• Journal of Korea Multimedia Society
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• v.22 no.9
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• IEMEK Journal of Embedded Systems and Applications
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• v.13 no.1
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• pp.45-51
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• 2018

In this paper, a tentative Kth order Newton-Raphson's floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Newton-Raphson root algorithm. Using the proposed algorithm, $F^{-1/N}$ and $F^{-(N-1)/N}$ can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration and iterates only until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.