Faster matmul

Author: christiangnrd

src/host/linalg.jl

@@ -325,37 +325,85 @@ function LinearAlgebra.ldiv!(B::AbstractGPUVecOrMat,
     B
 end
 
+# XXX: figure out how to do dynamically
+const TILE_DIM = 16
 
 ## matrix multiplication
 # legacy method
 generic_matmatmul!(C::AbstractArray, A::AbstractArray, B::AbstractArray, a::Number, b::Number) =
     generic_matmatmul!(C, A, B, MulAddMul(a, b))
 function generic_matmatmul!(C::AbstractArray{R}, A::AbstractArray{T}, B::AbstractArray{S}, add::MulAddMul) where {T,S,R}
-    if size(A,2) != size(B,1)
+    N = size(A,1)
+    Q = size(A,2)
+    M = size(B,2)
+    if Q != size(B,1)
         throw(DimensionMismatch("matrix A has dimensions $(size(A)), matrix B has dimensions $(size(B))"))
     end
-    if size(C,1) != size(A,1) || size(C,2) != size(B,2)
-        throw(DimensionMismatch("result C has dimensions $(size(C)), needs $((size(A,1),size(B,2)))"))
+    if size(C,1) != N || size(C,2) != M
+        throw(DimensionMismatch("result C has dimensions $(size(C)), needs $((N,M))"))
     end
     if isempty(A) || isempty(B)
         return fill!(C, zero(R))
     end
 
-    @kernel function matmatmul_kernel!(C, A, B)
-        assume.(size(C) .> 0)
-        idx = @index(Global, Linear)
-        i, j = @inbounds Tuple(CartesianIndices(C)[idx])..., 1
+    @kernel unsafe_indices=true function coalesced_matmul_kernel!(
+            output, @Const(input1), @Const(input2), N, Q, M,
+            ::Val{BANK} = Val(1),
+        ) where {BANK}
+        grow, gcol = @index(Group, NTuple)
+        tile_row, tile_col = @index(Local, NTuple)
 
-        @inbounds if i <= size(A,1) && j <= size(B,2)
-            z2 = zero(A[i, 1]*B[1, j] + A[i, 1]*B[1, j])
-            Cij = convert(promote_type(R, typeof(z2)), z2)
-            for k in 1:size(A,2)
-                Cij += A[i, k]*B[k, j]
+        # TILE_DIM = @uniform @groupsize()[1]
+
+        # +1 to avoid bank conflicts on shared memory
+        tile1 = @localmem(R, (TILE_DIM + BANK, TILE_DIM))
+        tile2 = @localmem(R, (TILE_DIM + BANK, TILE_DIM))
+
+        # private variable for tile output
+        outval = @private R 1
+        @inbounds outval[1] = -zero(R)
+
+        # @uniform N = size(output, 1)
+        # number of tiles depends on inner dimension
+        @uniform NUM_TILES = div(Q + TILE_DIM - 1, TILE_DIM)
+
+        I = (grow - 1) * TILE_DIM + tile_row
+        J = (gcol - 1) * TILE_DIM + tile_col
+
+        # loop over all tiles needed for this calculation
+        for t in 0:(NUM_TILES - 1)
+            # load inputs into tiles, with bounds checking for non-square matrices
+            if I <= N && t * TILE_DIM + tile_col <= Q
+                @inbounds tile1[tile_row, tile_col] = input1[I, t * TILE_DIM + tile_col]
+            else
+                @inbounds tile1[tile_row, tile_col] = zero(R)
+            end
+            if J <= M && t * TILE_DIM + tile_row <= Q
+                @inbounds tile2[tile_row, tile_col] = input2[t * TILE_DIM + tile_row, J]
+            else
+                @inbounds tile2[tile_row, tile_col] = zero(R)
             end
-            C[i,j] = add(Cij, C[i,j])
+
+            # wait for all tiles to be loaded
+            @synchronize
+
+            # calculate value of spot in output, use temporary value to allow for vectorization
+            out = zero(R)
+            @simd for k in 1:TILE_DIM
+                @inbounds out += tile1[tile_row, k] * tile2[k, tile_col]
+            end
+            outval[1] += out
+
+            @synchronize
+        end
+
+        # save if inbounds
+        if I <= N && J <= M
+            @inbounds output[I, J] = add(outval[1], output[I, J])
         end
     end
-    matmatmul_kernel!(get_backend(C))(C, A, B; ndrange = size(C))
+
+    coalesced_matmul_kernel!(get_backend(C), (TILE_DIM, TILE_DIM))(C, A, B, N, Q, M;ndrange=map(x -> ceil(Int,x/TILE_DIM)*TILE_DIM, size(C)))
     C
 end
 
@@ -744,7 +792,7 @@ function LinearAlgebra.kron!(z::AbstractGPUVector{T1}, x::AbstractGPUVector{T2},
 
     @kernel function kron_kernel!(z, @Const(x), @Const(y))
         i, j = @index(Global, NTuple)
-    
+
         @inbounds z[(i - 1) * length(y) + j] = x[i] * y[j]
     end
 
@@ -777,13 +825,13 @@ for (wrapa, transa, unwrapa) in trans_adj_wrappers, (wrapb, transb, unwrapb) in
 
         ta = $transa(T1)
         tb = $transb(T2)
-    
+
         @kernel function kron_kernel!(C, @Const(A), @Const(B))
             ai, aj = @index(Global, NTuple)  # Indices in the result matrix
-    
+
             # lb1, lb2 = size(B)  # Dimensions of B
             lb1, lb2 = tb == 'N' ? size(B) : reverse(size(B))
-    
+
             # Map global indices (ai, aj) to submatrices of the Kronecker product
             i_a = (ai - 1) ÷ lb1 + 1  # Corresponding row index in A
             i_b = (ai - 1) % lb1 + 1  # Corresponding row index in B
@@ -797,12 +845,12 @@ for (wrapa, transa, unwrapa) in trans_adj_wrappers, (wrapb, transb, unwrapb) in
                 C[ai, aj] = a_ij * b_ij
             end
         end
-    
+
         backend = KernelAbstractions.get_backend(C)
         kernel = kron_kernel!(backend)
-    
+
         kernel(C, $(unwrapa(:A)), $(unwrapb(:B)), ndrange=(size(C, 1), size(C, 2)))
-    
+
         return C
     end