredictable, in the language specification to which the computer code adheres. This is different from unspecified behavior, for which the language specification does not prescribe a result, and implementation-defined behavior that defers to the documentation of another component of the platform (such as the ABI or the translator documentation). In the C community, undefined behavior may be humorously referred to as "nasal demons", after a comp.std.c post that explained undefined behavior as allowing the compiler to do anything it chooses, even "to make demons fly out of your nose". Overview Some programming languages allow a program to operate differently or even have a different control flow than the source code, as long as it exhibits the same user-visible side effects, ''if undefined behavior never happens during program execution''. Undefined behavior ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Regehr
John Regehr is a computer scientist specializing in compiler correctness and undefined behavior. , he is a professor at the University of Utah. He is best known for the integer overflow sanitizer which was merged into the Clang C compiler, the C compiler fuzzer Csmith, and his widely read bloEmbedded in Academia He spent the 2015-2016 academic year on sabbatical in Paris, France, working with TrustInSoft on Frama-C Frama-C stands for ''Framework for Modular Analysis of C programs''. Frama-C is a set of interoperable program analyzers for C programs. Frama-C has been developed by the French Commissariat à l'Énergie Atomique et aux Énergies Alternativ ... and related code analysis tools. References External links John Regehr's home page* {{DEFAULTSORT:Regehr, John Living people American computer scientists University of Utah faculty Science bloggers Year of birth missing (living people) University of Virginia alumni Kansas State University alumni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ANSI C
ANSI C, ISO C, and Standard C are successive standards for the C programming language published by the American National Standards Institute (ANSI) and ISO/IEC JTC 1/SC 22/WG 14 of the International Organization for Standardization (ISO) and the International Electrotechnical Commission (IEC). Historically, the names referred specifically to the original and best-supported version of the standard (known as C89 or C90). Software developers writing in C are encouraged to conform to the standards, as doing so helps portability between compilers. History and outlook The first standard for C was published by ANSI. Although this document was subsequently adopted by ISO/IEC and subsequent revisions published by ISO/IEC have been adopted by ANSI, "ANSI C" is still used to refer to the standard. While some software developers use the term ISO C, others are standards-body neutral and use Standard C. Standardizing C In 1983, the American National Standards Institute formed a committee, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intrinsic Function
In computer software, in compiler theory, an intrinsic function (or built-in function) is a function (subroutine) available for use in a given programming language whose implementation is handled specially by the compiler. Typically, it may substitute a sequence of automatically generated instructions for the original function call, similar to an inline function. Unlike an inline function, the compiler has an intimate knowledge of an intrinsic function and can thus better integrate and optimize it for a given situation. Compilers that implement intrinsic functions generally enable them only when a program requests optimization, otherwise falling back to a default implementation provided by the language runtime system (environment). Intrinsic functions are often used to explicitly implement vectorization and parallelization in languages which do not address such constructs. Some application programming interfaces (API), for example, AltiVec and OpenMP, use intrinsic functions to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intel X86
x86 (also known as 80x86 or the 8086 family) is a family of complex instruction set computer (CISC) instruction set architectures initially developed by Intel based on the Intel 8086 microprocessor and its 8088 variant. The 8086 was introduced in 1978 as a fully 16-bit extension of Intel's 8-bit 8080 microprocessor, with memory segmentation as a solution for addressing more memory than can be covered by a plain 16-bit address. The term "x86" came into being because the names of several successors to Intel's 8086 processor end in "86", including the 80186, 80286, 80386 and 80486 processors. The term is not synonymous with IBM PC compatibility, as this implies a multitude of other computer hardware. Embedded systems and general-purpose computers used x86 chips before the PC-compatible market started, some of them before the IBM PC (1981) debut. , most desktop and laptop computers sold are based on the x86 architecture family, while mobile categories such as smartphones or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
