Vectorize pow for integer base / exponent types
diff --git a/test/array_cwise.cpp b/test/array_cwise.cpp
index 3e96e4c..64c4c2a 100644
--- a/test/array_cwise.cpp
+++ b/test/array_cwise.cpp
@@ -126,6 +126,72 @@
   VERIFY(all_pass);
 }
 
+template <typename Scalar, typename ScalarExponent>
+Scalar calc_overflow_threshold(const ScalarExponent exponent) {
+    EIGEN_USING_STD(exp2);
+    EIGEN_STATIC_ASSERT((NumTraits<Scalar>::digits() < 2 * NumTraits<double>::digits()), BASE_TYPE_IS_TOO_BIG);
+
+    if (exponent < 2)
+        return NumTraits<Scalar>::highest();
+    else {
+        const double max_exponent = static_cast<double>(NumTraits<Scalar>::digits());
+        const double clamped_exponent = exponent < max_exponent ? static_cast<double>(exponent) : max_exponent;
+        const double threshold = exp2(max_exponent / clamped_exponent);
+        return static_cast<Scalar>(threshold);
+    }
+}
+
+template <typename Base, typename Exponent>
+void test_exponent(Exponent exponent) {
+    EIGEN_USING_STD(pow);
+
+    const Base max_abs_bases = 10000;
+    // avoid integer overflow in Base type
+    Base threshold = calc_overflow_threshold<Base, Exponent>(numext::abs(exponent));
+    // avoid numbers that can't be verified with std::pow
+    double double_threshold = calc_overflow_threshold<double, Exponent>(numext::abs(exponent));
+    // use the lesser of these two thresholds
+    Base testing_threshold = threshold < double_threshold ? threshold : static_cast<Base>(double_threshold);
+    // avoid divide by zero
+    Base min_abs_base = exponent < 0 ? 1 : 0;
+    // avoid excessively long test
+    Base max_abs_base = numext::mini(testing_threshold, max_abs_bases);
+    // test both vectorized and non-vectorized code paths
+    const Index array_size = 2 * internal::packet_traits<Base>::size + 1;
+
+    Base max_base = numext::mini(testing_threshold, max_abs_bases);
+    Base min_base = NumTraits<Base>::IsSigned ? -max_base : 0;
+
+    ArrayX<Base> x(array_size), y(array_size);
+
+    bool all_pass = true;
+
+    for (Base base = min_base; base <= max_base; base++) {
+        if (exponent < 0 && base == 0) continue;
+        x.setConstant(base);
+        y = x.pow(exponent);
+        Base e = pow(base, exponent);
+        for (Base a : y) {
+            bool pass = a == e;
+            all_pass &= pass;
+            if (!pass) {
+                std::cout << "pow(" << base << "," << exponent << ")   =   " << a << " !=  " << e << std::endl;
+            }
+        }
+    }
+
+    VERIFY(all_pass);
+}
+template <typename Base, typename Exponent>
+void int_pow_test() {
+    Exponent max_exponent = NumTraits<Base>::digits();
+    Exponent min_exponent = NumTraits<Exponent>::IsSigned ? -max_exponent : 0;
+
+    for (Exponent exponent = min_exponent; exponent < max_exponent; exponent++) {
+        test_exponent<Base, Exponent>(exponent);
+    }
+}
+
 template<typename ArrayType> void array(const ArrayType& m)
 {
   typedef typename ArrayType::Scalar Scalar;
@@ -500,6 +566,14 @@
   VERIFY_IS_APPROX(m3.pow(RealScalar(-2)), m3.square().inverse());
   pow_test<Scalar>();
 
+  typedef typename internal::make_integer<Scalar>::type SignedInt;
+  typedef typename std::make_unsigned<SignedInt>::type UnsignedInt;
+
+  int_pow_test<SignedInt, SignedInt>();
+  int_pow_test<SignedInt, UnsignedInt>();
+  int_pow_test<UnsignedInt, SignedInt>();
+  int_pow_test<UnsignedInt, UnsignedInt>();
+
   VERIFY_IS_APPROX(log10(m3), log(m3)/numext::log(Scalar(10)));
   VERIFY_IS_APPROX(log2(m3), log(m3)/numext::log(Scalar(2)));