diff --git a/README.md b/README.md
index cbb55a8..e6bb118 100644
--- a/README.md
+++ b/README.md
@@ -373,6 +373,11 @@ using ptrdiff4x4 = mat<std::ptrdiff_t, 4>;
 template < typename T, size_t Size >
 constexpr vec<T, Size> operator-(const vec<T, Size>& xs);
 
+// !operator
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> operator!(const vec<T, Size>& xs);
+
 // operator+
 
 template < typename T, size_t Size >
@@ -471,6 +476,11 @@ constexpr bool operator<(const vec<T, Size>& xs, const vec<T, Size>& ys);
 template < typename T, size_t Size >
 constexpr mat<T, Size> operator-(const mat<T, Size>& xs);
 
+// !operator
+
+template < typename T, size_t Size >
+constexpr mat<bool, Size> operator!(const mat<T, Size>& xs);
+
 // operator+
 
 template < typename T, size_t Size >
@@ -569,9 +579,9 @@ constexpr bool operator<(const mat<T, Size>& xs, const mat<T, Size>& ys);
 
 ### Angle and Trigonometry Functions
 
-```cpp
-// Scalar
+#### Scalar
 
+```cpp
 template < floating_point T >
 constexpr T radians(T degrees) noexcept;
 
@@ -622,9 +632,11 @@ std::pair<T, T> sincos(T x) noexcept;
 
 template < floating_point T >
 void sincos(T x, T* s, T* c) noexcept;
+```
 
-// Vector
+#### Vector
 
+```cpp
 template < typename T, size_t Size >
 constexpr vec<T, Size> radians(const vec<T, Size>& degrees);
 
@@ -676,9 +688,9 @@ void sincos(const vec<T, Size>& xs, vec<T, Size>* ss, vec<T, Size>* cs);
 
 ### Exponential Functions
 
-```cpp
-// Scalar
+#### Scalar
 
+```cpp
 template < floating_point T >
 T pow(T x, T y) noexcept;
 
@@ -699,9 +711,11 @@ T sqrt(T x) noexcept;
 
 template < floating_point T >
 T rsqrt(T x) noexcept;
+```
 
-// Vector
+#### Vector
 
+```cpp
 template < typename T, size_t Size >
 vec<T, Size> pow(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
@@ -726,9 +740,9 @@ vec<T, Size> rsqrt(const vec<T, Size>& xs);
 
 ### Common Functions
 
-```cpp
-// Scalar
+#### Scalar
 
+```cpp
 template < arithmetic T >
 constexpr T abs(T x) noexcept;
 
@@ -803,9 +817,11 @@ T frexp(T x, int* exp) noexcept;
 
 template < floating_point T >
 T ldexp(T x, int exp) noexcept;
+```
 
-// Vector
+#### Vector
 
+```cpp
 template < typename T, size_t Size >
 constexpr vec<T, Size> abs(const vec<T, Size>& xs);
 
@@ -905,9 +921,9 @@ vec<T, Size> ldexp(const vec<T, Size>& xs, const vec<int, Size>& exps);
 
 ### Geometric Functions
 
-```cpp
-// Scalar
+#### Scalar
 
+```cpp
 template < arithmetic T >
 constexpr T dot(T x, T y) noexcept;
 
@@ -934,9 +950,11 @@ constexpr T reflect(T i, T n) noexcept;
 
 template < floating_point T >
 T refract(T i, T n, T eta) noexcept;
+```
 
-// Vector
+#### Vector
 
+```cpp
 template < typename T, size_t Size >
 constexpr T dot(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
@@ -973,9 +991,9 @@ vec<T, Size> refract(const vec<T, Size>& i, const vec<T, Size>& n, T eta);
 
 ### Relational Functions
 
-```cpp
-// Scalar
+#### Scalar
 
+```cpp
 template < arithmetic T >
 constexpr bool less(T x, T y) noexcept;
 
@@ -1005,31 +1023,81 @@ constexpr bool any(T x) noexcept;
 
 template < arithmetic T >
 constexpr bool all(T x) noexcept;
+```
 
-// Vector
+#### Vector
 
-template < typename T, size_t Size >
+```cpp
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> less(const vec<T, Size>& xs, T y);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> less(T x, const vec<T, Size>& ys);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> less(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
-template < typename T, size_t Size >
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> less_equal(const vec<T, Size>& xs, T y);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> less_equal(T x, const vec<T, Size>& ys);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> less_equal(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
-template < typename T, size_t Size >
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> greater(const vec<T, Size>& xs, T y);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> greater(T x, const vec<T, Size>& ys);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> greater(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
-template < typename T, size_t Size >
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> greater_equal(const vec<T, Size>& xs, T y);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> greater_equal(T x, const vec<T, Size>& ys);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> greater_equal(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
-template < typename T, size_t Size >
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, T y);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> equal_to(T x, const vec<T, Size>& ys);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
-template < typename T, size_t Size >
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, T y, T epsilon);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> equal_to(T x, const vec<T, Size>& ys, T epsilon);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys, T epsilon);
 
-template < typename T, size_t Size >
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, T y);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> not_equal_to(T x, const vec<T, Size>& ys);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys);
 
-template < typename T, size_t Size >
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, T y, T epsilon);
+
+template < typename T, std::size_t Size >
+constexpr vec<bool, Size> not_equal_to(T x, const vec<T, Size>& ys, T epsilon);
+
+template < typename T, std::size_t Size >
 constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys, T epsilon);
 
 template < typename T, size_t Size >
@@ -1192,8 +1260,6 @@ constexpr mat<T, 4> scale(const mat<T, 4>& m, T x, T y, T z);
 template < typename T >
 constexpr mat<T, 4> scale(const mat<T, 4>& m, const vec<T, 3>& v);
 
-// look_at
-
 template < typename T >
 mat<T, 4> look_at_lh(const vec<T, 3>& eye, const vec<T, 3>& at, const vec<T, 3>& up);
 
diff --git a/headers/vmath.hpp/vmath_mat_fun.hpp b/headers/vmath.hpp/vmath_mat_fun.hpp
index 8ffc74e..d9013ff 100644
--- a/headers/vmath.hpp/vmath_mat_fun.hpp
+++ b/headers/vmath.hpp/vmath_mat_fun.hpp
@@ -199,6 +199,13 @@ namespace vmath_hpp
         return map_join([](const vec<T, Size>& x){ return -x; }, xs);
     }
 
+    // !operator
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr mat<bool, Size> operator!(const mat<T, Size>& xs) {
+        return map_join([](const vec<T, Size>& x){ return !x; }, xs);
+    }
+
     // operator+
 
     template < typename T, std::size_t Size >
diff --git a/headers/vmath.hpp/vmath_vec_fun.hpp b/headers/vmath.hpp/vmath_vec_fun.hpp
index d9a0cf0..7e6bb00 100644
--- a/headers/vmath.hpp/vmath_vec_fun.hpp
+++ b/headers/vmath.hpp/vmath_vec_fun.hpp
@@ -172,6 +172,13 @@ namespace vmath_hpp
         return map_join([](T x){ return -x; }, xs);
     }
 
+    // !operator
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> operator!(const vec<T, Size>& xs) {
+        return map_join([](T x){ return !x; }, xs);
+    }
+
     // operator+
 
     template < typename T, std::size_t Size >
@@ -708,46 +715,140 @@ namespace vmath_hpp
 
 namespace vmath_hpp
 {
+    // less
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> less(const vec<T, Size>& xs, T y) {
+        return map_join([y](T x){ return less(x, y); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> less(T x, const vec<T, Size>& ys) {
+        return map_join([x](T y){ return less(x, y); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> less(const vec<T, Size>& xs, const vec<T, Size>& ys) {
         return map_join([](T x, T y){ return less(x, y); }, xs, ys);
     }
 
+    // less_equal
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> less_equal(const vec<T, Size>& xs, T y) {
+        return map_join([y](T x){ return less_equal(x, y); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> less_equal(T x, const vec<T, Size>& ys) {
+        return map_join([x](T y){ return less_equal(x, y); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> less_equal(const vec<T, Size>& xs, const vec<T, Size>& ys) {
         return map_join([](T x, T y){ return less_equal(x, y); }, xs, ys);
     }
 
+    // greater
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> greater(const vec<T, Size>& xs, T y) {
+        return map_join([y](T x){ return greater(x, y); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> greater(T x, const vec<T, Size>& ys) {
+        return map_join([x](T y){ return greater(x, y); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> greater(const vec<T, Size>& xs, const vec<T, Size>& ys) {
         return map_join([](T x, T y){ return greater(x, y); }, xs, ys);
     }
 
+    // greater_equal
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> greater_equal(const vec<T, Size>& xs, T y) {
+        return map_join([y](T x){ return greater_equal(x, y); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> greater_equal(T x, const vec<T, Size>& ys) {
+        return map_join([x](T y){ return greater_equal(x, y); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> greater_equal(const vec<T, Size>& xs, const vec<T, Size>& ys) {
         return map_join([](T x, T y){ return greater_equal(x, y); }, xs, ys);
     }
 
+    // equal_to
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, T y) {
+        return map_join([y](T x){ return equal_to(x, y); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> equal_to(T x, const vec<T, Size>& ys) {
+        return map_join([x](T y){ return equal_to(x, y); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys) {
         return map_join([](T x, T y){ return equal_to(x, y); }, xs, ys);
     }
 
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, T y, T epsilon) {
+        return map_join([y, epsilon](T x){ return equal_to(x, y, epsilon); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> equal_to(T x, const vec<T, Size>& ys, T epsilon) {
+        return map_join([x, epsilon](T y){ return equal_to(x, y, epsilon); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys, T epsilon) {
         return map_join([epsilon](T x, T y){ return equal_to(x, y, epsilon); }, xs, ys);
     }
 
+    // not_equal_to
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, T y) {
+        return map_join([y](T x){ return not_equal_to(x, y); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> not_equal_to(T x, const vec<T, Size>& ys) {
+        return map_join([x](T y){ return not_equal_to(x, y); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys) {
         return map_join([](T x, T y){ return not_equal_to(x, y); }, xs, ys);
     }
 
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, T y, T epsilon) {
+        return map_join([y, epsilon](T x){ return not_equal_to(x, y, epsilon); }, xs);
+    }
+
+    template < typename T, std::size_t Size >
+    [[nodiscard]] constexpr vec<bool, Size> not_equal_to(T x, const vec<T, Size>& ys, T epsilon) {
+        return map_join([x, epsilon](T y){ return not_equal_to(x, y, epsilon); }, ys);
+    }
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr vec<bool, Size> not_equal_to(const vec<T, Size>& xs, const vec<T, Size>& ys, T epsilon) {
         return map_join([epsilon](T x, T y){ return not_equal_to(x, y, epsilon); }, xs, ys);
     }
 
+    // any/all
+
     template < typename T, std::size_t Size >
     [[nodiscard]] constexpr bool any(const vec<T, Size>& xs) {
         return fold_join([](bool acc, T x){ return acc || any(x); }, false, xs);
diff --git a/untests/vmath_mat_fun_tests.cpp b/untests/vmath_mat_fun_tests.cpp
index c8b7069..6ceeac9 100644
--- a/untests/vmath_mat_fun_tests.cpp
+++ b/untests/vmath_mat_fun_tests.cpp
@@ -59,6 +59,7 @@ TEST_CASE("vmath/mat_fun") {
 
     SUBCASE("operators") {
         STATIC_REQUIRE(-int2x2(1,2,3,4) == int2x2(-1,-2,-3,-4));
+        STATIC_REQUIRE(!int2x2(-1,0,1,2) == bool2x2(false,true,false,false));
 
         STATIC_REQUIRE(int2x2(1,2,3,4) + 2 == int2x2(3,4,5,6));
         STATIC_REQUIRE(int2x2(1,2,3,4) - 2 == int2x2(-1,0,1,2));
diff --git a/untests/vmath_vec_fun_tests.cpp b/untests/vmath_vec_fun_tests.cpp
index f5f256a..ba1a79d 100644
--- a/untests/vmath_vec_fun_tests.cpp
+++ b/untests/vmath_vec_fun_tests.cpp
@@ -42,6 +42,7 @@ TEST_CASE("vmath/vec_fun") {
 
     SUBCASE("Operators") {
         STATIC_REQUIRE(-int2(1,-2) == int2(-1,2));
+        STATIC_REQUIRE(!int3(-1,0,1) == bool3(false, true, false));
 
         STATIC_REQUIRE(int2(1,2) + 3 == int2(4,5));
         STATIC_REQUIRE(int2(1,2) - 3 == int2(-2,-1));
@@ -211,20 +212,52 @@ TEST_CASE("vmath/vec_fun") {
 
     SUBCASE("Vector Relational Functions") {
         STATIC_REQUIRE(less(int3(1,1,1), int3(0,1,2)) == bool3(false, false, true));
+        STATIC_REQUIRE(less(int3(0,1,2),1) == bool3(true, false, false));
+        STATIC_REQUIRE(less(1,int3(0,1,2)) == bool3(false, false, true));
+
         STATIC_REQUIRE(less_equal(int3(1,1,1), int3(0,1,2)) == bool3(false, true, true));
+        STATIC_REQUIRE(less_equal(int3(0,1,2),1) == bool3(true, true, false));
+        STATIC_REQUIRE(less_equal(1,int3(0,1,2)) == bool3(false, true, true));
 
         STATIC_REQUIRE(greater(int3(1,1,1), int3(0,1,2)) == bool3(true, false, false));
+        STATIC_REQUIRE(greater(int3(0,1,2),1) == bool3(false, false, true));
+        STATIC_REQUIRE(greater(1,int3(0,1,2)) == bool3(true, false, false));
+
         STATIC_REQUIRE(greater_equal(int3(1,1,1), int3(0,1,2)) == bool3(true, true, false));
+        STATIC_REQUIRE(greater_equal(int3(0,1,2),1) == bool3(false, true, true));
+        STATIC_REQUIRE(greater_equal(1,int3(0,1,2)) == bool3(true, true, false));
 
         STATIC_REQUIRE(equal_to(int3(1,1,1), int3(0,1,2)) == bool3(false, true, false));
+        STATIC_REQUIRE(equal_to(int3(0,1,2),1) == bool3(false, true, false));
+        STATIC_REQUIRE(equal_to(1,int3(0,1,2)) == bool3(false, true, false));
+
         STATIC_REQUIRE(equal_to(int4(1,1,1,1), int4(0,1,2,3), 0) == bool4(false, true, false, false));
+        STATIC_REQUIRE(equal_to(int4(0,1,2,3), 1, 0) == bool4(false, true, false, false));
+        STATIC_REQUIRE(equal_to(1, int4(0,1,2,3), 0) == bool4(false, true, false, false));
+
         STATIC_REQUIRE(equal_to(int4(1,1,1,1), int4(0,1,2,3), 1) == bool4(true, true, true, false));
+        STATIC_REQUIRE(equal_to(int4(0,1,2,3), 1, 1) == bool4(true, true, true, false));
+        STATIC_REQUIRE(equal_to(1, int4(0,1,2,3), 1) == bool4(true, true, true, false));
+
         STATIC_REQUIRE(equal_to(int4(1,1,1,1), int4(0,1,2,3), 2) == bool4(true, true, true, true));
+        STATIC_REQUIRE(equal_to(int4(0,1,2,3), 1, 2) == bool4(true, true, true, true));
+        STATIC_REQUIRE(equal_to(1, int4(0,1,2,3), 2) == bool4(true, true, true, true));
 
         STATIC_REQUIRE(not_equal_to(int3(1,1,1), int3(0,1,2)) == bool3(true, false, true));
+        STATIC_REQUIRE(not_equal_to(int3(0,1,2),1) == bool3(true, false, true));
+        STATIC_REQUIRE(not_equal_to(1,int3(0,1,2)) == bool3(true, false, true));
+
         STATIC_REQUIRE(not_equal_to(int4(1,1,1,1), int4(0,1,2,3), 0) == bool4(true, false, true, true));
+        STATIC_REQUIRE(not_equal_to(int4(0,1,2,3), 1, 0) == bool4(true, false, true, true));
+        STATIC_REQUIRE(not_equal_to(1, int4(0,1,2,3), 0) == bool4(true, false, true, true));
+
         STATIC_REQUIRE(not_equal_to(int4(1,1,1,1), int4(0,1,2,3), 1) == bool4(false, false, false, true));
+        STATIC_REQUIRE(not_equal_to(int4(0,1,2,3), 1, 1) == bool4(false, false, false, true));
+        STATIC_REQUIRE(not_equal_to(1, int4(0,1,2,3), 1) == bool4(false, false, false, true));
+
         STATIC_REQUIRE(not_equal_to(int4(1,1,1,1), int4(0,1,2,3), 2) == bool4(false, false, false, false));
+        STATIC_REQUIRE(not_equal_to(int4(0,1,2,3), 1, 2) == bool4(false, false, false, false));
+        STATIC_REQUIRE(not_equal_to(1, int4(0,1,2,3), 2) == bool4(false, false, false, false));
 
         STATIC_REQUIRE_FALSE(any(bool2(false, false)));
         STATIC_REQUIRE(any(bool2(true, false)));