Clarify inverse of functions

[AHaumer]

First, the first box in chapter 12.7.3 Using the Inverse Annotation a bracket is missing:
annotation ( inverse (uk = f2(. . ., y, . . .));
annotation ( inverse (uk = f2(. . ., y, . . .)));

Second, to me it is not clear whether pairs of a function and its inverse should both have the inverse annotation,
i.e. looking at Modelica.Math:
sin is the inverse of asin and asin is the inverse of sin
and so on ... (cos, tan, sinh, cosh, tanh. exp)

see also: #4751

[HansOlsson]

The missing end-parenthesis shall be corrected.

For inverses of inverses:

• I don't see a need for inverses for the built-in functions.
• For other functions it depends, and I would say it depends on whether it is likely that the function needs to be inverted. Adding inverses increases the maintenance burden, so the benefits should outweigh that cost. For specific cases it varies:
  • Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_laminar_DP and Modelica.Fluid.Dissipation.PressureLoss.StraightPipe.dp_laminar_MFLOW are each other inverses
  • Modelica.Fluid.Fittings.BaseClasses.Bends.CurvedBend.massFlowRate has the inverse Modelica.Fluid.Fittings.BaseClasses.Bends.CurvedBend.pressureLoss - which instead is supposed to be inlined, and that inlined function version has an inverse.
  • Modelica.Media.Interfaces.PartialMedium.specificEnthalpy_pTX has an inverse without an inverse.

[AHaumer]

Are functions suggested for inlining inlined in ALL simulators? AFAIK this is only a recommendation.

[HansOlsson]

Are functions suggested for inlining inlined in ALL simulators? AFAIK this is only a recommendation.

They are not, and it's complicated: not all functions with Inline=true are inlined. It depends on the function, the tool, and the usage.

And similarly inverses are also just a recommendation.

[HansOlsson]

I just realized that the inverse-part is a bit more complicated, and I think it best to say nothing about the inverse of the inverse.

The inverse is defined so that it should be valid for all valid inputs - that means that asin has the inverse sin, but sin doesn't have the inverse asin (since sin isn't fully invertible). Tools can handle those built-in functions in a better way to avoid that problem.

But it indicates that one shouldn't automatically add inverse of inverse; and since it is already stressed that it must be a valid inverse for all values I don't think we need to add more.