Fix some tests

- Fix doctests
- Move _zeroed_backing() to a different file so it's defined before being
  used (otherwise causes failures on 1.13+)
- Use `mergewith(f)` instead of the deprecated `merge(f)`

Author: JamesWrigley

src/rules.jl

@@ -18,11 +18,11 @@ unary input, unary output scalar function:
 ```jldoctest frule
 julia> dself = NoTangent();
 
-julia> x = rand()
-0.8236475079774124
+julia> x = 1.23456
+1.23456
 
 julia> sinx, Δsinx = frule((dself, 1), sin, x)
-(0.7336293678134624, 0.6795498147167869)
+(0.9440031218347901, 0.3299365180851773)
 
 julia> sinx == sin(x)
 true
@@ -51,7 +51,7 @@ that return a single output that is iterable, like a `Tuple`.
 So this is actually a [`Tangent`](@ref):
 ```jldoctest frule
 julia> Δsincosx
-Tangent{Tuple{Float64, Float64}}(0.6795498147167869, -0.7336293678134624)
+Tangent{Tuple{Float64, Float64}}(0.3299365180851773, -0.9440031218347901)
 ```
 
 The optional [`RuleConfig`](@ref) option allows specifying frules only for AD systems that

src/tangent_arithmetic.jl

@@ -142,7 +142,7 @@ function Base.:+(a::P, d::StructuralTangent{P}) where {P}
         return construct(P, net_backing)
     end
 end
-Base.:+(a::Dict, d::Tangent{P}) where {P} = merge(+, a, backing(d))
+Base.:+(a::Dict, d::Tangent{P}) where {P} = mergewith(+, a, backing(d))
 Base.:+(a::StructuralTangent{P}, b::P) where {P} = b + a
 
 Base.:-(tangent::StructuralTangent{P}) where {P} = map(-, tangent)

src/tangent_types/abstract_zero.jl

@@ -201,3 +201,15 @@ zero_tangent(::Core.Compiler.AbstractInterpreter) = NoTangent()
 zero_tangent(::Core.Compiler.InstructionStream) = NoTangent()
 zero_tangent(::Core.CodeInfo) = NoTangent()
 zero_tangent(::Core.MethodInstance) = NoTangent()
+
+"""
+    _zeroed_backing(P)
+
+Returns a NamedTuple with same fields as `P`, and all values `ZeroTangent()`.
+"""
+@generated function _zeroed_backing(::Type{P}) where {P}
+    nil_base = ntuple(fieldcount(P)) do i
+        (fieldname(P, i), ZeroTangent())
+    end
+    return (; nil_base...)
+end

src/tangent_types/structural_tangent.jl

@@ -208,18 +208,6 @@ function backing(x::T)::NamedTuple where {T}
     end
 end
 
-"""
-    _zeroed_backing(P)
-
-Returns a NamedTuple with same fields as `P`, and all values `ZeroTangent()`.
-"""
-@generated function _zeroed_backing(::Type{P}) where {P}
-    nil_base = ntuple(fieldcount(P)) do i
-        (fieldname(P, i), ZeroTangent())
-    end
-    return (; nil_base...)
-end
-
 """
     construct(::Type{T}, fields::[NamedTuple|Tuple])
 
@@ -299,7 +287,7 @@ function elementwise_add(a::NamedTuple{an}, b::NamedTuple{bn}) where {an,bn}
     end
 end
 
-elementwise_add(a::Dict, b::Dict) = merge(+, a, b)
+elementwise_add(a::Dict, b::Dict) = mergewith(+, a, b)
 
 struct PrimalAdditionFailedException{P} <: Exception
     primal::P

src/tangent_types/thunks.jl

@@ -179,8 +179,7 @@ To evaluate the wrapped closure, call [`unthunk`](@ref) which is a no-op when th
 argument is not a `Thunk`.
 
 ```jldoctest
-julia> t = @thunk(3)
-Thunk(var"#4#5"())
+julia> t = @thunk(3);
 
 julia> unthunk(t)
 3

test/projection.jl

@@ -457,7 +457,12 @@ struct NoSuperType end
         @test 0 == @ballocated $pdiag(dx) setup = (dx = Diagonal(rand(10^3)))
 
         psymm = ProjectTo(Symmetric(rand(10^3, 10^3)))
-        @test_broken 0 == @ballocated $psymm(dx) setup = (dx = Symmetric(rand(10^3, 10^3)))  # 64
+        allocs = @ballocated $psymm(dx) setup = (dx = Symmetric(rand(10^3, 10^3)))  # 64
+        if VERSION > v"1.13"
+            @test 0 == allocs
+        else
+            @test_broken 0 == allocs
+        end
     end
 
     @testset "#685" begin