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Method for division with remainder
A division algorithm is an algorithm which, given two integers N and D (respectively the numerator and the denominator), computes their quotient and/or
Division_algorithm
Standard division algorithm for multi-digit numbers
In arithmetic, long division is a standard division algorithm suitable for dividing multi-digit numbers that is simple enough to perform by hand. It breaks
Long_division
Algorithm for computing greatest common divisors
In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers
Euclidean_algorithm
Algorithm for division of polynomials
In algebra, polynomial long division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree, a generalized version
Polynomial_long_division
Division with remainder of integers
computation are called integer division algorithms, the best known of which being long division. Euclidean division, and algorithms to compute it, are fundamental
Euclidean_division
Sequence of operations for a task
In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve
Algorithm
Computation method
arithmetic algorithms for addition, subtraction, multiplication, and division are described. For example, through the standard addition algorithm, the sum
Standard_algorithms
An algorithm is a fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem
List_of_algorithms
Algorithm for determinants of integers
In mathematics, the Bareiss algorithm, named after Erwin Bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer
Bareiss_algorithm
Number system extending the rational numbers
large values of n. This is commonly used by polynomial factorization algorithms. Both Z p {\displaystyle \mathbb {Z} _{p}} and Q p {\displaystyle \mathbb
P-adic_number
Arithmetic operation
International Encyclopedia article "Division in Mathematics". 400AD Sunzi division algorithm Division by two Galley division Inverse element Order of operations
Division_(mathematics)
Algorithm for computing Gröbner bases
In the theory of multivariate polynomials, Buchberger's algorithm is a method for transforming a given set of polynomials into a Gröbner basis, which
Buchberger's_algorithm
Mathematical construct in computer algebra
in his 1965 Ph.D. thesis, which also included an algorithm to compute them (Buchberger's algorithm). He named them after his advisor Wolfgang Gröbner
Gröbner_basis
Method for evaluating indefinite integrals
In symbolic computation, the Risch algorithm is a method of indefinite integration used in some computer algebra systems to find antiderivatives. It is
Risch_algorithm
Greatest common divisor of polynomials
may be computed as for the integer GCD, with the Euclidean algorithm using long division. The polynomial GCD is defined only up to the multiplication
Polynomial greatest common divisor
Polynomial_greatest_common_divisor
Bug in the Intel P5 Pentium floating-point unit
Missing values in a lookup table used by the FPU's floating-point division algorithm led to calculations acquiring small errors. In certain circumstances
Pentium_FDIV_bug
Algorithm in modular arithmetic
reduction is an algorithm designed to optimize the calculation of a mod n {\displaystyle a\,{\bmod {\,}}n\,} without needing a fast division algorithm. It replaces
Barrett_reduction
American mathematician
the direction of Heisuke Hironaka with a dissertation entitled The Division Algorithm and the Hilbert Scheme. He joined Columbia University thereafter.
Dave_Bayer
Topics referred to by the same term
the inverse of multiplication Division algorithm, a method for computing the result of mathematical division Division (military), a formation typically
Division
Algorithm for polynomial evaluation
mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. It is named after William George Horner, although
Horner's_method
Calculating method used in ancient China
Rod calculus or rod calculation was the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty
Rod_calculus
Way to break a division problem into smaller steps
short division is a division algorithm which breaks down a division problem into a series of easier steps. It is an abbreviated form of long division — whereby
Short_division
subtractions. Division of this type is efficiently realised in hardware by a modified shift register, and in software by a series of equivalent algorithms, starting
Computation of cyclic redundancy checks
Computation_of_cyclic_redundancy_checks
Ancient algorithm for generating prime numbers
In mathematics, the sieve of Eratosthenes is an ancient algorithm for finding all prime numbers up to any given limit. It does so by iteratively marking
Sieve_of_Eratosthenes
Complex number whose mapping on a coordinate plane produces a triangular lattice
Eisenstein integers into Eisenstein primes. One division algorithm is as follows. First perform the division in the field of complex numbers, and write the
Eisenstein_integer
Decimal representation of a number whose digits are periodic
repeating decimal can be obtained by long division if one uses a modified form of the usual division algorithm.) Any number that cannot be expressed as
Repeating_decimal
Problem of sharing resources
evaluating the quality of the division. The archetypal fair division algorithm is divide and choose. The research in fair division can be seen as an extension
Fair_division
Electronic circuit used to multiply binary numbers
product one at a time. Because some common digital signal processing algorithms spend most of their time multiplying, digital signal processor designers
Binary_multiplier
Fair division algorithm
achieve a proportional division. The first published algorithm for proportional division of a cake was the last diminisher algorithm, published in 1948.
Even–Paz_protocol
Integer factorization algorithm
Trial division is the most laborious but easiest to understand of the integer factorization algorithms. The essential idea behind trial division tests
Trial_division
Algorithms for calculating square roots
Square root algorithms compute the non-negative square root S {\displaystyle {\sqrt {S}}} of a positive real number S {\displaystyle S} . Since all square
Square_root_algorithms
Error-detecting code for detecting data changes
101 1 ----------------- 00000000000000 100 <--- remainder (3 bits). Division algorithm stops here as dividend is equal to zero. Since the leftmost divisor
Cyclic_redundancy_check
Property describing run-time complexity of algorithms
differentiate algorithms that would otherwise have identical asymptotic complexity. A simple example of an output-sensitive algorithm is given by the division algorithm
Output-sensitive_algorithm
Automated methods for the creation of mazes
Maze generation algorithms are automated methods for the creation of mazes. A maze can be generated by starting with a predetermined arrangement of cells
Maze_generation_algorithm
Algorithm for integer multiplication
The Karatsuba algorithm is a fast multiplication algorithm for integers. It was discovered by Anatoly Karatsuba in 1960 and published in 1962. It is a
Karatsuba_algorithm
Algorithm to multiply two numbers
multiplication algorithm is an algorithm (or method) to multiply two numbers. Depending on the size of the numbers, different algorithms are more efficient
Multiplication_algorithm
Type of digital adder
John. Collected Works. Parhami, Behrooz (2010). Computer arithmetic: algorithms and hardware designs (2nd ed.). New York: Oxford University Press.
Carry-save_adder
Binary representation for signed numbers
denominator is 8, giving a final result of 3/8. Division algorithm, including restoring and non-restoring division in two's-complement representations Offset
Two's_complement
Decomposition of a number into a product
factors. For example, naive trial division is a Category 1 algorithm. Trial division Wheel factorization Pollard's rho algorithm, which has two common flavors
Integer_factorization
Combinational digital circuit
multiple-precision arithmetic is an algorithm that operates on integers which are larger than the ALU word size. To do this, the algorithm treats each integer as an
Arithmetic_logic_unit
Most widely used method of division prior to 1600
The division described by Al-Khwarizmi in 825 was identical to the Sunzi algorithm for division. Group Field (algebra) Division algebra Division ring
Galley_division
Topics referred to by the same term
Telecommunications), Minot, North Dakota, US Sweeney–Robertson–Tocher division, computer division algorithm Secure Reliable Transport, video streaming protocol Smart
SRT
Digital circuit that produces sums from inputs
2017. Kogge, Peter Michael; Stone, Harold S. (August 1973). "A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations"
Adder_(electronics)
Method for computing the relation of two integers with their greatest common divisor
and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common
Extended_Euclidean_algorithm
Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions
simple and efficient algorithm to calculate trigonometric functions, hyperbolic functions, square roots, multiplications, divisions, exponentials, and logarithms
CORDIC
Mathematical algorithm
Kuṭṭaka is an algorithm for finding integer solutions of linear Diophantine equations. A linear Diophantine equation is an equation of the form ax + by
Kuṭṭaka
Replacing a number with a simpler value
proof of the correctness of the kernel of the AMD5K86 floating-point division algorithm" (PDF). IEEE Transactions on Computers. 47. CiteSeerX 10.1.1.43.3309
Rounding
Arithmetic operation, inverse of nth power
decimal form. The numbers are written similar to the long division algorithm, and, as in long division, the root will be written on the line above. Now separate
Nth_root
Efficient hardware implementation of a digital multiplier
than addition. From a complexity theoretic perspective, the Wallace tree algorithm puts multiplication in the class NC1. The downside of the Wallace tree
Wallace_tree
Arithmetic logic circuit
59–63, 114–116. Rojas, Raul (2014-06-07). "The Z1: Architecture and Algorithms of Konrad Zuse's First Computer". arXiv:1406.1886 [cs.AR]. Rosenberger
Carry-lookahead_adder
Amount left over after computation
of this result, see Euclidean division. For algorithms describing how to calculate the remainder, see Division algorithm.) The remainder, as defined above
Remainder
Arithmetic logic circuit
with carry-save adder. Parhami, Behrooz (2000). Computer arithmetic: Algorithms and Hardware Designs. Oxford University Press. p. 108. ISBN 0-19-512583-5
Carry-skip_adder
Type of fair division
gets the remainder of the cake. The Fink protocol is an algorithm that continues the division into successively smaller "equal" portions. The first partner
Proportional_cake-cutting
Algorithm for fast modular multiplication
significantly improving the speed of the algorithm. In binary computers, R is always a power of two, since division by powers of two can be implemented by
Montgomery modular multiplication
Montgomery_modular_multiplication
Algorithm for computing the greatest common divisor
nonnegative integers. Stein's algorithm uses simpler arithmetic operations than the conventional Euclidean algorithm; it replaces division with arithmetic shifts
Binary_GCD_algorithm
Concept in modular arithmetic
class modulo m is called a complete system of residues modulo m. The division algorithm shows that the set of integers, {0, 1, 2, ..., m − 1} form a complete
Modular multiplicative inverse
Modular_multiplicative_inverse
British computer scientist
from 1972 to 1973. Tocher was also one of the creators of the SRT division algorithm that is used in the hardware of many modern computers. Rivett, B.
K._D._Tocher
Computing circuit
Multiplication algorithm Booth's multiplication algorithm Wallace tree Dadda multiplier Booth encoding Divider (÷) Binary Divider Division algorithm Bitwise
Adder–subtractor
Theorem in number theory
/p\mathbb {Z} } . The fact that Z/pZ is a field allows to apply the division algorithm to f and the polynomial x − k (of degree 1), which yields the existence
Lagrange's theorem (number theory)
Lagrange's_theorem_(number_theory)
Model of computation used by algorithms
be given as inputs to a fair division algorithm. The RW model specifies two kinds of queries that a fair division algorithm may ask the agents: Eval and
Robertson–Webb_query_model
Computer approximation for real numbers
digital logic can be quite complex (see Booth's multiplication algorithm and Division algorithm). Literals for floating-point numbers depend on languages.
Floating-point_arithmetic
Middle ages book on arithmetics
India at his time. Part I mainly dealt with decimal algorithm of subtraction, multiplication, division, extraction of square root and cubic root in place
Principles_of_Hindu_Reckoning
Classification of algorithm
A galactic algorithm is an algorithm with record-breaking theoretical (asymptotic) performance, but which is not used due to practical constraints. Typical
Galactic_algorithm
Important algorithms in numerical statistics
Algorithms for calculating variance play a major role in computational statistics. A key difficulty in the design of good algorithms for this problem is
Algorithms for calculating variance
Algorithms_for_calculating_variance
Line-drawing algorithm
Bresenham's line algorithm is a line drawing algorithm that determines the points of an n-dimensional raster that should be selected in order to form
Bresenham's_line_algorithm
Fair division class using unique allocation methods
time. They present an algorithm that attains the optimal fairness-efficiency threshold. Several authors studied fair division problems in which one agent
Online_fair_division
Study of computation
since antiquity, aiding in computations such as multiplication and division. Algorithms for performing computations have existed since antiquity, even before
Computer_science
Arithmetic logic circuit
Multiplication algorithm Booth's multiplication algorithm Wallace tree Dadda multiplier Booth encoding Divider (÷) Binary Divider Division algorithm Bitwise
Brent–Kung_adder
Mathematical treatise
numerals: the reduction, addition, subtraction, and division of fractions, followed by mechanical algorithm for the extraction of square roots. Chapter 3 contains
Sunzi_Suanjing
Vector quantization algorithm minimizing the sum of squared deviations
efficient heuristic algorithms converge quickly to a local optimum. These are usually similar to the expectation–maximization algorithm for mixtures of Gaussian
K-means_clustering
Division algorithm — for computing quotient and/or remainder of two numbers Long division Restoring division Non-restoring division SRT division Newton–Raphson
List of numerical analysis topics
List_of_numerical_analysis_topics
Digital circuit implementation method
Multiplication algorithm Booth's multiplication algorithm Wallace tree Dadda multiplier Booth encoding Divider (÷) Binary Divider Division algorithm Bitwise
Carry-select_adder
Line algorithm with antialiasing
Xiaolin Wu's line algorithm is an algorithm for line antialiasing. Xiaolin Wu's line algorithm was presented in the article "An Efficient Antialiasing
Xiaolin_Wu's_line_algorithm
Mathematical function, inverse of an exponential function
bit-processing algorithm to compute the logarithm that is similar to long division and was later used in the Connection Machine. The algorithm relies on the
Logarithm
Discrete Fourier transform algorithm
A fast Fourier transform (FFT) is an algorithm that computes the discrete Fourier transform (DFT), or its inverse (IDFT), of a sequence. A Fourier transform
Fast_Fourier_transform
Recursive algorithm for matrix multiplication
Strassen algorithm, named after Volker Strassen, is an algorithm for matrix multiplication. It is faster than the standard matrix multiplication algorithm for
Strassen_algorithm
Arithmetic logic circuit
S. Stone, who published it in a seminal 1973 paper titled A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations
Kogge–Stone_adder
Mathematics used in Ancient Egypt
yield a quotient of 10 + 4 = 14. A more complicated example of the division algorithm is provided by Problem 66. A total of 3200 ro of fat are to be distributed
Ancient_Egyptian_mathematics
Fair division protocol
with Jaisingh Solanki. A proportional division of a cake can be achieved using the recursive halving algorithm in time O(n log n). Several hardness results
Edmonds–Pruhs_protocol
Scientific area at the interface between computer science and mathematics
division algorithm: for polynomials in several indeterminates Pollard's kangaroo algorithm (also known as Pollard's lambda algorithm): an algorithm for
Computer_algebra
Topics referred to by the same term
Multivariate optimization Multivariate cryptography Multivariate division algorithm Multivariate optical computing Multivariate analysis Multivariate
Multivariate
Estimate of time taken for running an algorithm
takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that
Time_complexity
Measure of algorithmic complexity
In computer science, a polynomial-time algorithm is – generally speaking – an algorithm whose running time is upper-bounded by some polynomial function
Strongly-polynomial_time
Circuit that performs subtraction
2 is added in the current digit. (This is similar to the subtraction algorithm in decimal. Instead of adding 2, we add 10 when we borrow.) Therefore
Subtractor
Programming language and theorem prover
proof of the correctness of the kernel of the AMD5K86 floating point division algorithm". IEEE Transactions on Computers. 47. CiteSeerX 10.1.1.43.3309. ACL2
ACL2
Standard for the encryption of electronic data
Standard (DES), which was published in 1977. The algorithm described by AES is a symmetric-key algorithm, meaning the same key is used for both encrypting
Advanced_Encryption_Standard
Scientific tests related to game theory
Genetic algorithms. Two pairs of players had to divide between them 10 indivisible goods. A genetic algorithm was used to search for the best division candidates:
Fair_division_experiments
reproduction is inspired by cell division, and variation is inspired by somatic hypermutation. Clonal selection algorithms are most commonly applied to optimization
Clonal_selection_algorithm
In mathematics, a statement that has been proven
well-known theorems have even more idiosyncratic names, for example, the division algorithm, Euler's formula, and the Banach–Tarski paradox. In English language
Theorem
Polynomial zeros related to linear factors
monic polynomial, and, therefore, the polynomial long division algorithm does not involve any division of coefficients. It is also a corollary of the polynomial
Factor_theorem
Calculations where numbers' precision is only limited by computer memory
The Karatsuba multiplication is such an algorithm. For division, see division algorithm. For a list of algorithms along with complexity estimates, see computational
Arbitrary-precision arithmetic
Arbitrary-precision_arithmetic
Type of fair division
where R is the number of regions. This algorithm can be generalized to piecewise-linear valuations. An exact division exists in the more general setting in
Consensus_splitting
Supercomputer built by the University of Illinois in 1962
Retch". The ILLIAC II had a division unit designed by faculty member James E. Robertson, a co-inventor of the SRT division algorithm. The ILLIAC II was one
ILLIAC_II
Algorithm for supervised learning of binary classifiers
In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A binary classifier is a function that can decide whether
Perceptron
Optimization algorithm
computer science and operations research, the ant colony optimization algorithm (ACO) is a probabilistic technique for solving computational problems
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Fast greatest common divisor algorithm
GCD algorithm, named after D. H. Lehmer, is a fast GCD algorithm for multiple-precision arithmetic, which improves on the simpler Euclidean algorithm by
Lehmer's_GCD_algorithm
Mathematics used in Ancient China
the most detailed step by step description of multiplication and division algorithm with counting rods. Intriguingly, Sunzi may have influenced the development
Chinese_mathematics
Method for finding minimum spanning trees
Borůvka's algorithm is a greedy algorithm for finding a minimum spanning tree in a graph, or a minimum spanning forest in the case of a graph that is
Borůvka's_algorithm
Algorithmic runtime requirements for common math procedures
The following tables list the computational complexity of various algorithms for common mathematical operations. Here, complexity refers to the time complexity
Computational complexity of mathematical operations
Computational_complexity_of_mathematical_operations
Algorithm for public-key cryptography
Ron Rivest, Adi Shamir and Leonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 at Government
RSA_cryptosystem
DIVISION ALGORITHM
DIVISION ALGORITHM
Girl/Female
Biblical
Separation, division.
Biblical
division
Biblical
divisions
Boy/Male
Australian, Scandinavian, Teutonic
A Division; The Barn
Girl/Female
Biblical
Rock of divisions.
Girl/Female
Biblical
Divisions.
Girl/Female
Indian, Telugu
Decision
Boy/Male
Indian
Decision
Boy/Male
Biblical
God of divisions.
Girl/Female
Biblical
Divisions.
Boy/Male
Muslim
Decision
Biblical
division; rupture
Biblical
rock of divisions
Boy/Male
American, Australian, British, English
Son of David; David's Son; Surname
Girl/Female
Biblical
Division.
Biblical
separation; division
Girl/Female
Biblical
Division.
Boy/Male
Biblical
Division, rupture.
Girl/Female
Biblical
Separation, division.
Boy/Male
English
David's son. Surname.
DIVISION ALGORITHM
DIVISION ALGORITHM
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Goddess Lakshmi; Worldly Wise
Female
English
Feminine form of English Dean, DEANA means "dean, head, leader."
Girl/Female
Hindu
Veneration, Goddess chamundi (Celebrity Name: Shakthi Kapoor)
Female
English
Variant spelling of English Kayley, KAYLIE means "slender."
Boy/Male
Shakespearean
Cymbeline' Son to Cymbeline, disguised under the name of Cadwal, a supposed son to Belarius.
Boy/Male
Indian
Rose.
Girl/Female
Indian, Tamil
As Like Golden God
Boy/Male
Gujarati, Hindu, Indian, Kannada
Humble
Boy/Male
Gaelic Irish
Strong; oak-hearted. See also Derek.
Boy/Male
English Teutonic
Son of Patrick.
DIVISION ALGORITHM
DIVISION ALGORITHM
DIVISION ALGORITHM
DIVISION ALGORITHM
DIVISION ALGORITHM
n.
One of the groups into which a fleet is divided.
a.
Indicating division or distribution.
n.
The quality of being decided; prompt and fixed determination; unwavering firmness; as, to manifest great decision.
n.
One of the larger districts into which a country is divided for administering military affairs.
n.
Two companies of infantry maneuvering as one subdivision of a battalion.
n.
Cutting off; division; detachment of a part.
n.
The act of revising; reexamination for correction; review; as, the revision of a book or writing, or of a proof sheet; a revision of statutes.
n.
An object of derision or scorn; a laughing-stock.
a.
That divides; pertaining to, making, or noting, a division; as, a divisional line; a divisional general; a divisional surgeon of police.
n.
A grade or rank in classification; a portion of a tribe or of a class; or, in some recent authorities, equivalent to a subkingdom.
n.
Want of vision or of the power of seeing.
n.
One of the larger divisions of the animal kingdom; a branch; a grand division.
n.
A course of notes so running into each other as to form one series or chain, to be sung in one breath to one syllable.
n.
The act of turning aside from any course, occupation, or object; as, the diversion of a stream from its channel; diversion of the mind from business.
n.
Vision.
a.
Creating, or tending to create, division, separation, or difference.
n.
The distribution of a discourse into parts; a part so distinguished.
n.
One who divides or makes division.
n.
An account or report of a conclusion, especially of a legal adjudication or judicial determination of a question or cause; as, a decision of arbitrators; a decision of the Supreme Court.
v. t.
To see in a vision; to dream.