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Faster (still slow) fallback matrix multiplication #590

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95 changes: 88 additions & 7 deletions src/host/linalg.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -325,11 +325,92 @@ function LinearAlgebra.ldiv!(B::AbstractGPUVecOrMat,
B
end

# XXX: figure out how to do dynamically
MAX_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::AbstractGPUMatrix{R}, A::AbstractGPUMatrix{T}, B::AbstractGPUMatrix{S}, add::MulAddMul) where {T<:Number,S<:Number,R<:Number}
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) != 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 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)

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)

# number of tiles depends on inner dimension
@uniform NUM_TILES = div(Q + TILE_DIM - 1, TILE_DIM)

# loop over all tiles needed for this calculation
for t in 0:(NUM_TILES - 1)
I = (grow - 1) * TILE_DIM + tile_row
J = (gcol - 1) * TILE_DIM + tile_col

# 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

# wait for all tiles to be loaded
@synchronize

I = (grow - 1) * TILE_DIM + tile_row
J = (gcol - 1) * TILE_DIM + tile_col

# 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

I = (grow - 1) * TILE_DIM + tile_row
J = (gcol - 1) * TILE_DIM + tile_col

# save if inbounds
if I <= N && J <= M
@inbounds output[I, J] = add(outval[1], output[I, J])
end
end

coalesced_matmul_kernel!(get_backend(C), (MAX_TILE_DIM, MAX_TILE_DIM))(C, A, B, N, Q, M;ndrange=map(x -> ceil(Int,x/MAX_TILE_DIM)*MAX_TILE_DIM, size(C)))
C
end
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)
throw(DimensionMismatch("matrix A has dimensions $(size(A)), matrix B has dimensions $(size(B))"))
Expand Down Expand Up @@ -744,7 +825,7 @@ 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

Expand Down Expand Up @@ -777,13 +858,13 @@ 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
Expand All @@ -797,12 +878,12 @@ 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

Expand Down
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