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Let's learn SQL

POWER and SQRT functions

S.I.Moiseenko

The SQL Server POWER (x, y) function raises x to the power of y.
x is an expression of type FLOAT or of a type that can be implicitly converted to FLOAT.
y is an expression of a numeric type.

The returned result has the same type as x.

The returned result is of FLOAT type.

SQRT is the inverse function of POWER(x, 2), so that SQRT(POWER(x,2)) should return x.

Let’s check this

select 3 x, power(3,2) y, sqrt(power(3,2)) sqrt_y;

x	y	sqrt_y
3	9	3

This is correct. However,

select 3.1 x, power(3.1,2) y, sqrt(power(3.1,2)) sqrt_y;

yields

x	y	sqrt_y
3.1	9.6	3,09838667696593

This unexpected result in most likelihood has to do with a loss of precision when the POWER function result type (which matches the type of the argument, NUMERIC) is implicitly converted to FLOAT.

Indeed,

select SQL_VARIANT_PROPERTY(3.1,'BASETYPE') basetype;

basetype
numeric

When we apply an equivalent conversion to retain the NUMERIC type for the result

select 3.1 x, power(3.1,2) y, power(power(3.1,2),0.5) sqrt_y;

everything works as expected.

x	y	sqrt_y
3.1	9.6	3.1

Read more...

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