Properly rounded variable precision square root

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Abstract
The square root function presented here returns a properly rounded approximation to the square root of its argument, or it raises an error condition if the argument is negative. Properly rounded means rounded to the nearest, or to nearest even in case of a tie. It is variable precision in that it is designed to return a p -digit approximation to a p -digit argument, for any p > 0. (Precision p means p decimal digits.) The program and the analysis are valid for all p > 0, but current implementations place some restrictions on p .

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