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Computing Square Roots in Quaternion Algebras

Koprowski Przemysław

Fundamenta Informaticae

2022

Vol. 190, nr 1

1--15

We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.

FPGA realization of an improved alpha max plus beta min algorithm

Czyżak M., Smyk R.

Poznan University of Technology Academic Journals. Electrical Engineering

2014

No. 80

151--160

The improved version of the alpha max plus beta min square-rooting algorithm and its realization in the Field Programmable Gate Array (FPGA) are presented. The algorithm computes the square root to calculate the approximate magnitude of a complex sample. It is especially useful for pipelined calculations in the DSP. The improved version allows to reduce the peak error from about 4% to 0.33%. This is attained by determination of the approximate ratio of arguments and adequate selection of algorithm coefficients. Four approximation regions are used and hence four sets of coefficients. Also a Xilinx FPGA implementation for 12-bit sign magnitude numbers is shown.