removed NaNs, codified behaviour with Ints

src/dual.jl

@@ -260,12 +260,14 @@ end
 
 Base.mod(z::Dual, n::Number) = Dual(mod(value(z), n), epsilon(z))
 
-# these two definitions are needed to fix ambiguity warnings
-Base.:^(z::Dual, n::Unsigned) = z^Signed(n)
-Base.:^(z::Dual, n::Integer) = Dual(value(z)^n, epsilon(z)*n*value(z)^(n-1))
-Base.:^(z::Dual, n::Rational) = Dual(value(z)^n, epsilon(z)*n*value(z)^(n-1))
+# introduce a boolean !iszero(n) for hard zero behaviour to combat NaNs
+pow(z::Dual, n) = Dual(value(z)^n, !iszero(n) * (epsilon(z) * n * value(z)^(n - 1)))
+# these last two definitions are needed to fix ambiguity warnings
+for T ∈ (:Integer, :Rational, :Number)
+    @eval Base.:^(z::Dual, n::$T) = pow(z, n)
+end
+
 
-Base.:^(z::Dual, n::Number) = Dual(value(z)^n, epsilon(z)*n*value(z)^(n-1))
 NaNMath.pow(z::Dual, n::Number) = Dual(NaNMath.pow(value(z),n), epsilon(z)*n*NaNMath.pow(value(z),n-1))
 NaNMath.pow(z::Number, w::Dual) = Dual(NaNMath.pow(z,value(w)), epsilon(w)*NaNMath.pow(z,value(w))*log(z))
 

test/automatic_differentiation_test.jl

@@ -15,6 +15,29 @@ y = x^3.0
 @test value(y) ≈ 2.0^3
 @test epsilon(y) ≈ 3.0*2^2
 
+# taking care with divides by zero where there shouldn't be any on paper
+for (y, n) ∈ Iterators.product((float(x), Dual(0.0, 1)), (0, 0.0))
+  z = y^n
+  @test value(z) == 1
+  @test !isnan(epsilon(z))
+  @test epsilon(z) == 0
+end
+
+# acting on floats works as expected
+for (y, n) ∈ ((float(x), Dual(0.0, 1)), -1:1)
+  @test float(x)^n == float(x)^float(n)
+end
+
+# power_by_squaring error for integers
+powwrap(z, n) = Dual(z, 1)^n # needs to be wrapped to make n a literal
+@test_throws DomainError powwrap(123, 0)
+@test_throws DomainError powwrap(2, -1)
+@test_throws DomainError powwrap(123, -1)
+# this one doesn't error!
+@test powwrap(1, -1) == Dual(1, -1)
+
+@test !isnan(epsilon(Dual(0, 1)^1))
+
 y = Dual(2.0, 1)^UInt64(0)
 @test !isnan(epsilon(y))