Better explanation of preparation (#536)

* Clarify documentation on preparation

* Handle Val in Enzyme

DifferentiationInterface/docs/src/explanation/backends.md

@@ -137,9 +137,12 @@ For every operator, preparation generates an [executable function](https://brian
 ### FiniteDiff
 
 Whenever possible, preparation creates a cache object.
+Pushforward is implemented rather slowly using a closure.
 
 ### FiniteDifferences
 
+Nothing specific to mention.
+
 ### ForwardDiff
 
 We implement [`pushforward`](@ref) directly using [`Dual` numbers](https://juliadiff.org/ForwardDiff.jl/stable/dev/how_it_works/), and preparation allocates the necessary space.
@@ -152,9 +155,12 @@ 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.
+It is control-flow dependent, so only one branch is recorded at each `if` statement.
 
-!!! warning
-    This tape is specific to the control flow inside the function, and cannot be reused if the control flow is value-dependent (like `if x[1] > 0`).
+!!! 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.
 
 ### Symbolics
 
@@ -176,4 +182,3 @@ Same-point preparation runs the forward sweep and returns the pullback closure a
 
 We implement `pullback` based on `Zygote.pullback`.
 Same-point preparation runs the forward sweep and returns the pullback closure at `x`.
-

DifferentiationInterface/docs/src/explanation/operators.md

@@ -125,13 +125,14 @@ Here are the general rules that we strive to implement:
 
 For different-point preparation, the output `prep` of `prepare_op(f, b, x, [t])` can be reused in `op(f, prep, b, other_x, [other_t])`, provided that:
 
-- the inputs `x` and `other_x` have similar types and equal shapes
-- the tangents in `t` and `other_t` have similar types and equal shapes
+- the inputs `x` and `other_x` have the same types and sizes
+- the tangents in `t` and `other_t` have the same types and sizes
 
 For same-point preparation, the output `prep` of `prepare_op_same_point(f, b, x, [t])` can be reused in `op(f, prep, b, x, other_t)`, provided that:
 
-- the input `x` remains the same (as well as the [`Context`](@ref) constants)
-- the tangents in `t` and `other_t` have similar types and equal shapes
+- the input `x` remains exactly the same (as well as any [`Constant`](@ref) context)
+- the tangents in `t` and `other_t` have the same types and sizes
 
 !!! warning
-    These rules hold for the majority of backends, but there are some exceptions.
+    These rules hold for the majority of backends, but there are some exceptions.
+    The most important exception is [ReverseDiff](@ref) and its taping mechanism, which is sensitive to control flow inside the function.

DifferentiationInterface/ext/DifferentiationInterfaceEnzymeExt/forward_onearg.jl

@@ -117,8 +117,8 @@ end
 function DI.prepare_gradient(
     f::F, backend::AutoEnzyme{<:ForwardMode,<:Union{Nothing,Const}}, x
 ) where {F}
-    B = pick_batchsize(backend, length(x))
-    shadows = create_shadows(Val(B), x)
+    valB = pick_batchsize(backend, length(x))
+    shadows = create_shadows(valB, x)
     return EnzymeForwardGradientPrep{B,typeof(shadows)}(shadows)
 end
 
@@ -180,8 +180,8 @@ function DI.prepare_jacobian(
     f::F, backend::AutoEnzyme{<:Union{ForwardMode,Nothing},<:Union{Nothing,Const}}, x
 ) where {F}
     y = f(x)
-    B = pick_batchsize(backend, length(x))
-    shadows = create_shadows(Val(B), x)
+    valB = pick_batchsize(backend, length(x))
+    shadows = create_shadows(valB, x)
     return EnzymeForwardOneArgJacobianPrep{B,typeof(shadows)}(shadows, length(y))
 end
 

DifferentiationInterface/ext/DifferentiationInterfaceEnzymeExt/reverse_onearg.jl

@@ -349,11 +349,15 @@ end
 
 struct EnzymeReverseOneArgJacobianPrep{Sy,B} <: JacobianPrep end
 
+function EnzymeReverseOneArgJacobianPrep(::Val{Sy}, ::Val{B}) where {Sy,B}
+    return EnzymeReverseOneArgJacobianPrep{Sy,B}()
+end
+
 function DI.prepare_jacobian(f::F, backend::AutoEnzyme{<:ReverseMode,Nothing}, x) where {F}
     y = f(x)
     Sy = size(y)
-    B = pick_batchsize(backend, prod(Sy))
-    return EnzymeReverseOneArgJacobianPrep{Sy,B}()
+    valB = pick_batchsize(backend, prod(Sy))
+    return EnzymeReverseOneArgJacobianPrep(Val(Sy), valB)
 end
 
 function DI.jacobian(