diff --git a/lib/JLArrays/src/JLArrays.jl b/lib/JLArrays/src/JLArrays.jl
index 632ea107..ac355538 100644
--- a/lib/JLArrays/src/JLArrays.jl
+++ b/lib/JLArrays/src/JLArrays.jl
@@ -13,6 +13,12 @@ import KernelAbstractions: Adapt, StaticArrays, Backend, Kernel, StaticSize, Dyn
 
 export JLArray, JLVector, JLMatrix, jl, JLBackend
 
+#
+# Device functionality
+#
+
+const MAXTHREADS = 256
+
 struct JLBackend <: KernelAbstractions.GPU
     static::Bool
     JLBackend(;static::Bool=false) = new(static)
diff --git a/src/host/broadcast.jl b/src/host/broadcast.jl
index c9295c3a..d117a24c 100644
--- a/src/host/broadcast.jl
+++ b/src/host/broadcast.jl
@@ -47,7 +47,8 @@ end
         @inbounds dest[I] = bc′[I]
     end
 
-    broadcast_kernel(get_backend(dest))(dest, bc′, ndrange = size(dest))
+    # ndrange set for a possible 0D evaluation
+    broadcast_kernel(get_backend(dest))(dest, bc′, ndrange = length(size(dest)) > 0 ? size(dest) : (1,))
 
     return dest
 end
diff --git a/src/host/construction.jl b/src/host/construction.jl
index 8cd926ad..2c1cf84d 100644
--- a/src/host/construction.jl
+++ b/src/host/construction.jl
@@ -15,7 +15,10 @@ function Base.fill!(A::AnyGPUArray{T}, x) where T
         idx = @index(Global, Linear)
         @inbounds a[idx] = val
     end
-    fill_kernel!(get_backend(A))(A, x, ndrange = size(A))
+
+    # ndrange set for a possible 0D evaluation
+    fill_kernel!(get_backend(A))(A, x,
+                                 ndrange = length(size(A)) > 0 ? size(A) : (1,))
     A
 end
 
diff --git a/src/host/linalg.jl b/src/host/linalg.jl
index ab5bd55b..6b31645a 100644
--- a/src/host/linalg.jl
+++ b/src/host/linalg.jl
@@ -92,7 +92,7 @@ function LinearAlgebra.copytri!(A::AbstractGPUMatrix{T}, uplo::AbstractChar, con
               @inbounds _A[j,i] = conj(_A[i,j])
             end
         end
-        U_conj!(get_backend(_A), ndrange = size(_A))
+        U_conj!(get_backend(A))(A, ndrange = size(A))
     elseif uplo == 'U' && !conjugate
         @kernel function U_noconj!(_A)
             I = @index(Global, Cartesian)
@@ -101,7 +101,7 @@ function LinearAlgebra.copytri!(A::AbstractGPUMatrix{T}, uplo::AbstractChar, con
               @inbounds _A[j,i] = _A[i,j]
             end
         end
-        U_noconj!(get_backend(_A))(_A, ndrange=size(_A))
+        U_noconj!(get_backend(A))(A, ndrange = size(A))
     elseif uplo == 'L' && conjugate
         @kernel function L_conj!(_A)
             I = @index(Global, Cartesian)
@@ -110,7 +110,7 @@ function LinearAlgebra.copytri!(A::AbstractGPUMatrix{T}, uplo::AbstractChar, con
               @inbounds _A[i,j] = conj(_A[j,i])
             end
         end
-        L_conj!(get_backend(_A))(_A, ndrange = size(_A))
+        L_conj!(get_backend(A))(A, ndrange = size(A))
     elseif uplo == 'L' && !conjugate
         @kernel function L_noconj!(_A)
             I = @index(Global, Cartesian)
@@ -119,7 +119,7 @@ function LinearAlgebra.copytri!(A::AbstractGPUMatrix{T}, uplo::AbstractChar, con
               @inbounds _A[i,j] = _A[j,i]
             end
         end
-        L_noconj!(get_backend(_A))(_A, ndrange = size(_A))
+        L_noconj!(get_backend(A))(A, ndrange = size(A))
     else
         throw(ArgumentError("uplo argument must be 'U' (upper) or 'L' (lower), got $uplo"))
     end
@@ -178,7 +178,7 @@ function LinearAlgebra.tril!(A::AbstractGPUMatrix{T}, d::Integer = 0) where T
       @inbounds _A[i, j] = zero(T)
     end
   end
-  tril_kernel!(get_backend(_A))(_A, _d, ndrange = size(_A))
+  tril_kernel!(get_backend(A))(A, d, ndrange = size(A))
   return A
 end
 
@@ -190,7 +190,7 @@ function LinearAlgebra.triu!(A::AbstractGPUMatrix{T}, d::Integer = 0) where T
       @inbounds _A[i, j] = zero(T)
     end
   end
-  triu_kernel!(get_backend(_A))(_A, _d, ndrange = length(_A))
+  triu_kernel!(get_backend(A))(A, d, ndrange = size(A))
   return A
 end
 
@@ -423,7 +423,7 @@ LinearAlgebra.rmul!(A::AbstractGPUArray, b::Number) = generic_rmul!(A, b)
 
 function generic_lmul!(s::Number, X::AbstractArray)
     @kernel function lmul_kernel!(X, s)
-        i = @index(Global, linear)
+        i = @index(Global, Linear)
         @inbounds X[i] = s*X[i]
     end
     lmul_kernel!(get_backend(X))(X, s, ndrange = size(X))
diff --git a/src/host/math.jl b/src/host/math.jl
index 9bd804a5..f96fb8ed 100644
--- a/src/host/math.jl
+++ b/src/host/math.jl
@@ -1,7 +1,7 @@
 # Base mathematical operations
 
 function Base.clamp!(A::AnyGPUArray, low, high)
-    @kernel function clamp_kernel!(A::AnyGPUArray, low, high)
+    @kernel function clamp_kernel!(A, low, high)
         I = @index(Global, Cartesian)
         A[I] = clamp(A[I], low, high)
     end
diff --git a/src/host/random.jl b/src/host/random.jl
index 2b08509b..d79b1a94 100644
--- a/src/host/random.jl
+++ b/src/host/random.jl
@@ -86,10 +86,9 @@ end
 function Random.rand!(rng::RNG, A::AnyGPUArray{T}) where T <: Number
     @kernel function rand!(a, randstate)
         idx = @index(Global, Linear)
-        @inbounds a[idx] = gpu_rand(T, idx, randstates)
+        @inbounds a[idx] = gpu_rand(T, idx, randstate)
     end
-    kernel = rand!(get_backend(A))
-    kernel(A, rng.state)
+    rand!(get_backend(A))(A, rng.state, ndrange = size(A))
     A
 end