Add support for dealiasing Adjoint and Transpose

And fixup the assumption that `broadcast!(f, C, A)` is safe

base/broadcast.jl

@@ -484,10 +484,13 @@ end
     return C
 end
 
-# In the one-argument case, we don't need to worry about aliasing as we only make one pass
+# In the one-argument case, we can avoid de-aliasing `A` from `C` if
+# `A === C`. Otherwise `A` might be something like `transpose(C)` or
+# another such re-ordering that won't iterate the two safely.
 @inline function _broadcast!(f, C, A)
     shape = broadcast_indices(C)
     @boundscheck check_broadcast_indices(shape, A)
+    A !== C && (A = unalias(C, A))
     keeps, Idefaults = map_newindexer(shape, A, ())
     iter = CartesianIndices(shape)
     _broadcast!(f, C, keeps, Idefaults, A, (), Val(0), iter)

stdlib/LinearAlgebra/src/adjtrans.jl

@@ -47,6 +47,10 @@ end
 Adjoint(A) = Adjoint{Base.promote_op(adjoint,eltype(A)),typeof(A)}(A)
 Transpose(A) = Transpose{Base.promote_op(transpose,eltype(A)),typeof(A)}(A)
 
+using Base: unalias, mightalias, dataids
+Base.unalias(dest, A::Union{Adjoint,Transpose}) = mightalias(dest, A) ? typeof(A)(unalias(dest, A.parent)) : A
+Base.dataids(A::Union{Adjoint,Transpose}) = dataids(A.parent)
+
 # wrapping lowercase quasi-constructors
 """
     adjoint(A)

stdlib/LinearAlgebra/test/adjtrans.jl

@@ -447,4 +447,17 @@ end
     @test adjoint!(b, a) === b
 end
 
+@testset "aliasing with adjoint and transpose" begin
+    A = collect(reshape(1:25, 5, 5)) .+ rand.().*im
+    B = copy(A)
+    B .= B'
+    @test B == A'
+    B = copy(A)
+    B .= transpose(B)
+    @test B == transpose(A)
+    B = copy(A)
+    B .= B .* B'
+    @test B == A .* A'
+end
+
 end # module TestAdjointTranspose