Add Base.literal_pow

src/dual.jl

@@ -425,6 +425,18 @@ for f in (:(Base.:^), :(NaNMath.pow))
     end
 end
 
+@inline Base.literal_pow(::typeof(^), x::Dual{T}, ::Type{Val{0}}) where {T} =
+    Dual{T}(one(value(x)), zero(partials(x)))
+
+for y in 1:3
+    @eval @inline function Base.literal_pow(::typeof(^), x::Dual{T}, ::Val{$y}) where {T}
+        v = value(x)
+        expv = v^$y
+        deriv = $y * v^$(y - 1)
+        return Dual{T}(expv, deriv * partials(x))
+    end
+end
+
 # hypot #
 #-------#
 

test/DualTest.jl

@@ -460,9 +460,10 @@ end
     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)
+    pow = ^  # to call non-literal power
+    @test pow(x3, 2) === x3^2 === x3 * x3
+    @test pow(x2, 1) === x2^1 === x2
+    @test pow(x1, 0) === x1^0 === Dual{:t1}(1.0, 0.0)
 end
 
 end # module