/* HandmadeMath.h v1.9.0 This is a single header file with a bunch of useful functions for game and graphics math operations. ============================================================================= You MUST #define HANDMADE_MATH_IMPLEMENTATION in EXACTLY one C or C++ file that includes this header, BEFORE the include, like this: #define HANDMADE_MATH_IMPLEMENTATION #include "HandmadeMath.h" All other files should just #include "HandmadeMath.h" without the #define. ============================================================================= To disable SSE intrinsics, you MUST #define HANDMADE_MATH_NO_SSE in EXACTLY one C or C++ file that includes this header, BEFORE the include, like this: #define HANDMADE_MATH_IMPLEMENTATION #define HANDMADE_MATH_NO_SSE #include "HandmadeMath.h" ============================================================================= To use HandmadeMath without the CRT, you MUST #define HMM_SINF MySinF #define HMM_COSF MyCosF #define HMM_TANF MyTanF #define HMM_SQRTF MySqrtF #define HMM_EXPF MyExpF #define HMM_LOGF MyLogF #define HMM_ACOSF MyACosF #define HMM_ATANF MyATanF #define HMM_ATAN2F MYATan2F Provide your own implementations of SinF, CosF, TanF, ACosF, ATanF, ATan2F, ExpF, and LogF in EXACTLY one C or C++ file that includes this header, BEFORE the include, like this: #define HMM_SINF MySinF #define HMM_COSF MyCosF #define HMM_TANF MyTanF #define HMM_SQRTF MySqrtF #define HMM_EXPF MyExpF #define HMM_LOGF MyLogF #define HMM_ACOSF MyACosF #define HMM_ATANF MyATanF #define HMM_ATAN2F MyATan2F #define HANDMADE_MATH_IMPLEMENTATION #include "HandmadeMath.h" If you do not define all of these, HandmadeMath.h will use the versions of these functions that are provided by the CRT. ============================================================================= LICENSE This software is in the public domain. Where that dedication is not recognized, you are granted a perpetual, irrevocable license to copy, distribute, and modify this file as you see fit. CREDITS Written by Zakary Strange (zak@strangedev.net && @strangezak) Functionality: Matt Mascarenhas (@miblo_) Aleph FieryDrake (@fierydrake) Gingerbill (@TheGingerBill) Ben Visness (@bvisness) Trinton Bullard (@Peliex_Dev) @AntonDan Fixes: Jeroen van Rijn (@J_vanRijn) Kiljacken (@Kiljacken) Insofaras (@insofaras) Daniel Gibson (@DanielGibson) */ /* let's figure out if SSE is really available (unless disabled anyway) (it isn't on non-x86/x86_64 platforms or even x86 without explicit SSE support) => only use "#ifdef HANDMADE_MATH__USE_SSE" to check for SSE support below this block! */ #ifndef HANDMADE_MATH_NO_SSE # ifdef _MSC_VER /* MSVC supports SSE in amd64 mode or _M_IX86_FP >= 1 (2 means SSE2) */ # if defined(_M_AMD64) || ( defined(_M_IX86_FP) && _M_IX86_FP >= 1 ) # define HANDMADE_MATH__USE_SSE 1 # endif # else /* not MSVC, probably GCC, clang, icc or something that doesn't support SSE anyway */ # ifdef __SSE__ /* they #define __SSE__ if it's supported */ # define HANDMADE_MATH__USE_SSE 1 # endif /* __SSE__ */ # endif /* not _MSC_VER */ #endif /* #ifndef HANDMADE_MATH_NO_SSE */ #include // This is for types #ifdef HANDMADE_MATH__USE_SSE #include #endif #ifndef HANDMADE_MATH_H #define HANDMADE_MATH_H #ifdef _MSC_VER #pragma warning(disable:4201) #endif #ifdef __clang__ #pragma GCC diagnostic push #pragma GCC diagnostic ignored "-Wgnu-anonymous-struct" #endif #ifdef __cplusplus extern "C" { #endif #define HMM_INLINE static inline #define HMM_EXTERN extern #if !defined(HMM_SINF) || !defined(HMM_COSF) || !defined(HMM_TANF) || \ !defined(HMM_SQRTF) || !defined(HMM_EXPF) || !defined(HMM_LOGF) || \ !defined(HMM_ACOSF) || !defined(HMM_ATANF)|| !defined(HMM_ATAN2F) #include #endif #ifndef HMM_SINF #define HMM_SINF sinf #endif #ifndef HMM_COSF #define HMM_COSF cosf #endif #ifndef HMM_TANF #define HMM_TANF tanf #endif #ifndef HMM_SQRTF #define HMM_SQRTF sqrtf #endif #ifndef HMM_EXPF #define HMM_EXPF expf #endif #ifndef HMM_LOGF #define HMM_LOGF logf #endif #ifndef HMM_ACOSF #define HMM_ACOSF acosf #endif #ifndef HMM_ATANF #define HMM_ATANF atanf #endif #ifndef HMM_ATAN2F #define HMM_ATAN2F atan2f #endif #define HMM_PI32 3.14159265359f #define HMM_PI 3.14159265358979323846 #define HMM_MIN(a, b) (a) > (b) ? (b) : (a) #define HMM_MAX(a, b) (a) < (b) ? (b) : (a) #define HMM_ABS(a) ((a) > 0 ? (a) : -(a)) #define HMM_MOD(a, m) ((a) % (m)) >= 0 ? ((a) % (m)) : (((a) % (m)) + (m)) #define HMM_SQUARE(x) ((x) * (x)) typedef union hmm_vec2 { struct { float X, Y; }; struct { float U, V; }; struct { float Left, Right; }; struct { float Width, Height; }; float Elements[2]; #ifdef __cplusplus inline float &operator[](const int &Index) { return Elements[Index]; } #endif } hmm_vec2; typedef union hmm_vec3 { struct { float X, Y, Z; }; struct { float U, V, W; }; struct { float R, G, B; }; struct { hmm_vec2 XY; float Ignored0_; }; struct { float Ignored1_; hmm_vec2 YZ; }; struct { hmm_vec2 UV; float Ignored2_; }; struct { float Ignored3_; hmm_vec2 VW; }; float Elements[3]; #ifdef __cplusplus inline float &operator[](const int &Index) { return Elements[Index]; } #endif } hmm_vec3; typedef union hmm_vec4 { struct { union { hmm_vec3 XYZ; struct { float X, Y, Z; }; }; float W; }; struct { union { hmm_vec3 RGB; struct { float R, G, B; }; }; float A; }; struct { hmm_vec2 XY; float Ignored0_; float Ignored1_; }; struct { float Ignored2_; hmm_vec2 YZ; float Ignored3_; }; struct { float Ignored4_; float Ignored5_; hmm_vec2 ZW; }; float Elements[4]; #ifdef HANDMADE_MATH__USE_SSE __m128 InternalElementsSSE; #endif #ifdef __cplusplus inline float &operator[](const int &Index) { return Elements[Index]; } #endif } hmm_vec4; 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) { float* col = Elements[Index]; hmm_vec4 result; result.Elements[0] = col[0]; result.Elements[1] = col[1]; result.Elements[2] = col[2]; result.Elements[3] = col[3]; return result; } #endif } hmm_mat4; typedef union hmm_quaternion { struct { union { hmm_vec3 XYZ; struct { float X, Y, Z; }; }; float W; }; float Elements[4]; #ifdef HANDMADE_MATH__USE_SSE __m128 InternalElementsSSE; #endif } hmm_quaternion; typedef int32_t hmm_bool; typedef hmm_vec2 hmm_v2; typedef hmm_vec3 hmm_v3; typedef hmm_vec4 hmm_v4; typedef hmm_mat4 hmm_m4; /* * Floating-point math functions */ HMM_INLINE float HMM_SinF(float Radians) { float Result = HMM_SINF(Radians); return (Result); } HMM_INLINE float HMM_CosF(float Radians) { float Result = HMM_COSF(Radians); return (Result); } HMM_INLINE float HMM_TanF(float Radians) { float Result = HMM_TANF(Radians); return (Result); } HMM_INLINE float HMM_ACosF(float Radians) { float Result = HMM_ACOSF(Radians); return (Result); } HMM_INLINE float HMM_ATanF(float Radians) { float Result = HMM_ATANF(Radians); return (Result); } HMM_INLINE float HMM_ATan2F(float Left, float Right) { float Result = HMM_ATAN2F(Left, Right); return (Result); } HMM_INLINE float HMM_ExpF(float Float) { float Result = HMM_EXPF(Float); return (Result); } HMM_INLINE float HMM_LogF(float Float) { float Result = HMM_LOGF(Float); return (Result); } HMM_INLINE float HMM_SquareRootF(float Float) { float Result; #ifdef HANDMADE_MATH__USE_SSE __m128 In = _mm_set_ss(Float); __m128 Out = _mm_sqrt_ss(In); Result = _mm_cvtss_f32(Out); #else Result = HMM_SQRTF(Float); #endif return(Result); } HMM_INLINE float HMM_RSquareRootF(float Float) { float Result; #ifdef HANDMADE_MATH__USE_SSE __m128 In = _mm_set_ss(Float); __m128 Out = _mm_rsqrt_ss(In); Result = _mm_cvtss_f32(Out); #else Result = 1.0f/HMM_SquareRootF(Float); #endif return(Result); } HMM_EXTERN float HMM_Power(float Base, int Exponent); HMM_INLINE float HMM_PowerF(float Base, float Exponent) { float Result = HMM_EXPF(Exponent * HMM_LOGF(Base)); return (Result); } /* * Utility functions */ HMM_INLINE float HMM_ToRadians(float Degrees) { float Result = Degrees * (HMM_PI32 / 180.0f); return (Result); } HMM_INLINE float HMM_Lerp(float A, float Time, float B) { float Result = (1.0f - Time) * A + Time * B; return (Result); } HMM_INLINE float HMM_Clamp(float Min, float Value, float Max) { float Result = Value; if(Result < Min) { Result = Min; } else if(Result > Max) { Result = Max; } return (Result); } /* * Vector initialization */ HMM_INLINE hmm_vec2 HMM_Vec2(float X, float Y) { hmm_vec2 Result; Result.X = X; Result.Y = Y; return (Result); } HMM_INLINE hmm_vec2 HMM_Vec2i(int X, int Y) { hmm_vec2 Result; Result.X = (float)X; Result.Y = (float)Y; return (Result); } HMM_INLINE hmm_vec3 HMM_Vec3(float X, float Y, float Z) { hmm_vec3 Result; Result.X = X; Result.Y = Y; Result.Z = Z; return (Result); } HMM_INLINE hmm_vec3 HMM_Vec3i(int X, int Y, int Z) { hmm_vec3 Result; Result.X = (float)X; Result.Y = (float)Y; Result.Z = (float)Z; return (Result); } HMM_INLINE hmm_vec4 HMM_Vec4(float X, float Y, float Z, float W) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_setr_ps(X, Y, Z, W); #else Result.X = X; Result.Y = Y; Result.Z = Z; Result.W = W; #endif return (Result); } HMM_INLINE hmm_vec4 HMM_Vec4i(int X, int Y, int Z, int W) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_setr_ps((float)X, (float)Y, (float)Z, (float)W); #else Result.X = (float)X; Result.Y = (float)Y; Result.Z = (float)Z; Result.W = (float)W; #endif return (Result); } HMM_INLINE hmm_vec4 HMM_Vec4v(hmm_vec3 Vector, float W) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_setr_ps(Vector.X, Vector.Y, Vector.Z, W); #else Result.XYZ = Vector; Result.W = W; #endif return (Result); } /* * Binary vector operations */ HMM_INLINE hmm_vec2 HMM_AddVec2(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result; Result.X = Left.X + Right.X; Result.Y = Left.Y + Right.Y; return (Result); } HMM_INLINE hmm_vec3 HMM_AddVec3(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result; Result.X = Left.X + Right.X; Result.Y = Left.Y + Right.Y; Result.Z = Left.Z + Right.Z; return (Result); } HMM_INLINE hmm_vec4 HMM_AddVec4(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_add_ps(Left.InternalElementsSSE, Right.InternalElementsSSE); #else Result.X = Left.X + Right.X; Result.Y = Left.Y + Right.Y; Result.Z = Left.Z + Right.Z; Result.W = Left.W + Right.W; #endif return (Result); } HMM_INLINE hmm_vec2 HMM_SubtractVec2(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result; Result.X = Left.X - Right.X; Result.Y = Left.Y - Right.Y; return (Result); } HMM_INLINE hmm_vec3 HMM_SubtractVec3(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result; Result.X = Left.X - Right.X; Result.Y = Left.Y - Right.Y; Result.Z = Left.Z - Right.Z; return (Result); } HMM_INLINE hmm_vec4 HMM_SubtractVec4(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_sub_ps(Left.InternalElementsSSE, Right.InternalElementsSSE); #else Result.X = Left.X - Right.X; Result.Y = Left.Y - Right.Y; Result.Z = Left.Z - Right.Z; Result.W = Left.W - Right.W; #endif return (Result); } HMM_INLINE hmm_vec2 HMM_MultiplyVec2(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result; Result.X = Left.X * Right.X; Result.Y = Left.Y * Right.Y; return (Result); } HMM_INLINE hmm_vec2 HMM_MultiplyVec2f(hmm_vec2 Left, float Right) { hmm_vec2 Result; Result.X = Left.X * Right; Result.Y = Left.Y * Right; return (Result); } HMM_INLINE hmm_vec3 HMM_MultiplyVec3(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result; Result.X = Left.X * Right.X; Result.Y = Left.Y * Right.Y; Result.Z = Left.Z * Right.Z; return (Result); } HMM_INLINE hmm_vec3 HMM_MultiplyVec3f(hmm_vec3 Left, float Right) { hmm_vec3 Result; Result.X = Left.X * Right; Result.Y = Left.Y * Right; Result.Z = Left.Z * Right; return (Result); } HMM_INLINE hmm_vec4 HMM_MultiplyVec4(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_mul_ps(Left.InternalElementsSSE, Right.InternalElementsSSE); #else Result.X = Left.X * Right.X; Result.Y = Left.Y * Right.Y; Result.Z = Left.Z * Right.Z; Result.W = Left.W * Right.W; #endif return (Result); } HMM_INLINE hmm_vec4 HMM_MultiplyVec4f(hmm_vec4 Left, float Right) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE __m128 Scalar = _mm_set1_ps(Right); Result.InternalElementsSSE = _mm_mul_ps(Left.InternalElementsSSE, Scalar); #else Result.X = Left.X * Right; Result.Y = Left.Y * Right; Result.Z = Left.Z * Right; Result.W = Left.W * Right; #endif return (Result); } HMM_INLINE hmm_vec2 HMM_DivideVec2(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result; Result.X = Left.X / Right.X; Result.Y = Left.Y / Right.Y; return (Result); } HMM_INLINE hmm_vec2 HMM_DivideVec2f(hmm_vec2 Left, float Right) { hmm_vec2 Result; Result.X = Left.X / Right; Result.Y = Left.Y / Right; return (Result); } HMM_INLINE hmm_vec3 HMM_DivideVec3(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result; Result.X = Left.X / Right.X; Result.Y = Left.Y / Right.Y; Result.Z = Left.Z / Right.Z; return (Result); } HMM_INLINE hmm_vec3 HMM_DivideVec3f(hmm_vec3 Left, float Right) { hmm_vec3 Result; Result.X = Left.X / Right; Result.Y = Left.Y / Right; Result.Z = Left.Z / Right; return (Result); } HMM_INLINE hmm_vec4 HMM_DivideVec4(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_div_ps(Left.InternalElementsSSE, Right.InternalElementsSSE); #else Result.X = Left.X / Right.X; Result.Y = Left.Y / Right.Y; Result.Z = Left.Z / Right.Z; Result.W = Left.W / Right.W; #endif return (Result); } HMM_INLINE hmm_vec4 HMM_DivideVec4f(hmm_vec4 Left, float Right) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE __m128 Scalar = _mm_set1_ps(Right); Result.InternalElementsSSE = _mm_div_ps(Left.InternalElementsSSE, Scalar); #else Result.X = Left.X / Right; Result.Y = Left.Y / Right; Result.Z = Left.Z / Right; Result.W = Left.W / Right; #endif return (Result); } HMM_INLINE hmm_bool HMM_EqualsVec2(hmm_vec2 Left, hmm_vec2 Right) { hmm_bool Result = (Left.X == Right.X && Left.Y == Right.Y); return (Result); } HMM_INLINE hmm_bool HMM_EqualsVec3(hmm_vec3 Left, hmm_vec3 Right) { hmm_bool Result = (Left.X == Right.X && Left.Y == Right.Y && Left.Z == Right.Z); return (Result); } HMM_INLINE hmm_bool HMM_EqualsVec4(hmm_vec4 Left, hmm_vec4 Right) { hmm_bool Result = (Left.X == Right.X && Left.Y == Right.Y && Left.Z == Right.Z && Left.W == Right.W); return (Result); } HMM_INLINE float HMM_DotVec2(hmm_vec2 VecOne, hmm_vec2 VecTwo) { float Result = (VecOne.X * VecTwo.X) + (VecOne.Y * VecTwo.Y); return (Result); } HMM_INLINE float HMM_DotVec3(hmm_vec3 VecOne, hmm_vec3 VecTwo) { float Result = (VecOne.X * VecTwo.X) + (VecOne.Y * VecTwo.Y) + (VecOne.Z * VecTwo.Z); return (Result); } HMM_INLINE float HMM_DotVec4(hmm_vec4 VecOne, hmm_vec4 VecTwo) { float Result; // NOTE(zak): IN the future if we wanna check what version SSE is support // we can use _mm_dp_ps (4.3) but for now we will use the old way. // Or a r = _mm_mul_ps(v1, v2), r = _mm_hadd_ps(r, r), r = _mm_hadd_ps(r, r) for SSE3 #ifdef HANDMADE_MATH__USE_SSE __m128 SSEResultOne = _mm_mul_ps(VecOne.InternalElementsSSE, VecTwo.InternalElementsSSE); __m128 SSEResultTwo = _mm_shuffle_ps(SSEResultOne, SSEResultOne, _MM_SHUFFLE(2, 3, 0, 1)); SSEResultOne = _mm_add_ps(SSEResultOne, SSEResultTwo); SSEResultTwo = _mm_shuffle_ps(SSEResultOne, SSEResultOne, _MM_SHUFFLE(0, 1, 2, 3)); SSEResultOne = _mm_add_ps(SSEResultOne, SSEResultTwo); _mm_store_ss(&Result, SSEResultOne); #else Result = (VecOne.X * VecTwo.X) + (VecOne.Y * VecTwo.Y) + (VecOne.Z * VecTwo.Z) + (VecOne.W * VecTwo.W); #endif return (Result); } HMM_INLINE hmm_vec3 HMM_Cross(hmm_vec3 VecOne, hmm_vec3 VecTwo) { hmm_vec3 Result; Result.X = (VecOne.Y * VecTwo.Z) - (VecOne.Z * VecTwo.Y); Result.Y = (VecOne.Z * VecTwo.X) - (VecOne.X * VecTwo.Z); Result.Z = (VecOne.X * VecTwo.Y) - (VecOne.Y * VecTwo.X); return (Result); } /* * Unary vector operations */ HMM_INLINE float HMM_LengthSquaredVec2(hmm_vec2 A) { float Result = HMM_DotVec2(A, A); return(Result); } HMM_INLINE float HMM_LengthSquaredVec3(hmm_vec3 A) { float Result = HMM_DotVec3(A, A); return (Result); } HMM_INLINE float HMM_LengthSquaredVec4(hmm_vec4 A) { float Result = HMM_DotVec4(A, A); return (Result); } HMM_INLINE float HMM_LengthVec2(hmm_vec2 A) { float Result = HMM_SquareRootF(HMM_LengthSquaredVec2(A)); return (Result); } HMM_INLINE float HMM_LengthVec3(hmm_vec3 A) { float Result = HMM_SquareRootF(HMM_LengthSquaredVec3(A)); return (Result); } HMM_INLINE float HMM_LengthVec4(hmm_vec4 A) { float Result = HMM_SquareRootF(HMM_LengthSquaredVec4(A)); return(Result); } HMM_INLINE hmm_vec2 HMM_NormalizeVec2(hmm_vec2 A) { hmm_vec2 Result = {0}; float VectorLength = HMM_LengthVec2(A); /* NOTE(kiljacken): We need a zero check to not divide-by-zero */ if (VectorLength != 0.0f) { Result.X = A.X * (1.0f / VectorLength); Result.Y = A.Y * (1.0f / VectorLength); } return (Result); } HMM_INLINE hmm_vec3 HMM_NormalizeVec3(hmm_vec3 A) { hmm_vec3 Result = {0}; float VectorLength = HMM_LengthVec3(A); /* NOTE(kiljacken): We need a zero check to not divide-by-zero */ if (VectorLength != 0.0f) { Result.X = A.X * (1.0f / VectorLength); Result.Y = A.Y * (1.0f / VectorLength); Result.Z = A.Z * (1.0f / VectorLength); } return (Result); } HMM_INLINE hmm_vec4 HMM_NormalizeVec4(hmm_vec4 A) { hmm_vec4 Result = {0}; float VectorLength = HMM_LengthVec4(A); /* NOTE(kiljacken): We need a zero check to not divide-by-zero */ if (VectorLength != 0.0f) { float Multiplier = 1.0f / VectorLength; #ifdef HANDMADE_MATH__USE_SSE __m128 SSEMultiplier = _mm_set1_ps(Multiplier); Result.InternalElementsSSE = _mm_mul_ps(A.InternalElementsSSE, SSEMultiplier); #else Result.X = A.X * Multiplier; Result.Y = A.Y * Multiplier; Result.Z = A.Z * Multiplier; Result.W = A.W * Multiplier; #endif } 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 */ #ifdef HANDMADE_MATH__USE_SSE HMM_INLINE __m128 HMM_LinearCombineSSE(__m128 Left, hmm_mat4 Right) { __m128 Result; 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); } #endif /* * Matrix functions */ HMM_INLINE hmm_mat4 HMM_Mat4(void) { hmm_mat4 Result = {0}; return (Result); } HMM_INLINE hmm_mat4 HMM_Mat4d(float Diagonal) { hmm_mat4 Result = HMM_Mat4(); Result.Elements[0][0] = Diagonal; Result.Elements[1][1] = Diagonal; Result.Elements[2][2] = Diagonal; Result.Elements[3][3] = Diagonal; return (Result); } #ifdef HANDMADE_MATH__USE_SSE HMM_INLINE hmm_mat4 HMM_Transpose(hmm_mat4 Matrix) { hmm_mat4 Result = Matrix; _MM_TRANSPOSE4_PS(Result.Columns[0], Result.Columns[1], Result.Columns[2], Result.Columns[3]); return (Result); } #else HMM_EXTERN hmm_mat4 HMM_Transpose(hmm_mat4 Matrix); #endif #ifdef HANDMADE_MATH__USE_SSE HMM_INLINE hmm_mat4 HMM_AddMat4(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result; 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); } #else HMM_EXTERN hmm_mat4 HMM_AddMat4(hmm_mat4 Left, hmm_mat4 Right); #endif #ifdef HANDMADE_MATH__USE_SSE HMM_INLINE hmm_mat4 HMM_SubtractMat4(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result; 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); } #else HMM_EXTERN hmm_mat4 HMM_SubtractMat4(hmm_mat4 Left, hmm_mat4 Right); #endif HMM_EXTERN hmm_mat4 HMM_MultiplyMat4(hmm_mat4 Left, hmm_mat4 Right); #ifdef HANDMADE_MATH__USE_SSE HMM_INLINE hmm_mat4 HMM_MultiplyMat4f(hmm_mat4 Matrix, float Scalar) { hmm_mat4 Result; __m128 SSEScalar = _mm_set1_ps(Scalar); 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); } #else HMM_EXTERN hmm_mat4 HMM_MultiplyMat4f(hmm_mat4 Matrix, float Scalar); #endif HMM_EXTERN hmm_vec4 HMM_MultiplyMat4ByVec4(hmm_mat4 Matrix, hmm_vec4 Vector); #ifdef HANDMADE_MATH__USE_SSE HMM_INLINE hmm_mat4 HMM_DivideMat4f(hmm_mat4 Matrix, float Scalar) { hmm_mat4 Result; __m128 SSEScalar = _mm_set1_ps(Scalar); 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); } #else HMM_EXTERN hmm_mat4 HMM_DivideMat4f(hmm_mat4 Matrix, float Scalar); #endif /* * Common graphics transformations */ HMM_INLINE hmm_mat4 HMM_Orthographic(float Left, float Right, float Bottom, float Top, float Near, float Far) { hmm_mat4 Result = HMM_Mat4(); Result.Elements[0][0] = 2.0f / (Right - Left); Result.Elements[1][1] = 2.0f / (Top - Bottom); Result.Elements[2][2] = 2.0f / (Near - Far); Result.Elements[3][3] = 1.0f; Result.Elements[3][0] = (Left + Right) / (Left - Right); Result.Elements[3][1] = (Bottom + Top) / (Bottom - Top); Result.Elements[3][2] = (Far + Near) / (Near - Far); return (Result); } HMM_INLINE hmm_mat4 HMM_Perspective(float FOV, float AspectRatio, float Near, float Far) { hmm_mat4 Result = HMM_Mat4(); // See https://www.khronos.org/registry/OpenGL-Refpages/gl2.1/xhtml/gluPerspective.xml float Cotangent = 1.0f / HMM_TanF(FOV * (HMM_PI32 / 360.0f)); Result.Elements[0][0] = Cotangent / AspectRatio; Result.Elements[1][1] = Cotangent; Result.Elements[2][3] = -1.0f; Result.Elements[2][2] = (Near + Far) / (Near - Far); Result.Elements[3][2] = (2.0f * Near * Far) / (Near - Far); Result.Elements[3][3] = 0.0f; return (Result); } HMM_INLINE hmm_mat4 HMM_Translate(hmm_vec3 Translation) { hmm_mat4 Result = HMM_Mat4d(1.0f); Result.Elements[3][0] = Translation.X; Result.Elements[3][1] = Translation.Y; Result.Elements[3][2] = Translation.Z; return (Result); } HMM_EXTERN hmm_mat4 HMM_Rotate(float Angle, hmm_vec3 Axis); HMM_INLINE hmm_mat4 HMM_Scale(hmm_vec3 Scale) { hmm_mat4 Result = HMM_Mat4d(1.0f); Result.Elements[0][0] = Scale.X; Result.Elements[1][1] = Scale.Y; Result.Elements[2][2] = Scale.Z; return (Result); } HMM_EXTERN hmm_mat4 HMM_LookAt(hmm_vec3 Eye, hmm_vec3 Center, hmm_vec3 Up); /* * Quaternion operations */ HMM_INLINE hmm_quaternion HMM_Quaternion(float X, float Y, float Z, float W) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_setr_ps(X, Y, Z, W); #else Result.X = X; Result.Y = Y; Result.Z = Z; Result.W = W; #endif return (Result); } HMM_INLINE hmm_quaternion HMM_QuaternionV4(hmm_vec4 Vector) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = Vector.InternalElementsSSE; #else Result.X = Vector.X; Result.Y = Vector.Y; Result.Z = Vector.Z; Result.W = Vector.W; #endif return (Result); } HMM_INLINE hmm_quaternion HMM_AddQuaternion(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_add_ps(Left.InternalElementsSSE, Right.InternalElementsSSE); #else Result.X = Left.X + Right.X; Result.Y = Left.Y + Right.Y; Result.Z = Left.Z + Right.Z; Result.W = Left.W + Right.W; #endif return (Result); } HMM_INLINE hmm_quaternion HMM_SubtractQuaternion(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = _mm_sub_ps(Left.InternalElementsSSE, Right.InternalElementsSSE); #else Result.X = Left.X - Right.X; Result.Y = Left.Y - Right.Y; Result.Z = Left.Z - Right.Z; Result.W = Left.W - Right.W; #endif return (Result); } HMM_INLINE hmm_quaternion HMM_MultiplyQuaternion(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE __m128 SSEResultOne = _mm_xor_ps(_mm_shuffle_ps(Left.InternalElementsSSE, Left.InternalElementsSSE, _MM_SHUFFLE(0, 0, 0, 0)), _mm_setr_ps(0.f, -0.f, 0.f, -0.f)); __m128 SSEResultTwo = _mm_shuffle_ps(Right.InternalElementsSSE, Right.InternalElementsSSE, _MM_SHUFFLE(0, 1, 2, 3)); __m128 SSEResultThree = _mm_mul_ps(SSEResultTwo, SSEResultOne); SSEResultOne = _mm_xor_ps(_mm_shuffle_ps(Left.InternalElementsSSE, Left.InternalElementsSSE, _MM_SHUFFLE(1, 1, 1, 1)) , _mm_setr_ps(0.f, 0.f, -0.f, -0.f)); SSEResultTwo = _mm_shuffle_ps(Right.InternalElementsSSE, Right.InternalElementsSSE, _MM_SHUFFLE(1, 0, 3, 2)); SSEResultThree = _mm_add_ps(SSEResultThree, _mm_mul_ps(SSEResultTwo, SSEResultOne)); SSEResultOne = _mm_xor_ps(_mm_shuffle_ps(Left.InternalElementsSSE, Left.InternalElementsSSE, _MM_SHUFFLE(2, 2, 2, 2)), _mm_setr_ps(-0.f, 0.f, 0.f, -0.f)); SSEResultTwo = _mm_shuffle_ps(Right.InternalElementsSSE, Right.InternalElementsSSE, _MM_SHUFFLE(2, 3, 0, 1)); SSEResultThree = _mm_add_ps(SSEResultThree, _mm_mul_ps(SSEResultTwo, SSEResultOne)); SSEResultOne = _mm_shuffle_ps(Left.InternalElementsSSE, Left.InternalElementsSSE, _MM_SHUFFLE(3, 3, 3, 3)); SSEResultTwo = _mm_shuffle_ps(Right.InternalElementsSSE, Right.InternalElementsSSE, _MM_SHUFFLE(3, 2, 1, 0)); Result.InternalElementsSSE = _mm_add_ps(SSEResultThree, _mm_mul_ps(SSEResultTwo, SSEResultOne)); #else Result.X = (Left.X * Right.W) + (Left.Y * Right.Z) - (Left.Z * Right.Y) + (Left.W * Right.X); Result.Y = (-Left.X * Right.Z) + (Left.Y * Right.W) + (Left.Z * Right.X) + (Left.W * Right.Y); Result.Z = (Left.X * Right.Y) - (Left.Y * Right.X) + (Left.Z * Right.W) + (Left.W * Right.Z); Result.W = (-Left.X * Right.X) - (Left.Y * Right.Y) - (Left.Z * Right.Z) + (Left.W * Right.W); #endif return (Result); } HMM_INLINE hmm_quaternion HMM_MultiplyQuaternionF(hmm_quaternion Left, float Multiplicative) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE __m128 Scalar = _mm_set1_ps(Multiplicative); Result.InternalElementsSSE = _mm_mul_ps(Left.InternalElementsSSE, Scalar); #else Result.X = Left.X * Multiplicative; Result.Y = Left.Y * Multiplicative; Result.Z = Left.Z * Multiplicative; Result.W = Left.W * Multiplicative; #endif return (Result); } HMM_INLINE hmm_quaternion HMM_DivideQuaternionF(hmm_quaternion Left, float Dividend) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE __m128 Scalar = _mm_set1_ps(Dividend); Result.InternalElementsSSE = _mm_div_ps(Left.InternalElementsSSE, Scalar); #else Result.X = Left.X / Dividend; Result.Y = Left.Y / Dividend; Result.Z = Left.Z / Dividend; Result.W = Left.W / Dividend; #endif return (Result); } HMM_EXTERN hmm_quaternion HMM_InverseQuaternion(hmm_quaternion Left); HMM_INLINE float HMM_DotQuaternion(hmm_quaternion Left, hmm_quaternion Right) { float Result; #ifdef HANDMADE_MATH__USE_SSE __m128 SSEResultOne = _mm_mul_ps(Left.InternalElementsSSE, Right.InternalElementsSSE); __m128 SSEResultTwo = _mm_shuffle_ps(SSEResultOne, SSEResultOne, _MM_SHUFFLE(2, 3, 0, 1)); SSEResultOne = _mm_add_ps(SSEResultOne, SSEResultTwo); SSEResultTwo = _mm_shuffle_ps(SSEResultOne, SSEResultOne, _MM_SHUFFLE(0, 1, 2, 3)); SSEResultOne = _mm_add_ps(SSEResultOne, SSEResultTwo); _mm_store_ss(&Result, SSEResultOne); #else Result = (Left.X * Right.X) + (Left.Y * Right.Y) + (Left.Z * Right.Z) + (Left.W * Right.W); #endif return (Result); } HMM_INLINE hmm_quaternion HMM_NormalizeQuaternion(hmm_quaternion Left) { hmm_quaternion Result; float Length = HMM_SquareRootF(HMM_DotQuaternion(Left, Left)); Result = HMM_DivideQuaternionF(Left, Length); return (Result); } HMM_INLINE hmm_quaternion HMM_NLerp(hmm_quaternion Left, float Time, hmm_quaternion Right) { hmm_quaternion Result; #ifdef HANDMADE_MATH__USE_SSE __m128 ScalarLeft = _mm_set1_ps(1.0f - Time); __m128 ScalarRight = _mm_set1_ps(Time); __m128 SSEResultOne = _mm_mul_ps(Left.InternalElementsSSE, ScalarLeft); __m128 SSEResultTwo = _mm_mul_ps(Right.InternalElementsSSE, ScalarRight); Result.InternalElementsSSE = _mm_add_ps(SSEResultOne, SSEResultTwo); #else Result.X = HMM_Lerp(Left.X, Time, Right.X); Result.Y = HMM_Lerp(Left.Y, Time, Right.Y); Result.Z = HMM_Lerp(Left.Z, Time, Right.Z); Result.W = HMM_Lerp(Left.W, Time, Right.W); #endif Result = HMM_NormalizeQuaternion(Result); return (Result); } HMM_EXTERN hmm_quaternion HMM_Slerp(hmm_quaternion Left, float Time, hmm_quaternion Right); HMM_EXTERN hmm_mat4 HMM_QuaternionToMat4(hmm_quaternion Left); HMM_EXTERN hmm_quaternion HMM_QuaternionFromAxisAngle(hmm_vec3 Axis, float AngleOfRotation); #ifdef __cplusplus } #endif #ifdef __cplusplus HMM_INLINE float HMM_Length(hmm_vec2 A) { float Result = HMM_LengthVec2(A); return (Result); } HMM_INLINE float HMM_Length(hmm_vec3 A) { float Result = HMM_LengthVec3(A); return (Result); } HMM_INLINE float HMM_Length(hmm_vec4 A) { float Result = HMM_LengthVec4(A); return (Result); } HMM_INLINE float HMM_LengthSquared(hmm_vec2 A) { float Result = HMM_LengthSquaredVec2(A); return (Result); } HMM_INLINE float HMM_LengthSquared(hmm_vec3 A) { float Result = HMM_LengthSquaredVec3(A); return (Result); } HMM_INLINE float HMM_LengthSquared(hmm_vec4 A) { float Result = HMM_LengthSquaredVec4(A); return (Result); } HMM_INLINE hmm_vec2 HMM_Normalize(hmm_vec2 A) { hmm_vec2 Result = HMM_NormalizeVec2(A); return (Result); } HMM_INLINE hmm_vec3 HMM_Normalize(hmm_vec3 A) { hmm_vec3 Result = HMM_NormalizeVec3(A); return (Result); } HMM_INLINE hmm_vec4 HMM_Normalize(hmm_vec4 A) { hmm_vec4 Result = HMM_NormalizeVec4(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); return (Result); } HMM_INLINE float HMM_Dot(hmm_vec2 VecOne, hmm_vec2 VecTwo) { float Result = HMM_DotVec2(VecOne, VecTwo); return (Result); } HMM_INLINE float HMM_Dot(hmm_vec3 VecOne, hmm_vec3 VecTwo) { float Result = HMM_DotVec3(VecOne, VecTwo); return (Result); } HMM_INLINE float HMM_Dot(hmm_vec4 VecOne, hmm_vec4 VecTwo) { float Result = HMM_DotVec4(VecOne, VecTwo); return (Result); } HMM_INLINE float HMM_Dot(hmm_quaternion QuatOne, hmm_quaternion QuatTwo) { float Result = HMM_DotQuaternion(QuatOne, QuatTwo); return (Result); } HMM_INLINE hmm_vec2 HMM_Add(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_AddVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec3 HMM_Add(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_AddVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec4 HMM_Add(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_AddVec4(Left, Right); return (Result); } HMM_INLINE hmm_mat4 HMM_Add(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result = HMM_AddMat4(Left, Right); return (Result); } HMM_INLINE hmm_quaternion HMM_Add(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result = HMM_AddQuaternion(Left, Right); return (Result); } HMM_INLINE hmm_vec2 HMM_Subtract(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_SubtractVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec3 HMM_Subtract(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_SubtractVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec4 HMM_Subtract(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_SubtractVec4(Left, Right); return (Result); } HMM_INLINE hmm_mat4 HMM_Subtract(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result = HMM_SubtractMat4(Left, Right); return (Result); } HMM_INLINE hmm_quaternion HMM_Subtract(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result = HMM_SubtractQuaternion(Left, Right); return (Result); } HMM_INLINE hmm_vec2 HMM_Multiply(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_MultiplyVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec2 HMM_Multiply(hmm_vec2 Left, float Right) { hmm_vec2 Result = HMM_MultiplyVec2f(Left, Right); return (Result); } HMM_INLINE hmm_vec3 HMM_Multiply(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_MultiplyVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec3 HMM_Multiply(hmm_vec3 Left, float Right) { hmm_vec3 Result = HMM_MultiplyVec3f(Left, Right); return (Result); } HMM_INLINE hmm_vec4 HMM_Multiply(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_MultiplyVec4(Left, Right); return (Result); } HMM_INLINE hmm_vec4 HMM_Multiply(hmm_vec4 Left, float Right) { hmm_vec4 Result = HMM_MultiplyVec4f(Left, Right); return (Result); } HMM_INLINE hmm_mat4 HMM_Multiply(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result = HMM_MultiplyMat4(Left, Right); return (Result); } HMM_INLINE hmm_mat4 HMM_Multiply(hmm_mat4 Left, float Right) { hmm_mat4 Result = HMM_MultiplyMat4f(Left, Right); return (Result); } HMM_INLINE hmm_vec4 HMM_Multiply(hmm_mat4 Matrix, hmm_vec4 Vector) { hmm_vec4 Result = HMM_MultiplyMat4ByVec4(Matrix, Vector); return (Result); } HMM_INLINE hmm_quaternion HMM_Multiply(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result = HMM_MultiplyQuaternion(Left, Right); return (Result); } HMM_INLINE hmm_quaternion HMM_Multiply(hmm_quaternion Left, float Right) { hmm_quaternion Result = HMM_MultiplyQuaternionF(Left, Right); return (Result); } HMM_INLINE hmm_vec2 HMM_Divide(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_DivideVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec2 HMM_Divide(hmm_vec2 Left, float Right) { hmm_vec2 Result = HMM_DivideVec2f(Left, Right); return (Result); } HMM_INLINE hmm_vec3 HMM_Divide(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_DivideVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec3 HMM_Divide(hmm_vec3 Left, float Right) { hmm_vec3 Result = HMM_DivideVec3f(Left, Right); return (Result); } HMM_INLINE hmm_vec4 HMM_Divide(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_DivideVec4(Left, Right); return (Result); } HMM_INLINE hmm_vec4 HMM_Divide(hmm_vec4 Left, float Right) { hmm_vec4 Result = HMM_DivideVec4f(Left, Right); return (Result); } HMM_INLINE hmm_mat4 HMM_Divide(hmm_mat4 Left, float Right) { hmm_mat4 Result = HMM_DivideMat4f(Left, Right); return (Result); } HMM_INLINE hmm_quaternion HMM_Divide(hmm_quaternion Left, float Right) { hmm_quaternion Result = HMM_DivideQuaternionF(Left, Right); return (Result); } HMM_INLINE hmm_bool HMM_Equals(hmm_vec2 Left, hmm_vec2 Right) { hmm_bool Result = HMM_EqualsVec2(Left, Right); return (Result); } HMM_INLINE hmm_bool HMM_Equals(hmm_vec3 Left, hmm_vec3 Right) { hmm_bool Result = HMM_EqualsVec3(Left, Right); return (Result); } HMM_INLINE hmm_bool HMM_Equals(hmm_vec4 Left, hmm_vec4 Right) { hmm_bool Result = HMM_EqualsVec4(Left, Right); return (Result); } HMM_INLINE hmm_vec2 operator+(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_AddVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec3 operator+(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_AddVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec4 operator+(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_AddVec4(Left, Right); return (Result); } HMM_INLINE hmm_mat4 operator+(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result = HMM_AddMat4(Left, Right); return (Result); } HMM_INLINE hmm_quaternion operator+(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result = HMM_AddQuaternion(Left, Right); return (Result); } HMM_INLINE hmm_vec2 operator-(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_SubtractVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec3 operator-(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_SubtractVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec4 operator-(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_SubtractVec4(Left, Right); return (Result); } HMM_INLINE hmm_mat4 operator-(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result = HMM_SubtractMat4(Left, Right); return (Result); } HMM_INLINE hmm_quaternion operator-(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result = HMM_SubtractQuaternion(Left, Right); return (Result); } HMM_INLINE hmm_vec2 operator*(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_MultiplyVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec3 operator*(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_MultiplyVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec4 operator*(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_MultiplyVec4(Left, Right); return (Result); } HMM_INLINE hmm_mat4 operator*(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result = HMM_MultiplyMat4(Left, Right); return (Result); } HMM_INLINE hmm_quaternion operator*(hmm_quaternion Left, hmm_quaternion Right) { hmm_quaternion Result = HMM_MultiplyQuaternion(Left, Right); return (Result); } HMM_INLINE hmm_vec2 operator*(hmm_vec2 Left, float Right) { hmm_vec2 Result = HMM_MultiplyVec2f(Left, Right); return (Result); } HMM_INLINE hmm_vec3 operator*(hmm_vec3 Left, float Right) { hmm_vec3 Result = HMM_MultiplyVec3f(Left, Right); return (Result); } HMM_INLINE hmm_vec4 operator*(hmm_vec4 Left, float Right) { hmm_vec4 Result = HMM_MultiplyVec4f(Left, Right); return (Result); } HMM_INLINE hmm_mat4 operator*(hmm_mat4 Left, float Right) { hmm_mat4 Result = HMM_MultiplyMat4f(Left, Right); return (Result); } HMM_INLINE hmm_quaternion operator*(hmm_quaternion Left, float Right) { hmm_quaternion Result = HMM_MultiplyQuaternionF(Left, Right); return (Result); } HMM_INLINE hmm_vec2 operator*(float Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_MultiplyVec2f(Right, Left); return (Result); } HMM_INLINE hmm_vec3 operator*(float Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_MultiplyVec3f(Right, Left); return (Result); } HMM_INLINE hmm_vec4 operator*(float Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_MultiplyVec4f(Right, Left); return (Result); } HMM_INLINE hmm_mat4 operator*(float Left, hmm_mat4 Right) { hmm_mat4 Result = HMM_MultiplyMat4f(Right, Left); return (Result); } HMM_INLINE hmm_quaternion operator*(float Left, hmm_quaternion Right) { hmm_quaternion Result = HMM_MultiplyQuaternionF(Right, Left); return (Result); } HMM_INLINE hmm_vec4 operator*(hmm_mat4 Matrix, hmm_vec4 Vector) { hmm_vec4 Result = HMM_MultiplyMat4ByVec4(Matrix, Vector); return (Result); } HMM_INLINE hmm_vec2 operator/(hmm_vec2 Left, hmm_vec2 Right) { hmm_vec2 Result = HMM_DivideVec2(Left, Right); return (Result); } HMM_INLINE hmm_vec3 operator/(hmm_vec3 Left, hmm_vec3 Right) { hmm_vec3 Result = HMM_DivideVec3(Left, Right); return (Result); } HMM_INLINE hmm_vec4 operator/(hmm_vec4 Left, hmm_vec4 Right) { hmm_vec4 Result = HMM_DivideVec4(Left, Right); return (Result); } HMM_INLINE hmm_vec2 operator/(hmm_vec2 Left, float Right) { hmm_vec2 Result = HMM_DivideVec2f(Left, Right); return (Result); } HMM_INLINE hmm_vec3 operator/(hmm_vec3 Left, float Right) { hmm_vec3 Result = HMM_DivideVec3f(Left, Right); return (Result); } HMM_INLINE hmm_vec4 operator/(hmm_vec4 Left, float Right) { hmm_vec4 Result = HMM_DivideVec4f(Left, Right); return (Result); } HMM_INLINE hmm_mat4 operator/(hmm_mat4 Left, float Right) { hmm_mat4 Result = HMM_DivideMat4f(Left, Right); return (Result); } HMM_INLINE hmm_quaternion operator/(hmm_quaternion Left, float Right) { hmm_quaternion Result = HMM_DivideQuaternionF(Left, Right); return (Result); } HMM_INLINE hmm_vec2 &operator+=(hmm_vec2 &Left, hmm_vec2 Right) { return (Left = Left + Right); } HMM_INLINE hmm_vec3 &operator+=(hmm_vec3 &Left, hmm_vec3 Right) { return (Left = Left + Right); } HMM_INLINE hmm_vec4 &operator+=(hmm_vec4 &Left, hmm_vec4 Right) { return (Left = Left + Right); } HMM_INLINE hmm_mat4 &operator+=(hmm_mat4 &Left, hmm_mat4 Right) { return (Left = Left + Right); } HMM_INLINE hmm_quaternion &operator+=(hmm_quaternion &Left, hmm_quaternion Right) { return (Left = Left + Right); } HMM_INLINE hmm_vec2 &operator-=(hmm_vec2 &Left, hmm_vec2 Right) { return (Left = Left - Right); } HMM_INLINE hmm_vec3 &operator-=(hmm_vec3 &Left, hmm_vec3 Right) { return (Left = Left - Right); } HMM_INLINE hmm_vec4 &operator-=(hmm_vec4 &Left, hmm_vec4 Right) { return (Left = Left - Right); } HMM_INLINE hmm_mat4 &operator-=(hmm_mat4 &Left, hmm_mat4 Right) { return (Left = Left - Right); } HMM_INLINE hmm_quaternion &operator-=(hmm_quaternion &Left, hmm_quaternion Right) { return (Left = Left - Right); } HMM_INLINE hmm_vec2 &operator*=(hmm_vec2 &Left, hmm_vec2 Right) { return (Left = Left * Right); } HMM_INLINE hmm_vec3 &operator*=(hmm_vec3 &Left, hmm_vec3 Right) { return (Left = Left * Right); } HMM_INLINE hmm_vec4 &operator*=(hmm_vec4 &Left, hmm_vec4 Right) { return (Left = Left * Right); } HMM_INLINE hmm_vec2 &operator*=(hmm_vec2 &Left, float Right) { return (Left = Left * Right); } HMM_INLINE hmm_vec3 &operator*=(hmm_vec3 &Left, float Right) { return (Left = Left * Right); } HMM_INLINE hmm_vec4 &operator*=(hmm_vec4 &Left, float Right) { return (Left = Left * Right); } HMM_INLINE hmm_mat4 &operator*=(hmm_mat4 &Left, float Right) { return (Left = Left * Right); } HMM_INLINE hmm_quaternion &operator*=(hmm_quaternion &Left, float Right) { return (Left = Left * Right); } HMM_INLINE hmm_vec2 &operator/=(hmm_vec2 &Left, hmm_vec2 Right) { return (Left = Left / Right); } HMM_INLINE hmm_vec3 &operator/=(hmm_vec3 &Left, hmm_vec3 Right) { return (Left = Left / Right); } HMM_INLINE hmm_vec4 &operator/=(hmm_vec4 &Left, hmm_vec4 Right) { return (Left = Left / Right); } HMM_INLINE hmm_vec2 &operator/=(hmm_vec2 &Left, float Right) { return (Left = Left / Right); } HMM_INLINE hmm_vec3 &operator/=(hmm_vec3 &Left, float Right) { return (Left = Left / Right); } HMM_INLINE hmm_vec4 &operator/=(hmm_vec4 &Left, float Right) { return (Left = Left / Right); } HMM_INLINE hmm_mat4 &operator/=(hmm_mat4 &Left, float Right) { return (Left = Left / Right); } HMM_INLINE hmm_quaternion &operator/=(hmm_quaternion &Left, float Right) { return (Left = Left / Right); } HMM_INLINE hmm_bool operator==(hmm_vec2 Left, hmm_vec2 Right) { return HMM_EqualsVec2(Left, Right); } HMM_INLINE hmm_bool operator==(hmm_vec3 Left, hmm_vec3 Right) { return HMM_EqualsVec3(Left, Right); } HMM_INLINE hmm_bool operator==(hmm_vec4 Left, hmm_vec4 Right) { return HMM_EqualsVec4(Left, Right); } HMM_INLINE hmm_bool operator!=(hmm_vec2 Left, hmm_vec2 Right) { return !HMM_EqualsVec2(Left, Right); } HMM_INLINE hmm_bool operator!=(hmm_vec3 Left, hmm_vec3 Right) { return !HMM_EqualsVec3(Left, Right); } HMM_INLINE hmm_bool operator!=(hmm_vec4 Left, hmm_vec4 Right) { return !HMM_EqualsVec4(Left, Right); } #endif /* __cplusplus */ #ifdef __clang__ #pragma GCC diagnostic pop #endif #endif /* HANDMADE_MATH_H */ #ifdef HANDMADE_MATH_IMPLEMENTATION float HMM_Power(float Base, int Exponent) { float Result = 1.0f; float Mul = Exponent < 0 ? 1.f / Base : Base; unsigned int X = Exponent < 0 ? -Exponent : Exponent; while (X) { if (X & 1) { Result *= Mul; } Mul *= Mul; X >>= 1; } return (Result); } #ifndef HANDMADE_MATH__USE_SSE hmm_mat4 HMM_Transpose(hmm_mat4 Matrix) { hmm_mat4 Result; int Columns; for(Columns = 0; Columns < 4; ++Columns) { int Rows; for(Rows = 0; Rows < 4; ++Rows) { Result.Elements[Rows][Columns] = Matrix.Elements[Columns][Rows]; } } return (Result); } #endif #ifndef HANDMADE_MATH__USE_SSE hmm_mat4 HMM_AddMat4(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result; int Columns; for(Columns = 0; Columns < 4; ++Columns) { int Rows; for(Rows = 0; Rows < 4; ++Rows) { Result.Elements[Columns][Rows] = Left.Elements[Columns][Rows] + Right.Elements[Columns][Rows]; } } return (Result); } #endif #ifndef HANDMADE_MATH__USE_SSE hmm_mat4 HMM_SubtractMat4(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result; int Columns; for(Columns = 0; Columns < 4; ++Columns) { int Rows; for(Rows = 0; Rows < 4; ++Rows) { Result.Elements[Columns][Rows] = Left.Elements[Columns][Rows] - Right.Elements[Columns][Rows]; } } return (Result); } #endif hmm_mat4 HMM_MultiplyMat4(hmm_mat4 Left, hmm_mat4 Right) { hmm_mat4 Result; #ifdef HANDMADE_MATH__USE_SSE 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; for(Columns = 0; Columns < 4; ++Columns) { int Rows; for(Rows = 0; Rows < 4; ++Rows) { float Sum = 0; int CurrentMatrice; for(CurrentMatrice = 0; CurrentMatrice < 4; ++CurrentMatrice) { Sum += Left.Elements[CurrentMatrice][Rows] * Right.Elements[Columns][CurrentMatrice]; } Result.Elements[Columns][Rows] = Sum; } } #endif return (Result); } #ifndef HANDMADE_MATH__USE_SSE hmm_mat4 HMM_MultiplyMat4f(hmm_mat4 Matrix, float Scalar) { hmm_mat4 Result; int Columns; for(Columns = 0; Columns < 4; ++Columns) { int Rows; for(Rows = 0; Rows < 4; ++Rows) { Result.Elements[Columns][Rows] = Matrix.Elements[Columns][Rows] * Scalar; } } return (Result); } #endif hmm_vec4 HMM_MultiplyMat4ByVec4(hmm_mat4 Matrix, hmm_vec4 Vector) { hmm_vec4 Result; #ifdef HANDMADE_MATH__USE_SSE Result.InternalElementsSSE = HMM_LinearCombineSSE(Vector.InternalElementsSSE, Matrix); #else int Columns, Rows; for(Rows = 0; Rows < 4; ++Rows) { float Sum = 0; for(Columns = 0; Columns < 4; ++Columns) { Sum += Matrix.Elements[Columns][Rows] * Vector.Elements[Columns]; } Result.Elements[Rows] = Sum; } #endif return (Result); } #ifndef HANDMADE_MATH__USE_SSE hmm_mat4 HMM_DivideMat4f(hmm_mat4 Matrix, float Scalar) { hmm_mat4 Result; int Columns; for(Columns = 0; Columns < 4; ++Columns) { int Rows; for(Rows = 0; Rows < 4; ++Rows) { Result.Elements[Columns][Rows] = Matrix.Elements[Columns][Rows] / Scalar; } } return (Result); } #endif hmm_mat4 HMM_Rotate(float Angle, hmm_vec3 Axis) { hmm_mat4 Result = HMM_Mat4d(1.0f); Axis = HMM_NormalizeVec3(Axis); float SinTheta = HMM_SinF(HMM_ToRadians(Angle)); float CosTheta = HMM_CosF(HMM_ToRadians(Angle)); float CosValue = 1.0f - CosTheta; Result.Elements[0][0] = (Axis.X * Axis.X * CosValue) + CosTheta; Result.Elements[0][1] = (Axis.X * Axis.Y * CosValue) + (Axis.Z * SinTheta); Result.Elements[0][2] = (Axis.X * Axis.Z * CosValue) - (Axis.Y * SinTheta); Result.Elements[1][0] = (Axis.Y * Axis.X * CosValue) - (Axis.Z * SinTheta); Result.Elements[1][1] = (Axis.Y * Axis.Y * CosValue) + CosTheta; Result.Elements[1][2] = (Axis.Y * Axis.Z * CosValue) + (Axis.X * SinTheta); Result.Elements[2][0] = (Axis.Z * Axis.X * CosValue) + (Axis.Y * SinTheta); Result.Elements[2][1] = (Axis.Z * Axis.Y * CosValue) - (Axis.X * SinTheta); Result.Elements[2][2] = (Axis.Z * Axis.Z * CosValue) + CosTheta; return (Result); } hmm_mat4 HMM_LookAt(hmm_vec3 Eye, hmm_vec3 Center, hmm_vec3 Up) { hmm_mat4 Result; hmm_vec3 F = HMM_NormalizeVec3(HMM_SubtractVec3(Center, Eye)); hmm_vec3 S = HMM_NormalizeVec3(HMM_Cross(F, Up)); hmm_vec3 U = HMM_Cross(S, F); Result.Elements[0][0] = S.X; Result.Elements[0][1] = U.X; Result.Elements[0][2] = -F.X; Result.Elements[0][3] = 0.0f; Result.Elements[1][0] = S.Y; Result.Elements[1][1] = U.Y; Result.Elements[1][2] = -F.Y; Result.Elements[1][3] = 0.0f; Result.Elements[2][0] = S.Z; Result.Elements[2][1] = U.Z; Result.Elements[2][2] = -F.Z; Result.Elements[2][3] = 0.0f; Result.Elements[3][0] = -HMM_DotVec3(S, Eye); Result.Elements[3][1] = -HMM_DotVec3(U, Eye); Result.Elements[3][2] = HMM_DotVec3(F, Eye); Result.Elements[3][3] = 1.0f; return (Result); } hmm_quaternion HMM_InverseQuaternion(hmm_quaternion Left) { hmm_quaternion Conjugate; hmm_quaternion Result; float Norm = 0; float NormSquared = 0; Conjugate.X = -Left.X; Conjugate.Y = -Left.Y; Conjugate.Z = -Left.Z; Conjugate.W = Left.W; Norm = HMM_SquareRootF(HMM_DotQuaternion(Left, Left)); NormSquared = Norm * Norm; Result = HMM_DivideQuaternionF(Conjugate, NormSquared); return (Result); } hmm_quaternion HMM_Slerp(hmm_quaternion Left, float Time, hmm_quaternion Right) { hmm_quaternion Result; hmm_quaternion QuaternionLeft; hmm_quaternion QuaternionRight; float Cos_Theta = HMM_DotQuaternion(Left, Right); float Angle = HMM_ACosF(Cos_Theta); float S1 = HMM_SinF((1.0f - Time) * Angle); float S2 = HMM_SinF(Time * Angle); float Is = 1.0f / HMM_SinF(Angle); QuaternionLeft = HMM_MultiplyQuaternionF(Left, S1); QuaternionRight = HMM_MultiplyQuaternionF(Right, S2); Result = HMM_AddQuaternion(QuaternionLeft, QuaternionRight); Result = HMM_MultiplyQuaternionF(Result, Is); return (Result); } hmm_mat4 HMM_QuaternionToMat4(hmm_quaternion Left) { hmm_mat4 Result; Result = HMM_Mat4d(1); hmm_quaternion NormalizedQuaternion = HMM_NormalizeQuaternion(Left); float XX, YY, ZZ, XY, XZ, YZ, WX, WY, WZ; XX = NormalizedQuaternion.X * NormalizedQuaternion.X; YY = NormalizedQuaternion.Y * NormalizedQuaternion.Y; ZZ = NormalizedQuaternion.Z * NormalizedQuaternion.Z; XY = NormalizedQuaternion.X * NormalizedQuaternion.Y; XZ = NormalizedQuaternion.X * NormalizedQuaternion.Z; YZ = NormalizedQuaternion.Y * NormalizedQuaternion.Z; WX = NormalizedQuaternion.W * NormalizedQuaternion.X; WY = NormalizedQuaternion.W * NormalizedQuaternion.Y; WZ = NormalizedQuaternion.W * NormalizedQuaternion.Z; Result.Elements[0][0] = 1.0f - 2.0f * (YY + ZZ); Result.Elements[0][1] = 2.0f * (XY + WZ); Result.Elements[0][2] = 2.0f * (XZ - WY); Result.Elements[1][0] = 2.0f * (XY - WZ); Result.Elements[1][1] = 1.0f - 2.0f * (XX + ZZ); Result.Elements[1][2] = 2.0f * (YZ + WX); Result.Elements[2][0] = 2.0f * (XZ + WY); Result.Elements[2][1] = 2.0f * (YZ - WX); Result.Elements[2][2] = 1.0f - 2.0f * (XX + YY); return (Result); } hmm_quaternion HMM_QuaternionFromAxisAngle(hmm_vec3 Axis, float AngleOfRotation) { hmm_quaternion Result; hmm_vec3 RotatedVector; float AxisNorm = 0; float SineOfRotation = 0; AxisNorm = HMM_SquareRootF(HMM_DotVec3(Axis, Axis)); SineOfRotation = HMM_SinF(AngleOfRotation / 2.0f); RotatedVector = HMM_MultiplyVec3f(Axis, SineOfRotation); Result.W = HMM_CosF(AngleOfRotation / 2.0f); Result.XYZ = HMM_DivideVec3f(RotatedVector, AxisNorm); return (Result); } #endif /* HANDMADE_MATH_IMPLEMENTATION */