Add in-place multiply-add #738
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| # 5-argument matrix multiplication | ||
| @inline LinearAlgebra.mul!(dest::StaticVecOrMat, A::StaticMatrix, B::StaticVecOrMat, α::Real, β::Real) = | ||
| _mul!(Size(dest), dest, Size(A), Size(B), A, B, α, β) | ||
| @inline mul!(dest::StaticVecOrMat, A::StaticVector, B::Transpose{<:Any, <:StaticVector}, α::Real, β::Real) = | ||
| _mul!(Size(dest), dest, Size(A), Size(B), A, B, α, β) | ||
| @inline mul!(dest::StaticVecOrMat, A::StaticVector, B::Adjoint{<:Any, <:StaticVector}, α::Real, β::Real) = | ||
| _mul!(Size(dest), dest, Size(A), Size(B), A, B, α, β) | ||
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| @inline mul!(dest::StaticVector, A::Transpose{<:Any, <:StaticMatrix}, B::StaticVector, α::Real, β::Real) = | ||
| _tmul!(Size(dest), dest, Size(A.parent), Size(B), A.parent, B, α, β) | ||
| @inline mul!(dest::StaticMatrix, A::Transpose{<:Any, <:StaticMatrix}, B::StaticMatrix, α::Real, β::Real) = | ||
| _mul!(Size(dest), dest, Size(A), Size(B), A, B, α, β) | ||
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| @inline multiplied_dimension(::Type{A}, ::Type{B}) where { | ||
| A<:Union{StaticMatrix,Transpose{<:Any,<:StaticMatrix}}, B<:StaticMatrix} = | ||
| prod(size(A)) * size(B,2) | ||
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| @inline multiplied_dimension(::Type{A}, ::Type{B}) where { | ||
| A<:Union{StaticMatrix,Transpose{<:Any,<:StaticMatrix}}, | ||
| B<:Transpose{<:Any, <:StaticMatrix}} = | ||
| prod(size(A)) * size(B,2) | ||
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| # Matrix-matrix multiplication | ||
| @generated function _mul!(Sc::Size{sc}, c::AbstractMatrix, | ||
| Sa::Size{sa}, Sb::Size{sb}, | ||
| a::AbstractMatrix, b::AbstractMatrix, | ||
| α::Real, β::Real) where {sa, sb, sc} | ||
| Ta,Tb,Tc = eltype(a), eltype(b), eltype(c) | ||
| can_blas = Tc == Ta && Tc == Tb && Tc <: BlasFloat | ||
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| mult_dim = multiplied_dimension(a,b) | ||
| if sa[1] * sa[2] * sb[2] < 4*4*4 | ||
| return quote | ||
| @_inline_meta | ||
| muladd_unrolled!(Sc, c, Sa, Sb, a, b, α, β) | ||
| return c | ||
| end | ||
| elseif sa[1] * sa[2] * sb[2] < 14*14*14 # Something seems broken for this one with large matrices (becomes allocating) | ||
| return quote | ||
| @_inline_meta | ||
| muladd_unrolled_chunks!(Sc, c, Sa, Sb, a, b, α, β) | ||
| return c | ||
| end | ||
| else | ||
| if can_blas | ||
| return quote | ||
| @_inline_meta | ||
| mul_blas!(Sc, c, Sa, Sb, a, b, α, β) | ||
| return c | ||
| end | ||
| else | ||
| return quote | ||
| @_inline_meta | ||
| muladd_unrolled_chunks!(Sc, c, Sa, Sb, a, b, α, β) | ||
| return c | ||
| end | ||
| end | ||
| end | ||
| end | ||
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| # Matrix-vector multiplication | ||
| @generated function _mul!(::Size{sc}, c::StaticVecOrMat, ::Size{sa}, ::Size{sb}, | ||
| a::StaticMatrix, b::StaticVector, α::Real, β::Real, ::Val{col}=Val(1)) where {sa, sb, sc,col} | ||
| if sb[1] != sa[2] || sc[1] != sa[1] | ||
| throw(DimensionMismatch("Tried to multiply arrays of size $sa and $sb and assign to array of size $sc")) | ||
| end | ||
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| if sa[2] != 0 | ||
| exprs = [:(c[$(LinearIndices(sc)[k,col])] = β * c[$(LinearIndices(sc)[k,col])] | ||
| + α * $(reduce((ex1,ex2) -> :(+($ex1,$ex2)), | ||
| [:(a[$(LinearIndices(sa)[k, j])]*b[$j]) for j = 1:sa[2]]))) for k = 1:sa[1]] | ||
| else | ||
| exprs = [:(c[$k] = zero(eltype(c))) for k = 1:sa[1]] | ||
| end | ||
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| return quote | ||
| @_inline_meta | ||
| @inbounds $(Expr(:block, exprs...)) | ||
| return c | ||
| end | ||
| end | ||
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| @generated function _tmul!(::Size{sc}, c::StaticVecOrMat, ::Size{sa}, ::Size{sb}, | ||
| a::StaticMatrix, b::StaticVector, α::Real, β::Real, ::Val{col}=Val(1)) where {sa, sb, sc,col} | ||
| if sb[1] != sa[1] || sc[1] != sa[2] | ||
| throw(DimensionMismatch("Tried to multiply arrays of size $sa and $sb and assign to array of size $sc")) | ||
| end | ||
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| if sa[2] != 0 | ||
| exprs = [:(c[$(LinearIndices(sc)[k,col])] = β * c[$(LinearIndices(sc)[k,col])] | ||
| + α * $(reduce((ex1,ex2) -> :(+($ex1,$ex2)), | ||
| [:(a[$(LinearIndices(sa)[j, k])]*b[$j]) for j = 1:sa[1]]))) for k = 1:sa[2]] | ||
| else | ||
| exprs = [:(c[$k] = zero(eltype(c))) for k = 1:sa[1]] | ||
| end | ||
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| return quote | ||
| @_inline_meta | ||
| @inbounds $(Expr(:block, exprs...)) | ||
| return c | ||
| end | ||
| end | ||
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| # Outer product | ||
| @generated function _mul!(::Size{sc}, c::StaticMatrix, ::Size{sa}, ::Size{sb}, a::StaticVector, | ||
| b::Union{Transpose{<:Any, <:StaticVector}, Adjoint{<:Any, <:StaticVector}}, | ||
| α::Real, β::Real) where {sa, sb, sc} | ||
| if sa[1] != sc[1] || sb[2] != sc[2] | ||
| throw(DimensionMismatch("Tried to multiply arrays of size $sa and $sb and assign to array of size $sc")) | ||
| end | ||
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| exprs = [:(c[$(LinearIndices(sc)[i, j])] = β * c[$(LinearIndices(sc)[i, j])] + α * | ||
| a[$i] * b[$j]) for i = 1:sa[1], j = 1:sb[2]] | ||
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| return quote | ||
| @_inline_meta | ||
| @inbounds $(Expr(:block, exprs...)) | ||
| return c | ||
| end | ||
| end | ||
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| @inline muladd_unrolled!(Sc::Size{sc}, c::StaticMatrix, Sa::Size{sa}, Sb::Size{sb}, | ||
| a::StaticMatrix, b::StaticMatrix, α::Real, β::Real) where {sa, sb, sc} = | ||
| _muladd_unrolled!(Sc, c, Sa, Sb, a, b, α, β) | ||
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| @inline muladd_unrolled!(Sc::Size{sc}, c::StaticMatrix, Sa::Size{sa}, Sb::Size{sb}, | ||
| a::Transpose{<:Any, <:StaticMatrix}, b::StaticMatrix, α::Real, β::Real) where {sa, sb, sc} = | ||
| _tmuladd_unrolled!(Sc, c, Size(a.parent), Sb, a.parent, b, α, β) | ||
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| @generated function _muladd_unrolled!(::Size{sc}, c::StaticMatrix, ::Size{sa}, ::Size{sb}, | ||
| a::StaticMatrix, b::StaticMatrix, α::Real, β::Real) where {sa, sb, sc} | ||
| if sb[1] != sa[2] || sa[1] != sc[1] || sb[2] != sc[2] | ||
| throw(DimensionMismatch("Tried to multiply arrays of size $sa and $sb and assign to array of size $sc")) | ||
| end | ||
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| if sa[2] != 0 | ||
| exprs = [:(c[$(LinearIndices(sc)[k1, k2])] = β*c[$(LinearIndices(sc)[k1, k2])] + α * | ||
| $(reduce((ex1,ex2) -> :(+($ex1,$ex2)), | ||
| [:(a[$(LinearIndices(sa)[k1, j])]*b[$(LinearIndices(sb)[j, k2])]) for j = 1:sa[2]] | ||
| ))) for k1 = 1:sa[1], k2 = 1:sb[2]] | ||
| else | ||
| exprs = [:(c[$(LinearIndices(sc)[k1, k2])] = zero(eltype(c))) for k1 = 1:sa[1], k2 = 1:sb[2]] | ||
| end | ||
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| return quote | ||
| @_inline_meta | ||
| @inbounds $(Expr(:block, exprs...)) | ||
| end | ||
| end | ||
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| @generated function _tmuladd_unrolled!(::Size{sc}, c::StaticMatrix, ::Size{sa}, ::Size{sb}, | ||
| a::StaticMatrix, b::StaticMatrix, α::Real, β::Real) where {sa, sb, sc} | ||
| if sb[1] != sa[1] || sa[2] != sc[1] || sb[2] != sc[2] | ||
| throw(DimensionMismatch("Tried to multiply arrays of size $(reverse(sa)) and $sb and assign to array of size $sc")) | ||
| end | ||
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| if sa[2] != 0 | ||
| exprs = [:(c[$(LinearIndices(sc)[k1, k2])] = β*c[$(LinearIndices(sc)[k1, k2])] + α * | ||
| $(reduce((ex1,ex2) -> :(+($ex1,$ex2)), | ||
| [:(a[$(LinearIndices(sa)[j, k1])]*b[$(LinearIndices(sb)[j, k2])]) for j = 1:sa[1]] | ||
| ))) for k1 = 1:sa[2], k2 = 1:sb[2]] | ||
| else | ||
| exprs = [:(c[$(LinearIndices(sc)[k1, k2])] = zero(eltype(c))) for k1 = 1:sa[1], k2 = 1:sb[2]] | ||
| end | ||
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| return quote | ||
| @_inline_meta | ||
| @inbounds $(Expr(:block, exprs...)) | ||
| end | ||
| end | ||
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| @inline muladd_unrolled_chunks!(Sc::Size{sc}, c::StaticMatrix, Sa::Size{sa}, Sb::Size{sb}, | ||
| a::StaticMatrix, b::StaticMatrix, α::Real, β::Real) where {sa, sb, sc} = | ||
| _muladd_unrolled_chunks!(Sc, c, Sa, Sb, a, b, α, β) | ||
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| @inline muladd_unrolled_chunks!(Sc::Size{sc}, c::StaticMatrix, Sa::Size{sa}, Sb::Size{sb}, | ||
| a::Transpose{<:Any, <:StaticMatrix}, b::StaticMatrix, α::Real, β::Real) where {sa, sb, sc} = | ||
| _tmuladd_unrolled_chunks!(Sc, c, Size(a.parent), Sb, a.parent, b, α, β) | ||
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| @generated function _muladd_unrolled_chunks!(::Size{sc}, c::StaticMatrix, | ||
| ::Size{sa}, ::Size{sb}, | ||
| a::Union{StaticMatrix, Transpose{<:Any, <:StaticMatrix}}, b::StaticMatrix, | ||
| α::Real, β::Real) where {sa, sb, sc} | ||
| if sb[1] != sa[2] || sa[1] != sc[1] || sb[2] != sc[2] | ||
| throw(DimensionMismatch("Tried to multiply arrays of size $sa and $sb and assign to array of size $sc")) | ||
| end | ||
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| #vect_exprs = [:($(Symbol("tmp_$k2")) = partly_unrolled_multiply(A, B[:, $k2])) for k2 = 1:sB[2]] | ||
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| # Do a custom b[:, k2] to return a SVector (an isbitstype type) rather than a mutable type. Avoids allocation == faster | ||
| tmp_type = SVector{sb[1], eltype(c)} | ||
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| col_mult = [:($(Symbol("tmp_$k2")) = | ||
| _mul!($(Size(sc)), c, $(Size(sa)), $(Size(sb[1])), a, | ||
| $(Expr(:call, tmp_type, | ||
| [Expr(:ref, :b, LinearIndices(sb)[i, k2]) for i = 1:sb[1]]...)),α,β,Val($k2))) for k2 = 1:sb[2]] | ||
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| return quote | ||
| @_inline_meta | ||
| return $(Expr(:block, col_mult...)) | ||
| end | ||
| end | ||
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| @generated function _tmuladd_unrolled_chunks!(::Size{sc}, c::StaticMatrix, | ||
| ::Size{sa}, ::Size{sb}, | ||
| a::Union{StaticMatrix, Transpose{<:Any, <:StaticMatrix}}, b::StaticMatrix, | ||
| α::Real, β::Real) where {sa, sb, sc} | ||
| if sb[1] != sa[1] || sa[2] != sc[1] || sb[2] != sc[2] | ||
| throw(DimensionMismatch("Tried to multiply arrays of size $(reverse(sa)) and $sb and assign to array of size $sc")) | ||
| end | ||
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| #vect_exprs = [:($(Symbol("tmp_$k2")) = partly_unrolled_multiply(A, B[:, $k2])) for k2 = 1:sB[2]] | ||
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| # Do a custom b[:, k2] to return a SVector (an isbitstype type) rather than a mutable type. Avoids allocation == faster | ||
| tmp_type = SVector{sb[1], eltype(c)} | ||
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| col_mult = [:($(Symbol("tmp_$k2")) = | ||
| _tmul!($(Size(sc)), c, $(Size(sa)), $(Size(sb[1])), a, | ||
| $(Expr(:call, tmp_type, | ||
| [Expr(:ref, :b, LinearIndices(sb)[i, k2]) for i = 1:sb[1]]...)),α,β,Val($k2))) for k2 = 1:sb[2]] | ||
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| return quote | ||
| @_inline_meta | ||
| return $(Expr(:block, col_mult...)) | ||
| end | ||
| end | ||
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| # Special-case SizedMatrix | ||
| # @inline mul!(dest::SizedMatrix{<:Any, <:Any, Tc}, A::SizedMatrix{<:Any, <:Any, Ta}, | ||
| # B::SizedMatrix{<:Any, <:Any, Tb}) where {Ta,Tb,Tc} = | ||
| # _mul!(Size(dest), dest, Size(A), Size(B), A, B, one(Ta), zero(Ta)) | ||
| # | ||
| # @generated function _mul!(Sc::Size{sc}, c::SizedMatrix{<:Any, <:Any, Tc}, | ||
| # Sa::Size{sa}, Sb::Size{sb}, | ||
| # a::SizedMatrix{<:Any, <:Any, Ta}, b::SizedMatrix{<:Any, <:Any, Tb}, | ||
| # α::Real, β::Real) where {sa, sb, sc, Ta, Tb, Tc} | ||
| # can_blas = Tc == Ta && Tc == Tb && Tc <: BlasFloat | ||
| # | ||
| # if can_blas | ||
| # if sa[1] * sa[2] * sb[2] < 4*4*4 | ||
| # return quote | ||
| # @_inline_meta | ||
| # muladd_unrolled!(Sc, c, Sa, Sb, a, b, α, β) | ||
| # return c | ||
| # end | ||
| # elseif sa[1] * sa[2] * sb[2] < 14*14*14 # Something seems broken for this one with large matrices (becomes allocating) | ||
| # return quote | ||
| # @_inline_meta | ||
| # muladd_unrolled_chunks!(Sc, c, Sa, Sb, a, b, α, β) | ||
| # return c | ||
| # end | ||
| # else | ||
| # return quote | ||
| # # @_inline_meta | ||
| # BLAS.gemm!('N','N', α, a.data, b.data, β, c.data) | ||
| # return c | ||
| # end | ||
| # end | ||
| # end | ||
| # end | ||
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This rather a lot of duplication which will be hard to maintain.
I think all you need is a utility function to "get the data pointer and transposed-ness" out of
a,b,c? Then you can collapse all these down again into one function.