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DirectXMathMisc.inl
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DirectXMathMisc.inl
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//-------------------------------------------------------------------------------------
// DirectXMathMisc.inl -- SIMD C++ Math library
//
// Copyright (c) Microsoft Corporation.
// Licensed under the MIT License.
//
// http://go.microsoft.com/fwlink/?LinkID=615560
//-------------------------------------------------------------------------------------
#pragma once
/****************************************************************************
*
* Quaternion
*
****************************************************************************/
//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionEqual
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
return XMVector4Equal(Q1, Q2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionNotEqual
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
return XMVector4NotEqual(Q1, Q2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionIsNaN(FXMVECTOR Q) noexcept
{
return XMVector4IsNaN(Q);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionIsInfinite(FXMVECTOR Q) noexcept
{
return XMVector4IsInfinite(Q);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMQuaternionIsIdentity(FXMVECTOR Q) noexcept
{
return XMVector4Equal(Q, g_XMIdentityR3.v);
}
//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionDot
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
return XMVector4Dot(Q1, Q2);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionMultiply
(
FXMVECTOR Q1,
FXMVECTOR Q2
) noexcept
{
// Returns the product Q2*Q1 (which is the concatenation of a rotation Q1 followed by the rotation Q2)
// [ (Q2.w * Q1.x) + (Q2.x * Q1.w) + (Q2.y * Q1.z) - (Q2.z * Q1.y),
// (Q2.w * Q1.y) - (Q2.x * Q1.z) + (Q2.y * Q1.w) + (Q2.z * Q1.x),
// (Q2.w * Q1.z) + (Q2.x * Q1.y) - (Q2.y * Q1.x) + (Q2.z * Q1.w),
// (Q2.w * Q1.w) - (Q2.x * Q1.x) - (Q2.y * Q1.y) - (Q2.z * Q1.z) ]
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 Result = { { {
(Q2.vector4_f32[3] * Q1.vector4_f32[0]) + (Q2.vector4_f32[0] * Q1.vector4_f32[3]) + (Q2.vector4_f32[1] * Q1.vector4_f32[2]) - (Q2.vector4_f32[2] * Q1.vector4_f32[1]),
(Q2.vector4_f32[3] * Q1.vector4_f32[1]) - (Q2.vector4_f32[0] * Q1.vector4_f32[2]) + (Q2.vector4_f32[1] * Q1.vector4_f32[3]) + (Q2.vector4_f32[2] * Q1.vector4_f32[0]),
(Q2.vector4_f32[3] * Q1.vector4_f32[2]) + (Q2.vector4_f32[0] * Q1.vector4_f32[1]) - (Q2.vector4_f32[1] * Q1.vector4_f32[0]) + (Q2.vector4_f32[2] * Q1.vector4_f32[3]),
(Q2.vector4_f32[3] * Q1.vector4_f32[3]) - (Q2.vector4_f32[0] * Q1.vector4_f32[0]) - (Q2.vector4_f32[1] * Q1.vector4_f32[1]) - (Q2.vector4_f32[2] * Q1.vector4_f32[2])
} } };
return Result.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
static const XMVECTORF32 ControlWZYX = { { { 1.0f, -1.0f, 1.0f, -1.0f } } };
static const XMVECTORF32 ControlZWXY = { { { 1.0f, 1.0f, -1.0f, -1.0f } } };
static const XMVECTORF32 ControlYXWZ = { { { -1.0f, 1.0f, 1.0f, -1.0f } } };
float32x2_t Q2L = vget_low_f32(Q2);
float32x2_t Q2H = vget_high_f32(Q2);
float32x4_t Q2X = vdupq_lane_f32(Q2L, 0);
float32x4_t Q2Y = vdupq_lane_f32(Q2L, 1);
float32x4_t Q2Z = vdupq_lane_f32(Q2H, 0);
XMVECTOR vResult = vmulq_lane_f32(Q1, Q2H, 1);
// Mul by Q1WZYX
float32x4_t vTemp = vrev64q_f32(Q1);
vTemp = vcombine_f32(vget_high_f32(vTemp), vget_low_f32(vTemp));
Q2X = vmulq_f32(Q2X, vTemp);
vResult = vmlaq_f32(vResult, Q2X, ControlWZYX);
// Mul by Q1ZWXY
vTemp = vreinterpretq_f32_u32(vrev64q_u32(vreinterpretq_u32_f32(vTemp)));
Q2Y = vmulq_f32(Q2Y, vTemp);
vResult = vmlaq_f32(vResult, Q2Y, ControlZWXY);
// Mul by Q1YXWZ
vTemp = vreinterpretq_f32_u32(vrev64q_u32(vreinterpretq_u32_f32(vTemp)));
vTemp = vcombine_f32(vget_high_f32(vTemp), vget_low_f32(vTemp));
Q2Z = vmulq_f32(Q2Z, vTemp);
vResult = vmlaq_f32(vResult, Q2Z, ControlYXWZ);
return vResult;
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 ControlWZYX = { { { 1.0f, -1.0f, 1.0f, -1.0f } } };
static const XMVECTORF32 ControlZWXY = { { { 1.0f, 1.0f, -1.0f, -1.0f } } };
static const XMVECTORF32 ControlYXWZ = { { { -1.0f, 1.0f, 1.0f, -1.0f } } };
// Copy to SSE registers and use as few as possible for x86
XMVECTOR Q2X = Q2;
XMVECTOR Q2Y = Q2;
XMVECTOR Q2Z = Q2;
XMVECTOR vResult = Q2;
// Splat with one instruction
vResult = XM_PERMUTE_PS(vResult, _MM_SHUFFLE(3, 3, 3, 3));
Q2X = XM_PERMUTE_PS(Q2X, _MM_SHUFFLE(0, 0, 0, 0));
Q2Y = XM_PERMUTE_PS(Q2Y, _MM_SHUFFLE(1, 1, 1, 1));
Q2Z = XM_PERMUTE_PS(Q2Z, _MM_SHUFFLE(2, 2, 2, 2));
// Retire Q1 and perform Q1*Q2W
vResult = _mm_mul_ps(vResult, Q1);
XMVECTOR Q1Shuffle = Q1;
// Shuffle the copies of Q1
Q1Shuffle = XM_PERMUTE_PS(Q1Shuffle, _MM_SHUFFLE(0, 1, 2, 3));
// Mul by Q1WZYX
Q2X = _mm_mul_ps(Q2X, Q1Shuffle);
Q1Shuffle = XM_PERMUTE_PS(Q1Shuffle, _MM_SHUFFLE(2, 3, 0, 1));
// Flip the signs on y and z
vResult = XM_FMADD_PS(Q2X, ControlWZYX, vResult);
// Mul by Q1ZWXY
Q2Y = _mm_mul_ps(Q2Y, Q1Shuffle);
Q1Shuffle = XM_PERMUTE_PS(Q1Shuffle, _MM_SHUFFLE(0, 1, 2, 3));
// Flip the signs on z and w
Q2Y = _mm_mul_ps(Q2Y, ControlZWXY);
// Mul by Q1YXWZ
Q2Z = _mm_mul_ps(Q2Z, Q1Shuffle);
// Flip the signs on x and w
Q2Y = XM_FMADD_PS(Q2Z, ControlYXWZ, Q2Y);
vResult = _mm_add_ps(vResult, Q2Y);
return vResult;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionLengthSq(FXMVECTOR Q) noexcept
{
return XMVector4LengthSq(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionReciprocalLength(FXMVECTOR Q) noexcept
{
return XMVector4ReciprocalLength(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionLength(FXMVECTOR Q) noexcept
{
return XMVector4Length(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionNormalizeEst(FXMVECTOR Q) noexcept
{
return XMVector4NormalizeEst(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionNormalize(FXMVECTOR Q) noexcept
{
return XMVector4Normalize(Q);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionConjugate(FXMVECTOR Q) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 Result = { { {
-Q.vector4_f32[0],
-Q.vector4_f32[1],
-Q.vector4_f32[2],
Q.vector4_f32[3]
} } };
return Result.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
static const XMVECTORF32 NegativeOne3 = { { { -1.0f, -1.0f, -1.0f, 1.0f } } };
return vmulq_f32(Q, NegativeOne3.v);
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 NegativeOne3 = { { { -1.0f, -1.0f, -1.0f, 1.0f } } };
return _mm_mul_ps(Q, NegativeOne3);
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionInverse(FXMVECTOR Q) noexcept
{
XMVECTOR L = XMVector4LengthSq(Q);
XMVECTOR Conjugate = XMQuaternionConjugate(Q);
XMVECTOR Control = XMVectorLessOrEqual(L, g_XMEpsilon.v);
XMVECTOR Result = XMVectorDivide(Conjugate, L);
Result = XMVectorSelect(Result, g_XMZero, Control);
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionLn(FXMVECTOR Q) noexcept
{
static const XMVECTORF32 OneMinusEpsilon = { { { 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f } } };
XMVECTOR QW = XMVectorSplatW(Q);
XMVECTOR Q0 = XMVectorSelect(g_XMSelect1110.v, Q, g_XMSelect1110.v);
XMVECTOR ControlW = XMVectorInBounds(QW, OneMinusEpsilon.v);
XMVECTOR Theta = XMVectorACos(QW);
XMVECTOR SinTheta = XMVectorSin(Theta);
XMVECTOR S = XMVectorDivide(Theta, SinTheta);
XMVECTOR Result = XMVectorMultiply(Q0, S);
Result = XMVectorSelect(Q0, Result, ControlW);
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionExp(FXMVECTOR Q) noexcept
{
XMVECTOR Theta = XMVector3Length(Q);
XMVECTOR SinTheta, CosTheta;
XMVectorSinCos(&SinTheta, &CosTheta, Theta);
XMVECTOR S = XMVectorDivide(SinTheta, Theta);
XMVECTOR Result = XMVectorMultiply(Q, S);
const XMVECTOR Zero = XMVectorZero();
XMVECTOR Control = XMVectorNearEqual(Theta, Zero, g_XMEpsilon.v);
Result = XMVectorSelect(Result, Q, Control);
Result = XMVectorSelect(CosTheta, Result, g_XMSelect1110.v);
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSlerp
(
FXMVECTOR Q0,
FXMVECTOR Q1,
float t
) noexcept
{
XMVECTOR T = XMVectorReplicate(t);
return XMQuaternionSlerpV(Q0, Q1, T);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSlerpV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR T
) noexcept
{
assert((XMVectorGetY(T) == XMVectorGetX(T)) && (XMVectorGetZ(T) == XMVectorGetX(T)) && (XMVectorGetW(T) == XMVectorGetX(T)));
// Result = Q0 * sin((1.0 - t) * Omega) / sin(Omega) + Q1 * sin(t * Omega) / sin(Omega)
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)
const XMVECTORF32 OneMinusEpsilon = { { { 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f } } };
XMVECTOR CosOmega = XMQuaternionDot(Q0, Q1);
const XMVECTOR Zero = XMVectorZero();
XMVECTOR Control = XMVectorLess(CosOmega, Zero);
XMVECTOR Sign = XMVectorSelect(g_XMOne.v, g_XMNegativeOne.v, Control);
CosOmega = XMVectorMultiply(CosOmega, Sign);
Control = XMVectorLess(CosOmega, OneMinusEpsilon);
XMVECTOR SinOmega = XMVectorNegativeMultiplySubtract(CosOmega, CosOmega, g_XMOne.v);
SinOmega = XMVectorSqrt(SinOmega);
XMVECTOR Omega = XMVectorATan2(SinOmega, CosOmega);
XMVECTOR SignMask = XMVectorSplatSignMask();
XMVECTOR V01 = XMVectorShiftLeft(T, Zero, 2);
SignMask = XMVectorShiftLeft(SignMask, Zero, 3);
V01 = XMVectorXorInt(V01, SignMask);
V01 = XMVectorAdd(g_XMIdentityR0.v, V01);
XMVECTOR InvSinOmega = XMVectorReciprocal(SinOmega);
XMVECTOR S0 = XMVectorMultiply(V01, Omega);
S0 = XMVectorSin(S0);
S0 = XMVectorMultiply(S0, InvSinOmega);
S0 = XMVectorSelect(V01, S0, Control);
XMVECTOR S1 = XMVectorSplatY(S0);
S0 = XMVectorSplatX(S0);
S1 = XMVectorMultiply(S1, Sign);
XMVECTOR Result = XMVectorMultiply(Q0, S0);
Result = XMVectorMultiplyAdd(Q1, S1, Result);
return Result;
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 OneMinusEpsilon = { { { 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f, 1.0f - 0.00001f } } };
static const XMVECTORU32 SignMask2 = { { { 0x80000000, 0x00000000, 0x00000000, 0x00000000 } } };
XMVECTOR CosOmega = XMQuaternionDot(Q0, Q1);
const XMVECTOR Zero = XMVectorZero();
XMVECTOR Control = XMVectorLess(CosOmega, Zero);
XMVECTOR Sign = XMVectorSelect(g_XMOne, g_XMNegativeOne, Control);
CosOmega = _mm_mul_ps(CosOmega, Sign);
Control = XMVectorLess(CosOmega, OneMinusEpsilon);
XMVECTOR SinOmega = _mm_mul_ps(CosOmega, CosOmega);
SinOmega = _mm_sub_ps(g_XMOne, SinOmega);
SinOmega = _mm_sqrt_ps(SinOmega);
XMVECTOR Omega = XMVectorATan2(SinOmega, CosOmega);
XMVECTOR V01 = XM_PERMUTE_PS(T, _MM_SHUFFLE(2, 3, 0, 1));
V01 = _mm_and_ps(V01, g_XMMaskXY);
V01 = _mm_xor_ps(V01, SignMask2);
V01 = _mm_add_ps(g_XMIdentityR0, V01);
XMVECTOR S0 = _mm_mul_ps(V01, Omega);
S0 = XMVectorSin(S0);
S0 = _mm_div_ps(S0, SinOmega);
S0 = XMVectorSelect(V01, S0, Control);
XMVECTOR S1 = XMVectorSplatY(S0);
S0 = XMVectorSplatX(S0);
S1 = _mm_mul_ps(S1, Sign);
XMVECTOR Result = _mm_mul_ps(Q0, S0);
S1 = _mm_mul_ps(S1, Q1);
Result = _mm_add_ps(Result, S1);
return Result;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSquad
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR Q3,
float t
) noexcept
{
XMVECTOR T = XMVectorReplicate(t);
return XMQuaternionSquadV(Q0, Q1, Q2, Q3, T);
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionSquadV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR Q3,
HXMVECTOR T
) noexcept
{
assert((XMVectorGetY(T) == XMVectorGetX(T)) && (XMVectorGetZ(T) == XMVectorGetX(T)) && (XMVectorGetW(T) == XMVectorGetX(T)));
XMVECTOR TP = T;
const XMVECTOR Two = XMVectorSplatConstant(2, 0);
XMVECTOR Q03 = XMQuaternionSlerpV(Q0, Q3, T);
XMVECTOR Q12 = XMQuaternionSlerpV(Q1, Q2, T);
TP = XMVectorNegativeMultiplySubtract(TP, TP, TP);
TP = XMVectorMultiply(TP, Two);
XMVECTOR Result = XMQuaternionSlerpV(Q03, Q12, TP);
return Result;
}
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV XMQuaternionSquadSetup
(
XMVECTOR* pA,
XMVECTOR* pB,
XMVECTOR* pC,
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR Q3
) noexcept
{
assert(pA);
assert(pB);
assert(pC);
XMVECTOR LS12 = XMQuaternionLengthSq(XMVectorAdd(Q1, Q2));
XMVECTOR LD12 = XMQuaternionLengthSq(XMVectorSubtract(Q1, Q2));
XMVECTOR SQ2 = XMVectorNegate(Q2);
XMVECTOR Control1 = XMVectorLess(LS12, LD12);
SQ2 = XMVectorSelect(Q2, SQ2, Control1);
XMVECTOR LS01 = XMQuaternionLengthSq(XMVectorAdd(Q0, Q1));
XMVECTOR LD01 = XMQuaternionLengthSq(XMVectorSubtract(Q0, Q1));
XMVECTOR SQ0 = XMVectorNegate(Q0);
XMVECTOR LS23 = XMQuaternionLengthSq(XMVectorAdd(SQ2, Q3));
XMVECTOR LD23 = XMQuaternionLengthSq(XMVectorSubtract(SQ2, Q3));
XMVECTOR SQ3 = XMVectorNegate(Q3);
XMVECTOR Control0 = XMVectorLess(LS01, LD01);
XMVECTOR Control2 = XMVectorLess(LS23, LD23);
SQ0 = XMVectorSelect(Q0, SQ0, Control0);
SQ3 = XMVectorSelect(Q3, SQ3, Control2);
XMVECTOR InvQ1 = XMQuaternionInverse(Q1);
XMVECTOR InvQ2 = XMQuaternionInverse(SQ2);
XMVECTOR LnQ0 = XMQuaternionLn(XMQuaternionMultiply(InvQ1, SQ0));
XMVECTOR LnQ2 = XMQuaternionLn(XMQuaternionMultiply(InvQ1, SQ2));
XMVECTOR LnQ1 = XMQuaternionLn(XMQuaternionMultiply(InvQ2, Q1));
XMVECTOR LnQ3 = XMQuaternionLn(XMQuaternionMultiply(InvQ2, SQ3));
const XMVECTOR NegativeOneQuarter = XMVectorSplatConstant(-1, 2);
XMVECTOR ExpQ02 = XMVectorMultiply(XMVectorAdd(LnQ0, LnQ2), NegativeOneQuarter);
XMVECTOR ExpQ13 = XMVectorMultiply(XMVectorAdd(LnQ1, LnQ3), NegativeOneQuarter);
ExpQ02 = XMQuaternionExp(ExpQ02);
ExpQ13 = XMQuaternionExp(ExpQ13);
*pA = XMQuaternionMultiply(Q1, ExpQ02);
*pB = XMQuaternionMultiply(SQ2, ExpQ13);
*pC = SQ2;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionBaryCentric
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
float f,
float g
) noexcept
{
float s = f + g;
XMVECTOR Result;
if ((s < 0.00001f) && (s > -0.00001f))
{
Result = Q0;
}
else
{
XMVECTOR Q01 = XMQuaternionSlerp(Q0, Q1, s);
XMVECTOR Q02 = XMQuaternionSlerp(Q0, Q2, s);
Result = XMQuaternionSlerp(Q01, Q02, g / s);
}
return Result;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionBaryCentricV
(
FXMVECTOR Q0,
FXMVECTOR Q1,
FXMVECTOR Q2,
GXMVECTOR F,
HXMVECTOR G
) noexcept
{
assert((XMVectorGetY(F) == XMVectorGetX(F)) && (XMVectorGetZ(F) == XMVectorGetX(F)) && (XMVectorGetW(F) == XMVectorGetX(F)));
assert((XMVectorGetY(G) == XMVectorGetX(G)) && (XMVectorGetZ(G) == XMVectorGetX(G)) && (XMVectorGetW(G) == XMVectorGetX(G)));
const XMVECTOR Epsilon = XMVectorSplatConstant(1, 16);
XMVECTOR S = XMVectorAdd(F, G);
XMVECTOR Result;
if (XMVector4InBounds(S, Epsilon))
{
Result = Q0;
}
else
{
XMVECTOR Q01 = XMQuaternionSlerpV(Q0, Q1, S);
XMVECTOR Q02 = XMQuaternionSlerpV(Q0, Q2, S);
XMVECTOR GS = XMVectorReciprocal(S);
GS = XMVectorMultiply(G, GS);
Result = XMQuaternionSlerpV(Q01, Q02, GS);
}
return Result;
}
//------------------------------------------------------------------------------
// Transformation operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionIdentity() noexcept
{
return g_XMIdentityR3.v;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationRollPitchYaw
(
float Pitch,
float Yaw,
float Roll
) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
const float halfpitch = Pitch * 0.5f;
float cp = cosf(halfpitch);
float sp = sinf(halfpitch);
const float halfyaw = Yaw * 0.5f;
float cy = cosf(halfyaw);
float sy = sinf(halfyaw);
const float halfroll = Roll * 0.5f;
float cr = cosf(halfroll);
float sr = sinf(halfroll);
XMVECTORF32 vResult = { { {
cr * sp * cy + sr * cp * sy,
cr * cp * sy - sr * sp * cy,
sr * cp * cy - cr * sp * sy,
cr * cp * cy + sr * sp * sy
} } };
return vResult;
#else
XMVECTOR Angles = XMVectorSet(Pitch, Yaw, Roll, 0.0f);
return XMQuaternionRotationRollPitchYawFromVector(Angles);
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationRollPitchYawFromVector
(
FXMVECTOR Angles // <Pitch, Yaw, Roll, 0>
) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
const float halfpitch = Angles.vector4_f32[0] * 0.5f;
float cp = cosf(halfpitch);
float sp = sinf(halfpitch);
const float halfyaw = Angles.vector4_f32[1] * 0.5f;
float cy = cosf(halfyaw);
float sy = sinf(halfyaw);
const float halfroll = Angles.vector4_f32[2] * 0.5f;
float cr = cosf(halfroll);
float sr = sinf(halfroll);
XMVECTORF32 vResult = { { {
cr * sp * cy + sr * cp * sy,
cr * cp * sy - sr * sp * cy,
sr * cp * cy - cr * sp * sy,
cr * cp * cy + sr * sp * sy
} } };
return vResult;
#else
static const XMVECTORF32 Sign = { { { 1.0f, -1.0f, -1.0f, 1.0f } } };
XMVECTOR HalfAngles = XMVectorMultiply(Angles, g_XMOneHalf.v);
XMVECTOR SinAngles, CosAngles;
XMVectorSinCos(&SinAngles, &CosAngles, HalfAngles);
XMVECTOR P0 = XMVectorPermute<XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X>(SinAngles, CosAngles);
XMVECTOR Y0 = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y>(SinAngles, CosAngles);
XMVECTOR R0 = XMVectorPermute<XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z>(SinAngles, CosAngles);
XMVECTOR P1 = XMVectorPermute<XM_PERMUTE_0X, XM_PERMUTE_1X, XM_PERMUTE_1X, XM_PERMUTE_1X>(CosAngles, SinAngles);
XMVECTOR Y1 = XMVectorPermute<XM_PERMUTE_1Y, XM_PERMUTE_0Y, XM_PERMUTE_1Y, XM_PERMUTE_1Y>(CosAngles, SinAngles);
XMVECTOR R1 = XMVectorPermute<XM_PERMUTE_1Z, XM_PERMUTE_1Z, XM_PERMUTE_0Z, XM_PERMUTE_1Z>(CosAngles, SinAngles);
XMVECTOR Q1 = XMVectorMultiply(P1, Sign.v);
XMVECTOR Q0 = XMVectorMultiply(P0, Y0);
Q1 = XMVectorMultiply(Q1, Y1);
Q0 = XMVectorMultiply(Q0, R0);
XMVECTOR Q = XMVectorMultiplyAdd(Q1, R1, Q0);
return Q;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationNormal
(
FXMVECTOR NormalAxis,
float Angle
) noexcept
{
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)
XMVECTOR N = XMVectorSelect(g_XMOne.v, NormalAxis, g_XMSelect1110.v);
float SinV, CosV;
XMScalarSinCos(&SinV, &CosV, 0.5f * Angle);
XMVECTOR Scale = XMVectorSet(SinV, SinV, SinV, CosV);
return XMVectorMultiply(N, Scale);
#elif defined(_XM_SSE_INTRINSICS_)
XMVECTOR N = _mm_and_ps(NormalAxis, g_XMMask3);
N = _mm_or_ps(N, g_XMIdentityR3);
XMVECTOR Scale = _mm_set_ps1(0.5f * Angle);
XMVECTOR vSine;
XMVECTOR vCosine;
XMVectorSinCos(&vSine, &vCosine, Scale);
Scale = _mm_and_ps(vSine, g_XMMask3);
vCosine = _mm_and_ps(vCosine, g_XMMaskW);
Scale = _mm_or_ps(Scale, vCosine);
N = _mm_mul_ps(N, Scale);
return N;
#endif
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationAxis
(
FXMVECTOR Axis,
float Angle
) noexcept
{
assert(!XMVector3Equal(Axis, XMVectorZero()));
assert(!XMVector3IsInfinite(Axis));
XMVECTOR Normal = XMVector3Normalize(Axis);
XMVECTOR Q = XMQuaternionRotationNormal(Normal, Angle);
return Q;
}
//------------------------------------------------------------------------------
inline XMVECTOR XM_CALLCONV XMQuaternionRotationMatrix(FXMMATRIX M) noexcept
{
#if defined(_XM_NO_INTRINSICS_)
XMVECTORF32 q;
float r22 = M.m[2][2];
if (r22 <= 0.f) // x^2 + y^2 >= z^2 + w^2
{
float dif10 = M.m[1][1] - M.m[0][0];
float omr22 = 1.f - r22;
if (dif10 <= 0.f) // x^2 >= y^2
{
float fourXSqr = omr22 - dif10;
float inv4x = 0.5f / sqrtf(fourXSqr);
q.f[0] = fourXSqr * inv4x;
q.f[1] = (M.m[0][1] + M.m[1][0]) * inv4x;
q.f[2] = (M.m[0][2] + M.m[2][0]) * inv4x;
q.f[3] = (M.m[1][2] - M.m[2][1]) * inv4x;
}
else // y^2 >= x^2
{
float fourYSqr = omr22 + dif10;
float inv4y = 0.5f / sqrtf(fourYSqr);
q.f[0] = (M.m[0][1] + M.m[1][0]) * inv4y;
q.f[1] = fourYSqr * inv4y;
q.f[2] = (M.m[1][2] + M.m[2][1]) * inv4y;
q.f[3] = (M.m[2][0] - M.m[0][2]) * inv4y;
}
}
else // z^2 + w^2 >= x^2 + y^2
{
float sum10 = M.m[1][1] + M.m[0][0];
float opr22 = 1.f + r22;
if (sum10 <= 0.f) // z^2 >= w^2
{
float fourZSqr = opr22 - sum10;
float inv4z = 0.5f / sqrtf(fourZSqr);
q.f[0] = (M.m[0][2] + M.m[2][0]) * inv4z;
q.f[1] = (M.m[1][2] + M.m[2][1]) * inv4z;
q.f[2] = fourZSqr * inv4z;
q.f[3] = (M.m[0][1] - M.m[1][0]) * inv4z;
}
else // w^2 >= z^2
{
float fourWSqr = opr22 + sum10;
float inv4w = 0.5f / sqrtf(fourWSqr);
q.f[0] = (M.m[1][2] - M.m[2][1]) * inv4w;
q.f[1] = (M.m[2][0] - M.m[0][2]) * inv4w;
q.f[2] = (M.m[0][1] - M.m[1][0]) * inv4w;
q.f[3] = fourWSqr * inv4w;
}
}
return q.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
static const XMVECTORF32 XMPMMP = { { { +1.0f, -1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMPMP = { { { -1.0f, +1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMMPP = { { { -1.0f, -1.0f, +1.0f, +1.0f } } };
static const XMVECTORU32 Select0110 = { { { XM_SELECT_0, XM_SELECT_1, XM_SELECT_1, XM_SELECT_0 } } };
static const XMVECTORU32 Select0010 = { { { XM_SELECT_0, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0 } } };
float32x4_t r0 = M.r[0];
float32x4_t r1 = M.r[1];
float32x4_t r2 = M.r[2];
float32x4_t r00 = vdupq_lane_f32(vget_low_f32(r0), 0);
float32x4_t r11 = vdupq_lane_f32(vget_low_f32(r1), 1);
float32x4_t r22 = vdupq_lane_f32(vget_high_f32(r2), 0);
// x^2 >= y^2 equivalent to r11 - r00 <= 0
float32x4_t r11mr00 = vsubq_f32(r11, r00);
uint32x4_t x2gey2 = vcleq_f32(r11mr00, g_XMZero);
// z^2 >= w^2 equivalent to r11 + r00 <= 0
float32x4_t r11pr00 = vaddq_f32(r11, r00);
uint32x4_t z2gew2 = vcleq_f32(r11pr00, g_XMZero);
// x^2 + y^2 >= z^2 + w^2 equivalent to r22 <= 0
uint32x4_t x2py2gez2pw2 = vcleq_f32(r22, g_XMZero);
// (4*x^2, 4*y^2, 4*z^2, 4*w^2)
float32x4_t t0 = vmulq_f32(XMPMMP, r00);
float32x4_t x2y2z2w2 = vmlaq_f32(t0, XMMPMP, r11);
x2y2z2w2 = vmlaq_f32(x2y2z2w2, XMMMPP, r22);
x2y2z2w2 = vaddq_f32(x2y2z2w2, g_XMOne);
// (r01, r02, r12, r11)
t0 = vextq_f32(r0, r0, 1);
float32x4_t t1 = vextq_f32(r1, r1, 1);
t0 = vcombine_f32(vget_low_f32(t0), vrev64_f32(vget_low_f32(t1)));
// (r10, r20, r21, r10)
t1 = vextq_f32(r2, r2, 3);
float32x4_t r10 = vdupq_lane_f32(vget_low_f32(r1), 0);
t1 = vbslq_f32(Select0110, t1, r10);
// (4*x*y, 4*x*z, 4*y*z, unused)
float32x4_t xyxzyz = vaddq_f32(t0, t1);
// (r21, r20, r10, r10)
t0 = vcombine_f32(vrev64_f32(vget_low_f32(r2)), vget_low_f32(r10));
// (r12, r02, r01, r12)
float32x4_t t2 = vcombine_f32(vrev64_f32(vget_high_f32(r0)), vrev64_f32(vget_low_f32(r0)));
float32x4_t t3 = vdupq_lane_f32(vget_high_f32(r1), 0);
t1 = vbslq_f32(Select0110, t2, t3);
// (4*x*w, 4*y*w, 4*z*w, unused)
float32x4_t xwywzw = vsubq_f32(t0, t1);
xwywzw = vmulq_f32(XMMPMP, xwywzw);
// (4*x*x, 4*x*y, 4*x*z, 4*x*w)
t0 = vextq_f32(xyxzyz, xyxzyz, 3);
t1 = vbslq_f32(Select0110, t0, x2y2z2w2);
t2 = vdupq_lane_f32(vget_low_f32(xwywzw), 0);
float32x4_t tensor0 = vbslq_f32(g_XMSelect1110, t1, t2);
// (4*y*x, 4*y*y, 4*y*z, 4*y*w)
t0 = vbslq_f32(g_XMSelect1011, xyxzyz, x2y2z2w2);
t1 = vdupq_lane_f32(vget_low_f32(xwywzw), 1);
float32x4_t tensor1 = vbslq_f32(g_XMSelect1110, t0, t1);
// (4*z*x, 4*z*y, 4*z*z, 4*z*w)
t0 = vextq_f32(xyxzyz, xyxzyz, 1);
t1 = vcombine_f32(vget_low_f32(t0), vrev64_f32(vget_high_f32(xwywzw)));
float32x4_t tensor2 = vbslq_f32(Select0010, x2y2z2w2, t1);
// (4*w*x, 4*w*y, 4*w*z, 4*w*w)
float32x4_t tensor3 = vbslq_f32(g_XMSelect1110, xwywzw, x2y2z2w2);
// Select the row of the tensor-product matrix that has the largest
// magnitude.
t0 = vbslq_f32(x2gey2, tensor0, tensor1);
t1 = vbslq_f32(z2gew2, tensor2, tensor3);
t2 = vbslq_f32(x2py2gez2pw2, t0, t1);
// Normalize the row. No division by zero is possible because the
// quaternion is unit-length (and the row is a nonzero multiple of
// the quaternion).
t0 = XMVector4Length(t2);
return XMVectorDivide(t2, t0);
#elif defined(_XM_SSE_INTRINSICS_)
static const XMVECTORF32 XMPMMP = { { { +1.0f, -1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMPMP = { { { -1.0f, +1.0f, -1.0f, +1.0f } } };
static const XMVECTORF32 XMMMPP = { { { -1.0f, -1.0f, +1.0f, +1.0f } } };
XMVECTOR r0 = M.r[0]; // (r00, r01, r02, 0)
XMVECTOR r1 = M.r[1]; // (r10, r11, r12, 0)
XMVECTOR r2 = M.r[2]; // (r20, r21, r22, 0)
// (r00, r00, r00, r00)
XMVECTOR r00 = XM_PERMUTE_PS(r0, _MM_SHUFFLE(0, 0, 0, 0));
// (r11, r11, r11, r11)
XMVECTOR r11 = XM_PERMUTE_PS(r1, _MM_SHUFFLE(1, 1, 1, 1));
// (r22, r22, r22, r22)
XMVECTOR r22 = XM_PERMUTE_PS(r2, _MM_SHUFFLE(2, 2, 2, 2));
// x^2 >= y^2 equivalent to r11 - r00 <= 0
// (r11 - r00, r11 - r00, r11 - r00, r11 - r00)
XMVECTOR r11mr00 = _mm_sub_ps(r11, r00);
XMVECTOR x2gey2 = _mm_cmple_ps(r11mr00, g_XMZero);
// z^2 >= w^2 equivalent to r11 + r00 <= 0
// (r11 + r00, r11 + r00, r11 + r00, r11 + r00)
XMVECTOR r11pr00 = _mm_add_ps(r11, r00);
XMVECTOR z2gew2 = _mm_cmple_ps(r11pr00, g_XMZero);
// x^2 + y^2 >= z^2 + w^2 equivalent to r22 <= 0
XMVECTOR x2py2gez2pw2 = _mm_cmple_ps(r22, g_XMZero);
// (4*x^2, 4*y^2, 4*z^2, 4*w^2)
XMVECTOR t0 = XM_FMADD_PS(XMPMMP, r00, g_XMOne);
XMVECTOR t1 = _mm_mul_ps(XMMPMP, r11);
XMVECTOR t2 = XM_FMADD_PS(XMMMPP, r22, t0);
XMVECTOR x2y2z2w2 = _mm_add_ps(t1, t2);
// (r01, r02, r12, r11)
t0 = _mm_shuffle_ps(r0, r1, _MM_SHUFFLE(1, 2, 2, 1));
// (r10, r10, r20, r21)
t1 = _mm_shuffle_ps(r1, r2, _MM_SHUFFLE(1, 0, 0, 0));
// (r10, r20, r21, r10)
t1 = XM_PERMUTE_PS(t1, _MM_SHUFFLE(1, 3, 2, 0));
// (4*x*y, 4*x*z, 4*y*z, unused)
XMVECTOR xyxzyz = _mm_add_ps(t0, t1);
// (r21, r20, r10, r10)
t0 = _mm_shuffle_ps(r2, r1, _MM_SHUFFLE(0, 0, 0, 1));
// (r12, r12, r02, r01)
t1 = _mm_shuffle_ps(r1, r0, _MM_SHUFFLE(1, 2, 2, 2));
// (r12, r02, r01, r12)
t1 = XM_PERMUTE_PS(t1, _MM_SHUFFLE(1, 3, 2, 0));
// (4*x*w, 4*y*w, 4*z*w, unused)
XMVECTOR xwywzw = _mm_sub_ps(t0, t1);
xwywzw = _mm_mul_ps(XMMPMP, xwywzw);
// (4*x^2, 4*y^2, 4*x*y, unused)
t0 = _mm_shuffle_ps(x2y2z2w2, xyxzyz, _MM_SHUFFLE(0, 0, 1, 0));
// (4*z^2, 4*w^2, 4*z*w, unused)
t1 = _mm_shuffle_ps(x2y2z2w2, xwywzw, _MM_SHUFFLE(0, 2, 3, 2));
// (4*x*z, 4*y*z, 4*x*w, 4*y*w)
t2 = _mm_shuffle_ps(xyxzyz, xwywzw, _MM_SHUFFLE(1, 0, 2, 1));
// (4*x*x, 4*x*y, 4*x*z, 4*x*w)
XMVECTOR tensor0 = _mm_shuffle_ps(t0, t2, _MM_SHUFFLE(2, 0, 2, 0));
// (4*y*x, 4*y*y, 4*y*z, 4*y*w)
XMVECTOR tensor1 = _mm_shuffle_ps(t0, t2, _MM_SHUFFLE(3, 1, 1, 2));
// (4*z*x, 4*z*y, 4*z*z, 4*z*w)
XMVECTOR tensor2 = _mm_shuffle_ps(t2, t1, _MM_SHUFFLE(2, 0, 1, 0));
// (4*w*x, 4*w*y, 4*w*z, 4*w*w)
XMVECTOR tensor3 = _mm_shuffle_ps(t2, t1, _MM_SHUFFLE(1, 2, 3, 2));
// Select the row of the tensor-product matrix that has the largest
// magnitude.
t0 = _mm_and_ps(x2gey2, tensor0);
t1 = _mm_andnot_ps(x2gey2, tensor1);
t0 = _mm_or_ps(t0, t1);
t1 = _mm_and_ps(z2gew2, tensor2);
t2 = _mm_andnot_ps(z2gew2, tensor3);
t1 = _mm_or_ps(t1, t2);
t0 = _mm_and_ps(x2py2gez2pw2, t0);
t1 = _mm_andnot_ps(x2py2gez2pw2, t1);
t2 = _mm_or_ps(t0, t1);
// Normalize the row. No division by zero is possible because the
// quaternion is unit-length (and the row is a nonzero multiple of
// the quaternion).
t0 = XMVector4Length(t2);
return _mm_div_ps(t2, t0);
#endif
}
//------------------------------------------------------------------------------
// Conversion operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV XMQuaternionToAxisAngle
(
XMVECTOR* pAxis,
float* pAngle,
FXMVECTOR Q
) noexcept
{
assert(pAxis);
assert(pAngle);
*pAxis = Q;
*pAngle = 2.0f * XMScalarACos(XMVectorGetW(Q));
}
/****************************************************************************
*
* Plane
*
****************************************************************************/
//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneEqual
(
FXMVECTOR P1,
FXMVECTOR P2
) noexcept
{
return XMVector4Equal(P1, P2);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneNearEqual
(
FXMVECTOR P1,
FXMVECTOR P2,
FXMVECTOR Epsilon
) noexcept
{
XMVECTOR NP1 = XMPlaneNormalize(P1);
XMVECTOR NP2 = XMPlaneNormalize(P2);
return XMVector4NearEqual(NP1, NP2, Epsilon);
}
//------------------------------------------------------------------------------
inline bool XM_CALLCONV XMPlaneNotEqual