Math: added IsUnitless type trait.

doc/changelog.dox

@@ -123,9 +123,9 @@ See also:
     @ref Corrade::Utility::Debug::color modifier
 -   Added convenience @ref BoolVector2, @ref BoolVector3 and @ref BoolVector4
     typedefs to the root namespace
--   New @ref Math::IsScalar, @ref Math::IsVector, @ref Math::IsIntegral and
-    @ref Math::IsFloatingPoint type traits and a @ref Math::UnderlyingTypeOf
-    utility
+-   New @ref Math::IsScalar, @ref Math::IsVector, @ref Math::IsIntegral,
+    @ref Math::IsFloatingPoint and @ref Math::IsUnitless type traits and a
+    @ref Math::UnderlyingTypeOf utility
 
 @subsubsection changelog-latest-new-platform Platform libraries
 

src/Magnum/Math/Test/TypeTraitsTest.cpp

@@ -43,6 +43,7 @@ struct TypeTraitsTest: Corrade::TestSuite::Tester {
     void isVector();
     void isIntegral();
     void isFloatingPoint();
+    void isUnitless();
 
     void underlyingTypeOf();
 
@@ -107,6 +108,7 @@ TypeTraitsTest::TypeTraitsTest() {
               &TypeTraitsTest::isVector,
               &TypeTraitsTest::isIntegral,
               &TypeTraitsTest::isFloatingPoint,
+              &TypeTraitsTest::isUnitless,
 
               &TypeTraitsTest::underlyingTypeOf,
 
@@ -231,6 +233,14 @@ void TypeTraitsTest::isFloatingPoint() {
     CORRADE_VERIFY(!IsFloatingPoint<char*>::value);
 }
 
+void TypeTraitsTest::isUnitless() {
+    CORRADE_VERIFY(IsUnitless<Int>::value);
+    CORRADE_VERIFY(IsUnitless<Color4<Float>>::value);
+    CORRADE_VERIFY(!IsUnitless<Deg<Float>>::value);
+    CORRADE_VERIFY(!(IsUnitless<Unit<Rad, Double>>::value));
+    CORRADE_VERIFY(!IsUnitless<char*>::value);
+}
+
 void TypeTraitsTest::underlyingTypeOf() {
     CORRADE_VERIFY((std::is_same<UnderlyingTypeOf<Int>, Int>::value));
     CORRADE_VERIFY((std::is_same<UnderlyingTypeOf<Deg<Float>>, Float>::value));

src/Magnum/Math/TypeTraits.h

@@ -222,6 +222,24 @@ template<class T> struct IsFloatingPoint<Deg<T>>: IsFloatingPoint<T> {};
 template<class T> struct IsFloatingPoint<Rad<T>>: IsFloatingPoint<T> {};
 #endif
 
+/**
+@brief Whether @p T is a unitless tpye
+
+Equivalent to @ref std::true_type for scalar or vector types that have an
+unitless underlying type (i.e., not @ref Deg or @ref Rad); @ref std::false_type
+otherwise. Some math functions such as @ref sqrt() or @ref log() work only with
+unitless types because the resulting unit couldn't be expressed otherwise.
+@see @ref IsScalar, @ref IsVector
+*/
+template<class T> struct IsUnitless
+    #ifndef DOXYGEN_GENERATING_OUTPUT
+    : std::integral_constant<bool, IsScalar<T>::value || IsVector<T>::value>
+    #endif
+    {};
+template<template<class> class Derived, class T> struct IsUnitless<Unit<Derived, T>>: std::false_type {};
+template<class T> struct IsUnitless<Deg<T>>: std::false_type {};
+template<class T> struct IsUnitless<Rad<T>>: std::false_type {};
+
 namespace Implementation {
     template<class T> struct UnderlyingType {
         static_assert(IsScalar<T>::value, "type is not scalar");