fix: correct interpretation for compile with AutoReverseDiff (#613)

* fix: correct interpretation for `compile` with `AutoReverseDiff`

* Fix static arrays

* Wrong arg order

Author: gdalle

DifferentiationInterface/Project.toml

@@ -1,7 +1,7 @@
 name = "DifferentiationInterface"
 uuid = "a0c0ee7d-e4b9-4e03-894e-1c5f64a51d63"
 authors = ["Guillaume Dalle", "Adrian Hill"]
-version = "0.6.20"
+version = "0.6.21"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"

DifferentiationInterface/docs/src/explanation/backends.md

@@ -144,14 +144,18 @@ Most operators fall back on `AutoForwardDiff`.
 
 ### ReverseDiff
 
-Wherever possible, preparation records a [tape](https://juliadiff.org/ReverseDiff.jl/dev/api/#The-AbstractTape-API) of the function's execution.
-This tape is computed from the arguments `x` and `contexts...` provided at preparation time.
+With `AutoReverseDiff(compile=false)`, preparation preallocates a [config](https://juliadiff.org/ReverseDiff.jl/dev/api/#The-AbstractConfig-API).
+
+With `AutoReverseDiff(compile=true)`, preparation records a [tape](https://juliadiff.org/ReverseDiff.jl/dev/api/#The-AbstractTape-API) of the function's execution.
+This tape is computed from the input `x` provided at preparation time.
 It is control-flow dependent, so only one branch is recorded at each `if` statement.
 
 !!! danger
     If your function has value-specific control flow (like `if x[1] > 0` or `if c == 1`), you may get silently wrong results whenever it takes new branches that were not taken during preparation.
     You must make sure to run preparation with an input and contexts whose values trigger the correct control flow for future executions.
 
+Whenever contexts are provided, tape recording is deactivated in all cases, because otherwise the context values would be hardcoded into a tape.
+
 ### Symbolics
 
 For all operators, preparation generates an [executable function](https://docs.sciml.ai/Symbolics/stable/manual/build_function/) from the symbolic expression of the differentiated function.

DifferentiationInterface/ext/DifferentiationInterfaceReverseDiffExt/DifferentiationInterfaceReverseDiffExt.jl

@@ -20,6 +20,7 @@ using ReverseDiff.DiffResults:
     DiffResults, DiffResult, GradientResult, HessianResult, MutableDiffResult
 using LinearAlgebra: dot, mul!
 using ReverseDiff:
+    ReverseDiff,
     CompiledGradient,
     CompiledHessian,
     CompiledJacobian,
@@ -29,7 +30,6 @@ using ReverseDiff:
     HessianTape,
     JacobianConfig,
     JacobianTape,
-    compile,
     gradient,
     gradient!,
     hessian,