This information is part of the Modelica Standard Library maintained by the Modelica Association.

This function approximates sqrt(abs(x))*sgn(x), such that the derivative is finite and smooth in x=0.

Function	Approximation	Range
y = regRoot(x)	y ~= sqrt(abs(x))*sgn(x)	abs(x) >>delta
y = regRoot(x)	y ~= x/sqrt(delta)	abs(x) << delta

With the default value of delta=0.01, the difference between sqrt(x) and regRoot(x) is 16% around x=0.01, 0.25% around x=0.1 and 0.0025% around x=1.

y = regRoot(x, delta)

x	Type: Real
delta	Default Value: 0.01 Type: Real Description: Range of significant deviation from sqrt(abs(x))*sgn(x)

y	Type: Real