test/methods: (in progress) add explicit adapt parameter cases to Unitful tests

These seem to at least produce correct units, but the numerical value is
wrong for the adapt=0 case (not surprising, based on the documentation).

The question is, why the heck do things go wrong, when you do not give
an explicit adapt value, but leave it to the compiler-generated method
that inserts the value adapt=1 automatically.

Author: SeSodesa

test/methods.jl

@@ -91,10 +91,27 @@ struct NotAFunction end # not <: Function on purpose, cf #224
 
     # Integration test to ensure that Unitful-output functions can be tested.
     @testset "Unitful output" begin
+
         fn(x) = 5.0u"J/s" * x
-        @show derivativeVal = central_fdm(5, 1)(fn, 1.0u"s/J")
-        @test unit(derivativeVal) == u"J/s"
-        @test isapprox(derivativeVal, 5.0u"J/s"; rtol=1e-12, atol=1e-12u"J/s")
+
+        derivativeVal = 5.0u"J/s"
+
+        # NOTE: the input value unit is wrong here to make this run at all!
+        # The unit should be u"s", but it has to be the inverse of the desired output unit.
+        # TODO: Find out the faulty code path using a debugger.
+        twoPlaceDerivativeVal = central_fdm(5, 1)(fn, 1.0u"s/J")
+
+        unadaptedDerivativeVal = central_fdm(5, 1)(fn, 1.0u"s",0)
+
+        adaptedDerivativeVal = central_fdm(5, 1)(fn, 1.0u"s",1)
+
+        @test unit(twoPlaceDerivativeVal) == u"J/s"
+        @test unit(unadaptedDerivativeVal) == u"J/s"
+        @test unit(adaptedDerivativeVal) == u"J/s"
+
+        @test isapprox(twoPlaceDerivativeVal, 5.0u"J/s"; rtol=1e-12, atol=1e-12u"J/s")
+        @test isapprox(unadaptedDerivativeVal, 5.0u"J/s"; rtol=1e-12, atol=1e-12u"J/s")
+        @test isapprox(adaptedDerivativeVal, 5.0u"J/s"; rtol=1e-12, atol=1e-12u"J/s")
     end
 
     @testset "Adaptation improves estimate" begin