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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Alpha max plus beta min algorithm ： ウィキペディア英語版 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. :$|z|\; =\; \backslash sqrt$ 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: :$|z|\; =\; \backslash alpha\backslash ,\backslash !\; \backslash mathbf\; +\; \backslash beta\backslash ,\backslash !\; \backslash mathbf$ Where $\backslash mathbf$ is the maximum absolute value of a and b and $\backslash mathbf$ is the minimum absolute value of a and b. For the closest approximation, the optimum values for $\backslash alpha\backslash ,\backslash !$ and $\backslash beta\backslash ,\backslash !$ are $\backslash alpha\_0\; =\; \backslash frac\}\}\; =\; 0.96043387...$ and $\backslash beta\_0\; =\; \backslash frac\}\}\; =\; 0.39782473...$, giving a maximum error of 3.96%. ==See also== *Hypot, a precise function or algorithm that is also safe against overflow and underflow 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Alpha max plus beta min algorithm」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.