If either argument is NaN, then the result is NaN. If the first argument is positive zero and the second argument is positive, or the first argument is positive and finite and the second argument is positive infinity, then the result is positive zero. If the first argument is negative zero and the second argument is positive, or the first argument is negative and finite and the second argument is positive infinity, then the result is negative zero.
At the time, floating-point division was generally expensive compared to multiplication; the fast inverse square root algorithm bypassed the division step, giving it its performance advantage.
Quake III Arena, a first-person shooter video game, used the fast inverse square root algorithm to accelerate graphics computation, but the algorithm has since been implemented in some dedicated hardware vertex shaders using field-programmable gate arrays FPGA.
Common software methods in the early s drew approximations from a lookup table. The algorithm was approximately four times faster than computing the square root with another method and calculating the reciprocal via floating-point division.
The purpose of the constant is not immediately clear to someone viewing the code, so, like other such constants found in code, it is often called a magic number.
One iteration of Newton's method is performed to gain some accuracy, and the code is finished. The algorithm generates reasonably accurate results using a unique first approximation for Newton's method ; however, it is much slower and less accurate than using the SSE instruction rsqrtss on x86 processors also released in The proper way to accomplish the fast inverse square root, in a more standard conforming way, is to type-pun floating point values and integers through a union type.
The first steps of the algorithm are illustrated below: Single-precision floating-point format Since this algorithm relies heavily on the bit-level representation of single-precision floating-point numbers, a short overview of this representation is provided here.
In order to encode a non-zero real number x as a single precision float, the first step is to write x as a normalized binary number:B = sqrt(X) returns the square root of each element of the array X. For the elements of X that are negative or complex, sqrt(X) produces complex results.
The sqrt function’s domain includes negative and complex numbers, which can lead to unexpected results if used unintentionally. A Computer Science portal for geeks.
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Perhaps the first algorithm used for approximating is known as the Babylonian method, named after the Babylonians, or "Heron's method", named after the first-century Greek mathematician Hero of Alexandria who gave the first explicit description of the method. It can be derived from (but predates by 16 centuries) Newton's rutadeltambor.com basic idea is that if x .
Floor of square root of x cannot be more than x/2 when x > 1. Thanks to vinit for suggesting above optimization. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
ruby: Capitalized variables contain constants and class/module names. By convention, constants are all caps and class/module names are camel case.