diff --git a/include/cglm/vec4.h b/include/cglm/vec4.h
index 0ef6bff..c50b4f9 100644
--- a/include/cglm/vec4.h
+++ b/include/cglm/vec4.h
@@ -146,7 +146,15 @@ glm_vec4_dot(vec4 a, vec4 b) {
 CGLM_INLINE
 float
 glm_vec4_norm2(vec4 v) {
-  return glm_vec4_dot(v, v);
+#if defined( __SSE__ ) || defined( __SSE2__ )
+  __m128 x0;
+  x0 = _mm_load_ps(v);
+  x0 = _mm_mul_ps(x0, x0);
+  x0 = _mm_add_ps(x0, _mm_shuffle1_ps(x0, 1, 0, 3, 2));
+  return _mm_cvtss_f32(_mm_add_ss(x0, _mm_shuffle1_ps(x0, 0, 1, 0, 1)));
+#else
+  return a[0] * b[0] + a[1] * b[1] + a[2] * b[2] + a[3] * b[3];
+#endif
 }
 
 /*!
@@ -159,7 +167,13 @@ glm_vec4_norm2(vec4 v) {
 CGLM_INLINE
 float
 glm_vec4_norm(vec4 vec) {
+#if defined( __SSE__ ) || defined( __SSE2__ )
+  __m128 x0;
+  x0 = _mm_load_ps(vec);
+  return _mm_cvtss_f32(_mm_sqrt_ss(glm_simd_dot(x0, x0)));
+#else
   return sqrtf(glm_vec4_norm2(vec));
+#endif
 }
 
 /*!
diff --git a/test/src/test_common.c b/test/src/test_common.c
index a559087..60baac3 100644
--- a/test/src/test_common.c
+++ b/test/src/test_common.c
@@ -84,6 +84,11 @@ test_assert_mat4_eq2(mat4 m1, mat4 m2, float eps) {
   }
 }
 
+void
+test_assert_eqf(float a, float b) {
+  assert_true(fabsf(a - b) <= 0.000009); /* rounding errors */
+}
+
 void
 test_assert_vec3_eq(vec3 v1, vec3 v2) {
   assert_true(fabsf(v1[0] - v2[0]) <= 0.000009); /* rounding errors */
diff --git a/test/src/test_common.h b/test/src/test_common.h
index 50e84d6..db113a4 100644
--- a/test/src/test_common.h
+++ b/test/src/test_common.h
@@ -25,6 +25,9 @@
 void
 test_rand_mat4(mat4 dest);
 
+void
+test_assert_eqf(float a, float b);
+
 void
 test_assert_mat4_eq(mat4 m1, mat4 m2);
 
diff --git a/test/src/test_vec4.c b/test/src/test_vec4.c
index 994bab7..51986f1 100644
--- a/test/src/test_vec4.c
+++ b/test/src/test_vec4.c
@@ -28,6 +28,16 @@ test_vec4_normalize_to(vec4 vec, vec4 dest) {
   glm_vec4_scale(vec, 1.0f / norm, dest);
 }
 
+float
+test_vec4_norm2(vec4 vec) {
+  return test_vec4_dot(vec, vec);
+}
+
+float
+test_vec4_norm(vec4 vec) {
+  return sqrtf(test_vec4_dot(vec, vec));
+}
+
 void
 test_vec4(void **state) {
   vec4  v, v1, v2;
@@ -35,7 +45,7 @@ test_vec4(void **state) {
   float d1, d2;
 
 
-  for (i = 0; i < 100; i++) {
+  for (i = 0; i < 1000; i++) {
     /* 1. test SSE/SIMD dot product */
     test_rand_vec4(v);
     d1 = glm_vec4_dot(v, v);
@@ -51,5 +61,13 @@ test_vec4(void **state) {
     /* all must be same */
     test_assert_vec4_eq(v1, v2);
     test_assert_vec4_eq(v, v2);
+
+    /* 3. test SIMD norm */
+    test_rand_vec4(v);
+    test_assert_eqf(test_vec4_norm(v), glm_vec4_norm(v));
+
+    /* 3. test SIMD norm2 */
+    test_rand_vec4(v);
+    test_assert_eqf(test_vec4_norm2(v), glm_vec4_norm2(v));
   }
 }