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Division Algorithm
A division algorithm is an algorithm which, given two integers ''N'' and ''D'' (respectively the numerator and the denominator), computes their quotient and/or remainder, the result of Euclidean division. Some are applied by hand, while others are employed by digital circuit designs and software. Division algorithms fall into two main categories: slow division and fast division. Slow division algorithms produce one digit of the final quotient per iteration. Examples of slow division include restoring, non-performing restoring, non-restoring, and SRT division. Fast division methods start with a close approximation to the final quotient and produce twice as many digits of the final quotient on each iteration. Newton–Raphson and Goldschmidt algorithms fall into this category. Variants of these algorithms allow using fast multiplication algorithms. It results that, for large integers, the computer time needed for a division is the same, up to a constant factor, as the time n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algorithm
In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algorithms are used as specifications for performing calculations and data processing. More advanced algorithms can use Conditional (computer programming), conditionals to divert the code execution through various routes (referred to as automated decision-making) and deduce valid inferences (referred to as automated reasoning). In contrast, a Heuristic (computer science), heuristic is an approach to solving problems without well-defined correct or optimal results.David A. Grossman, Ophir Frieder, ''Information Retrieval: Algorithms and Heuristics'', 2nd edition, 2004, For example, although social media recommender systems are commonly called "algorithms", they actually rely on heuristics as there is no truly "correct" recommendation. As an e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chunking (division)
In mathematics education at the primary school level, chunking (sometimes also called the partial quotients method) is an elementary approach for solving simple division questions by repeated subtraction. It is also known as the hangman method with the addition of a line separating the divisor, dividend, and partial quotients. It has a counterpart in the grid method for multiplication as well. In general, chunking is more flexible than the traditional method in that the calculation of quotient is less dependent on the place values. As a result, it is often considered to be a more intuitive, but a less systematic approach to divisionswhere the efficiency is highly dependent upon one's numeracy skills. To calculate the whole number quotient of dividing a large number by a small number, the student repeatedly takes away "chunks" of the large number, where each "chunk" is an easy multiple (for example 100×, 10×, 5× 2×, etc.) of the small number, until the large number has been r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multiplicative Inverse
In mathematics, a multiplicative inverse or reciprocal for a number ''x'', denoted by 1/''x'' or ''x''−1, is a number which when Multiplication, multiplied by ''x'' yields the multiplicative identity, 1. The multiplicative inverse of a rational number, fraction ''a''/''b'' is ''b''/''a''. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4. The reciprocal function, the Function (mathematics), function ''f''(''x'') that maps ''x'' to 1/''x'', is one of the simplest examples of a function which is its own inverse (an Involution (mathematics), involution). Multiplying by a number is the same as Division (mathematics), dividing by its reciprocal and vice versa. For example, multiplication by 4/5 (or 0.8) will give the same result as division by 5/4 (or 1.25). Therefore, multiplication by a number followed by multiplication by its reciprocal yie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Method
In numerical analysis, the Newton–Raphson method, also known simply as Newton's method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real-valued function. The most basic version starts with a real-valued function , its derivative , and an initial guess for a root of . If satisfies certain assumptions and the initial guess is close, then x_ = x_0 - \frac is a better approximation of the root than . Geometrically, is the x-intercept of the tangent of the graph of at : that is, the improved guess, , is the unique root of the linear approximation of at the initial guess, . The process is repeated as x_ = x_n - \frac until a sufficiently precise value is reached. The number of correct digits roughly doubles with each step. This algorithm is first in the class of Householder's methods, and was succeeded by Halley's method. The method can also be extended t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pentium FDIV Bug
The Pentium FDIV bug is a hardware bug affecting the floating-point unit (FPU) of the early Intel Pentium processors. Because of the bug, the processor would return incorrect binary floating point results when dividing certain pairs of high-precision numbers. The bug was discovered in 1994 by Thomas R. Nicely, a professor of mathematics at Lynchburg College. Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors. In certain circumstances the errors can occur frequently and lead to significant deviations. The severity of the FDIV bug is debated. Though rarely encountered by most users (''Byte'' magazine estimated that 1 in 9 billion floating point divides with random parameters would produce inaccurate results), both the flaw and Intel's initial handling of the matter were heavily criticized by the tech community. In December 1994, Intel recalled the defective processors in what was the first full r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Original Intel Pentium (P5 Microarchitecture)
The Pentium (also referred to as the i586 or P5 Pentium) is a microprocessor introduced by Intel on March 22, 1993. It is the first CPU using the Pentium brand. Considered the fifth generation in the x86 (8086) compatible line of processors, succeeding the i486, its implementation and microarchitecture was internally called ''P5''. Like the Intel i486, the Pentium is instruction set compatible with the 32-bit i386. It uses a very similar microarchitecture to the i486, but was extended enough to implement a dual integer pipeline design, as well as a more advanced floating-point unit (FPU) that was noted to be ten times faster than its predecessor. The Pentium was succeeded by the Pentium Pro in November 1995. In October 1996, the Pentium MMX was introduced, complementing the same basic microarchitecture of the original Pentium with the MMX instruction set, larger caches, and some other enhancements. Intel discontinued the P5 Pentium processors (sold as a cheaper product sinc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lookup Table
In computer science, a lookup table (LUT) is an array data structure, array that replaces runtime (program lifecycle phase), runtime computation of a mathematical function (mathematics), function with a simpler array indexing operation, in a process termed as ''direct addressing''. The savings in processing time can be significant, because retrieving a value from memory is often faster than carrying out an "expensive" computation or input/output operation. The tables may be precomputation, precalculated and stored in static memory allocation, static program storage, calculated (or prefetcher, "pre-fetched") as part of a program's initialization phase (''memoization''), or even stored in hardware in application-specific platforms. Lookup tables are also used extensively to validate input values by matching against a list of valid (or invalid) items in an array and, in some programming languages, may include pointer functions (or offsets to labels) to process the matching input. Fiel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Imperial College London
Imperial College London, also known as Imperial, is a Public university, public research university in London, England. Its history began with Prince Albert of Saxe-Coburg and Gotha, Prince Albert, husband of Queen Victoria, who envisioned a Albertopolis, cultural district in South Kensington that included museums, colleges, and the Royal Albert Hall. In 1907, these colleges – the Royal College of Science, the Royal School of Mines, and the City and Guilds of London Institute – merged to form the Imperial College of Science and Technology. In 1988, Imperial merged with St Mary's Hospital, London, St Mary's Hospital Medical School and then with Charing Cross and Westminster Medical School to form the Imperial College School of Medicine. The Imperial Business School was established in 2003 and officially opened by Elizabeth II, Queen Elizabeth II. Formerly a constituent college of the University of London, Imperial became an independent university in 2007. Imperial is o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
University Of Illinois
The University of Illinois Urbana-Champaign (UIUC, U of I, Illinois, or University of Illinois) is a public university, public land-grant university, land-grant research university in the Champaign–Urbana metropolitan area, Illinois, United States. Established in 1867, it is the founding campus and Flagship#Colleges and universities in the United States, flagship institution of the University of Illinois System. With over 59,000 students, the University of Illinois is one of the List of United States public university campuses by enrollment, largest public universities by enrollment in the United States. The university contains 16 schools and colleges and offers more than 150 undergraduate and over 100 graduate programs of study. The university holds 651 buildings on and its annual operating budget in 2016 was over $2 billion. The University of Illinois Urbana-Champaign also operates Research Park at the University of Illinois Urbana-Champaign, a research park home to innova ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Microprocessor
A microprocessor is a computer processor (computing), processor for which the data processing logic and control is included on a single integrated circuit (IC), or a small number of ICs. The microprocessor contains the arithmetic, logic, and control circuitry required to perform the functions of a computer's central processing unit (CPU). The IC is capable of interpreting and executing program instructions and performing arithmetic operations. The microprocessor is a multipurpose, Clock signal, clock-driven, Processor register, register-based, digital integrated circuit that accepts binary code, binary data as input, processes it according to instruction (computing), instructions stored in its computer memory, memory, and provides results (also in binary form) as output. Microprocessors contain both combinational logic and sequential logic, sequential digital logic, and operate on numbers and symbols represented in the binary number system. The integration of a whole CPU on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Two's Complement
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, and more generally, fixed point binary values. Two's complement uses the binary digit with the ''greatest'' value as the ''sign'' to indicate whether the binary number is positive or negative; when the most significant bit is ''1'' the number is signed as negative and when the most significant bit is ''0'' the number is signed as positive. As a result, non-negative numbers are represented as themselves: 6 is 0110, zero is 0000, and −6 is 1010 (the result of applying the bitwise NOT operator to 6 and adding 1). However, while the number of binary bits is fixed throughout a computation it is otherwise arbitrary. Unlike the ones' complement scheme, the two's complement scheme has only one representation for zero. Furthermore, arithmetic implementations can be used on signed as well as unsigned integers and differ only in the integer overflow situations. Proce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ones' Complement
The ones' complement of a binary number is the value obtained by inverting (flipping) all the bits in the Binary number, binary representation of the number. The name "ones' complement" refers to the fact that such an inverted value, if added to the original, would always produce an "all ones" number (the term "Method of complements, complement" refers to such pairs of mutually additive inverse numbers, here in respect to a non-0 base number). This mathematical operation is primarily of interest in computer science, where it has varying effects depending on how a specific computer represents numbers. A ones' complement system or ones' complement arithmetic is a system in which negative numbers are represented by the inverse of the binary representations of their corresponding positive numbers. In such a system, a number is negated (converted from positive to negative or vice versa) by computing its ones' complement. An N-bit ones' complement numeral system can only represent int ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
