Add math::dual weak comparison operators & some transcendental functions

libs/math/include/psemek/math/dual.hpp

@@ -3,6 +3,7 @@
 #include <psemek/math/vector.hpp>
 
 #include <iostream>
+#include <compare>
 
 namespace psemek::math
 {
@@ -148,6 +149,50 @@ namespace psemek::math
 		return v * inverse(d);
 	}
 
+	// Exists mostly to make max/min/clamp/etc work
+	template <typename T, std::size_t N>
+	std::partial_ordering operator <=> (dual<T, N> const & d1, dual<T, N> const & d2)
+	{
+		return d1.scalar <=> d2.scalar;
+	}
+
+	template <typename T, std::size_t N>
+	dual<T, N> abs(dual<T, N> const & d)
+	{
+		return d.scalar > T{0} ? d : -d;
+	}
+
+	template <typename T, std::size_t N>
+	dual<T, N> exp(dual<T, N> const & d)
+	{
+		auto e = std::exp(d.scalar);
+		return {e, e * d.delta};
+	}
+
+	template <typename T, std::size_t N>
+	dual<T, N> log(dual<T, N> const & d)
+	{
+		return {std::log(d.scalar), d.delta / d.scalar};
+	}
+
+	template <typename T, std::size_t N>
+	dual<T, N> sin(dual<T, N> const & d)
+	{
+		return {std::sin(d.scalar), std::cos(d.scalar) * d.delta};
+	}
+
+	template <typename T, std::size_t N>
+	dual<T, N> cos(dual<T, N> const & d)
+	{
+		return {std::cos(d.scalar), - std::sin(d.scalar) * d.delta};
+	}
+
+	template <typename T, std::size_t N>
+	dual<T, N> pow(dual<T, N> const & d1, dual<T, N> const & d2)
+	{
+		return exp(log(d1) * d2);
+	}
+
 	template <typename T, std::size_t N>
 	std::ostream & operator << (std::ostream & os, dual<T, N> const & d)
 	{