Alpha Max Plus Beta Min Algorithm

The alpha max plus beta min algorithm is a computational shortcut for approximating the square root of the sum of two squares without performing an actual squaring or square-root operation. Instead it computes alpha times the larger of the two absolute values plus beta times the smaller, using fixed constants alpha and beta chosen to minimize error; with commonly used optimal constants, alpha approximately 0.9604 and beta approximately 0.3978, the maximum error is about 3.96 percent. Because it replaces expensive squaring and square-root operations with comparison, multiplication and addition, and because well-chosen constants can reduce the multiplications to simple binary shifts, the algorithm is particularly useful in digital circuit implementations where speed matters more than exact precision; typical applications include estimating a right triangle's hypotenuse from its two other sides, the magnitude of a two-dimensional vector, or the absolute value of a complex number from its real and imaginary parts. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/