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update strided implementation (#191)
* update strided implementation * move blascontract * fix forgotten conj argument * add lts to ci
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,165 @@ | ||
| # general implementation for backends that implement tensor contractions by permuting and | ||
| # reshaping the input tensors and then calling a BLAS routine to perform the contraction | ||
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| # all of the following methods expect that basic argument checks on dimensionality and | ||
| # permutation validity have already been performed | ||
| function blas_contract!(C, A, pA, B, pB, pAB, α, β, backend, allocator) | ||
| rpA = reverse(pA) | ||
| rpB = reverse(pB) | ||
| indCinoBA = let N₁ = numout(pA), N₂ = numin(pB) | ||
| map(n -> ifelse(n > N₁, n - N₁, n + N₂), linearize(pAB)) | ||
| end | ||
| tpAB = trivialpermutation(pAB) | ||
| rpAB = (TupleTools.getindices(indCinoBA, tpAB[1]), | ||
| TupleTools.getindices(indCinoBA, tpAB[2])) | ||
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| if contract_memcost(C, A, pA, B, pB, pAB) <= contract_memcost(C, B, rpB, A, rpA, rpAB) | ||
| return _blas_contract!(C, A, pA, B, pB, pAB, α, β, backend, allocator) | ||
| else | ||
| return _blas_contract!(C, B, rpB, A, rpA, rpAB, α, β, backend, allocator) | ||
| end | ||
| end | ||
| # specialised fast path for matrix matrix multiplication | ||
| function blas_contract!(C::StridedView{T,2}, | ||
| A::StridedView{T,2}, pA::Index2Tuple{1,1}, | ||
| B::StridedView{T,2}, pB::Index2Tuple{1,1}, | ||
| pAB::Index2Tuple{1,1}, | ||
| α::Number, β::Number, | ||
| backend, allocator) where {T} | ||
| A′ = pA == ((1,), (2,)) ? A : transpose(A) | ||
| B′ = pB == ((1,), (2,)) ? B : transpose(B) | ||
| if pAB == ((1,), (2,)) | ||
| mul!(C, A′, B′, α, β) | ||
| elseif pAB == ((2,), (1,)) | ||
| mul!(C, transpose(B′), transpose(A′), α, β) | ||
| end | ||
| return C | ||
| end | ||
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| # implement necessary permutations | ||
| function _blas_contract!(C, A, pA, B, pB, pAB, α, β, backend, allocator) | ||
| TC = eltype(C) | ||
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| A_, pA, flagA = makeblascontractable(A, pA, TC, backend, allocator) | ||
| B_, pB, flagB = makeblascontractable(B, pB, TC, backend, allocator) | ||
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| ipAB = oindABinC(pAB, pA, pB) | ||
| flagC = isblasdestination(C, ipAB) | ||
| if flagC | ||
| C_ = C | ||
| _unsafe_blas_contract!(C_, A_, pA, B_, pB, ipAB, α, β) | ||
| else | ||
| C_ = SV(tensoralloc_add(TC, C, ipAB, false, Val(true), allocator)) | ||
| _unsafe_blas_contract!(C_, A_, pA, B_, pB, trivialpermutation(ipAB), | ||
| one(TC), zero(TC)) | ||
| tensoradd!(C, C_, pAB, false, α, β, backend, allocator) | ||
| tensorfree!(C_.parent, allocator) | ||
| end | ||
| flagA || tensorfree!(A_.parent, allocator) | ||
| flagB || tensorfree!(B_.parent, allocator) | ||
| return C | ||
| end | ||
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| # perform the actual contraction, assuming it can be done as matrix multiplication by simply | ||
| # reshaping without any further allocations | ||
| function _unsafe_blas_contract!(C::StridedView{T}, | ||
| A::StridedView{T}, pA, | ||
| B::StridedView{T}, pB, | ||
| pAB, α, β) where {T<:BlasFloat} | ||
| sizeA = size(A) | ||
| sizeB = size(B) | ||
| csizeA = TupleTools.getindices(sizeA, pA[2]) | ||
| csizeB = TupleTools.getindices(sizeB, pB[1]) | ||
| osizeA = TupleTools.getindices(sizeA, pA[1]) | ||
| osizeB = TupleTools.getindices(sizeB, pB[2]) | ||
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| mul!(sreshape(permutedims(C, linearize(pAB)), (prod(osizeA), prod(osizeB))), | ||
| sreshape(permutedims(A, linearize(pA)), (prod(osizeA), prod(csizeA))), | ||
| sreshape(permutedims(B, linearize(pB)), (prod(csizeB), prod(osizeB))), | ||
| α, β) | ||
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| return C | ||
| end | ||
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| @inline function makeblascontractable(A, pA, TC, backend, allocator) | ||
| flagA = isblascontractable(A, pA) && eltype(A) == TC | ||
| if !flagA | ||
| A_ = tensoralloc_add(TC, A, pA, false, Val(true), allocator) | ||
| Anew = SV(A_, size(A_), strides(A_), 0, A.op) | ||
| Anew = tensoradd!(Anew, A, pA, false, One(), Zero(), backend, allocator) | ||
| pAnew = trivialpermutation(pA) | ||
| else | ||
| Anew = A | ||
| pAnew = pA | ||
| end | ||
| return Anew, pAnew, flagA | ||
| end | ||
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| function isblascontractable(A::StridedView, p::Index2Tuple) | ||
| eltype(A) <: LinearAlgebra.BlasFloat || return false | ||
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| sizeA = size(A) | ||
| stridesA = strides(A) | ||
| sizeA1 = TupleTools.getindices(sizeA, p[1]) | ||
| sizeA2 = TupleTools.getindices(sizeA, p[2]) | ||
| stridesA1 = TupleTools.getindices(stridesA, p[1]) | ||
| stridesA2 = TupleTools.getindices(stridesA, p[2]) | ||
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| canfuse1, _, s1 = _canfuse(sizeA1, stridesA1) | ||
| canfuse2, _, s2 = _canfuse(sizeA2, stridesA2) | ||
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| if A.op == conj | ||
| return canfuse1 && canfuse2 && s2 == 1 | ||
| else | ||
| return canfuse1 && canfuse2 && (s1 == 1 || s2 == 1) | ||
| end | ||
| end | ||
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| function isblasdestination(A::StridedView, p::Index2Tuple) | ||
| (eltype(A) <: LinearAlgebra.BlasFloat && A.op == identity) || return false | ||
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| sizeA = size(A) | ||
| stridesA = strides(A) | ||
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| sizeA1 = TupleTools.getindices(sizeA, p[1]) | ||
| stridesA1 = TupleTools.getindices(stridesA, p[1]) | ||
| canfuse1, _, s1 = _canfuse(sizeA1, stridesA1) | ||
| (canfuse1 && s1 == 1) || return false | ||
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| sizeA2 = TupleTools.getindices(sizeA, p[2]) | ||
| stridesA2 = TupleTools.getindices(stridesA, p[2]) | ||
| canfuse2, _, _ = _canfuse(sizeA2, stridesA2) | ||
| return canfuse2 | ||
| end | ||
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| _canfuse(::Dims{0}, ::Dims{0}) = true, 1, 1 | ||
| _canfuse(dims::Dims{1}, strides::Dims{1}) = true, dims[1], strides[1] | ||
| @inline function _canfuse(dims::Dims{N}, strides::Dims{N}) where {N} | ||
| if dims[1] == 0 | ||
| return true, 0, 1 | ||
| elseif dims[1] == 1 | ||
| return _canfuse(Base.tail(dims), Base.tail(strides)) | ||
| else | ||
| b, d, s = _canfuse(Base.tail(dims), Base.tail(strides)) | ||
| if b && (s == dims[1] * strides[1] || d == 1) | ||
| dnew = dims[1] * d | ||
| return true, dnew, (dnew == 0 || dnew == 1) ? 1 : strides[1] | ||
| else | ||
| return false, dims[1] * d, strides[1] | ||
| end | ||
| end | ||
| end | ||
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| function oindABinC(pAB, pA, pB) | ||
| ipAB = invperm(linearize(pAB)) | ||
| oindAinC = TupleTools.getindices(ipAB, trivialpermutation(pA[1])) | ||
| oindBinC = TupleTools.getindices(ipAB, numout(pA) .+ trivialpermutation(pB[2])) | ||
| return (oindAinC, oindBinC) | ||
| end | ||
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| function contract_memcost(C, A, pA, B, pB, pAB) | ||
| ipAB = oindABinC(pAB, pA, pB) | ||
| return length(A) * (!isblascontractable(A, pA) || eltype(A) !== eltype(C)) + | ||
| length(B) * (!isblascontractable(B, pB) || eltype(B) !== eltype(C)) + | ||
| length(C) * !isblasdestination(C, ipAB) | ||
| end |
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