diff --git a/math/math.hpp b/math/math.hpp
index d66df29..4a79a8c 100644
--- a/math/math.hpp
+++ b/math/math.hpp
@@ -39,13 +39,13 @@ constexpr float abs(const float n) noexcept
 constexpr float pi = 3.141592653589793;
 
 template <typename T>
-inline constexpr float max(const T a, const T b) noexcept
+inline constexpr T max(const T a, const T b) noexcept
 {
   return (a > b) ? a : b;
 }
 
 template <typename T>
-inline constexpr float min(const T a, const T b) noexcept
+inline constexpr T min(const T a, const T b) noexcept
 {
   return (a < b) ? a : b;
 }
diff --git a/math/vec.hpp b/math/vec.hpp
index a63d225..930fe10 100644
--- a/math/vec.hpp
+++ b/math/vec.hpp
@@ -2,3 +2,27 @@
 
 template <int L, typename T>
 struct vec;
+
+template <int L, typename T>
+inline constexpr T magnitude(vec<L, T> const& v)
+{
+  return sqrt(dot(v, v));
+}
+
+template <int L, typename T>
+inline constexpr T magnitude_squared(vec<L, T> const& v)
+{
+  return dot(v, v);
+}
+
+template <int L, typename T>
+inline constexpr vec<3, T> normalize(vec<L, T> const& v)
+{
+  return v / magnitude(v);
+}
+
+template <int L, typename T>
+inline constexpr vec<3, T> reflect(vec<L, T> const& i, vec<L, T> const& n)
+{
+  return i - dot(n, i) * n * static_cast<T>(2.0);
+}
diff --git a/math/vec3.hpp b/math/vec3.hpp
index 9ae7e2b..98240aa 100644
--- a/math/vec3.hpp
+++ b/math/vec3.hpp
@@ -137,8 +137,10 @@ inline constexpr vec<3, T> operator/(vec<3, T> const& v1, T const& scalar)
 template <typename T>
 inline constexpr T dot(vec<3, T> const& v1, vec<3, T> const& v2)
 {
-  vec<3, T> tmp(v1 * v2);
-  return tmp.x + tmp.y + tmp.z;
+  return
+    v1.x * v2.x +
+    v1.y * v2.y +
+    v1.z * v2.z;
 }
 
 template <typename T>
@@ -160,21 +162,3 @@ inline constexpr vec<3, U> functor1(U (&func) (T const& x), vec<3, T> const& v)
 {
   return vec<3, U>(func(v.x), func(v.y), func(v.z));
 }
-
-template <typename T>
-inline constexpr T magnitude(vec<3, T> const& v)
-{
-  return sqrt(dot(v, v));
-}
-
-template <typename T>
-inline constexpr vec<3, T> normalize(vec<3, T> const& v)
-{
-  return v / magnitude(v);
-}
-
-template <typename T>
-inline constexpr vec<3, T> reflect(vec<3, T> const& i, vec<3, T> const& n)
-{
-  return i - dot(n, i) * n * static_cast<T>(2.0);
-}