From 86cf22675fd82ddab34d111aa36002a728284f15 Mon Sep 17 00:00:00 2001
From: Mike Innes <mike.j.innes@gmail.com>
Date: Fri, 24 Aug 2018 14:07:08 +0100
Subject: [PATCH] rewrite broadcast

---
 src/tracker/array.jl | 44 +++++++++++++++++++++-----------------------
 1 file changed, 21 insertions(+), 23 deletions(-)

diff --git a/src/tracker/array.jl b/src/tracker/array.jl
index cef4463d..5e76ddf4 100644
--- a/src/tracker/array.jl
+++ b/src/tracker/array.jl
@@ -327,35 +327,33 @@ end
 
 using ForwardDiff: Dual, partials, value
 
-_size(x::AbstractArray) = size(x)
-_size(x) = ()
+trim(x, Δ) = reshape(Δ, ntuple(i -> size(Δ, i), Val(ndims(x))))
 
-dualify(xs, n) = xs
-dualify(xs::AbstractArray, ps) = map(x -> Dual(x, ps), xs)
-dualify(xs::Real, ps) = Dual(xs, ps)
+unbroadcast(x::AbstractArray, Δ) =
+  size(x) == size(Δ) ? Δ :
+  length(x) == length(Δ) ? trim(x, Δ) :
+    trim(x, sum(Δ, dims = ntuple(i -> size(x, i) == 1 ? i : ndims(Δ)+1, Val(ndims(Δ)))))
 
-unbroadcast(x::Tuple, Δ) =
-  x == size(Δ) ? Δ :
-    reshape(sum(Δ, dims = filter(n -> n > length(x) || x[n] == 1, 1:ndims(Δ))), x)
+unbroadcast(x::Number, Δ) = sum(Δ)
+unbroadcast(x::Base.RefValue{<:Function}, _) = nothing
+unbroadcast(x::Base.RefValue{<:Val}, _) = nothing
 
-unbroadcast(x::Tuple{}, Δ) = sum(Δ)
+dual(x, p) = x
+dual(x::Real, p) = Dual(x, p)
 
-function getpartial(Δ, x, i)
-  @inbounds p = getindex(partials(x), i)
-  return Δ * p
+function partial(f::F, Δ, i, args::Vararg{Any,N}) where {F,N}
+  dargs = ntuple(j -> dual(args[j], i==j), Val(N))
+  return Δ * f(dargs...).partials[1]
 end
 
-function ∇broadcast(f, args::Vararg{Any,N}) where N
-  sizes = _size.(args)
-  dargs = map((x,i) -> dualify(data(x), ntuple(j -> i==j, Val(N))), args, ntuple(identity, Val(N)))
-  out = broadcast(f, dargs...)
-  eltype(out) <: Dual || return out
-  y = value.(out)
-  back = function (Δ_)
-    Δ = data(Δ_)
-    Δargs = ntuple(i -> getpartial.(Δ, out, i), Val(N))
-    dxs = map((x, Δ) -> unbroadcast(x, Δ), sizes, Δargs)
-    nobacksies(:broadcast, dxs)
+@inline function ∇broadcast(f::F, args::Vararg{Any,N}) where {F,N}
+  y = broadcast(f, data.(args)...)
+  eltype(y) <: Real || return y
+  eltype(y) == Bool && return y
+  function back(Δ)
+    Δargs = ntuple(i -> partial.(f, data(Δ), i, args...), Val(N))
+    dxs = unbroadcast.(args, Δargs)
+    return nobacksies(:broadcast, dxs)
   end
   # So we can return non-tracked arrays
   track(Call(back, tracker.(args)), y)