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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. 

65 relations: Analysis of algorithms, Angle of incidence (optics), Approximation error, C preprocessor, Cambridge, Cambridge University Press, Cleve Moler, Comment (computer programming), Computer graphics, Derivative, Digital signal processing, Dimension (vector space), Euclidean vector, Exponent bias, Field-programmable gate array, First-person shooter, Floating-point arithmetic, Hexadecimal, Id Software, Id Tech 3, IEEE 754-1985, IEEE Computer Society, Institute of Electrical and Electronics Engineers, International Federation for Information Processing, Irvine, California, Jim Blinn, John Carmack, Kludge, Lambert's cosine law, Lighting, List of IEEE publications, Logical shift, Lookup table, Magic number (programming), Mathematical table, MATLAB, Methods of computing square roots, Multiplicative inverse, Newton's method, Norm (mathematics), Normal number (computing), Normalized number, O'Reilly Media, Quake III Arena, QuakeCon, Rate of convergence, Reflection (computer graphics), Root-finding algorithm, SGI Indigo, Shader, ... Expand index (15 more) »

## Analysis of algorithms

In computer science, the analysis of algorithms is the determination of the computational complexity of algorithms, that is the amount of time, storage and/or other resources necessary to execute them.

## Angle of incidence (optics)

In geometric optics, the angle of incidence is the angle between a ray incident on a surface and the line perpendicular to the surface at the point of incidence, called the normal.

## Approximation error

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

## C preprocessor

The C preprocessor or cpp is the macro preprocessor for the C and C++ computer programming languages.

## Cambridge

Cambridge is a university city and the county town of Cambridgeshire, England, on the River Cam approximately north of London.

## Cambridge University Press

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

## Cleve Moler

Cleve Barry Moler is an American mathematician and computer programmer specializing in numerical analysis.

## Comment (computer programming)

In computer programming, a comment is a programmer-readable explanation or annotation in the source code of a computer program.

## Computer graphics

Computer graphics are pictures and films created using computers.

## Derivative

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).

## Digital signal processing

Digital signal processing (DSP) is the use of digital processing, such as by computers or more specialized digital signal processors, to perform a wide variety of signal processing operations.

## Dimension (vector space)

In mathematics, the dimension of a vector space V is the cardinality (i.e. the number of vectors) of a basis of V over its base field.

## Euclidean vector

In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction.

## 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.

## Field-programmable gate array

A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturing hence "field-programmable".

## First-person shooter

First-person shooter (FPS) is a video game genre centered around gun and other weapon-based combat in a first-person perspective; that is, the player experiences the action through the eyes of the protagonist.

## Floating-point arithmetic

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.

## Hexadecimal

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

## Id Software

id Software LLC (see Company name) is an American video game developer headquartered in Dallas, Texas.

## Id Tech 3

id Tech 3, popularly known as the Quake III Arena engine, is a game engine developed by id Software for their video game Quake III Arena.

## IEEE 754-1985

IEEE 754-1985 was an industry standard for representing floating-point numbers in computers, officially adopted in 1985 and superseded in 2008 by IEEE 754-2008.

## IEEE Computer Society

IEEE Computer Society (sometimes abbreviated Computer Society or CS) is a professional society of IEEE.

## 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.

## International Federation for Information Processing

The International Federation for Information Processing (IFIP) is a global organisation for researchers and professionals working in the field of information and communication technologies (ICT) to conduct research, develop standards and promote information sharing.

## Irvine, California

Irvine is a master-planned city in Orange County, California, United States.

## Jim Blinn

James F. Blinn (born 1949) is an American computer scientist who first became widely known for his work as a computer graphics expert at NASA's Jet Propulsion Laboratory (JPL), particularly his work on the pre-encounter animations for the Voyager project, his work on the Carl Sagan documentary series Cosmos, and the research of the Blinn–Phong shading model.

## John Carmack

John D. Carmack (born August 20, 1970) is an American computer programmer, engineer, and businessman.

## Kludge

A kludge or kluge is a workaround or quick-and-dirty solution that is clumsy, inelegant, inefficient, difficult to extend and hard to maintain.

## Lambert's cosine law

In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the direction of the incident light and the surface normal.

## Lighting

Lighting or illumination is the deliberate use of light to achieve a practical or aesthetic effect.

## List of IEEE publications

The publications of the Institute of Electrical and Electronics Engineers publications (IEEE) constitute around 30% of the world literature in the electrical and electronics engineering and computer science fields, publishing well over 100 peer-reviewed journals.

## Logical shift

In computer science, a logical shift is a bitwise operation that shifts all the bits of its operand.

## Lookup table

In computer science, a lookup table is an array that replaces runtime computation with a simpler array indexing operation.

## Magic number (programming)

In computer programming, the term magic number has multiple meanings.

## Mathematical table

Mathematical tables are lists of numbers showing the results of calculation with varying arguments.

## MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

## Methods of computing square roots

In numerical analysis, a branch of mathematics, there are several square root algorithms or methods of computing the principal square root of a non-negative real number.

## Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x&minus;1, is a number which when multiplied by x yields the multiplicative identity, 1.

## Newton's method

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

## Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

## Normal number (computing)

In computing, a normal number is a non-zero number in a floating-point representation which is within the balanced range supported by a given floating-point format: it is a floating point number that can be represented without leading zeros in its significand.

## Normalized number

In applied mathematics, a number is normalized when it is written in scientific notation with one non-zero decimal digit before the decimal point.

## O'Reilly Media

O'Reilly Media (formerly O'Reilly & Associates) is an American media company established by Tim O'Reilly that publishes books and Web sites and produces conferences on computer technology topics.

## Quake III Arena

Quake III Arena is a multiplayer-focused first-person shooter video game released in December 1999.

## QuakeCon

QuakeCon is a yearly convention held by ZeniMax Media to celebrate and promote the major franchises of id Software and other studios owned by ZeniMax.

## Rate of convergence

In numerical analysis, the speed at which a convergent sequence approaches its limit is called the rate of convergence.

## Reflection (computer graphics)

Reflection in computer graphics is used to emulate reflective objects like mirrors and shiny surfaces.

## Root-finding algorithm

In mathematics and computing, a root-finding algorithm is an algorithm for finding roots of continuous functions.

## SGI Indigo

The Indigo, introduced as the IRIS Indigo, is a line of workstation computers developed and manufactured by Silicon Graphics, Inc. (SGI).

## Shader

In computer graphics, a shader is a type of computer program that was originally used for shading (the production of appropriate levels of light, darkness, and color within an image) but which now performs a variety of specialized functions in various fields of computer graphics special effects or does video post-processing unrelated to shading, or even functions unrelated to graphics at all.

## Shading

Shading refers to depicting depth perception in 3D models or illustrations by varying levels of darkness.

## 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.

## Stardent Inc.

Stardent Computer, Inc. was a manufacturer of graphics supercomputer workstations in the late 1990s.

## Streaming SIMD Extensions

In computing, Streaming SIMD Extensions (SSE) is an SIMD instruction set extension to the x86 architecture, designed by Intel and introduced in 1999 in their Pentium III series of processors shortly after the appearance of AMD's 3DNow!.

## Transform, clipping, and lighting

Transform, clipping, and lighting (T&L or sometimes TCL) is a term used in computer graphics.

## Trial and error

Trial and error is a fundamental method of problem solving.

## Undefined behavior

In computer programming, undefined behavior (UB) is the result of executing computer code whose behavior is not prescribed by the language specification to which the code adheres, for the current state of the program.

## Uniform norm

In mathematical analysis, the uniform norm (or sup norm) assigns to real- or complex-valued bounded functions f defined on a set S the non-negative number This norm is also called the supremum norm, the Chebyshev norm, or the infinity norm. The name "uniform norm" derives from the fact that a sequence of functions \ converges to f under the metric derived from the uniform norm if and only if f_n converges to f uniformly.

## Union type

In computer science, a union is a value that may have any of several representations or formats within the same position in memory; or it is a data structure that consists of a variable that may hold such a value.

## Unit vector

In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1.

## Usenet

Usenet is a worldwide distributed discussion system available on computers.

## 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.

## 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).

## 3D computer graphics

3D computer graphics or three-dimensional computer graphics, (in contrast to 2D computer graphics) are graphics that use a three-dimensional representation of geometric data (often Cartesian) that is stored in the computer for the purposes of performing calculations and rendering 2D images.

## 3dfx Interactive

3dfx Interactive was a company headquartered in San Jose, California, founded in 1994, that specialized in the manufacturing of 3D graphics processing units, and later, graphics cards.

## References

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