Special case x^0 (#331)

fixes #330

src/dual.jl

@@ -408,8 +408,12 @@ for f in (:(Base.:^), :(NaNMath.pow))
             begin
                 v = value(x)
                 expv = ($f)(v, y)
-                deriv = y * ($f)(v, y - 1)
-                return Dual{Tx}(expv, deriv * partials(x))
+                if y == zero(y)
+                    new_partials = zero(partials(x))
+                else
+                    new_partials = partials(x) * y * ($f)(v, y - 1)
+                end
+                return Dual{Tx}(expv, new_partials)
             end,
             begin
                 v = value(y)

test/DualTest.jl

@@ -455,4 +455,14 @@ for N in (0,3), M in (0,4), V in (Int, Float32)
     end
 end
 
+@testset "Exponentiation of zero" begin
+    x0 = 0.0
+    x1 = Dual{:t1}(x0, 1.0)
+    x2 = Dual{:t2}(x1, 1.0)
+    x3 = Dual{:t3}(x2, 1.0)
+    @test x3^2 === x3 * x3
+    @test x2^1 === x2
+    @test x1^0 === Dual{:t1}(1.0, 0.0)
+end
+
 end # module