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Square Rooting Algorithms for Integer and Floating-Point Numbers
August 1990 (vol. 39 no. 8)
pp. 1025-1029

An algorithm for evaluating the square root of integers and real numbers is developed. The procedure consists of two parts: one to obtain a close estimate of the square root and the other to modify the initial value, iteratively, until a precise root is evaluated. The major effort in this development has been concentrated on two objectives: high speed and no division operation other than division by 2. The first objective is achieved through a simple two-step procedure for getting the first estimate, and then modifying it by employing a fast converging iteration technique. The second objective is also fulfilled through applying bit-shift operation rather than division operation. The algorithm is simulated for both integer and real numbers, and the results are compared to two methods being widely used. The results (tabulated) show considerable improvement in speed compared to these other two methods.

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Index Terms:
square rooting algorithms; integer numbers; initial value modification; floating-point numbers; real numbers; close estimate; precise root; division by 2; fast converging iteration; bit-shift operation; digital arithmetic; iterative methods; number theory.
R. Hashemian, "Square Rooting Algorithms for Integer and Floating-Point Numbers," IEEE Transactions on Computers, vol. 39, no. 8, pp. 1025-1029, Aug. 1990, doi:10.1109/12.57041
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