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Popcount
The Hamming weight of a string is the number of symbols that are different from the zero-symbol of the alphabet used. It is thus equivalent to the Hamming distance from the all-zero string of the same length. For the most typical case, a string of bits, this is the number of 1's in the string, or the digit sum of the binary representation of a given number and the ''β''β norm of a bit vector. In this binary case, it is also called the population count, popcount, sideways sum, or bit summation. History and usage The Hamming weight is named after Richard Hamming although he did not originate the notion. The Hamming weight of binary numbers was already used in 1899 by James W. L. Glaisher to give a formula for the number of odd binomial coefficients in a single row of Pascal's triangle. Irving S. Reed introduced a concept, equivalent to Hamming weight in the binary case, in 1954. Hamming weight is used in several disciplines including information theory, coding theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Find First Set
In computer software and hardware, find first set (ffs) or find first one is a bit operation that, given an unsigned machine word, designates the index or position of the least significant bit set to one in the word counting from the least significant bit position. A nearly equivalent operation is count trailing zeros (ctz) or number of trailing zeros (ntz), which counts the number of zero bits following the least significant one bit. The complementary operation that finds the index or position of the most significant set bit is log base 2, so called because it computes the binary logarithm . This is closely related to count leading zeros (clz) or number of leading zeros (nlz), which counts the number of zero bits preceding the most significant one bit. There are two common variants of find first set, the POSIX definition which starts indexing of bits at 1, herein labelled ffs, and the variant which starts indexing of bits at zero, which is equivalent to ctz and so will be called by ... [...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] |
IrisCode
Iris recognition is an automated method of biometric identification that uses mathematical pattern-recognition techniques on video images of one or both of the irises of an individual's eyes, whose complex patterns are unique, stable, and can be seen from some distance. The discriminating powers of all biometric technologies depend on the amount of entropy they are able to encode and use in matching. Iris recognition is exceptional in this regard, enabling the avoidance of "collisions" (False Matches) even in cross-comparisons across massive populations. Its major limitation is that image acquisition from distances greater than a meter or two, or without cooperation, can be very difficult. Retinal scanning is a different, ocular-based biometric technology that uses the unique patterns on a person's retina blood vessels and is often confused with iris recognition. Iris recognition uses video camera technology with subtle near infrared illumination to acquire images of the detail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bitwise AND
In computer programming, a bitwise operation operates on a bit string, a bit array or a binary numeral (considered as a bit string) at the level of its individual bits. It is a fast and simple action, basic to the higher-level arithmetic operations and directly supported by the processor. Most bitwise operations are presented as two-operand instructions where the result replaces one of the input operands. On simple low-cost processors, typically, bitwise operations are substantially faster than division, several times faster than multiplication, and sometimes significantly faster than addition. While modern processors usually perform addition and multiplication just as fast as bitwise operations due to their longer instruction pipelines and other architectural design choices, bitwise operations do commonly use less power because of the reduced use of resources. Bitwise operators In the explanations below, any indication of a bit's position is counted from the right (least signif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Processor Support
Processor may refer to: Computing Hardware * Processor (computing) **Central processing unit (CPU), the hardware within a computer that executes a program *** Microprocessor, a central processing unit contained on a single integrated circuit (IC) **** Application-specific instruction set processor (ASIP), a component used in system-on-a-chip design **** Graphics processing unit (GPU), a processor designed for doing dedicated graphics-rendering computations **** Physics processing unit (PPU), a dedicated microprocessor designed to handle the calculations of physics **** Digital signal processor (DSP), a specialized microprocessor designed specifically for digital signal processing *****Image processor, a specialized DSP used for image processing in digital cameras, mobile phones or other devices **** Coprocessor **** Floating-point unit **** Network processor, a microprocessor specifically targeted at the networking application domain ** Multi-core processor, single component with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Array
A bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores ''kw'' bits, where ''w'' is the number of bits in the unit of storage, such as a byte or word, and ''k'' is some nonnegative integer. If ''w'' does not divide the number of bits to be stored, some space is wasted due to internal fragmentation. Definition A bit array is a mapping from some domain (almost always a range of integers) to values in the set . The values can be interpreted as dark/light, absent/present, locked/unlocked, valid/invalid, et cetera. The point is that there are only two possible values, so they can be stored in one bit. As with other arrays, the access to a single bit can be managed by applying an index to the array. Assuming its size ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wavelet Tree
The Wavelet Tree is a succinct data structure to store strings in compressed space. It generalizes the \mathbf_q and \mathbf_q operations defined on bitvectors to arbitrary alphabets. Originally introduced to represent compressed suffix arrays, it has found application in several contexts. The tree is defined by recursively partitioning the alphabet into pairs of subsets; the leaves correspond to individual symbols of the alphabet, and at each node a bitvector stores whether a symbol of the string belongs to one subset or the other. The name derives from an analogy with the wavelet transform for signals, which recursively decomposes a signal into low-frequency and high-frequency components. Properties Let \Sigma be a finite alphabet with \sigma=, \Sigma, . By using succinct dictionaries in the nodes, a string s \in \Sigma^* can be stored in , s, H_0(s) + o(, s, \log \sigma), where H_0(s) is the order-0 empirical entropy of s. If the tree is balanced, the operations \mathbf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Array
A bit array (also known as bitmask, bit map, bit set, bit string, or bit vector) is an array data structure that compactly stores bits. It can be used to implement a simple set data structure. A bit array is effective at exploiting bit-level parallelism in hardware to perform operations quickly. A typical bit array stores ''kw'' bits, where ''w'' is the number of bits in the unit of storage, such as a byte or word, and ''k'' is some nonnegative integer. If ''w'' does not divide the number of bits to be stored, some space is wasted due to internal fragmentation. Definition A bit array is a mapping from some domain (almost always a range of integers) to values in the set . The values can be interpreted as dark/light, absent/present, locked/unlocked, valid/invalid, et cetera. The point is that there are only two possible values, so they can be stored in one bit. As with other arrays, the access to a single bit can be managed by applying an index to the array. Assuming its size ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Succinct Data Structure
In computer science, a succinct data structure is a data structure which uses an amount of space that is "close" to the information-theoretic lower bound, but (unlike other compressed representations) still allows for efficient query operations. The concept was originally introduced by Jacobson to encode bit vectors, (unlabeled) trees, and planar graphs. Unlike general lossless data compression algorithms, succinct data structures retain the ability to use them in-place, without decompressing them first. A related notion is that of a compressed data structure, in which the size of the data structure depends upon the particular data being represented. Suppose that Z is the information-theoretical optimal number of bits needed to store some data. A representation of this data is called: * ''implicit'' if it takes Z + O(1) bits of space, * ''succinct'' if it takes Z + o(Z) bits of space, and * ''compact'' if it takes O(Z) bits of space. For example, a data structure that uses 2Z bits ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Number
A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" ( one). The base-2 numeral system is a positional notation with a radix of 2. Each digit is referred to as a bit, or binary digit. Because of its straightforward implementation in digital electronic circuitry using logic gates, the binary system is used by almost all modern computers and computer-based devices, as a preferred system of use, over various other human techniques of communication, because of the simplicity of the language and the noise immunity in physical implementation. History The modern binary number system was studied in Europe in the 16th and 17th centuries by Thomas Harriot, Juan Caramuel y Lobkowitz, and Gottfried Leibniz. However, systems related to binary numbers have appeared earlier in multiple cultures including ancient Egypt, China, and India. Leibniz was specifica ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unary Numeral System
The unary numeral system is the simplest numeral system to represent natural numbers: to represent a number ''N'', a symbol representing 1 is repeated ''N'' times. In the unary system, the number 0 (zero) is represented by the empty string, that is, the absence of a symbol. Numbers 1, 2, 3, 4, 5, 6, ... are represented in unary as 1, 11, 111, 1111, 11111, 111111, ... Unary is a Bijective numeration, bijective numeral system. However, because the value of a digit does not depend on its position, it is not a form of positional notation, and it is unclear whether it would be appropriate to say that it has a Radix, base (or "radix") of 1 (number), 1, as it behaves differently from all other bases. The use of tally marks in counting is an application of the unary numeral system. For example, using the tally mark | (π·), the number 3 is represented as |||. In East Asian cultures, the number 3 is represented as wikt:δΈ#Translingual, δΈ, a character drawn with th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
