diff --git a/Project.toml b/Project.toml
index 10e73faf..ba5fe8e4 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "GPUArrays"
 uuid = "0c68f7d7-f131-5f86-a1c3-88cf8149b2d7"
-version = "12.0.0"
+version = "12.0.1"
 
 [workspace]
 projects = ["lib/GPUArraysCore", "lib/JLArrays", "test", "docs"]
diff --git a/src/host/mapreduce.jl b/src/host/mapreduce.jl
index d14ac37d..75583a0c 100644
--- a/src/host/mapreduce.jl
+++ b/src/host/mapreduce.jl
@@ -19,15 +19,18 @@ Base.mapreducedim!(f, op, R::AnyGPUArray, A::AbstractArray) =
     _ak_mapreducedim!(f, op, R, A; backend=get_backend(R))
 Base.mapreducedim!(f, op, R::AnyGPUArray, A::Broadcast.Broadcasted) =
     _ak_mapreducedim!(f, op, R, A; backend=get_backend(R))
-# (LinearAlgebra's methods for adjoint and transposed matrices are ambiguous with these)
-for W in (:Adjoint, :Transpose)
+# (LinearAlgebra's methods for adjoint and transposed matrices, and Base's for permuted
+# arrays, are ambiguous with these)
+for (W, Wnum) in ((:(Adjoint{<:Any, <:AbstractMatrix}), :(Adjoint{<:Union{Real, Complex}, <:AbstractMatrix})),
+                  (:(Transpose{<:Any, <:AbstractMatrix}), :(Transpose{<:Union{Real, Complex}, <:AbstractMatrix})),
+                  (:PermutedDimsArray, :(PermutedDimsArray{<:Union{Real, Complex}})))
     @eval begin
         Base.mapreducedim!(f, op::Union{typeof(&), typeof(|), typeof(+), typeof(Base.add_sum),
                                         typeof(max), typeof(min), typeof(Base._extrema_rf)},
-                           R::AnyGPUArray, A::$W{<:Any, <:AbstractMatrix}) =
+                           R::AnyGPUArray, A::$W) =
             _ak_mapreducedim!(f, op, R, A; backend=get_backend(R))
         Base.mapreducedim!(f::typeof(identity), op::Union{typeof(*), typeof(Base.mul_prod)},
-                           R::AnyGPUArray, A::$W{<:Union{Real, Complex}, <:AbstractMatrix}) =
+                           R::AnyGPUArray, A::$Wnum) =
             _ak_mapreducedim!(f, op, R, A; backend=get_backend(R))
     end
 end
diff --git a/test/testsuite/reductions.jl b/test/testsuite/reductions.jl
index b9f258dd..f6b926f6 100644
--- a/test/testsuite/reductions.jl
+++ b/test/testsuite/reductions.jl
@@ -41,7 +41,9 @@ end
             @test compare((A,R)->Base.mapreducedim!(abs2, +, R, A), AT, rand(range, (3,2,10)), t(zeros(ET, (2,3))))
             # ... and from them (LinearAlgebra has methods for these sources)
             @test compare((A,R)->Base.mapreducedim!(identity, +, R, t(A)), AT, rand(range, (3,4)), zeros(ET, (4,)))
-            @test compare((A,R)->Base.mapreducedim!(abs2, max, R, t(A)), AT, rand(range, (3,4)), zeros(real(ET), (1,3)))
+            # (small values: Intel's compiler gets `abs2` of an overflowing `Complex{Int16}` wrong)
+            small = ET <: Complex ? ET.(complex.(rand(-9:9, 3, 4), rand(-9:9, 3, 4))) : rand(range, (3,4))
+            @test compare((A,R)->Base.mapreducedim!(abs2, max, R, t(A)), AT, small, zeros(real(ET), (1,3)))
             @test compare((A,R)->Base.mapreducedim!(identity, *, R, t(A)), AT, rand(range, (3,4)), ones(ET, (4,)))
 
             # TODO: reenable once https://github.com/JuliaGPU/Metal.jl/issues/907 is fixed
@@ -50,6 +52,12 @@ end
             A, R = AT(rand(range, (3,2,10))), t(AT(zeros(ET, (2,3))))
             @test Base.mapreducedim!(identity, *, R, A) === R
         end
+
+        # ... and from permuted arrays (Base has methods for these sources)
+        p(A) = PermutedDimsArray(A, (3, 1, 2))
+        @test compare((A,R)->Base.mapreducedim!(identity, +, R, p(A)), AT, rand(range, (3,2,4)), zeros(ET, (4,1,1)))
+        ET <: Real && @test compare((A,R)->Base.mapreducedim!(identity, max, R, p(A)), AT, rand(range, (3,2,4)), fill(typemin(ET), (1,3,1)))
+        @test compare((A,R)->Base.mapreducedim!(identity, *, R, p(A)), AT, rand(range, (3,2,4)), ones(ET, (4,1,2)))
     end
 end