Question

Does F# have a built in cube root function? I know I can use exponentiation to compute cuberoots but it won’t type check in my case since I want to take the cuberoot of a quantity of type float and get a float.

Answer 1

I don’t think there is a built-in function to calculate the cube root with units of measure (I assume it would be in the primitive operators module where sqrt and others are), so I think the only option is to use exponentiation.

However, you can use exponentiation without units and wrap the unit-unsafe operation in a function that adds units, so you get function with correct units:

let cuberoot (f:float<'m^3>) : float<'m> = 
  System.Math.Pow(float f, 1.0/3.0) |> LanguagePrimitives.FloatWithMeasure

Note that F# does not support fractional units so you can write cuberoot (10.0<m^3>) or cuberoot (10.0<m^9>), but if you write cuberoot (10.0<m>) then it will not type-check, because the result would be meters to 1/3 (and that’s a fractional unit).

This sample is only implementing cuberoot for float. If you wanted to write overloaded function that works with other numeric types (I guess you might need float32) then it gets a bit uglier (so I would not recommend that unless necessary), but you can use a trick with intermediate type with multiple overloads like, for example, in this answer.