Lighting and reflection calculations, as in the video game OpenArena, use the fast inverse square root code to compute angles of incidence and reflection.
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. The algorithm is best known for its implementation in 1999 in Quake III Arena, a first-person shooter video game heavily based on 3D graphics. With subsequent hardware advancements, especially the x86 SSE instruction rsqrtss, this algorithm is not generally the best choice for modern computers,[1] though it remains an interesting historical example.[2]
The algorithm accepts a 32-bit floating-point number as the input and stores a halved value for later use. Then, treating the bits representing the floating-point number as a 32-bit integer, a logical shift right by one bit is performed and the result subtracted from the number 0x5F3759DF, which is a floating-point representation of an approximation of .[3] This results in the first approximation of the inverse square root of the input. Treating the bits again as a floating-point number, it runs one iteration of Newton's method, yielding a more precise approximation.
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Fastinversesquareroot, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF, is an algorithm that estimates 1 x {\textstyle...
may be preferable to compute the inversesquareroot instead. Other methods are available to compute the squareroot digit by digit, or using Taylor series...
with approximately 9,400 active players in 2018. Fastinversesquareroot, sometimes referred to as Fast InvSqrt() or by the hexadecimal constant 0x5F3759DF...
example the model outputted the training data code implementing the fastinversesquareroot algorithm, including comments and an incorrect copyright notice...
function is bijective and so, invertible. The inverse function here is called the (positive) squareroot function and is denoted by x ↦ x {\displaystyle...
undefined behaviour. For example, passing a negative number to the fastinversesquareroot function will produce a number. Not a very useful number, but the...
{\displaystyle (x_{0},y_{0},z_{0})} is the center of the metaball. The fastinversesquareroot technique may be used in this calculation. Various other falloff...
information. Binomial inverse theorem LU decomposition Matrix decomposition Matrix squareroot Minor (linear algebra) Partial inverse of a matrix Pseudoinverse...
allows for a fast approximation of the base-2 logarithm, leading to algorithms e.g. for computing the fastsquare-root and fastinverse-square-root. The implicit...
Practical examples of floating-point punning include fastinversesquareroot popularized by Quake III, fast FP comparison as integers, and finding neighboring...
radical sign 3 . {\displaystyle {\sqrt[{3}]{~^{~}}}.} The cube root is the inverse function of the cube function if considering only real numbers, but...
and complex numbers. The two inverses of tetration are called super-root and super-logarithm, analogous to the nth root and the logarithmic functions...
first used in Enemy Territory: Quake Wars. Quake 3 popularized the fastinversesquareroot algorithm. Carmack's engines have also been licensed for use in...
the principal branch of the natural log and squareroot functions to the usual principal branch of the inverse trig functions, the particular form of the...
y2)1/2 Alpha max plus beta min algorithm — approximates hypot(x,y) Fastinversesquareroot — calculates 1 / √x using details of the IEEE floating-point system...
than in a square wave (proportional to the inversesquare of the harmonic number as opposed to just the inverse). A triangle wave of period p that spans...
expensive computation (3 ** x) to be replaced by the cheaper (3 * z). Fastinversesquareroot Hacker's Delight Partial evaluation Steven Muchnick; Muchnick and...
inverse golden ratio and minus golden ratio. For n = 8, for any root of unity z + z equals to either 0, ±2, or ±√2 (D = 2). For n = 12, for any root of...
A Fast Fourier Transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). Fourier analysis...
According to the inverse function theorem, the matrix inverse of the Jacobian matrix of an invertible function is the Jacobian matrix of the inverse function...
attributes of the complex DFT, including the inverse transform, the convolution theorem, and most fast Fourier transform (FFT) algorithms, depend only...
crucially on the availability of a fast algorithm to compute discrete Fourier transforms and their inverses, a fast Fourier transform. When the DFT is...
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