Avoid cartesian iteration where possible.

src/host/broadcast.jl

@@ -51,22 +51,53 @@ end
     bc′ = Broadcast.preprocess(dest, bc)
 
     # grid-stride kernel
-    function broadcast_kernel(ctx, dest, bc′, nelem)
-        i = 0
-        while i < nelem
-            i += 1
-            I = @cartesianidx(dest, i)
-            @inbounds dest[I] = bc′[I]
+    function broadcast_kernel(ctx, dest, ::Val{Is}, bc′, nelem) where Is
+        j = 0
+        while j < nelem
+            j += 1
+
+            i = @linearidx(dest, j)
+
+            # cartesian indexing is slow, so avoid it if possible
+            if isa(IndexStyle(dest), IndexCartesian) || isa(IndexStyle(bc′), IndexCartesian)
+                # this performs an integer division, which is expensive. to make it possible
+                # for the compiler to optimize it away, we put the iterator in the type
+                # domain so that the indices are available at compile time. note that LLVM
+                # only seems to replace pow2 divisions (with bitshifts), but other back-ends
+                # may be smarter and replace arbitrary divisions by bit operations.
+                #
+                # also see maleadt/StaticCartesian.jl, which implements this in Julia,
+                # but does not result in an additional speed-up on tested back-ends.
+                #
+                # in addition, we use @inbounds to avoid bounds checks, but we also need to
+                # inform the compiler about the bounds that we are assuming. this is done
+                # using the assume intrinsic, and in case of Metal yields a 8x speed-up.
+                assume(1 <= i <= length(Is))
+                I = @inbounds Is[i]
+            end
+
+            val = if isa(IndexStyle(bc′), IndexCartesian)
+                @inbounds bc′[I]
+            else
+                @inbounds bc′[i]
+            end
+
+            if isa(IndexStyle(dest), IndexCartesian)
+                @inbounds dest[I] = val
+            else
+                @inbounds dest[i] = val
+            end
         end
         return
     end
     elements = length(dest)
     elements_per_thread = typemax(Int)
-    heuristic = launch_heuristic(backend(dest), broadcast_kernel, dest, bc′, 1;
+    Is = CartesianIndices(dest)
+    heuristic = launch_heuristic(backend(dest), broadcast_kernel, dest, Val(Is), bc′, 1;
                                  elements, elements_per_thread)
     config = launch_configuration(backend(dest), heuristic;
                                   elements, elements_per_thread)
-    gpu_call(broadcast_kernel, dest, bc′, config.elements_per_thread;
+    gpu_call(broadcast_kernel, dest, Val(Is), bc′, config.elements_per_thread;
              threads=config.threads, blocks=config.blocks)
 
     return dest

src/host/math.jl

@@ -2,7 +2,7 @@
 
 function Base.clamp!(A::AnyGPUArray, low, high)
     gpu_call(A, low, high) do ctx, A, low, high
-        I = @cartesianidx A
+        I = @linearidx A
         A[I] = clamp(A[I], low, high)
         return
     end