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Sep 29, 2020
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Change order of function definition in matrix multiplication code #833

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f4f9504
rearrange order of function definitions in matrix multiplication
mateuszbaran Sep 25, 2020
7df98ef
moving gen_by_access as well
mateuszbaran Sep 28, 2020
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262 changes: 0 additions & 262 deletions src/matrix_multiply.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -15,150 +15,6 @@ import LinearAlgebra: BlasFloat, matprod, mul!
@inline *(A::StaticArray{Tuple{N,1},<:Any,2}, B::Adjoint{<:Any,<:StaticVector}) where {N} = vec(A) * B
@inline *(A::StaticArray{Tuple{N,1},<:Any,2}, B::Transpose{<:Any,<:StaticVector}) where {N} = vec(A) * B

"""
gen_by_access(expr_gen, a::Type{<:AbstractArray}, asym = :wrapped_a)

Statically generate outer code for fully unrolled multiplication loops.
Returned code does wrapper-specific tests (for example if a symmetric matrix view is
`U` or `L`) and the body of the if expression is then generated by function `expr_gen`.
The function `expr_gen` receives access pattern description symbol as its argument
and this symbol is then consumed by uplo_access to generate the right code for matrix
element access.

The name of the matrix to test is indicated by `asym`.
"""
function gen_by_access(expr_gen, a::Type{<:StaticVecOrMat}, asym = :wrapped_a)
return expr_gen(:any)
end
function gen_by_access(expr_gen, a::Type{<:Symmetric{<:Any, <:StaticMatrix}}, asym = :wrapped_a)
return quote
if $(asym).uplo == 'U'
$(expr_gen(:up))
else
$(expr_gen(:lo))
end
end
end
function gen_by_access(expr_gen, a::Type{<:Hermitian{<:Any, <:StaticMatrix}}, asym = :wrapped_a)
return quote
if $(asym).uplo == 'U'
$(expr_gen(:up_herm))
else
$(expr_gen(:lo_herm))
end
end
end
function gen_by_access(expr_gen, a::Type{<:UpperTriangular{<:Any, <:StaticMatrix}}, asym = :wrapped_a)
return expr_gen(:upper_triangular)
end
function gen_by_access(expr_gen, a::Type{<:LowerTriangular{<:Any, <:StaticMatrix}}, asym = :wrapped_a)
return expr_gen(:lower_triangular)
end
function gen_by_access(expr_gen, a::Type{<:UnitUpperTriangular{<:Any, <:StaticMatrix}}, asym = :wrapped_a)
return expr_gen(:unit_upper_triangular)
end
function gen_by_access(expr_gen, a::Type{<:UnitLowerTriangular{<:Any, <:StaticMatrix}}, asym = :wrapped_a)
return expr_gen(:unit_lower_triangular)
end
function gen_by_access(expr_gen, a::Type{<:Transpose{<:Any, <:StaticVecOrMat}}, asym = :wrapped_a)
return expr_gen(:transpose)
end
function gen_by_access(expr_gen, a::Type{<:Adjoint{<:Any, <:StaticVecOrMat}}, asym = :wrapped_a)
return expr_gen(:adjoint)
end
function gen_by_access(expr_gen, a::Type{<:SDiagonal}, asym = :wrapped_a)
return expr_gen(:diagonal)
end
"""
gen_by_access(expr_gen, a::Type{<:AbstractArray}, b::Type{<:AbstractArray})

Simiar to gen_by_access with only one type argument. The difference is that tests for both
arrays of type `a` and `b` are generated and `expr_gen` receives two access arguments,
first for matrix `a` and the second for matrix `b`.
"""
function gen_by_access(expr_gen, a::Type{<:StaticMatrix}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:any, access_b)
end)
end
end
function gen_by_access(expr_gen, a::Type{<:Symmetric{<:Any, <:StaticMatrix}}, b::Type)
return quote
if wrapped_a.uplo == 'U'
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:up, access_b)
end)
else
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:lo, access_b)
end)
end
end
end
function gen_by_access(expr_gen, a::Type{<:Hermitian{<:Any, <:StaticMatrix}}, b::Type)
return quote
if wrapped_a.uplo == 'U'
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:up_herm, access_b)
end)
else
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:lo_herm, access_b)
end)
end
end
end
function gen_by_access(expr_gen, a::Type{<:UpperTriangular{<:Any, <:StaticMatrix}}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:upper_triangular, access_b)
end)
end
end
function gen_by_access(expr_gen, a::Type{<:LowerTriangular{<:Any, <:StaticMatrix}}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:lower_triangular, access_b)
end)
end
end
function gen_by_access(expr_gen, a::Type{<:UnitUpperTriangular{<:Any, <:StaticMatrix}}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:unit_upper_triangular, access_b)
end)
end
end
function gen_by_access(expr_gen, a::Type{<:UnitLowerTriangular{<:Any, <:StaticMatrix}}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:unit_lower_triangular, access_b)
end)
end
end
function gen_by_access(expr_gen, a::Type{<:Transpose{<:Any, <:StaticMatrix}}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:transpose, access_b)
end)
end
end
function gen_by_access(expr_gen, a::Type{<:Adjoint{<:Any, <:StaticMatrix}}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:adjoint, access_b)
end)
end
end
function gen_by_access(expr_gen, a::Type{<:SDiagonal}, b::Type)
return quote
return $(gen_by_access(b, :wrapped_b) do access_b
expr_gen(:diagonal, access_b)
end)
end
end

"""
mul_result_structure(a::Type, b::Type)

Expand Down Expand Up @@ -202,99 +58,6 @@ function mul_result_structure(::SDiagonal, ::SDiagonal)
return Diagonal
end

"""
uplo_access(sa, asym, k, j, uplo)

Generate code for matrix element access, for a matrix of size `sa` locally referred to
as `asym` in the context where the result will be used. Both indices `k` and `j` need to be
statically known for this function to work. `uplo` is the access pattern mode generated
by the `gen_by_access` function.
"""
function uplo_access(sa, asym, k, j, uplo)
TAsym = Symbol("T"*string(asym))
if uplo == :any
return :($asym[$(LinearIndices(sa)[k, j])])
elseif uplo == :up
if k < j
return :($asym[$(LinearIndices(sa)[k, j])])
elseif k == j
return :(LinearAlgebra.symmetric($asym[$(LinearIndices(sa)[k, j])], :U))
else
return :(transpose($asym[$(LinearIndices(sa)[j, k])]))
end
elseif uplo == :lo
if k > j
return :($asym[$(LinearIndices(sa)[k, j])])
elseif k == j
return :(LinearAlgebra.symmetric($asym[$(LinearIndices(sa)[k, j])], :L))
else
return :(transpose($asym[$(LinearIndices(sa)[j, k])]))
end
elseif uplo == :up_herm
if k < j
return :($asym[$(LinearIndices(sa)[k, j])])
elseif k == j
return :(LinearAlgebra.hermitian($asym[$(LinearIndices(sa)[k, j])], :U))
else
return :(adjoint($asym[$(LinearIndices(sa)[j, k])]))
end
elseif uplo == :lo_herm
if k > j
return :($asym[$(LinearIndices(sa)[k, j])])
elseif k == j
return :(LinearAlgebra.hermitian($asym[$(LinearIndices(sa)[k, j])], :L))
else
return :(adjoint($asym[$(LinearIndices(sa)[j, k])]))
end
elseif uplo == :upper_triangular
if k <= j
return :($asym[$(LinearIndices(sa)[k, j])])
else
return :(zero($TAsym))
end
elseif uplo == :lower_triangular
if k >= j
return :($asym[$(LinearIndices(sa)[k, j])])
else
return :(zero($TAsym))
end
elseif uplo == :unit_upper_triangular
if k < j
return :($asym[$(LinearIndices(sa)[k, j])])
elseif k == j
return :(oneunit($TAsym))
else
return :(zero($TAsym))
end
elseif uplo == :unit_lower_triangular
if k > j
return :($asym[$(LinearIndices(sa)[k, j])])
elseif k == j
return :(oneunit($TAsym))
else
return :(zero($TAsym))
end
elseif uplo == :upper_hessenberg
if k <= j+1
return :($asym[$(LinearIndices(sa)[k, j])])
else
return :(zero($TAsym))
end
elseif uplo == :transpose
return :(transpose($asym[$(LinearIndices(reverse(sa))[j, k])]))
elseif uplo == :adjoint
return :(adjoint($asym[$(LinearIndices(reverse(sa))[j, k])]))
elseif uplo == :diagonal
if k == j
return :($asym[$k])
else
return :(zero($TAsym))
end
else
error("Unknown uplo: $uplo")
end
end

# Implementations

function mul_smat_vec_exprs(sa, access_a)
Expand Down Expand Up @@ -369,31 +132,6 @@ for TWR in [Adjoint, Transpose, Symmetric, Hermitian, LowerTriangular, UpperTria
@eval _unstatic_array(::Type{$TWR{T,TSA}}) where {S, T, N, TSA<:StaticArray{S,T,N}} = $TWR{T,<:AbstractArray{T,N}}
end

function combine_products(expr_list)
filtered = filter(expr_list) do expr
if expr.head != :call || expr.args[1] != :*
error("expected call to *")
end
for arg in expr.args[2:end]
if isa(arg, Expr) && arg.head == :call && arg.args[1] == :zero
return false
end
end
return true
end
if isempty(filtered)
return :(zero(T))
else
return reduce(filtered) do ex1, ex2
if ex2.head != :call || ex2.args[1] != :*
error("expected call to *")
end

return :(muladd($(ex2.args[2]), $(ex2.args[3]), $ex1))
end
end
end

@generated function _mul(Sa::Size{sa}, Sb::Size{sb}, a::StaticMatMulLike{<:Any, <:Any, Ta}, b::StaticMatMulLike{<:Any, <:Any, Tb}) where {sa, sb, Ta, Tb}
S = Size(sa[1], sb[2])
# Heuristic choice for amount of codegen
Expand Down
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