Math: added sqrt() overload for Dual.

src/Math/Dual.h

@@ -19,6 +19,7 @@
  * @brief Class Magnum::Math::Dual
  */
 
+#include <cmath>
 #include <Utility/Debug.h>
 
 #include "Math/MathTypeTraits.h"
@@ -191,6 +192,19 @@ template<class T> Corrade::Utility::Debug operator<<(Corrade::Utility::Debug deb
     return debug;
 }
 
+/** @relates Dual
+@brief Square root of dual number
+
+@f[
+    \sqrt{\hat a} = \sqrt{a_0} + \epsilon \frac{a_\epsilon}{2 \sqrt{a_0}}
+@f]
+@see Math::sqrt(const T&)
+*/
+template<class T> Dual<T> sqrt(const Dual<T>& dual) {
+    T sqrt0 = std::sqrt(dual.real());
+    return {sqrt0, dual.dual()/(2*sqrt0)};
+}
+
 }}
 
 #endif

src/Math/Test/DualTest.cpp

@@ -33,6 +33,7 @@ class DualTest: public Corrade::TestSuite::Tester {
         void multiplyDivide();
 
         void conjugated();
+        void sqrt();
 
         void debug();
 };
@@ -49,6 +50,7 @@ DualTest::DualTest() {
              &DualTest::multiplyDivide,
 
              &DualTest::conjugated,
+             &DualTest::sqrt,
 
              &DualTest::debug);
 }
@@ -104,6 +106,10 @@ void DualTest::conjugated() {
     CORRADE_COMPARE(Dual(1.0f, -6.5f).conjugated(), Dual(1.0f, 6.5f));
 }
 
+void DualTest::sqrt() {
+    CORRADE_COMPARE(Math::sqrt(Dual(16.0f, 2.0f)), Dual(4.0f, 0.25f));
+}
+
 void DualTest::debug() {
     std::ostringstream o;