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Add XMMatrixInverseTranspose for optimal normal vector transformation #336

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cff3cc1
Add XMMatrixInverseTranspose for normal vector transforms (Fixes #9)
RohithPariki Aug 3, 2026
c5d86c3
Fix PREfast missing SAL annotation warning on XMMatrixInverseTranspose
RohithPariki Aug 4, 2026
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1 change: 1 addition & 0 deletions Inc/DirectXMath.h
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Original file line number Diff line number Diff line change
Expand Up @@ -1605,6 +1605,7 @@ namespace DirectX
XMMATRIX XM_CALLCONV XMMatrixMultiplyTranspose(FXMMATRIX M1, CXMMATRIX M2) noexcept;
XMMATRIX XM_CALLCONV XMMatrixTranspose(FXMMATRIX M) noexcept;
XMMATRIX XM_CALLCONV XMMatrixInverse(_Out_opt_ XMVECTOR* pDeterminant, _In_ FXMMATRIX M) noexcept;
XMMATRIX XM_CALLCONV XMMatrixInverseTranspose(_Out_opt_ XMVECTOR* pDeterminant, _In_ FXMMATRIX M) noexcept;
XMMATRIX XM_CALLCONV XMMatrixVectorTensorProduct(FXMVECTOR V1, FXMVECTOR V2) noexcept;
XMVECTOR XM_CALLCONV XMMatrixDeterminant(FXMMATRIX M) noexcept;

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220 changes: 220 additions & 0 deletions Inc/DirectXMathMatrix.inl
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Original file line number Diff line number Diff line change
@@ -1,3 +1,3 @@
//-------------------------------------------------------------------------------------
// DirectXMathMatrix.inl -- SIMD C++ Math library
//
Expand Down Expand Up @@ -1005,6 +1005,226 @@

//------------------------------------------------------------------------------

inline XMMATRIX XM_CALLCONV XMMatrixInverseTranspose
(
XMVECTOR* pDeterminant,
FXMMATRIX M
) noexcept
{
// Computes (M^-1)^T = adj(M) / det(M), used for transforming surface normals.
//
// XMMatrixInverse internally transposes M first (MT = M^T), then computes
// cofactors of MT to produce adj(M^T) = adj(M)^T. The final transpose requested
// by the caller cancels that internal one, so InverseTranspose simply runs the
// same cofactor algorithm directly on M — skipping the initial transpose entirely.

#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)

// No initial transpose — use M directly (was MT in XMMatrixInverse)
XMVECTOR V0[4], V1[4];
V0[0] = XMVectorSwizzle<XM_SWIZZLE_X, XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_Y>(M.r[2]);
V1[0] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_W>(M.r[3]);
V0[1] = XMVectorSwizzle<XM_SWIZZLE_X, XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_Y>(M.r[0]);
V1[1] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_W>(M.r[1]);
V0[2] = XMVectorPermute<XM_PERMUTE_0X, XM_PERMUTE_0Z, XM_PERMUTE_1X, XM_PERMUTE_1Z>(M.r[2], M.r[0]);
V1[2] = XMVectorPermute<XM_PERMUTE_0Y, XM_PERMUTE_0W, XM_PERMUTE_1Y, XM_PERMUTE_1W>(M.r[3], M.r[1]);

XMVECTOR D0 = XMVectorMultiply(V0[0], V1[0]);
XMVECTOR D1 = XMVectorMultiply(V0[1], V1[1]);
XMVECTOR D2 = XMVectorMultiply(V0[2], V1[2]);

V0[0] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_W>(M.r[2]);
V1[0] = XMVectorSwizzle<XM_SWIZZLE_X, XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_Y>(M.r[3]);
V0[1] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_W>(M.r[0]);
V1[1] = XMVectorSwizzle<XM_SWIZZLE_X, XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_Y>(M.r[1]);
V0[2] = XMVectorPermute<XM_PERMUTE_0Y, XM_PERMUTE_0W, XM_PERMUTE_1Y, XM_PERMUTE_1W>(M.r[2], M.r[0]);
V1[2] = XMVectorPermute<XM_PERMUTE_0X, XM_PERMUTE_0Z, XM_PERMUTE_1X, XM_PERMUTE_1Z>(M.r[3], M.r[1]);

D0 = XMVectorNegativeMultiplySubtract(V0[0], V1[0], D0);
D1 = XMVectorNegativeMultiplySubtract(V0[1], V1[1], D1);
D2 = XMVectorNegativeMultiplySubtract(V0[2], V1[2], D2);

V0[0] = XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_Z, XM_SWIZZLE_X, XM_SWIZZLE_Y>(M.r[1]);
V1[0] = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_0W, XM_PERMUTE_0X>(D0, D2);
V0[1] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_X>(M.r[0]);
V1[1] = XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_0Z>(D0, D2);
V0[2] = XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_Z, XM_SWIZZLE_X, XM_SWIZZLE_Y>(M.r[3]);
V1[2] = XMVectorPermute<XM_PERMUTE_1W, XM_PERMUTE_0Y, XM_PERMUTE_0W, XM_PERMUTE_0X>(D1, D2);
V0[3] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_X, XM_SWIZZLE_Y, XM_SWIZZLE_X>(M.r[2]);
V1[3] = XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_1W, XM_PERMUTE_0Y, XM_PERMUTE_0Z>(D1, D2);

XMVECTOR C0 = XMVectorMultiply(V0[0], V1[0]);
XMVECTOR C2 = XMVectorMultiply(V0[1], V1[1]);
XMVECTOR C4 = XMVectorMultiply(V0[2], V1[2]);
XMVECTOR C6 = XMVectorMultiply(V0[3], V1[3]);

V0[0] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Y, XM_SWIZZLE_Z>(M.r[1]);
V1[0] = XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_0X, XM_PERMUTE_0Y, XM_PERMUTE_1X>(D0, D2);
V0[1] = XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Y>(M.r[0]);
V1[1] = XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0Y, XM_PERMUTE_1X, XM_PERMUTE_0X>(D0, D2);
V0[2] = XMVectorSwizzle<XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Y, XM_SWIZZLE_Z>(M.r[3]);
V1[2] = XMVectorPermute<XM_PERMUTE_0W, XM_PERMUTE_0X, XM_PERMUTE_0Y, XM_PERMUTE_1Z>(D1, D2);
V0[3] = XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_Z, XM_SWIZZLE_W, XM_SWIZZLE_Y>(M.r[2]);
V1[3] = XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_0Y, XM_PERMUTE_1Z, XM_PERMUTE_0X>(D1, D2);

C0 = XMVectorNegativeMultiplySubtract(V0[0], V1[0], C0);
C2 = XMVectorNegativeMultiplySubtract(V0[1], V1[1], C2);
C4 = XMVectorNegativeMultiplySubtract(V0[2], V1[2], C4);
C6 = XMVectorNegativeMultiplySubtract(V0[3], V1[3], C6);

V0[0] = XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_X>(M.r[1]);
V1[0] = XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_1Y, XM_PERMUTE_1X, XM_PERMUTE_0Z>(D0, D2);
V0[1] = XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Z>(M.r[0]);
V1[1] = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_1X>(D0, D2);
V0[2] = XMVectorSwizzle<XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_W, XM_SWIZZLE_X>(M.r[3]);
V1[2] = XMVectorPermute<XM_PERMUTE_0Z, XM_PERMUTE_1W, XM_PERMUTE_1Z, XM_PERMUTE_0Z>(D1, D2);
V0[3] = XMVectorSwizzle<XM_SWIZZLE_Y, XM_SWIZZLE_W, XM_SWIZZLE_X, XM_SWIZZLE_Z>(M.r[2]);
V1[3] = XMVectorPermute<XM_PERMUTE_1W, XM_PERMUTE_0X, XM_PERMUTE_0W, XM_PERMUTE_1Z>(D1, D2);

XMVECTOR C1 = XMVectorNegativeMultiplySubtract(V0[0], V1[0], C0);
C0 = XMVectorMultiplyAdd(V0[0], V1[0], C0);
XMVECTOR C3 = XMVectorMultiplyAdd(V0[1], V1[1], C2);
C2 = XMVectorNegativeMultiplySubtract(V0[1], V1[1], C2);
XMVECTOR C5 = XMVectorNegativeMultiplySubtract(V0[2], V1[2], C4);
C4 = XMVectorMultiplyAdd(V0[2], V1[2], C4);
XMVECTOR C7 = XMVectorMultiplyAdd(V0[3], V1[3], C6);
C6 = XMVectorNegativeMultiplySubtract(V0[3], V1[3], C6);

XMMATRIX R;
R.r[0] = XMVectorSelect(C0, C1, g_XMSelect0101.v);
R.r[1] = XMVectorSelect(C2, C3, g_XMSelect0101.v);
R.r[2] = XMVectorSelect(C4, C5, g_XMSelect0101.v);
R.r[3] = XMVectorSelect(C6, C7, g_XMSelect0101.v);

XMVECTOR Determinant = XMVector4Dot(R.r[0], M.r[0]);

if (pDeterminant != nullptr)
*pDeterminant = Determinant;

XMVECTOR Reciprocal = XMVectorReciprocal(Determinant);

XMMATRIX Result;
Result.r[0] = XMVectorMultiply(R.r[0], Reciprocal);
Result.r[1] = XMVectorMultiply(R.r[1], Reciprocal);
Result.r[2] = XMVectorMultiply(R.r[2], Reciprocal);
Result.r[3] = XMVectorMultiply(R.r[3], Reciprocal);
return Result;

#elif defined(_XM_SSE_INTRINSICS_)
// No initial transpose block — cofactors are computed from M.r directly.
// This gives adj(M)/det(M) = (M^-1)^T without any redundant shuffles.

XMVECTOR V00 = XM_PERMUTE_PS(M.r[2], _MM_SHUFFLE(1, 1, 0, 0));
XMVECTOR V10 = XM_PERMUTE_PS(M.r[3], _MM_SHUFFLE(3, 2, 3, 2));
XMVECTOR V01 = XM_PERMUTE_PS(M.r[0], _MM_SHUFFLE(1, 1, 0, 0));
XMVECTOR V11 = XM_PERMUTE_PS(M.r[1], _MM_SHUFFLE(3, 2, 3, 2));
XMVECTOR V02 = _mm_shuffle_ps(M.r[2], M.r[0], _MM_SHUFFLE(2, 0, 2, 0));
XMVECTOR V12 = _mm_shuffle_ps(M.r[3], M.r[1], _MM_SHUFFLE(3, 1, 3, 1));

XMVECTOR D0 = _mm_mul_ps(V00, V10);
XMVECTOR D1 = _mm_mul_ps(V01, V11);
XMVECTOR D2 = _mm_mul_ps(V02, V12);

V00 = XM_PERMUTE_PS(M.r[2], _MM_SHUFFLE(3, 2, 3, 2));
V10 = XM_PERMUTE_PS(M.r[3], _MM_SHUFFLE(1, 1, 0, 0));
V01 = XM_PERMUTE_PS(M.r[0], _MM_SHUFFLE(3, 2, 3, 2));
V11 = XM_PERMUTE_PS(M.r[1], _MM_SHUFFLE(1, 1, 0, 0));
V02 = _mm_shuffle_ps(M.r[2], M.r[0], _MM_SHUFFLE(3, 1, 3, 1));
V12 = _mm_shuffle_ps(M.r[3], M.r[1], _MM_SHUFFLE(2, 0, 2, 0));

D0 = XM_FNMADD_PS(V00, V10, D0);
D1 = XM_FNMADD_PS(V01, V11, D1);
D2 = XM_FNMADD_PS(V02, V12, D2);
// V11 = D0Y,D0W,D2Y,D2Y
V11 = _mm_shuffle_ps(D0, D2, _MM_SHUFFLE(1, 1, 3, 1));
V00 = XM_PERMUTE_PS(M.r[1], _MM_SHUFFLE(1, 0, 2, 1));
V10 = _mm_shuffle_ps(V11, D0, _MM_SHUFFLE(0, 3, 0, 2));
V01 = XM_PERMUTE_PS(M.r[0], _MM_SHUFFLE(0, 1, 0, 2));
V11 = _mm_shuffle_ps(V11, D0, _MM_SHUFFLE(2, 1, 2, 1));
// V13 = D1Y,D1W,D2W,D2W
XMVECTOR V13 = _mm_shuffle_ps(D1, D2, _MM_SHUFFLE(3, 3, 3, 1));
V02 = XM_PERMUTE_PS(M.r[3], _MM_SHUFFLE(1, 0, 2, 1));
V12 = _mm_shuffle_ps(V13, D1, _MM_SHUFFLE(0, 3, 0, 2));
XMVECTOR V03 = XM_PERMUTE_PS(M.r[2], _MM_SHUFFLE(0, 1, 0, 2));
V13 = _mm_shuffle_ps(V13, D1, _MM_SHUFFLE(2, 1, 2, 1));

XMVECTOR C0 = _mm_mul_ps(V00, V10);
XMVECTOR C2 = _mm_mul_ps(V01, V11);
XMVECTOR C4 = _mm_mul_ps(V02, V12);
XMVECTOR C6 = _mm_mul_ps(V03, V13);

// V11 = D0X,D0Y,D2X,D2X
V11 = _mm_shuffle_ps(D0, D2, _MM_SHUFFLE(0, 0, 1, 0));
V00 = XM_PERMUTE_PS(M.r[1], _MM_SHUFFLE(2, 1, 3, 2));
V10 = _mm_shuffle_ps(D0, V11, _MM_SHUFFLE(2, 1, 0, 3));
V01 = XM_PERMUTE_PS(M.r[0], _MM_SHUFFLE(1, 3, 2, 3));
V11 = _mm_shuffle_ps(D0, V11, _MM_SHUFFLE(0, 2, 1, 2));
// V13 = D1X,D1Y,D2Z,D2Z
V13 = _mm_shuffle_ps(D1, D2, _MM_SHUFFLE(2, 2, 1, 0));
V02 = XM_PERMUTE_PS(M.r[3], _MM_SHUFFLE(2, 1, 3, 2));
V12 = _mm_shuffle_ps(D1, V13, _MM_SHUFFLE(2, 1, 0, 3));
V03 = XM_PERMUTE_PS(M.r[2], _MM_SHUFFLE(1, 3, 2, 3));
V13 = _mm_shuffle_ps(D1, V13, _MM_SHUFFLE(0, 2, 1, 2));

C0 = XM_FNMADD_PS(V00, V10, C0);
C2 = XM_FNMADD_PS(V01, V11, C2);
C4 = XM_FNMADD_PS(V02, V12, C4);
C6 = XM_FNMADD_PS(V03, V13, C6);

V00 = XM_PERMUTE_PS(M.r[1], _MM_SHUFFLE(0, 3, 0, 3));
// V10 = D0Z,D0Z,D2X,D2Y
V10 = _mm_shuffle_ps(D0, D2, _MM_SHUFFLE(1, 0, 2, 2));
V10 = XM_PERMUTE_PS(V10, _MM_SHUFFLE(0, 2, 3, 0));
V01 = XM_PERMUTE_PS(M.r[0], _MM_SHUFFLE(2, 0, 3, 1));
// V11 = D0X,D0W,D2X,D2Y
V11 = _mm_shuffle_ps(D0, D2, _MM_SHUFFLE(1, 0, 3, 0));
V11 = XM_PERMUTE_PS(V11, _MM_SHUFFLE(2, 1, 0, 3));
V02 = XM_PERMUTE_PS(M.r[3], _MM_SHUFFLE(0, 3, 0, 3));
// V12 = D1Z,D1Z,D2Z,D2W
V12 = _mm_shuffle_ps(D1, D2, _MM_SHUFFLE(3, 2, 2, 2));
V12 = XM_PERMUTE_PS(V12, _MM_SHUFFLE(0, 2, 3, 0));
V03 = XM_PERMUTE_PS(M.r[2], _MM_SHUFFLE(2, 0, 3, 1));
// V13 = D1X,D1W,D2Z,D2W
V13 = _mm_shuffle_ps(D1, D2, _MM_SHUFFLE(3, 2, 3, 0));
V13 = XM_PERMUTE_PS(V13, _MM_SHUFFLE(2, 1, 0, 3));

V00 = _mm_mul_ps(V00, V10);
V01 = _mm_mul_ps(V01, V11);
V02 = _mm_mul_ps(V02, V12);
V03 = _mm_mul_ps(V03, V13);
XMVECTOR C1 = _mm_sub_ps(C0, V00);
C0 = _mm_add_ps(C0, V00);
XMVECTOR C3 = _mm_add_ps(C2, V01);
C2 = _mm_sub_ps(C2, V01);
XMVECTOR C5 = _mm_sub_ps(C4, V02);
C4 = _mm_add_ps(C4, V02);
XMVECTOR C7 = _mm_add_ps(C6, V03);
C6 = _mm_sub_ps(C6, V03);

C0 = _mm_shuffle_ps(C0, C1, _MM_SHUFFLE(3, 1, 2, 0));
C2 = _mm_shuffle_ps(C2, C3, _MM_SHUFFLE(3, 1, 2, 0));
C4 = _mm_shuffle_ps(C4, C5, _MM_SHUFFLE(3, 1, 2, 0));
C6 = _mm_shuffle_ps(C6, C7, _MM_SHUFFLE(3, 1, 2, 0));
C0 = XM_PERMUTE_PS(C0, _MM_SHUFFLE(3, 1, 2, 0));
C2 = XM_PERMUTE_PS(C2, _MM_SHUFFLE(3, 1, 2, 0));
C4 = XM_PERMUTE_PS(C4, _MM_SHUFFLE(3, 1, 2, 0));
C6 = XM_PERMUTE_PS(C6, _MM_SHUFFLE(3, 1, 2, 0));
// Determinant — det(M) == det(M^T), same value as XMMatrixInverse
XMVECTOR vTemp = XMVector4Dot(C0, M.r[0]);
if (pDeterminant != nullptr)
*pDeterminant = vTemp;
vTemp = _mm_div_ps(g_XMOne, vTemp);
XMMATRIX mResult;
mResult.r[0] = _mm_mul_ps(C0, vTemp);
mResult.r[1] = _mm_mul_ps(C2, vTemp);
mResult.r[2] = _mm_mul_ps(C4, vTemp);
mResult.r[3] = _mm_mul_ps(C6, vTemp);
return mResult;
#endif
}

//------------------------------------------------------------------------------

inline XMMATRIX XM_CALLCONV XMMatrixVectorTensorProduct
(
FXMVECTOR V1,
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