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Floating-point arithmetic

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In computing, floating-point arithmetic is arithmetic using formulaic representation of real numbers as an approximation so as to support a trade-off between range and precision. [1]

183 relations: Accuracy and precision, ACM Computing Surveys, Addison-Wesley, Al Hussein (missile), Analytical Engine, Approximation error, Arbitrary-precision arithmetic, Archimedes, Arithmetic underflow, Association for Computing Machinery, Associative property, Base (exponentiation), Binary number, Binary-coded decimal, Birkhäuser, Bit, Booth's multiplication algorithm, C Sharp (programming language), C11 (C standard revision), C99, Cambridge University Press, Cg (programming language), Charles Babbage, Cluster (spacecraft), Coefficient, Commutative property, Compiler, Complex number, Computable number, Computational geometry, Computational science, Computer, Computer algebra system, Computing, Concurrency (computer science), Condition number, Conjugate element (field theory), Continuous function, Coprocessor, Cosmic distance ladder, Cray SV1, Cray T90, Decimal floating point, Decimal representation, Decimal separator, Decimal128 floating-point format, Decimal32 floating-point format, Decimal64 floating-point format, Denormal number, Derivative, ..., Dhahran, Discretization error, Distributive property, Division algorithm, Division by zero, Double-precision floating-point format, Dynamic range, Eigenvalues and eigenvectors, Electromechanics, Endianness, English Electric DEUCE, Exception handling, Exclusive or, Experimental mathematics, Exponent bias, Exponentiation, Extended precision, Extended real number line, Fast inverse square root, Financial calculator, Fixed-point arithmetic, Floating point error mitigation, Floating-point unit, Floor and ceiling functions, FLOPS, Fraction (mathematics), Gal's accurate tables, GNU Multiple Precision Arithmetic Library, Government Accountability Office, Half-precision floating-point format, Hewlett-Packard, Hexadecimal, IAS machine, IBM 704, IBM 7090, IBM Floating Point Architecture, IBM System/360, IEEE 754, IEEE 754 revision, IEEE Annals of the History of Computing, Infinity, Institute of Electrical and Electronics Engineers, Integer, Integer overflow, Intel 8087, Interval arithmetic, Invertible matrix, Io (moon), Iterative refinement, James H. Wilkinson, John von Neumann, John Wiley & Sons, Johns Hopkins University Press, Jupiter, Kahan summation algorithm, Konrad Zuse, Leonardo Torres y Quevedo, Logarithm, Logarithmic number system, Long double, Loss of significance, Machine epsilon, Maple (software), Maxima (software), Mechanical computer, Microsoft Binary Format, Microsoft Developer Network, MIM-104 Patriot, Minifloat, Motorola 68000, NaN, National Physical Laboratory (United Kingdom), Numeral system, Numerical analysis, Numerical linear algebra, Numerical stability, Orders of magnitude (numbers), Overload (magazine), Oxford University Press, Pentium, Pentium FDIV bug, Pi, Pilot ACE, Porting, Precision (computer science), Prentice Hall, Proton, Python (programming language), Q (number format), Quadruple-precision floating-point format, Radix, Radix point, Rational number, Real number, Relay, Round-off error, Rounding, Runtime system, Saudi Arabia, Scientific calculator, Scientific notation, Setun, Sign function, Signed zero, Significand, Significant figures, Single-precision floating-point format, Society for Industrial and Applied Mathematics, Springer Nature, Springer Science+Business Media, Square root, Subatomic scale, Symmetric level-index arithmetic, Taylor series, Ternary numeral system, Thread-local storage, Trade-off, Trap (computing), Truncation, Turing Award, Two's complement, Unit in the last place, UNIVAC 1100/2200 series, William Kahan, Wolfram Mathematica, Word (computer architecture), X86, Z/Architecture, Z1 (computer), Z3 (computer), Z4 (computer), Zero of a function, 14th Quartermaster Detachment. Expand index (133 more) »

Accuracy and precision

Precision is a description of random errors, a measure of statistical variability.

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ACM Computing Surveys

ACM Computing Surveys (CSUR) is a peer reviewed scientific journal published by the Association for Computing Machinery.

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Addison-Wesley is a publisher of textbooks and computer literature.

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Al Hussein (missile)

Al Hussein or al-Husayn (Arabic: الحسين) is the designation of an Iraqi short-range ballistic missile.

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Analytical Engine

The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage.

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Approximation error

The approximation error in some data is the discrepancy between an exact value and some approximation to it.

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Arbitrary-precision arithmetic

In computer science, arbitrary-precision arithmetic, also called bignum arithmetic, multiple-precision arithmetic, or sometimes infinite-precision arithmetic, indicates that calculations are performed on numbers whose digits of precision are limited only by the available memory of the host system.

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Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

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Arithmetic underflow

The term arithmetic underflow (or "floating point underflow", or just "underflow") is a condition in a computer program where the result of a calculation is a number of smaller absolute value than the computer can actually represent in memory on its CPU.

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Association for Computing Machinery

The Association for Computing Machinery (ACM) is an international learned society for computing.

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Associative property

In mathematics, the associative property is a property of some binary operations.

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Base (exponentiation)

In exponentiation, the base is the number b in an expression of the form bn.

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Binary number

In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically 0 (zero) and 1 (one).

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Binary-coded decimal

In computing and electronic systems, binary-coded decimal (BCD) is a class of binary encodings of decimal numbers where each decimal digit is represented by a fixed number of bits, usually four or eight.

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Birkhäuser is a former Swiss publisher founded in 1879 by Emil Birkhäuser.

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The bit (a portmanteau of binary digit) is a basic unit of information used in computing and digital communications.

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Booth's multiplication algorithm

Booth's multiplication algorithm is a multiplication algorithm that multiplies two signed binary numbers in two's complement notation.

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C Sharp (programming language)

C# (/si: ʃɑːrp/) is a multi-paradigm programming language encompassing strong typing, imperative, declarative, functional, generic, object-oriented (class-based), and component-oriented programming disciplines.

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C11 (C standard revision)

C11 (formerly C1X) is an informal name for ISO/IEC 9899:2011, the current standard for the C programming language.

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C99 (previously known as C9X) is an informal name for ISO/IEC 9899:1999, a past version of the C programming language standard.

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Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

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Cg (programming language)

Cg (short for C for Graphics) is a high-level shading language developed by Nvidia in close collaboration with Microsoft for programming vertex and pixel shaders.

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Charles Babbage

Charles Babbage (26 December 1791 – 18 October 1871) was an English polymath.

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Cluster (spacecraft)

Cluster was a constellation of four European Space Agency spacecraft which were launched on the maiden flight of the Ariane 5 rocket, Flight 501, and subsequently lost when that rocket failed to achieve orbit.

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In mathematics, a coefficient is a multiplicative factor in some term of a polynomial, a series or any expression; it is usually a number, but may be any expression.

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Commutative property

In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.

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A compiler is computer software that transforms computer code written in one programming language (the source language) into another programming language (the target language).

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Complex number

A complex number is a number that can be expressed in the form, where and are real numbers, and is a solution of the equation.

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Computable number

In mathematics, computable numbers are the real numbers that can be computed to within any desired precision by a finite, terminating algorithm.

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Computational geometry

Computational geometry is a branch of computer science devoted to the study of algorithms which can be stated in terms of geometry.

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Computational science

Computational science (also scientific computing or scientific computation (SC)) is a rapidly growing multidisciplinary field that uses advanced computing capabilities to understand and solve complex problems.

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A computer is a device that can be instructed to carry out sequences of arithmetic or logical operations automatically via computer programming.

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Computer algebra system

A computer algebra system (CAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists.

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Computing is any goal-oriented activity requiring, benefiting from, or creating computers.

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Concurrency (computer science)

In computer science, concurrency refers to the ability of different parts or units of a program, algorithm, or problem to be executed out-of-order or in partial order, without affecting the final outcome.

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Condition number

In the field of numerical analysis, the condition number of a function with respect to an argument measures how much the output value of the function can change for a small change in the input argument.

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Conjugate element (field theory)

In mathematics, in particular field theory, the conjugate elements of an algebraic element α, over a field extension L/K, are the roots of the minimal polynomial pK,α(x) of α over K. Conjugate elements are also called Galois conjugates or simply conjugates.

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Continuous function

In mathematics, a continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output.

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A coprocessor is a computer processor used to supplement the functions of the primary processor (the CPU).

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Cosmic distance ladder

The cosmic distance ladder (also known as the extragalactic distance scale) is the succession of methods by which astronomers determine the distances to celestial objects.

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Cray SV1

The Cray SV1 is a vector processor supercomputer from the Cray Research division of Silicon Graphics introduced in 1998.

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Cray T90

The Cray T90 series (code-named Triton during development) was the last of a line of vector processing supercomputers manufactured by Cray Research, Inc, superseding the Cray C90 series.

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Decimal floating point

Decimal floating-point (DFP) arithmetic refers to both a representation and operations on decimal floating-point numbers.

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Decimal representation

A decimal representation of a non-negative real number r is an expression in the form of a series, traditionally written as a sum where a0 is a nonnegative integer, and a1, a2,...

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Decimal separator

A decimal separator is a symbol used to separate the integer part from the fractional part of a number written in decimal form.

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Decimal128 floating-point format

In computing, decimal128 is a decimal floating-point computer numbering format that occupies 16 bytes (128 bits) in computer memory.

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Decimal32 floating-point format

In computing, decimal32 is a decimal floating-point computer numbering format that occupies 4 bytes (32 bits) in computer memory.

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Decimal64 floating-point format

In computing, decimal64 is a decimal floating-point computer numbering format that occupies 8 bytes (64 bits) in computer memory.

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Denormal number

In computer science, denormal numbers or denormalized numbers (now often called subnormal numbers) fill the underflow gap around zero in floating-point arithmetic.

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The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Dhahran (Arabic الظهران aẓ-Ẓahrān) is a city located in Eastern Province, Saudi Arabia.

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Discretization error

In numerical analysis, computational physics, and simulation, discretization error is the error resulting from the fact that a function of a continuous variable is represented in the computer by a finite number of evaluations, for example, on a lattice.

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Distributive property

In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.

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Division algorithm

A division algorithm is an algorithm which, given two integers N and D, computes their quotient and/or remainder, the result of division.

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Division by zero

In mathematics, division by zero is division where the divisor (denominator) is zero.

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Double-precision floating-point format

Double-precision floating-point format is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.

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Dynamic range

Dynamic range, abbreviated DR, DNR, or DYR is the ratio between the largest and smallest values that a certain quantity can assume.

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Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

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In engineering, electromechanics combines processes and procedures drawn from electrical engineering and mechanical engineering.

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Endianness refers to the sequential order in which bytes are arranged into larger numerical values when stored in memory or when transmitted over digital links.

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English Electric DEUCE

The DEUCE (Digital Electronic Universal Computing Engine) was one of the earliest British commercially available computers, built by English Electric from 1955.

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Exception handling

Exception handling is the process of responding to the occurrence, during computation, of exceptions – anomalous or exceptional conditions requiring special processing – often changing the normal flow of program execution.

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Exclusive or

Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).

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Experimental mathematics

Experimental mathematics is an approach to mathematics in which computation is used to investigate mathematical objects and identify properties and patterns.

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Exponent bias

In IEEE 754 floating point numbers, the exponent is biased in the engineering sense of the word – the value stored is offset from the actual value by the exponent bias.

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Exponentiation is a mathematical operation, written as, involving two numbers, the base and the exponent.

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Extended precision

Extended precision refers to floating point number formats that provide greater precision than the basic floating point formats.

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Extended real number line

In mathematics, the affinely extended real number system is obtained from the real number system by adding two elements: and (read as positive infinity and negative infinity respectively).

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Fast inverse square root

Fast inverse square root, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates, the reciprocal (or multiplicative inverse) of the square root of a 32-bit floating-point number in IEEE 754 floating-point format.

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Financial calculator

A financial calculator or business calculator is an electronic calculator that performs financial functions commonly needed in business and commerce communities.

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Fixed-point arithmetic

In computing, a fixed-point number representation is a real data type for a number that has a fixed number of digits after (and sometimes also before) the radix point (after the decimal point '.' in English decimal notation).

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Floating point error mitigation

Floating point error arises because real numbers cannot, in general, be accurately represented in a fixed space.

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Floating-point unit

A floating-point unit (FPU, colloquially a math coprocessor) is a part of a computer system specially designed to carry out operations on floating point numbers.

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Floor and ceiling functions

In mathematics and computer science, the floor function is the function that takes as input a real number x and gives as output the greatest integer less than or equal to x, denoted \operatorname(x).

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In computing, floating point operations per second (FLOPS, flops or flop/s) is a measure of computer performance, useful in fields of scientific computations that require floating-point calculations.

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Fraction (mathematics)

A fraction (from Latin fractus, "broken") represents a part of a whole or, more generally, any number of equal parts.

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Gal's accurate tables

Gal's accurate tables is a method devised by Shmuel Gal to provide accurate values of special functions using a lookup table and interpolation.

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GNU Multiple Precision Arithmetic Library

GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating point numbers.

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Government Accountability Office

The Government Accountability Office (GAO) is a legislative branch government agency that provides auditing, evaluation, and investigative services for the United States Congress.

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Half-precision floating-point format

In computing, half precision is a binary floating-point computer number format that occupies 16 bits (two bytes in modern computers) in computer memory.

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The Hewlett-Packard Company (commonly referred to as HP) or shortened to Hewlett-Packard was an American multinational information technology company headquartered in Palo Alto, California.

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In mathematics and computing, hexadecimal (also base, or hex) is a positional numeral system with a radix, or base, of 16.

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IAS machine

The IAS machine was the first electronic computer to be built at the Institute for Advanced Study (IAS) in Princeton, New Jersey.

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IBM 704

The IBM 704, introduced by IBM in 1954, is the first mass-produced computer with floating-point arithmetic hardware.

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IBM 7090

The IBM 7090 is a second-generation transistorized version of the earlier IBM 709 vacuum tube mainframe computers that was designed for "large-scale scientific and technological applications".

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IBM Floating Point Architecture

IBM System/360 computers, and subsequent machines based on that architecture (mainframes), support a hexadecimal floating-point format.

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IBM System/360

The IBM System/360 (S/360) is a family of mainframe computer systems that was announced by IBM on April 7, 1964, and delivered between 1965 and 1978.

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IEEE 754

The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point computation established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE).

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IEEE 754 revision

IEEE 754-2008 (previously known as IEEE 754r) was published in August 2008 and is a significant revision to, and replaces, the IEEE 754-1985 floating point standard.

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IEEE Annals of the History of Computing

The IEEE Annals of the History of Computing is a quarterly peer-reviewed academic journal published by the IEEE Computer Society.

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Infinity (symbol) is a concept describing something without any bound or larger than any natural number.

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Institute of Electrical and Electronics Engineers

The Institute of Electrical and Electronics Engineers (IEEE) is a professional association with its corporate office in New York City and its operations center in Piscataway, New Jersey.

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An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Integer overflow

In computer programming, an integer overflow occurs when an arithmetic operation attempts to create a numeric value that is outside of the range that can be represented with a given number of bits – either larger than the maximum or lower than the minimum representable value.

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Intel 8087

The Intel 8087, announced in 1980, was the first x87 floating-point coprocessor for the 8086 line of microprocessors.

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Interval arithmetic

Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s, as an approach to putting bounds on rounding errors and measurement errors in mathematical computation and thus developing numerical methods that yield reliable results.

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Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular or nondegenerate) if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication.

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Io (moon)

Io (Jupiter I) is the innermost of the four Galilean moons of the planet Jupiter.

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Iterative refinement

Iterative refinement is an iterative method proposed by James H. Wilkinson to improve the accuracy of numerical solutions to systems of linear equations.

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James H. Wilkinson

James Hardy Wilkinson FRS (27 September 1919 – 5 October 1986) was a prominent figure in the field of numerical analysis, a field at the boundary of applied mathematics and computer science particularly useful to physics and engineering.

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John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

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John Wiley & Sons

John Wiley & Sons, Inc., also referred to as Wiley, is a global publishing company that specializes in academic publishing.

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Johns Hopkins University Press

The Johns Hopkins University Press (also referred to as JHU Press or JHUP) is the publishing division of Johns Hopkins University.

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Jupiter is the fifth planet from the Sun and the largest in the Solar System.

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Kahan summation algorithm

In numerical analysis, the Kahan summation algorithm (also known as compensated summation) significantly reduces the numerical error in the total obtained by adding a sequence of finite precision floating point numbers, compared to the obvious approach.

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Konrad Zuse

Konrad Zuse (22 June 1910 – 18 December 1995) was a German civil engineer, inventor and computer pioneer.

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Leonardo Torres y Quevedo

Leonardo Torres y Quevedo (28 December 1852 – 18 December 1936) was a Spanish civil engineer and mathematician of the late nineteenth and early twentieth centuries.

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In mathematics, the logarithm is the inverse function to exponentiation.

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Logarithmic number system

A logarithmic number system (LNS) is an arithmetic system used for representing real numbers in computer and digital hardware, especially for digital signal processing.

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Long double

In C and related programming languages, long double refers to a floating-point data type that is often more precise than double-precision.

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Loss of significance

Loss of significance is an undesirable effect in calculations using finite-precision arithmetic such as floating-point arithmetic.

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Machine epsilon

Machine epsilon gives an upper bound on the relative error due to rounding in floating point arithmetic.

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Maple (software)

Maple is a symbolic and numeric computing environment, and is also a multi-paradigm programming language.

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Maxima (software)

Maxima is a computer algebra system (CAS) based on a 1982 version of Macsyma.

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Mechanical computer

A mechanical computer is built from mechanical components such as levers and gears, rather than electronic components.

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Microsoft Binary Format

In computing, Microsoft Binary Format (MBF) was a format for floating-point numbers used in Microsoft's BASIC language products, including MBASIC, GW-BASIC and QuickBasic prior to version 4.00.

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Microsoft Developer Network

Microsoft Developer Network (MSDN) is the portion of Microsoft responsible for managing the firm's relationship with developers and testers, such as hardware developers interested in the operating system (OS), and software developers developing on the various OS platforms or using the API or scripting languages of Microsoft's applications.

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MIM-104 Patriot

The MIM-104 Patriot is a surface-to-air missile (SAM) system, the primary of its kind used by the United States Army and several allied nations.

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In computing, minifloats are floating-point values represented with very few bits.

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Motorola 68000

The Motorola 68000 ("'sixty-eight-thousand'"; also called the m68k or Motorola 68k, "sixty-eight-kay") is a 16/32-bit CISC microprocessor, which implements a 32-bit instruction set, with 32-bit registers and 32-bit internal data bus, but with a 16-bit data ALU and two 16-bit arithmetic ALUs and a 16-bit external data bus, designed and marketed by Motorola Semiconductor Products Sector.

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In computing, NaN, standing for not a number, is a numeric data type value representing an undefined or unrepresentable value, especially in floating-point calculations.

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National Physical Laboratory (United Kingdom)

The National Physical Laboratory (NPL) is the national measurement standards laboratory for the United Kingdom, based at Bushy Park in Teddington, London, England.

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Numeral system

A numeral system (or system of numeration) is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set, using digits or other symbols in a consistent manner.

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Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics).

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Numerical linear algebra

Numerical linear algebra is the study of algorithms for performing linear algebra computations, most notably matrix operations, on computers.

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Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms.

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Orders of magnitude (numbers)

This list contains selected positive numbers in increasing order, including counts of things, dimensionless quantity and probabilities.

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Overload (magazine)

Overload is a bi-monthly professional computer magazine published by ACCU, that was established in 1993 and is edited by Frances Buontempo.

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Oxford University Press

Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.

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Pentium is a brand used for a series of x86 architecture-compatible microprocessors produced by Intel since 1993.

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Pentium FDIV bug

The Pentium FDIV bug was a computer bug that affected the floating point unit (FPU) of the early Intel Pentium processors.

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The number is a mathematical constant.

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Pilot ACE

The Pilot ACE (Automatic Computing Engine) was one of the first computers built in the United Kingdom at the National Physical Laboratory (NPL) in the early 1950s.

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In software engineering, porting is the process of adapting software for the purpose of achieving some form of execution in a computing environment that is different from the one that a given program (meant for such execution) was originally designed for (e.g. different CPU, operating system, or third party library).

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Precision (computer science)

In computer science, the precision of a numerical quantity is a measure of the detail in which the quantity is expressed.

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Prentice Hall

Prentice Hall is a major educational publisher owned by Pearson plc.

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| magnetic_moment.

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Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

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Q (number format)

Q is a fixed point number format where the number of fractional bits (and optionally the number of integer bits) is specified.

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Quadruple-precision floating-point format

In computing, quadruple precision (or quad precision) is a binary floating-point-based computer number format that occupies 16 bytes (128 bits) in with precision more than twice the 53-bit double precision.

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In mathematical numeral systems, the radix or base is the number of unique digits, including zero, used to represent numbers in a positional numeral system.

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Radix point

In mathematics and computing, a radix point (or radix character) is the symbol used in numerical representations to separate the integer part of a number (to the left of the radix point) from its fractional part (to the right of the radix point).

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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A relay is an electrically operated switch.

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Round-off error

A round-off error, also called rounding error, is the difference between the calculated approximation of a number and its exact mathematical value due to rounding.

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Rounding a numerical value means replacing it by another value that is approximately equal but has a shorter, simpler, or more explicit representation; for example, replacing $ with $, or the fraction 312/937 with 1/3, or the expression with.

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Runtime system

A runtime system, also called run-time system, primarily implements portions of an execution model.

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Saudi Arabia

Saudi Arabia, officially the Kingdom of Saudi Arabia (KSA), is a sovereign Arab state in Western Asia constituting the bulk of the Arabian Peninsula.

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Scientific calculator

A scientific calculator is a type of electronic calculator, usually but not always handheld, designed to calculate problems in science, engineering, and mathematics.

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Scientific notation

Scientific notation (also referred to as scientific form or standard index form, or standard form in the UK) is a way of expressing numbers that are too big or too small to be conveniently written in decimal form.

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Setun (Сетунь) was a computer developed in 1958 at Moscow State University.

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Sign function

In mathematics, the sign function or signum function (from signum, Latin for "sign") is an odd mathematical function that extracts the sign of a real number.

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Signed zero

Signed zero is zero with an associated sign.

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The significand (also mantissa or coefficient) is part of a number in scientific notation or a floating-point number, consisting of its significant digits.

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Significant figures

The significant figures (also known as the significant digits) of a number are digits that carry meaning contributing to its measurement resolution.

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Single-precision floating-point format

Single-precision floating-point format is a computer number format, usually occupying 32 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.

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Society for Industrial and Applied Mathematics

The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.

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Springer Nature

Springer Nature is an academic publishing company created by the May 2015 merger of Springer Science+Business Media and Holtzbrinck Publishing Group's Nature Publishing Group, Palgrave Macmillan, and Macmillan Education.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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Square root

In mathematics, a square root of a number a is a number y such that; in other words, a number y whose square (the result of multiplying the number by itself, or) is a. For example, 4 and −4 are square roots of 16 because.

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Subatomic scale

The subatomic scale is the domain of physical size that encompasses objects smaller than an atom.

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Symmetric level-index arithmetic

The level-index (LI) representation of numbers, and its algorithms for arithmetic operations, were introduced by Clenshaw and Olver in 1984.

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Taylor series

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.

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Ternary numeral system

The ternary numeral system (also called base 3) has three as its base.

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Thread-local storage

Thread-local storage (TLS) is a computer programming method that uses static or global memory local to a thread.

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A trade-off (or tradeoff) is a situational decision that involves diminishing or losing one quality, quantity or property of a set or design in return for gains in other aspects.

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Trap (computing)

In computing and operating systems, a trap, also known as an exception or a fault, is typicallyThere is a wide variation in the nomenclature.

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In mathematics and computer science, truncation is limiting the number of digits right of the decimal point.

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Turing Award

The ACM A.M. Turing Award is an annual prize given by the Association for Computing Machinery (ACM) to an individual selected for contributions "of lasting and major technical importance to the computer field".

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Two's complement

Two's complement is a mathematical operation on binary numbers, best known for its role in computing as a method of signed number representation.

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Unit in the last place

In computer science and numerical analysis, unit in the last place or unit of least precision (ULP) is the spacing between floating-point numbers, i.e., the value the least significant digit represents if it is 1.

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UNIVAC 1100/2200 series

The UNIVAC 1100/2200 series is a series of compatible 36-bit computer systems, beginning with the UNIVAC 1107 in 1962, initially made by Sperry Rand.

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William Kahan

William "Velvel" Morton Kahan (born June 5, 1933) is a Canadian mathematician and computer scientist who received the Turing Award in 1989 for "his fundamental contributions to numerical analysis", was named an ACM Fellow in 1994, and inducted into the National Academy of Engineering in 2005.

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Wolfram Mathematica

Wolfram Mathematica (usually termed Mathematica) is a modern technical computing system spanning most areas of technical computing — including neural networks, machine learning, image processing, geometry, data science, visualizations, and others.

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Word (computer architecture)

In computing, a word is the natural unit of data used by a particular processor design.

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x86 is a family of backward-compatible instruction set architectures based on the Intel 8086 CPU and its Intel 8088 variant.

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z/Architecture, initially and briefly called ESA Modal Extensions (ESAME), is IBM's 64-bit instruction set architecture implemented by its mainframe computers.

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Z1 (computer)

The Z1 was a mechanical computer designed by Konrad Zuse from 1935 to 1936 and built by him from 1936 to 1938.

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Z3 (computer)

The Z3 was a German electromechanical computer designed by Konrad Zuse.

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Z4 (computer)

The Z4 was the world's first commercial digital computer, designed by German engineer Konrad Zuse and built by his company Zuse Apparatebau in 1945.

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Zero of a function

In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation f(x).

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14th Quartermaster Detachment

The 14th Quartermaster Detachment, is a United States Army Reserve water purification unit stationed in Greensburg, Pennsylvania.

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[1] https://en.wikipedia.org/wiki/Floating-point_arithmetic

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