use istracked instead of pure type checking to decide whether to update partials cache for pow/div broadcast methods (#37)

Author: jrevels

src/derivatives/elementwise.jl

@@ -433,9 +433,7 @@ denom_partials(n, d) = broadcast(denom_partials_kernel, n, d)
 denom_partials!(out::Ref, n, d) = (out[] = denom_partials_kernel(n, d); nothing)
 denom_partials!(out::AbstractArray, n, d) = (broadcast!(denom_partials_kernel, out, n, d); nothing)
 
-rdiv_cache(x::TrackedType, y::TrackedType) = (numer_partials(value(y)), denom_partials(value(x), value(y)))
-rdiv_cache(x::TrackedType, y) = (numer_partials(value(y)), nothing)
-rdiv_cache(x, y::TrackedType) = (nothing, denom_partials(value(x), value(y)))
+rdiv_cache(x, y) = (numer_partials(value(y)), denom_partials(value(x), value(y)))
 
 function broadcast_rdiv{D}(x, y, ::Type{D})
     tp = tape(x, y)
@@ -452,8 +450,8 @@ end
     pull_value!(a)
     pull_value!(b)
     broadcast!(/, value(output), a_value, b_value)
-    !(isa(n_partials, Void)) && numer_partials!(n_partials, b_value)
-    !(isa(d_partials, Void)) && denom_partials!(d_partials, a_value, b_value)
+    istracked(a) && numer_partials!(n_partials, b_value)
+    istracked(b) && denom_partials!(d_partials, a_value, b_value)
     return nothing
 end
 
@@ -485,8 +483,8 @@ end
     pull_value!(a)
     pull_value!(b)
     broadcast!(\, value(output), a_value, b_value)
-    !(isa(n_partials, Void)) && numer_partials!(n_partials, a_value)
-    !(isa(d_partials, Void)) && denom_partials!(d_partials, b_value, a_value)
+    istracked(b) && numer_partials!(n_partials, a_value)
+    istracked(a) && denom_partials!(d_partials, b_value, a_value)
     return nothing
 end
 
@@ -515,9 +513,7 @@ exp_partials(b, e) = broadcast(exp_partials_kernel, b, e)
 exp_partials!(out::Ref, b, e) = (out[] = exp_partials_kernel(b, e); nothing)
 exp_partials!(out::AbstractArray, b, e) = (broadcast!(exp_partials_kernel, out, b, e); nothing)
 
-pow_cache(x::TrackedType, y::TrackedType) = (base_partials(value(x), value(y)), exp_partials(value(x), value(y)))
-pow_cache(x::TrackedType, y) = (base_partials(value(x), value(y)), nothing)
-pow_cache(x, y::TrackedType) = (nothing, exp_partials(value(x), value(y)))
+pow_cache(x, y) = (base_partials(value(x), value(y)), exp_partials(value(x), value(y)))
 
 function broadcast_pow{D}(x, y, ::Type{D})
     tp = tape(x, y)
@@ -534,8 +530,8 @@ end
     pull_value!(a)
     pull_value!(b)
     broadcast!(^, value(output), a_value, b_value)
-    !(isa(bs_partials, Void)) && base_partials!(bs_partials, a_value, b_value)
-    !(isa(ex_partials, Void)) && exp_partials!(ex_partials, a_value, b_value)
+    istracked(a) && base_partials!(bs_partials, a_value, b_value)
+    istracked(b) && exp_partials!(ex_partials, a_value, b_value)
     return nothing
 end