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forward.jl
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forward.jl
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#========== backward gradient using ForwardDiff ==========#
function insert_forward_gradient(create, apply!, store)
store.verbose && @info "using ForwardDiff for $create ~ $(store.right[])"
store.epsilonright[] = MacroTools.postwalk(epsilonwalk(store), store.right[])
# # Version of right with (A[i,j] + 𝜀A′) etc, with dict[:𝜀A′] = A[i,j]
# epsilonright = Ref{ExprSym}(),
# epsilondict = Dict{Symbol,Expr}(),
dZ = Symbol(DEL, ZED)
∇apply! = Symbol(:∇, apply!)
gradarrays = map(A -> Symbol(DEL, A), store.arrays)
# loopind = vcat(store.leftind, store.redind)
# shared = map(i -> Symbol(AXIS, i), store.sharedind)
# nonshared = map(i -> Symbol(AXIS, i), setdiff(loopind, store.sharedind))
nonshared = setdiff(vcat(store.leftind, store.redind), store.sharedind)
axislist = map(i -> Symbol(AXIS, i), vcat(store.sharedind, nonshared))
# defineepsilons = map(enumerate(store.epsilondict)) do (d, (Aepsilon,_))
# tup = ntuple(i -> i==d ? 1 : 0, length(store.epsilondict))
# :($Aepsilon = $ForwardDiff.Dual(0, $tup))
# end
# readepsilons = map(enumerate(store.epsilondict)) do (d, (_,Aex))
# :($Aex += $ForwardDiff.partials($ZED, $d) * $dZ[$(store.leftraw...)])
# end
defineepsilons, readepsilons = [], []
for (d, (Aepsilon, Aex)) in enumerate(store.epsilondict) # order isn't consistent? so do it once
basis = [i==d ? :(one($TYP)) : :(zero($TYP)) for i in 1:length(store.epsilondict)]
push!(defineepsilons, :($Aepsilon = $ForwardDiff.Dual(zero($TYP), ($(basis...),))))
push!(readepsilons, :($Aex = $Aex + $ForwardDiff.partials($ZED, $d) * $dZ[$(store.leftraw...)]))
# push!(readepsilons, :($Aex = $Aex + $ZED.partials.values[$d] * $dZ[$(store.leftraw...)])) # doesn't work with avx
end
ex_iter = :($ZED = $(store.epsilonright[]); $(readepsilons...))
make_many_workers(∇apply!,
vcat(gradarrays, :($dZ::AbstractArray{$TYP}), store.arrays, store.scalars, axislist),
:(($(defineepsilons...);)), store.sharedind, nothing, nonshared, ex_iter, nothing, store)
# to special-case dZ::FillArray, you'd need to build a different readepsilons ... loopex
# Or you'd have to edit it:
# fillarrayloop = MacroTools.postwalk(loopex) do ex
# x == :($dZ[$(store.leftraw...)]) ? :($dZ.val) : ex # ??
# end
# And you'd have to make storage_type not trip on this.
end
epsilonwalk(store) = ex -> begin
@capture(ex, A_[inds__]) || return ex
return arrayplusepsilon(A, inds, store)
end
arrayplusepsilon(A::Symbol, inds, store) = begin # the same array may occur twice!
Aepsilon = Symbol(EPS, A)
while haskey(store.epsilondict, Aepsilon)
Aepsilon = Symbol(Aepsilon, "′")
end
store.epsilondict[Aepsilon] = :( $(Symbol(DEL, A))[$(inds...)] )
:(( $A[$(inds...)] + $Aepsilon ))
end
arrayplusepsilon(A, inds, store) = begin
push!(store.flags, :nograd)
@debug "expression ", string(A), " is the problem"
:🐳
end
#========== making ForwardDiff work with LoopVectorization ==========#
# using Tullio.LoopVectorization: LoopVectorization, SVec, vconvert, SIMDPirates
using LoopVectorization
using LoopVectorization: SVec, vconvert, SIMDPirates
using Core: VecElement
s1 = SVec{2,Float64}(5.5, 6.6) # SVec{2,Float64}<5.5, 6.6>
# dump(s1)
# SVec{2,Float64}
# data: Tuple{VecElement{Float64},VecElement{Float64}}
# 1: VecElement{Float64}
# value: Float64 5.5
# 2: VecElement{Float64}
# value: Float64 6.6
s1[2]
s1 |> typeof |> parentmodule # VectorizationBase
@inline svec(tup::NTuple{N,T}) where {N,T} = SVec{N,T}(tup...)
# Base.inv(sv::SVec{N,<:Integer}) where {N} = svec(ntuple(n -> inv(sv[n]), N))
# Base.sqrt(sv::SVec{N,<:Integer}) where {N} = svec(ntuple(n -> sqrt(sv[n]), N))
# Base.trunc(T::Type, sv::SVec{N}) where {N} = svec(ntuple(n -> trunc(T, sv[n]), N))
@inline Base.inv(sv::SVec{N,<:Integer}) where {N} = svec(ntuple(n -> inv(sv[n]), N))
@inline Base.sqrt(sv::SVec{N,<:Integer}) where {N} = svec(ntuple(n -> sqrt(sv[n]), N))
@inline Base.trunc(T::Type, sv::SVec{N}) where {N} = svec(ntuple(n -> trunc(T, sv[n]), N))
using ForwardDiff
using ForwardDiff: Dual, Partials, partials
d1 = Dual(1.23, (4,0,0))
typeof(d1) # Dual{Nothing,Float64,3}
# dump(d1)
# Dual{Nothing,Float64,2}
# value: Float64 1.23
# partials: Partials{2,Float64}
# values: Tuple{Float64,Float64}
# 1: Float64 4.0
# 2: Float64 0.0
# 3: Float64 0.0
d1.partials # Partials{3,Float64}
d1.partials[1]
partials(d1, 1)
# @inline val(d::Dual) = d.value
ForwardDiff.can_dual(::Type{<:SVec}) = true
@inline function Base.:+(x::Dual{Z,T,D}, sv::SVec{N,S}) where {Z,T<:Number,D,N,S}
y = x.value + sv
ps = ntuple(d -> x.partials.values[d] + zero(sv), Val(D))
TS = SVec{N,promote_type(T,S)}
Dual{Z,TS,D}(y, Partials{D,TS}(ps))
end
@inline function Base.:+(sv::SVec{N,S}, x::Dual{Z,T,D}) where {Z,T<:Number,D,N,S}
y = x.value + sv
ps = ntuple(d -> x.partials.values[d] + zero(sv), Val(D))
TS = SVec{N,promote_type(T,S)}
Dual{Z,TS,D}(y, Partials{D,TS}(ps))
end
@inline function Base.:*(x::Dual{Z,SVec{N,T},D}, sv::SVec{N,S}) where {Z,T,D,N,S}
y = x.value * sv
ps = ntuple(d -> x.partials.values[d] * sv, Val(D))
TS = SVec{N,promote_type(T,S)}
Dual{Z,typeof(y),D}(y, Partials{D,typeof(y)}(ps))
end
@inline function Base.:*(sv::SVec{N,S}, x::Dual{Z,SVec{N,T},D}) where {Z,T,D,N,S}
y = sv * x.value
ps = ntuple(d -> sv * x.partials.values[d], Val(D))
TS = SVec{N,promote_type(T,S)}
Dual{Z,TS,D}(y, Partials{D,TS}(ps))
end
@inline function Base.:*(p::Partials{D,SVec{N,T}}, sv::SVec{N,S}) where {T,D,N,S}
TS = SVec{N,promote_type(T,S)}
Partials{D,TS}(ntuple(d -> p.values[d] * sv, Val(D)))
end
@inline function Base.:*(sv::SVec{N,S}, p::Partials{D,SVec{N,T}}) where {T,D,N,S}
TS = SVec{N,promote_type(T,S)}
Partials{D,TS}(ntuple(d -> sv * p.values[d], Val(D)))
end
#========== the end ==========#