The justification for this definition is to preserve the sign of the result in case of arithmetic underflow.
2.
The log form of the geometric mean is generally the preferred alternative for implementation in computer languages because calculating the product of many numbers can lead to an arithmetic overflow or arithmetic underflow.
3.
In a computer implementation, as the three " s " " j " sums become large, we need to consider round-off error, arithmetic overflow, and arithmetic underflow.
4.
However the squares of very large or small values of " x " and " y " may exceed the range of machine precision when calculated on a computer, leading to an inaccurate result caused by arithmetic underflow and / or arithmetic overflow.
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