Add fast vector normalization (#94)

* Add fast normalization routines

* Update readme and remove version history from main file

* Update version at top of file

HandmadeMath.h

@@ -1,5 +1,5 @@
 /*
-  HandmadeMath.h v1.6.0
+  HandmadeMath.h v1.8.0
   
   This is a single header file with a bunch of useful functions for game and
   graphics math operations.
@@ -65,114 +65,6 @@
   versions of these functions that are provided by the CRT.
   
   =============================================================================
-  
-  Version History:
-      0.2 (*) Updated documentation
-          (*) Better C compliance
-          (*) Prefix all handmade math functions 
-          (*) Better operator overloading
-      0.2a
-          (*) Prefixed Macros
-      0.2b
-          (*) Disabled warning 4201 on MSVC as it is legal is C11
-          (*) Removed the f at the end of HMM_PI to get 64bit precision
-      0.3
-          (*) Added +=, -=, *=, /= for hmm_vec2, hmm_vec3, hmm_vec4
-      0.4
-          (*) SSE Optimized HMM_SqrtF
-          (*) SSE Optimized HMM_RSqrtF
-          (*) Removed CRT
-      0.5
-          (*) Added scalar multiplication and division for vectors
-              and matrices
-          (*) Added matrix subtraction and += for hmm_mat4
-          (*) Reconciled all headers and implementations
-          (*) Tidied up, and filled in a few missing operators
-      0.5.1
-          (*) Ensured column-major order for matrices throughout
-          (*) Fixed HMM_Translate producing row-major matrices
-      0.5.2
-          (*) Fixed SSE code in HMM_SqrtF
-          (*) Fixed SSE code in HMM_RSqrtF
-      0.6
-          (*) Added Unit testing
-          (*) Made HMM_Power faster
-          (*) Fixed possible efficiency problem with HMM_Normalize 
-          (*) RENAMED HMM_LengthSquareRoot to HMM_LengthSquared
-          (*) RENAMED HMM_RSqrtF to HMM_RSquareRootF
-          (*) RENAMED HMM_SqrtF to HMM_SquareRootF
-          (*) REMOVED Inner function (user should use Dot now)
-          (*) REMOVED HMM_FastInverseSquareRoot function declaration
-      0.7 
-          (*) REMOVED HMM_LengthSquared in HANDMADE_MATH_IMPLEMENTATION (should
-              use HMM_LengthSquaredVec3, or HANDMADE_MATH_CPP_MODE for function
-              overloaded version)
-          (*) REMOVED HMM_Length in HANDMADE_MATH_IMPLEMENTATION (should use
-              HMM_LengthVec3, HANDMADE_MATH_CPP_MODE for function
-              overloaded version)
-          (*) REMOVED HMM_Normalize in HANDMADE_MATH_IMPLEMENTATION (should use
-              HMM_NormalizeVec3, or HANDMADE_MATH_CPP_MODE for function
-              overloaded version)
-          (*) Added HMM_LengthSquaredVec2
-          (*) Added HMM_LengthSquaredVec4
-          (*) Addd HMM_LengthVec2
-          (*) Added HMM_LengthVec4
-          (*) Added HMM_NormalizeVec2
-          (*) Added HMM_NormalizeVec4
-     1.0
-          (*) Lots of testing!
-     1.1
-          (*) Quaternion support
-          (*) Added type hmm_quaternion
-          (*) Added HMM_Quaternion
-          (*) Added HMM_QuaternionV4
-          (*) Added HMM_AddQuaternion
-          (*) Added HMM_SubtractQuaternion
-          (*) Added HMM_MultiplyQuaternion
-          (*) Added HMM_MultiplyQuaternionF
-          (*) Added HMM_DivideQuaternionF
-          (*) Added HMM_InverseQuaternion
-          (*) Added HMM_DotQuaternion
-          (*) Added HMM_NormalizeQuaternion
-          (*) Added HMM_Slerp
-          (*) Added HMM_QuaternionToMat4
-          (*) Added HMM_QuaternionFromAxisAngle
-     1.1.1
-          (*) Resolved compiler warnings on gcc and g++
-     1.1.2
-          (*) Fixed invalid HMMDEF's in the function definitions
-     1.1.3
-          (*) Fixed compile error in C mode
-     1.1.4
-          (*) Fixed SSE being included on platforms that don't support it
-          (*) Fixed divide-by-zero errors when normalizing zero vectors.
-     1.1.5
-          (*) Add Width and Height to HMM_Vec2
-          (*) Made it so you can supply your own SqrtF 
-     1.2.0
-          (*) Added equality functions for HMM_Vec2, HMM_Vec3, and HMM_Vec4.
-              (*) Added HMM_EqualsVec2, HMM_EqualsVec3, and HMM_EqualsVec4
-              (*) Added C++ overloaded HMM_Equals for all three
-              (*) Added C++ == and != operators for all three
-          (*) SSE'd HMM_MultiplyMat4 (this is _WAY_ faster)
-          (*) SSE'd HMM_Transpose
-     1.3.0
-          (*) Remove need to #define HANDMADE_MATH_CPP_MODE
-     1.4.0
-          (*) Fixed bug when using HandmadeMath in C mode
-          (*) SSEd all vec4 operations          
-          (*) Removed all zero-ing
-     1.5.0
-          (*) Changed internal structure for better performance and inlining.
-          (*) As a result, HANDMADE_MATH_NO_INLINE has been removed and no
-              longer has any effect.
-     1.5.1
-          (*) Fixed a bug with uninitialized elements in HMM_LookAt.
-     1.6.0
-          (*) Added array subscript operators for vector and matrix types in
-              C++. This is provided as a convenience, but be aware that it may
-              incur an extra function call in unoptimized builds.
-
 
   LICENSE
   
@@ -320,7 +212,7 @@ typedef union hmm_vec2
     float Elements[2];
 
 #ifdef __cplusplus
-    inline float &operator[](int Index)
+    inline float &operator[](const int &Index)
     {
         return Elements[Index];
     }
@@ -371,7 +263,7 @@ typedef union hmm_vec3
     float Elements[3];
 
 #ifdef __cplusplus
-    inline float &operator[](int Index)
+    inline float &operator[](const int &Index)
     {
         return Elements[Index];
     }
@@ -435,7 +327,7 @@ typedef union hmm_vec4
 #endif
 
 #ifdef __cplusplus
-    inline float &operator[](int Index)
+    inline float &operator[](const int &Index)
     {
         return Elements[Index];
     }
@@ -447,11 +339,15 @@ typedef union hmm_mat4
     float Elements[4][4];
         
 #ifdef HANDMADE_MATH__USE_SSE
+    __m128 Columns[4];
+
+    // DEPRECATED. Our matrices are column-major, so this was named
+    // incorrectly. Use Columns instead.
     __m128 Rows[4];
 #endif
 
 #ifdef __cplusplus
-    inline hmm_vec4 operator[](const int Index)
+    inline hmm_vec4 operator[](const int &Index)
     {
         float* col = Elements[Index];
 
@@ -1120,6 +1016,21 @@ HMM_INLINE hmm_vec4 HMM_NormalizeVec4(hmm_vec4 A)
     return (Result);
 }
 
+HMM_INLINE hmm_vec2 HMM_FastNormalizeVec2(hmm_vec2 A)
+{
+    return HMM_MultiplyVec2f(A, HMM_RSquareRootF(HMM_DotVec2(A, A)));
+}
+
+HMM_INLINE hmm_vec3 HMM_FastNormalizeVec3(hmm_vec3 A)
+{
+    return HMM_MultiplyVec3f(A, HMM_RSquareRootF(HMM_DotVec3(A, A)));
+}
+
+HMM_INLINE hmm_vec4 HMM_FastNormalizeVec4(hmm_vec4 A)
+{
+    return HMM_MultiplyVec4f(A, HMM_RSquareRootF(HMM_DotVec4(A, A)));
+}
+
 
 /*
  * SSE stuff
@@ -1129,10 +1040,10 @@ HMM_INLINE hmm_vec4 HMM_NormalizeVec4(hmm_vec4 A)
 HMM_INLINE __m128 HMM_LinearCombineSSE(__m128 Left, hmm_mat4 Right)
 {
     __m128 Result;
-    Result = _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0x00), Right.Rows[0]);
-    Result = _mm_add_ps(Result, _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0x55), Right.Rows[1]));
-    Result = _mm_add_ps(Result, _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0xaa), Right.Rows[2]));
-    Result = _mm_add_ps(Result, _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0xff), Right.Rows[3]));
+    Result = _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0x00), Right.Columns[0]);
+    Result = _mm_add_ps(Result, _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0x55), Right.Columns[1]));
+    Result = _mm_add_ps(Result, _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0xaa), Right.Columns[2]));
+    Result = _mm_add_ps(Result, _mm_mul_ps(_mm_shuffle_ps(Left, Left, 0xff), Right.Columns[3]));
     
     return (Result);
 }
@@ -1167,7 +1078,7 @@ HMM_INLINE hmm_mat4 HMM_Transpose(hmm_mat4 Matrix)
 {
     hmm_mat4 Result = Matrix;
     
-    _MM_TRANSPOSE4_PS(Result.Rows[0], Result.Rows[1], Result.Rows[2], Result.Rows[3]);
+    _MM_TRANSPOSE4_PS(Result.Columns[0], Result.Columns[1], Result.Columns[2], Result.Columns[3]);
 
     return (Result);
 }
@@ -1180,10 +1091,10 @@ HMM_INLINE hmm_mat4 HMM_AddMat4(hmm_mat4 Left, hmm_mat4 Right)
 {
     hmm_mat4 Result;
 
-    Result.Rows[0] = _mm_add_ps(Left.Rows[0], Right.Rows[0]);
-    Result.Rows[1] = _mm_add_ps(Left.Rows[1], Right.Rows[1]);
-    Result.Rows[2] = _mm_add_ps(Left.Rows[2], Right.Rows[2]);
-    Result.Rows[3] = _mm_add_ps(Left.Rows[3], Right.Rows[3]);    
+    Result.Columns[0] = _mm_add_ps(Left.Columns[0], Right.Columns[0]);
+    Result.Columns[1] = _mm_add_ps(Left.Columns[1], Right.Columns[1]);
+    Result.Columns[2] = _mm_add_ps(Left.Columns[2], Right.Columns[2]);
+    Result.Columns[3] = _mm_add_ps(Left.Columns[3], Right.Columns[3]);    
 
     return (Result);
 }
@@ -1196,10 +1107,10 @@ HMM_INLINE hmm_mat4 HMM_SubtractMat4(hmm_mat4 Left, hmm_mat4 Right)
 {
     hmm_mat4 Result;
 
-    Result.Rows[0] = _mm_sub_ps(Left.Rows[0], Right.Rows[0]);
-    Result.Rows[1] = _mm_sub_ps(Left.Rows[1], Right.Rows[1]);
-    Result.Rows[2] = _mm_sub_ps(Left.Rows[2], Right.Rows[2]);
-    Result.Rows[3] = _mm_sub_ps(Left.Rows[3], Right.Rows[3]);
+    Result.Columns[0] = _mm_sub_ps(Left.Columns[0], Right.Columns[0]);
+    Result.Columns[1] = _mm_sub_ps(Left.Columns[1], Right.Columns[1]);
+    Result.Columns[2] = _mm_sub_ps(Left.Columns[2], Right.Columns[2]);
+    Result.Columns[3] = _mm_sub_ps(Left.Columns[3], Right.Columns[3]);
 
     return (Result);
 }
@@ -1215,10 +1126,10 @@ HMM_INLINE hmm_mat4 HMM_MultiplyMat4f(hmm_mat4 Matrix, float Scalar)
     hmm_mat4 Result;
 
     __m128 SSEScalar = _mm_set1_ps(Scalar);
-    Result.Rows[0] = _mm_mul_ps(Matrix.Rows[0], SSEScalar);
-    Result.Rows[1] = _mm_mul_ps(Matrix.Rows[1], SSEScalar);
-    Result.Rows[2] = _mm_mul_ps(Matrix.Rows[2], SSEScalar);
-    Result.Rows[3] = _mm_mul_ps(Matrix.Rows[3], SSEScalar);
+    Result.Columns[0] = _mm_mul_ps(Matrix.Columns[0], SSEScalar);
+    Result.Columns[1] = _mm_mul_ps(Matrix.Columns[1], SSEScalar);
+    Result.Columns[2] = _mm_mul_ps(Matrix.Columns[2], SSEScalar);
+    Result.Columns[3] = _mm_mul_ps(Matrix.Columns[3], SSEScalar);
 
     return (Result);
 }
@@ -1234,10 +1145,10 @@ HMM_INLINE hmm_mat4 HMM_DivideMat4f(hmm_mat4 Matrix, float Scalar)
     hmm_mat4 Result;
     
     __m128 SSEScalar = _mm_set1_ps(Scalar);
-    Result.Rows[0] = _mm_div_ps(Matrix.Rows[0], SSEScalar);
-    Result.Rows[1] = _mm_div_ps(Matrix.Rows[1], SSEScalar);
-    Result.Rows[2] = _mm_div_ps(Matrix.Rows[2], SSEScalar);
-    Result.Rows[3] = _mm_div_ps(Matrix.Rows[3], SSEScalar);    
+    Result.Columns[0] = _mm_div_ps(Matrix.Columns[0], SSEScalar);
+    Result.Columns[1] = _mm_div_ps(Matrix.Columns[1], SSEScalar);
+    Result.Columns[2] = _mm_div_ps(Matrix.Columns[2], SSEScalar);
+    Result.Columns[3] = _mm_div_ps(Matrix.Columns[3], SSEScalar);    
 
     return (Result);
 }
@@ -1503,6 +1414,27 @@ HMM_INLINE hmm_vec4 HMM_Normalize(hmm_vec4 A)
     return (Result);
 }
 
+HMM_INLINE hmm_vec2 HMM_FastNormalize(hmm_vec2 A)
+{
+    hmm_vec2 Result = HMM_FastNormalizeVec2(A);
+
+    return (Result);
+}
+
+HMM_INLINE hmm_vec3 HMM_FastNormalize(hmm_vec3 A)
+{
+    hmm_vec3 Result = HMM_FastNormalizeVec3(A);
+
+    return (Result);
+}
+
+HMM_INLINE hmm_vec4 HMM_FastNormalize(hmm_vec4 A)
+{
+    hmm_vec4 Result = HMM_FastNormalizeVec4(A);
+
+    return (Result);
+}
+
 HMM_INLINE hmm_quaternion HMM_Normalize(hmm_quaternion A)
 {
     hmm_quaternion Result = HMM_NormalizeQuaternion(A);
@@ -2252,10 +2184,10 @@ hmm_mat4 HMM_MultiplyMat4(hmm_mat4 Left, hmm_mat4 Right)
 
 #ifdef HANDMADE_MATH__USE_SSE
 
-    Result.Rows[0] = HMM_LinearCombineSSE(Right.Rows[0], Left);
-    Result.Rows[1] = HMM_LinearCombineSSE(Right.Rows[1], Left);
-    Result.Rows[2] = HMM_LinearCombineSSE(Right.Rows[2], Left);
-    Result.Rows[3] = HMM_LinearCombineSSE(Right.Rows[3], Left);     
+    Result.Columns[0] = HMM_LinearCombineSSE(Right.Columns[0], Left);
+    Result.Columns[1] = HMM_LinearCombineSSE(Right.Columns[1], Left);
+    Result.Columns[2] = HMM_LinearCombineSSE(Right.Columns[2], Left);
+    Result.Columns[3] = HMM_LinearCombineSSE(Right.Columns[3], Left);     
     
 #else
     int Columns;

README.md

@@ -10,6 +10,9 @@ To get started, go download [the latest release](https://github.com/HandmadeMath
 
 Version         | Changes        |
 ----------------|----------------|
+**1.8.0** | Added fast vector normalization routines that use fast inverse square roots.
+**1.7.1** | Changed operator[] to take a const ref int instead of an int.
+**1.7.0** | Renamed the 'Rows' member of hmm_mat4 to 'Columns'. Since our matrices are column-major, this should have been named 'Columns' from the start. 'Rows' is still present, but has been deprecated.
 **1.6.0** | Added array subscript operators for vector and matrix types in C++. This is provided as a convenience, but be aware that it may incur an extra function call in unoptimized builds.
 **1.5.1** | Fixed a bug with uninitialized elements in HMM_LookAt.
 **1.5.0** | Changed internal structure for better performance and inlining. As a result, `HANDMADE_MATH_NO_INLINE` has been removed and no longer has any effect.

test/categories/SSE.h

@@ -8,10 +8,10 @@ TEST(SSE, LinearCombine)
     hmm_mat4 MatrixTwo = HMM_Mat4d(4.0f);
     hmm_mat4 Result;
     
-    Result.Rows[0] = HMM_LinearCombineSSE(MatrixOne.Rows[0], MatrixTwo);
-    Result.Rows[1] = HMM_LinearCombineSSE(MatrixOne.Rows[1], MatrixTwo);
-    Result.Rows[2] = HMM_LinearCombineSSE(MatrixOne.Rows[2], MatrixTwo);
-    Result.Rows[3] = HMM_LinearCombineSSE(MatrixOne.Rows[3], MatrixTwo);
+    Result.Columns[0] = HMM_LinearCombineSSE(MatrixOne.Columns[0], MatrixTwo);
+    Result.Columns[1] = HMM_LinearCombineSSE(MatrixOne.Columns[1], MatrixTwo);
+    Result.Columns[2] = HMM_LinearCombineSSE(MatrixOne.Columns[2], MatrixTwo);
+    Result.Columns[3] = HMM_LinearCombineSSE(MatrixOne.Columns[3], MatrixTwo);
     
     {
         EXPECT_FLOAT_EQ(Result.Elements[0][0], 8.0f);
@@ -23,14 +23,12 @@ TEST(SSE, LinearCombine)
         EXPECT_FLOAT_EQ(Result.Elements[1][1], 8.0f);                
         EXPECT_FLOAT_EQ(Result.Elements[1][2], 0.0f);
         EXPECT_FLOAT_EQ(Result.Elements[1][3], 0.0f);
-
                         
         EXPECT_FLOAT_EQ(Result.Elements[2][0], 0.0f);
         EXPECT_FLOAT_EQ(Result.Elements[2][1], 0.0f);                
         EXPECT_FLOAT_EQ(Result.Elements[2][2], 8.0f);
         EXPECT_FLOAT_EQ(Result.Elements[2][3], 0.0f);
 
-        
         EXPECT_FLOAT_EQ(Result.Elements[3][0], 0.0f);
         EXPECT_FLOAT_EQ(Result.Elements[3][1], 0.0f);                
         EXPECT_FLOAT_EQ(Result.Elements[3][2], 0.0f);

test/categories/VectorOps.h

@@ -134,6 +134,106 @@ TEST(VectorOps, NormalizeZero)
 #endif
 }
 
+TEST(VectorOps, FastNormalize)
+{
+    hmm_vec2 v2 = HMM_Vec2(1.0f, -2.0f);
+    hmm_vec3 v3 = HMM_Vec3(1.0f, -2.0f, 3.0f);
+    hmm_vec4 v4 = HMM_Vec4(1.0f, -2.0f, 3.0f, -1.0f);
+
+    {
+        hmm_vec2 result = HMM_FastNormalizeVec2(v2);
+        EXPECT_NEAR(HMM_LengthVec2(result), 1.0f, 0.001f);
+        EXPECT_GT(result.X, 0.0f);
+        EXPECT_LT(result.Y, 0.0f);
+    }
+    {
+        hmm_vec3 result = HMM_FastNormalizeVec3(v3);
+        EXPECT_NEAR(HMM_LengthVec3(result), 1.0f, 0.001f);
+        EXPECT_GT(result.X, 0.0f);
+        EXPECT_LT(result.Y, 0.0f);
+        EXPECT_GT(result.Z, 0.0f);
+    }
+    {
+        hmm_vec4 result = HMM_FastNormalizeVec4(v4);
+        EXPECT_NEAR(HMM_LengthVec4(result), 1.0f, 0.001f);
+        EXPECT_GT(result.X, 0.0f);
+        EXPECT_LT(result.Y, 0.0f);
+        EXPECT_GT(result.Z, 0.0f);
+        EXPECT_LT(result.W, 0.0f);
+    }
+
+#ifdef __cplusplus
+    {
+        hmm_vec2 result = HMM_FastNormalize(v2);
+        EXPECT_NEAR(HMM_LengthVec2(result), 1.0f, 0.001f);
+        EXPECT_GT(result.X, 0.0f);
+        EXPECT_LT(result.Y, 0.0f);
+    }
+    {
+        hmm_vec3 result = HMM_FastNormalize(v3);
+        EXPECT_NEAR(HMM_LengthVec3(result), 1.0f, 0.001f);
+        EXPECT_GT(result.X, 0.0f);
+        EXPECT_LT(result.Y, 0.0f);
+        EXPECT_GT(result.Z, 0.0f);
+    }
+    {
+        hmm_vec4 result = HMM_FastNormalize(v4);
+        EXPECT_NEAR(HMM_LengthVec4(result), 1.0f, 0.001f);
+        EXPECT_GT(result.X, 0.0f);
+        EXPECT_LT(result.Y, 0.0f);
+        EXPECT_GT(result.Z, 0.0f);
+        EXPECT_LT(result.W, 0.0f);
+    }
+#endif
+}
+
+TEST(VectorOps, FastNormalizeZero)
+{
+    hmm_vec2 v2 = HMM_Vec2(0.0f, 0.0f);
+    hmm_vec3 v3 = HMM_Vec3(0.0f, 0.0f, 0.0f);
+    hmm_vec4 v4 = HMM_Vec4(0.0f, 0.0f, 0.0f, 0.0f);
+
+    {
+        hmm_vec2 result = HMM_FastNormalizeVec2(v2);
+        EXPECT_FLOAT_EQ(result.X, 0.0f);
+        EXPECT_FLOAT_EQ(result.Y, 0.0f);
+    }
+    {
+        hmm_vec3 result = HMM_FastNormalizeVec3(v3);
+        EXPECT_FLOAT_EQ(result.X, 0.0f);
+        EXPECT_FLOAT_EQ(result.Y, 0.0f);
+        EXPECT_FLOAT_EQ(result.Z, 0.0f);
+    }
+    {
+        hmm_vec4 result = HMM_FastNormalizeVec4(v4);
+        EXPECT_FLOAT_EQ(result.X, 0.0f);
+        EXPECT_FLOAT_EQ(result.Y, 0.0f);
+        EXPECT_FLOAT_EQ(result.Z, 0.0f);
+        EXPECT_FLOAT_EQ(result.W, 0.0f);
+    }
+
+#ifdef __cplusplus
+    {
+        hmm_vec2 result = HMM_FastNormalize(v2);
+        EXPECT_FLOAT_EQ(result.X, 0.0f);
+        EXPECT_FLOAT_EQ(result.Y, 0.0f);
+    }
+    {
+        hmm_vec3 result = HMM_FastNormalize(v3);
+        EXPECT_FLOAT_EQ(result.X, 0.0f);
+        EXPECT_FLOAT_EQ(result.Y, 0.0f);
+        EXPECT_FLOAT_EQ(result.Z, 0.0f);
+    }
+    {
+        hmm_vec4 result = HMM_FastNormalize(v4);
+        EXPECT_FLOAT_EQ(result.X, 0.0f);
+        EXPECT_FLOAT_EQ(result.Y, 0.0f);
+        EXPECT_FLOAT_EQ(result.Z, 0.0f);
+        EXPECT_FLOAT_EQ(result.W, 0.0f);
+    }
+#endif
+}
+
 TEST(VectorOps, Cross)
 {
     hmm_vec3 v1 = HMM_Vec3(1.0f, 2.0f, 3.0f);