Root-finding algorithms | Pythagorean theorem | Approximation algorithms
Alpha max plus beta min algorithm
The alpha max plus beta min algorithm is a high-speed approximation of the square root of the sum of two squares. The square root of the sum of two squares, also known as Pythagorean addition, is a useful function, because it finds the hypotenuse of a right triangle given the two side lengths, the norm of a 2-D vector, or the magnitude of a complex number z = a + bi given the real and imaginary parts. The algorithm avoids performing the square and square-root operations, instead using simple operations such as comparison, multiplication, and addition. Some choices of the α and β parameters of the algorithm allow the multiplication operation to be reduced to a simple shift of binary digits that is particularly well suited to implementation in high-speed digital circuitry. The approximation is expressed as where is the maximum absolute value of a and b, and is the minimum absolute value of a and b. For the closest approximation, the optimum values for and are and , giving a maximum error of 3.96%. (Wikipedia).
