Add the Enzyme rules example.

Author: ludgerpaehler

julia_custom/custom.jl

@@ -0,0 +1,49 @@
+using Enzyme
+using Enzyme: EnzymeRules
+
+# Defining our function
+f(x) = x^2;
+
+function f_ip(x)
+    x[1] *= x[1]
+    return nothing
+ end
+ 
+ import .EnzymeRules: augmented_primal, reverse, Annotation, has_rrule, has_rrule_from_sig
+ using .EnzymeRules
+
+ function augmented_primal(config::ConfigWidth{1}, func::Const{typeof(f)}, ::Type{<:Active}, x::Active)
+    if needs_primal(config)
+        return AugmentedReturn(func.val(x.val), nothing, nothing)
+    else
+        return AugmentedReturn(nothing, nothing, nothing)
+    end
+end
+
+function reverse(config::ConfigWidth{1}, ::Const{typeof(f)}, dret::Active, tape, x::Active)
+    if needs_primal(config)
+        return (10+2*x.val*dret.val,)
+    else
+        return (100+2*x.val*dret.val,)
+    end
+end
+
+function augmented_primal(::Config{false, false, 1}, func::Const{typeof(f_ip)}, ::Type{<:Const}, x::Duplicated)
+    v = x.val[1]
+    x.val[1] *= v
+    return AugmentedReturn(nothing, nothing, v)
+end
+
+function reverse(::Config{false, false, 1}, ::Const{typeof(f_ip)}, ::Type{<:Const}, tape, x::Duplicated)
+    x.dval[1] = 100 + x.dval[1] * tape
+    return ()
+end
+
+# To which we can then apply the Enzyme calls
+Enzyme.autodiff(Enzyme.Reverse, f, Active(2.0))[1][1];
+Enzyme.autodiff(Enzyme.Reverse, x->f(x)^2, Active(2.0))[1][1];
+
+x = [2.0];
+dx = [1.0];
+
+Enzyme.autodiff(Enzyme.Reverse, f_ip, Duplicated(x, dx));