Optimal starting approximations for generating square root for slow or no divide
Communications of the ACM
A class of algorithms for automatic evaluation of certain elementary functions in a binary computer
A class of algorithms for automatic evaluation of certain elementary functions in a binary computer
The logic of computer arithmetic
The logic of computer arithmetic
IEEE Transactions on Computers
Fast multiplication cellular arrays for LSI implementation
AFIPS '69 (Fall) Proceedings of the November 18-20, 1969, fall joint computer conference
The IBM system/360 model 91: floating-point execution unit
IBM Journal of Research and Development
CMOS floating-point unit for the S/390 parallel enterprise server G4
IBM Journal of Research and Development - Special issue: IBM S/390 G3 and G4
Radix-16 Evaluation of Certain Elementary Functions
IEEE Transactions on Computers
The S/390 G5 floating-point unit
IBM Journal of Research and Development
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With the increasing availability of high-speed multiplication units in large computers it is attractive to develop an iterative procedure to compute division and square root, using multiplication as the primary operation. In this paper, we present three new methods of performing square rooting rapidly which utilize multiplication and no division. Each algorithm is considered for convergence rate, efficiency, and implementation. The most typical and efficient one of the already-known algorithms which utilizes multiplication, here called the N algorithm, is introduced for the purpose of comparison with the new algorithms. The effect and importance of the initial approximation is considered. (One of the algorithms, here called the G algorithm, is described in detail with the emphasis on its high efficiency.)