EsenthalEngine/ThirdPartyLibs/DirectXMath/DirectXMathMisc.inl

//-------------------------------------------------------------------------------------
// DirectXMathMisc.inl -- SIMD C++ Math library
//
// THIS CODE AND INFORMATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF
// ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING BUT NOT LIMITED TO
// THE IMPLIED WARRANTIES OF MERCHANTABILITY AND/OR FITNESS FOR A
// PARTICULAR PURPOSE.
//  
// Copyright (c) Microsoft Corporation. All rights reserved.
//
// http://go.microsoft.com/fwlink/?LinkID=615560
//-------------------------------------------------------------------------------------

#pragma once

/****************************************************************************
 *
 * Quaternion
 *
 ****************************************************************************/

//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------

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

inline bool XM_CALLCONV XMQuaternionEqual
(
    FXMVECTOR Q1,
    FXMVECTOR Q2
)
{
    return XMVector4Equal(Q1, Q2);
}

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

inline bool XM_CALLCONV XMQuaternionNotEqual
(
    FXMVECTOR Q1,
    FXMVECTOR Q2
)
{
    return XMVector4NotEqual(Q1, Q2);
}

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

inline bool XM_CALLCONV XMQuaternionIsNaN
(
    FXMVECTOR Q
)
{
    return XMVector4IsNaN(Q);
}

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

inline bool XM_CALLCONV XMQuaternionIsInfinite
(
    FXMVECTOR Q
)
{
    return XMVector4IsInfinite(Q);
}

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

inline bool XM_CALLCONV XMQuaternionIsIdentity
(
    FXMVECTOR Q
)
{
    return XMVector4Equal(Q, g_XMIdentityR3.v);
}

//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------

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

inline XMVECTOR XM_CALLCONV XMQuaternionDot
(
    FXMVECTOR Q1,
    FXMVECTOR Q2
)
{
    return XMVector4Dot(Q1, Q2);
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionMultiply
(
    FXMVECTOR Q1,
    FXMVECTOR Q2
)
{
    // 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 = vrev64q_u32(vTemp);
    Q2Y = vmulq_f32(Q2Y,vTemp);
    vResult = vmlaq_f32(vResult, Q2Y, ControlZWXY);

    // Mul by Q1YXWZ
    vTemp = vrev64q_u32(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
    Q2X = _mm_mul_ps(Q2X,ControlWZYX);
    // 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);
    vResult = _mm_add_ps(vResult,Q2X);
    // Flip the signs on x and w
    Q2Z = _mm_mul_ps(Q2Z,ControlYXWZ);
    Q2Y = _mm_add_ps(Q2Y,Q2Z);
    vResult = _mm_add_ps(vResult,Q2Y);
    return vResult;
#endif
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionLengthSq
(
    FXMVECTOR Q
)
{
    return XMVector4LengthSq(Q);
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionReciprocalLength
(
    FXMVECTOR Q
)
{
    return XMVector4ReciprocalLength(Q);
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionLength
(
    FXMVECTOR Q
)
{
    return XMVector4Length(Q);
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionNormalizeEst
(
    FXMVECTOR Q
)
{
    return XMVector4NormalizeEst(Q);
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionNormalize
(
    FXMVECTOR Q
)
{
    return XMVector4Normalize(Q);
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionConjugate
(
    FXMVECTOR Q
)
{
#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
)
{
    const XMVECTOR  Zero = XMVectorZero();

    XMVECTOR L = XMVector4LengthSq(Q);
    XMVECTOR Conjugate = XMQuaternionConjugate(Q);

    XMVECTOR Control = XMVectorLessOrEqual(L, g_XMEpsilon.v);

    XMVECTOR Result = XMVectorDivide(Conjugate, L);

    Result = XMVectorSelect(Result, Zero, Control);

    return Result;
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionLn
(
    FXMVECTOR Q
)
{
    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
)
{
    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
)
{
    XMVECTOR T = XMVectorReplicate(t);
    return XMQuaternionSlerpV(Q0, Q1, T);
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionSlerpV
(
    FXMVECTOR Q0,
    FXMVECTOR Q1,
    FXMVECTOR T
)
{
    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
)
{
    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
)
{
    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
)
{
    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
)
{
    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
)
{
    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()
{
    return g_XMIdentityR3.v;
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionRotationRollPitchYaw
(
    float Pitch,
    float Yaw,
    float Roll
)
{
    XMVECTOR Angles = XMVectorSet(Pitch, Yaw, Roll, 0.0f);
    XMVECTOR Q = XMQuaternionRotationRollPitchYawFromVector(Angles);
    return Q;
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionRotationRollPitchYawFromVector
(
    FXMVECTOR Angles // <Pitch, Yaw, Roll, 0>
)
{
    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;
}

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

inline XMVECTOR XM_CALLCONV XMQuaternionRotationNormal
(
    FXMVECTOR NormalAxis,
    float    Angle
)
{
#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
)
{
    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
)
{
#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 } } };

    XMVECTOR r0 = M.r[0];
    XMVECTOR r1 = M.r[1];
    XMVECTOR r2 = M.r[2];

    XMVECTOR r00 = vdupq_lane_f32(vget_low_f32(r0), 0);
    XMVECTOR r11 = vdupq_lane_f32(vget_low_f32(r1), 1);
    XMVECTOR r22 = vdupq_lane_f32(vget_high_f32(r2), 0);

    // x^2 >= y^2 equivalent to r11 - r00 <= 0
    XMVECTOR r11mr00 = vsubq_f32(r11, r00);
    XMVECTOR x2gey2 = vcleq_f32(r11mr00, g_XMZero);

    // z^2 >= w^2 equivalent to r11 + r00 <= 0
    XMVECTOR r11pr00 = vaddq_f32(r11, r00);
    XMVECTOR z2gew2 = vcleq_f32(r11pr00, g_XMZero);
    
    // x^2 + y^2 >= z^2 + w^2 equivalent to r22 <= 0
    XMVECTOR x2py2gez2pw2 = vcleq_f32(r22, g_XMZero);

    // (4*x^2, 4*y^2, 4*z^2, 4*w^2)
    XMVECTOR t0 = vmulq_f32( XMPMMP, r00 );
    XMVECTOR 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);
    XMVECTOR 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);
    XMVECTOR 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)
    XMVECTOR 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)
    XMVECTOR t2 = vcombine_f32( vrev64_f32( vget_high_f32(r0) ), vrev64_f32( vget_low_f32(r0) ) );
    XMVECTOR 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)
    XMVECTOR 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 );
    XMVECTOR 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 );
    XMVECTOR 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) ) );
    XMVECTOR tensor2 = vbslq_f32( Select0010, x2y2z2w2, t1 );

    // (4*w*x, 4*w*y, 4*w*z, 4*w*w)
    XMVECTOR 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);

    // (+r00, -r00, -r00, +r00)
    XMVECTOR t0 = _mm_mul_ps(XMPMMP, r00);

    // (-r11, +r11, -r11, +r11)
    XMVECTOR t1 = _mm_mul_ps(XMMPMP, r11);

    // (-r22, -r22, +r22, +r22)
    XMVECTOR t2 = _mm_mul_ps(XMMMPP, r22);

    // (4*x^2, 4*y^2, 4*z^2, 4*w^2)
    XMVECTOR x2y2z2w2 = _mm_add_ps(t0, t1);
    x2y2z2w2 = _mm_add_ps(t2, x2y2z2w2);
    x2y2z2w2 = _mm_add_ps(x2y2z2w2, g_XMOne);

    // (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
)
{
    assert(pAxis);
    assert(pAngle);

    *pAxis = Q;

    *pAngle = 2.0f * XMScalarACos(XMVectorGetW(Q));
}

/****************************************************************************
 *
 * Plane
 *
 ****************************************************************************/

//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------

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

inline bool XM_CALLCONV XMPlaneEqual
(
    FXMVECTOR P1,
    FXMVECTOR P2
)
{
    return XMVector4Equal(P1, P2);
}

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

inline bool XM_CALLCONV XMPlaneNearEqual
(
    FXMVECTOR P1,
    FXMVECTOR P2,
    FXMVECTOR Epsilon
)
{
    XMVECTOR NP1 = XMPlaneNormalize(P1);
    XMVECTOR NP2 = XMPlaneNormalize(P2);
    return XMVector4NearEqual(NP1, NP2, Epsilon);
}

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

inline bool XM_CALLCONV XMPlaneNotEqual
(
    FXMVECTOR P1,
    FXMVECTOR P2
)
{
    return XMVector4NotEqual(P1, P2);
}

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

inline bool XM_CALLCONV XMPlaneIsNaN
(
    FXMVECTOR P
)
{
    return XMVector4IsNaN(P);
}

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

inline bool XM_CALLCONV XMPlaneIsInfinite
(
    FXMVECTOR P
)
{
    return XMVector4IsInfinite(P);
}

//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------

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

inline XMVECTOR XM_CALLCONV XMPlaneDot
(
    FXMVECTOR P,
    FXMVECTOR V
)
{
    return XMVector4Dot(P, V);
}

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

inline XMVECTOR XM_CALLCONV XMPlaneDotCoord
(
    FXMVECTOR P,
    FXMVECTOR V
)
{
    // Result = P[0] * V[0] + P[1] * V[1] + P[2] * V[2] + P[3]

    XMVECTOR V3 = XMVectorSelect(g_XMOne.v, V, g_XMSelect1110.v);
    XMVECTOR Result = XMVector4Dot(P, V3);
    return Result;
}

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

inline XMVECTOR XM_CALLCONV XMPlaneDotNormal
(
    FXMVECTOR P,
    FXMVECTOR V
)
{
    return XMVector3Dot(P, V);
}

//------------------------------------------------------------------------------
// XMPlaneNormalizeEst uses a reciprocal estimate and
// returns QNaN on zero and infinite vectors.

inline XMVECTOR XM_CALLCONV XMPlaneNormalizeEst
(
    FXMVECTOR P
)
{
#if defined(_XM_NO_INTRINSICS_) || defined(_XM_ARM_NEON_INTRINSICS_)

    XMVECTOR Result = XMVector3ReciprocalLengthEst(P);
    return XMVectorMultiply(P, Result);

#elif defined(_XM_SSE4_INTRINSICS_)
    XMVECTOR vTemp = _mm_dp_ps( P, P, 0x7f );
    XMVECTOR vResult = _mm_rsqrt_ps( vTemp );
    return _mm_mul_ps(vResult, P);
#elif defined(_XM_SSE_INTRINSICS_)
    // Perform the dot product
    XMVECTOR vDot = _mm_mul_ps(P,P);
    // x=Dot.y, y=Dot.z
    XMVECTOR vTemp = XM_PERMUTE_PS(vDot,_MM_SHUFFLE(2,1,2,1));
    // Result.x = x+y
    vDot = _mm_add_ss(vDot,vTemp);
    // x=Dot.z
    vTemp = XM_PERMUTE_PS(vTemp,_MM_SHUFFLE(1,1,1,1));
    // Result.x = (x+y)+z
    vDot = _mm_add_ss(vDot,vTemp);
    // Splat x
    vDot = XM_PERMUTE_PS(vDot,_MM_SHUFFLE(0,0,0,0));
    // Get the reciprocal
    vDot = _mm_rsqrt_ps(vDot);
    // Get the reciprocal
    vDot = _mm_mul_ps(vDot,P);
    return vDot;
#endif
}

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

inline XMVECTOR XM_CALLCONV XMPlaneNormalize
(
    FXMVECTOR P
)
{
#if defined(_XM_NO_INTRINSICS_)
    float fLengthSq = sqrtf((P.vector4_f32[0]*P.vector4_f32[0])+(P.vector4_f32[1]*P.vector4_f32[1])+(P.vector4_f32[2]*P.vector4_f32[2]));
    // Prevent divide by zero
    if (fLengthSq)
    {
        fLengthSq = 1.0f/fLengthSq;
    }
    XMVECTORF32 vResult = { { {
            P.vector4_f32[0] * fLengthSq,
            P.vector4_f32[1] * fLengthSq,
            P.vector4_f32[2] * fLengthSq,
            P.vector4_f32[3] * fLengthSq
        } } };
    return vResult.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
    XMVECTOR vLength = XMVector3ReciprocalLength(P);
    return XMVectorMultiply( P, vLength );
#elif defined(_XM_SSE4_INTRINSICS_)
    XMVECTOR vLengthSq = _mm_dp_ps( P, P, 0x7f );
    // Prepare for the division
    XMVECTOR vResult = _mm_sqrt_ps(vLengthSq);
    // Failsafe on zero (Or epsilon) length planes
    // If the length is infinity, set the elements to zero
    vLengthSq = _mm_cmpneq_ps(vLengthSq,g_XMInfinity);
    // Reciprocal mul to perform the normalization
    vResult = _mm_div_ps(P,vResult);
    // Any that are infinity, set to zero
    vResult = _mm_and_ps(vResult,vLengthSq);
    return vResult;
#elif defined(_XM_SSE_INTRINSICS_)
    // Perform the dot product on x,y and z only
    XMVECTOR vLengthSq = _mm_mul_ps(P,P);
    XMVECTOR vTemp = XM_PERMUTE_PS(vLengthSq,_MM_SHUFFLE(2,1,2,1));
    vLengthSq = _mm_add_ss(vLengthSq,vTemp);
    vTemp = XM_PERMUTE_PS(vTemp,_MM_SHUFFLE(1,1,1,1));
    vLengthSq = _mm_add_ss(vLengthSq,vTemp);
    vLengthSq = XM_PERMUTE_PS(vLengthSq,_MM_SHUFFLE(0,0,0,0));
    // Prepare for the division
    XMVECTOR vResult = _mm_sqrt_ps(vLengthSq);
    // Failsafe on zero (Or epsilon) length planes
    // If the length is infinity, set the elements to zero
    vLengthSq = _mm_cmpneq_ps(vLengthSq,g_XMInfinity);
    // Reciprocal mul to perform the normalization
    vResult = _mm_div_ps(P,vResult);
    // Any that are infinity, set to zero
    vResult = _mm_and_ps(vResult,vLengthSq);
    return vResult;
#endif
}

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

inline XMVECTOR XM_CALLCONV XMPlaneIntersectLine
(
    FXMVECTOR P,
    FXMVECTOR LinePoint1,
    FXMVECTOR LinePoint2
)
{
    XMVECTOR V1 = XMVector3Dot(P, LinePoint1);
    XMVECTOR V2 = XMVector3Dot(P, LinePoint2);
    XMVECTOR D = XMVectorSubtract(V1, V2);

    XMVECTOR VT = XMPlaneDotCoord(P, LinePoint1);
    VT = XMVectorDivide(VT, D);

    XMVECTOR Point = XMVectorSubtract(LinePoint2, LinePoint1);
    Point = XMVectorMultiplyAdd(Point, VT, LinePoint1);

    const XMVECTOR Zero = XMVectorZero();
    XMVECTOR Control = XMVectorNearEqual(D, Zero, g_XMEpsilon.v);

    return XMVectorSelect(Point, g_XMQNaN.v, Control);
}

//------------------------------------------------------------------------------
_Use_decl_annotations_
inline void XM_CALLCONV XMPlaneIntersectPlane
(
    XMVECTOR* pLinePoint1,
    XMVECTOR* pLinePoint2,
    FXMVECTOR  P1,
    FXMVECTOR  P2
)
{
    assert(pLinePoint1);
    assert(pLinePoint2);

    XMVECTOR V1 = XMVector3Cross(P2, P1);

    XMVECTOR LengthSq = XMVector3LengthSq(V1);

    XMVECTOR V2 = XMVector3Cross(P2, V1);

    XMVECTOR P1W = XMVectorSplatW(P1);
    XMVECTOR Point = XMVectorMultiply(V2, P1W);

    XMVECTOR V3 = XMVector3Cross(V1, P1);

    XMVECTOR P2W = XMVectorSplatW(P2);
    Point = XMVectorMultiplyAdd(V3, P2W, Point);

    XMVECTOR LinePoint1 = XMVectorDivide(Point, LengthSq);

    XMVECTOR LinePoint2 = XMVectorAdd(LinePoint1, V1);

    XMVECTOR Control = XMVectorLessOrEqual(LengthSq, g_XMEpsilon.v);
    *pLinePoint1 = XMVectorSelect(LinePoint1,g_XMQNaN.v, Control);
    *pLinePoint2 = XMVectorSelect(LinePoint2,g_XMQNaN.v, Control);
}

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

inline XMVECTOR XM_CALLCONV XMPlaneTransform
(
    FXMVECTOR P,
    FXMMATRIX M
)
{
    XMVECTOR W = XMVectorSplatW(P);
    XMVECTOR Z = XMVectorSplatZ(P);
    XMVECTOR Y = XMVectorSplatY(P);
    XMVECTOR X = XMVectorSplatX(P);

    XMVECTOR Result = XMVectorMultiply(W, M.r[3]);
    Result = XMVectorMultiplyAdd(Z, M.r[2], Result);
    Result = XMVectorMultiplyAdd(Y, M.r[1], Result);
    Result = XMVectorMultiplyAdd(X, M.r[0], Result);
    return Result;
}

//------------------------------------------------------------------------------
_Use_decl_annotations_
inline XMFLOAT4* XM_CALLCONV XMPlaneTransformStream
(
    XMFLOAT4*       pOutputStream,
    size_t          OutputStride,
    const XMFLOAT4* pInputStream,    
    size_t          InputStride,
    size_t          PlaneCount,
    FXMMATRIX       M
)
{
    return XMVector4TransformStream(pOutputStream,
                                    OutputStride,
                                    pInputStream,
                                    InputStride,
                                    PlaneCount,
                                    M);
}

//------------------------------------------------------------------------------
// Conversion operations
//------------------------------------------------------------------------------

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

inline XMVECTOR XM_CALLCONV XMPlaneFromPointNormal
(
    FXMVECTOR Point,
    FXMVECTOR Normal
)
{
    XMVECTOR W = XMVector3Dot(Point, Normal);
    W = XMVectorNegate(W);
    return XMVectorSelect(W, Normal, g_XMSelect1110.v);
}

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

inline XMVECTOR XM_CALLCONV XMPlaneFromPoints
(
    FXMVECTOR Point1,
    FXMVECTOR Point2,
    FXMVECTOR Point3
)
{
    XMVECTOR V21 = XMVectorSubtract(Point1, Point2);
    XMVECTOR V31 = XMVectorSubtract(Point1, Point3);

    XMVECTOR N = XMVector3Cross(V21, V31);
    N = XMVector3Normalize(N);

    XMVECTOR D = XMPlaneDotNormal(N, Point1);
    D = XMVectorNegate(D);

    XMVECTOR Result = XMVectorSelect(D, N, g_XMSelect1110.v);

    return Result;
}

/****************************************************************************
 *
 * Color
 *
 ****************************************************************************/

//------------------------------------------------------------------------------
// Comparison operations
//------------------------------------------------------------------------------

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

inline bool XM_CALLCONV XMColorEqual
(
    FXMVECTOR C1,
    FXMVECTOR C2
)
{
    return XMVector4Equal(C1, C2);
}

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

inline bool XM_CALLCONV XMColorNotEqual
(
    FXMVECTOR C1,
    FXMVECTOR C2
)
{
    return XMVector4NotEqual(C1, C2);
}

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

inline bool XM_CALLCONV XMColorGreater
(
    FXMVECTOR C1,
    FXMVECTOR C2
)
{
    return XMVector4Greater(C1, C2);
}

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

inline bool XM_CALLCONV XMColorGreaterOrEqual
(
    FXMVECTOR C1,
    FXMVECTOR C2
)
{
    return XMVector4GreaterOrEqual(C1, C2);
}

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

inline bool XM_CALLCONV XMColorLess
(
    FXMVECTOR C1,
    FXMVECTOR C2
)
{
    return XMVector4Less(C1, C2);
}

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

inline bool XM_CALLCONV XMColorLessOrEqual
(
    FXMVECTOR C1,
    FXMVECTOR C2
)
{
    return XMVector4LessOrEqual(C1, C2);
}

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

inline bool XM_CALLCONV XMColorIsNaN
(
    FXMVECTOR C
)
{
    return XMVector4IsNaN(C);
}

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

inline bool XM_CALLCONV XMColorIsInfinite
(
    FXMVECTOR C
)
{
    return XMVector4IsInfinite(C);
}

//------------------------------------------------------------------------------
// Computation operations
//------------------------------------------------------------------------------

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

inline XMVECTOR XM_CALLCONV XMColorNegative
(
    FXMVECTOR vColor
)
{
#if defined(_XM_NO_INTRINSICS_)
    XMVECTORF32 vResult = { { {
            1.0f - vColor.vector4_f32[0],
            1.0f - vColor.vector4_f32[1],
            1.0f - vColor.vector4_f32[2],
            vColor.vector4_f32[3]
        } } };
    return vResult.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
    XMVECTOR vTemp = veorq_u32(vColor,g_XMNegate3);
    return vaddq_f32(vTemp,g_XMOne3);
#elif defined(_XM_SSE_INTRINSICS_)
    // Negate only x,y and z.
    XMVECTOR vTemp = _mm_xor_ps(vColor,g_XMNegate3);
    // Add 1,1,1,0 to -x,-y,-z,w
    return _mm_add_ps(vTemp,g_XMOne3);
#endif
}

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

inline XMVECTOR XM_CALLCONV XMColorModulate
(
    FXMVECTOR C1,
    FXMVECTOR C2
)
{
    return XMVectorMultiply(C1, C2);
}

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

inline XMVECTOR XM_CALLCONV XMColorAdjustSaturation
(
    FXMVECTOR vColor,
    float    fSaturation
)
{
    // Luminance = 0.2125f * C[0] + 0.7154f * C[1] + 0.0721f * C[2];
    // Result = (C - Luminance) * Saturation + Luminance;

    const XMVECTORF32 gvLuminance = { { { 0.2125f, 0.7154f, 0.0721f, 0.0f } } };
#if defined(_XM_NO_INTRINSICS_)
    float fLuminance = (vColor.vector4_f32[0]*gvLuminance.f[0])+(vColor.vector4_f32[1]*gvLuminance.f[1])+(vColor.vector4_f32[2]*gvLuminance.f[2]);
    XMVECTOR vResult;
    vResult.vector4_f32[0] = ((vColor.vector4_f32[0] - fLuminance)*fSaturation)+fLuminance;
    vResult.vector4_f32[1] = ((vColor.vector4_f32[1] - fLuminance)*fSaturation)+fLuminance;
    vResult.vector4_f32[2] = ((vColor.vector4_f32[2] - fLuminance)*fSaturation)+fLuminance;
    vResult.vector4_f32[3] = vColor.vector4_f32[3];
    return vResult;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
    XMVECTOR vLuminance = XMVector3Dot( vColor, gvLuminance );
    XMVECTOR vResult = vsubq_f32(vColor, vLuminance);
    vResult = vmlaq_n_f32( vLuminance, vResult, fSaturation );
    return vbslq_f32( g_XMSelect1110, vResult, vColor );
#elif defined(_XM_SSE_INTRINSICS_)
    XMVECTOR vLuminance = XMVector3Dot( vColor, gvLuminance );
// Splat fSaturation
    XMVECTOR vSaturation = _mm_set_ps1(fSaturation);
// vResult = ((vColor-vLuminance)*vSaturation)+vLuminance;
    XMVECTOR vResult = _mm_sub_ps(vColor,vLuminance);
    vResult = _mm_mul_ps(vResult,vSaturation);
    vResult = _mm_add_ps(vResult,vLuminance);
// Retain w from the source color
    vLuminance = _mm_shuffle_ps(vResult,vColor,_MM_SHUFFLE(3,2,2,2));   // x = vResult.z,y = vResult.z,z = vColor.z,w=vColor.w
    vResult = _mm_shuffle_ps(vResult,vLuminance,_MM_SHUFFLE(3,0,1,0));  // x = vResult.x,y = vResult.y,z = vResult.z,w=vColor.w
    return vResult;
#endif
}

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

inline XMVECTOR XM_CALLCONV XMColorAdjustContrast
(
    FXMVECTOR vColor,
    float    fContrast
)
{
    // Result = (vColor - 0.5f) * fContrast + 0.5f;

#if defined(_XM_NO_INTRINSICS_)
    XMVECTORF32 vResult = { { {
            ((vColor.vector4_f32[0] - 0.5f) * fContrast) + 0.5f,
            ((vColor.vector4_f32[1] - 0.5f) * fContrast) + 0.5f,
            ((vColor.vector4_f32[2] - 0.5f) * fContrast) + 0.5f,
            vColor.vector4_f32[3]        // Leave W untouched
        } } };
    return vResult.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
    XMVECTOR vResult = vsubq_f32(vColor, g_XMOneHalf.v);
    vResult = vmlaq_n_f32( g_XMOneHalf.v, vResult, fContrast );
    return vbslq_f32( g_XMSelect1110, vResult, vColor );
#elif defined(_XM_SSE_INTRINSICS_)
    XMVECTOR vScale = _mm_set_ps1(fContrast);           // Splat the scale
    XMVECTOR vResult = _mm_sub_ps(vColor,g_XMOneHalf);  // Subtract 0.5f from the source (Saving source)
    vResult = _mm_mul_ps(vResult,vScale);               // Mul by scale
    vResult = _mm_add_ps(vResult,g_XMOneHalf);          // Add 0.5f
// Retain w from the source color
    vScale = _mm_shuffle_ps(vResult,vColor,_MM_SHUFFLE(3,2,2,2));   // x = vResult.z,y = vResult.z,z = vColor.z,w=vColor.w
    vResult = _mm_shuffle_ps(vResult,vScale,_MM_SHUFFLE(3,0,1,0));  // x = vResult.x,y = vResult.y,z = vResult.z,w=vColor.w
    return vResult;
#endif
}

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

inline XMVECTOR XM_CALLCONV XMColorRGBToHSL( FXMVECTOR rgb )
{
    XMVECTOR r = XMVectorSplatX( rgb );
    XMVECTOR g = XMVectorSplatY( rgb );
    XMVECTOR b = XMVectorSplatZ( rgb );

    XMVECTOR min = XMVectorMin( r, XMVectorMin( g, b ) );
    XMVECTOR max = XMVectorMax( r, XMVectorMax( g, b ) );

    XMVECTOR l = XMVectorMultiply( XMVectorAdd( min, max ), g_XMOneHalf );

    XMVECTOR d = XMVectorSubtract( max, min );

    XMVECTOR la = XMVectorSelect( rgb, l, g_XMSelect1110 );

    if ( XMVector3Less( d, g_XMEpsilon ) )
    {
        // Achromatic, assume H and S of 0
        return XMVectorSelect( la, g_XMZero, g_XMSelect1100 );
    }
    else
    {
        XMVECTOR s, h;

        XMVECTOR d2 = XMVectorAdd( min, max );

        if ( XMVector3Greater( l, g_XMOneHalf ) )
        {
            // d / (2-max-min)
            s = XMVectorDivide( d, XMVectorSubtract( g_XMTwo, d2 ) ); 
        }
        else
        {
            // d / (max+min)
            s = XMVectorDivide( d, d2 ); 
        }

        if ( XMVector3Equal( r, max ) )
        {
            // Red is max
            h = XMVectorDivide( XMVectorSubtract( g, b ), d );
        }
        else if ( XMVector3Equal( g, max ) )
        {
            // Green is max
            h = XMVectorDivide( XMVectorSubtract( b, r ), d );
            h = XMVectorAdd( h, g_XMTwo );
        }
        else
        {
            // Blue is max
            h = XMVectorDivide( XMVectorSubtract( r, g ), d );
            h = XMVectorAdd( h, g_XMFour );
        }

        h = XMVectorDivide( h, g_XMSix );

        if ( XMVector3Less( h, g_XMZero ) )
            h = XMVectorAdd( h, g_XMOne );

        XMVECTOR lha = XMVectorSelect( la, h, g_XMSelect1100 );
        return XMVectorSelect( s, lha, g_XMSelect1011 );
    }
}

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

namespace Internal
{

inline XMVECTOR XM_CALLCONV XMColorHue2Clr( FXMVECTOR p, FXMVECTOR q, FXMVECTOR h )
{
    static const XMVECTORF32 oneSixth = { { { 1.0f / 6.0f, 1.0f / 6.0f, 1.0f / 6.0f, 1.0f / 6.0f } } };
    static const XMVECTORF32 twoThirds = { { { 2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f, 2.0f / 3.0f } } };
    
    XMVECTOR t = h;

    if ( XMVector3Less( t, g_XMZero ) )
        t = XMVectorAdd( t, g_XMOne );

    if ( XMVector3Greater( t, g_XMOne ) )
        t = XMVectorSubtract( t, g_XMOne );

    if ( XMVector3Less( t, oneSixth ) )
    {
        // p + (q - p) * 6 * t
        XMVECTOR t1 = XMVectorSubtract( q, p );
        XMVECTOR t2 = XMVectorMultiply( g_XMSix, t );
        return XMVectorMultiplyAdd( t1, t2, p );
    }

    if ( XMVector3Less( t, g_XMOneHalf ) )
        return q;

    if ( XMVector3Less( t, twoThirds ) )
    {
        // p + (q - p) * 6 * (2/3 - t)
        XMVECTOR t1 = XMVectorSubtract( q, p );
        XMVECTOR t2 = XMVectorMultiply( g_XMSix, XMVectorSubtract( twoThirds, t ) );
        return XMVectorMultiplyAdd( t1, t2, p );
    }

    return p;
}

}; // namespace Internal

inline XMVECTOR XM_CALLCONV XMColorHSLToRGB( FXMVECTOR hsl )
{
    static const XMVECTORF32 oneThird = { { { 1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f, 1.0f / 3.0f } } };

    XMVECTOR s = XMVectorSplatY( hsl );
    XMVECTOR l = XMVectorSplatZ( hsl );

    if ( XMVector3NearEqual( s, g_XMZero, g_XMEpsilon ) )
    {
        // Achromatic
        return XMVectorSelect( hsl, l, g_XMSelect1110 );
    }
    else
    {
        XMVECTOR h = XMVectorSplatX( hsl );

        XMVECTOR q;
        if ( XMVector3Less( l, g_XMOneHalf ) )
        {
            q = XMVectorMultiply( l, XMVectorAdd ( g_XMOne, s ) );
        }
        else
        {
            q = XMVectorSubtract( XMVectorAdd( l, s ), XMVectorMultiply( l, s ) );
        }

        XMVECTOR p = XMVectorSubtract( XMVectorMultiply( g_XMTwo, l ), q );

        XMVECTOR r = DirectX::Internal::XMColorHue2Clr( p, q, XMVectorAdd( h, oneThird ) );
        XMVECTOR g = DirectX::Internal::XMColorHue2Clr( p, q, h );
        XMVECTOR b = DirectX::Internal::XMColorHue2Clr( p, q, XMVectorSubtract( h, oneThird ) );

        XMVECTOR rg = XMVectorSelect( g, r, g_XMSelect1000 );
        XMVECTOR ba = XMVectorSelect( hsl, b, g_XMSelect1110 );

        return XMVectorSelect( ba, rg, g_XMSelect1100 );
    }
}

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

inline XMVECTOR XM_CALLCONV XMColorRGBToHSV( FXMVECTOR rgb )
{
    XMVECTOR r = XMVectorSplatX( rgb );
    XMVECTOR g = XMVectorSplatY( rgb );
    XMVECTOR b = XMVectorSplatZ( rgb );

    XMVECTOR min = XMVectorMin( r, XMVectorMin( g, b ) );
    XMVECTOR v = XMVectorMax( r, XMVectorMax( g, b ) );

    XMVECTOR d = XMVectorSubtract( v, min );

    XMVECTOR s = ( XMVector3NearEqual( v, g_XMZero, g_XMEpsilon ) ) ? g_XMZero : XMVectorDivide( d, v );

    if ( XMVector3Less( d, g_XMEpsilon ) )
    {
        // Achromatic, assume H of 0
        XMVECTOR hv = XMVectorSelect( v, g_XMZero, g_XMSelect1000 );
        XMVECTOR hva = XMVectorSelect( rgb, hv, g_XMSelect1110 );
        return XMVectorSelect( s, hva, g_XMSelect1011 );
    }
    else
    {
        XMVECTOR h;

        if ( XMVector3Equal( r, v ) )
        {
            // Red is max
            h = XMVectorDivide( XMVectorSubtract( g, b ), d );

            if ( XMVector3Less( g, b ) )
                h = XMVectorAdd( h, g_XMSix );
        }
        else if ( XMVector3Equal( g, v ) )
        {
            // Green is max
            h = XMVectorDivide( XMVectorSubtract( b, r ), d );
            h = XMVectorAdd( h, g_XMTwo );
        }
        else
        {
            // Blue is max
            h = XMVectorDivide( XMVectorSubtract( r, g ), d );
            h = XMVectorAdd( h, g_XMFour );
        }

        h = XMVectorDivide( h, g_XMSix );

        XMVECTOR hv = XMVectorSelect( v, h, g_XMSelect1000 );
        XMVECTOR hva = XMVectorSelect( rgb, hv, g_XMSelect1110 );
        return XMVectorSelect( s, hva, g_XMSelect1011 );
    }
}

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

inline XMVECTOR XM_CALLCONV XMColorHSVToRGB( FXMVECTOR hsv )
{
    XMVECTOR h = XMVectorSplatX( hsv );
    XMVECTOR s = XMVectorSplatY( hsv );
    XMVECTOR v = XMVectorSplatZ( hsv );

    XMVECTOR h6 = XMVectorMultiply( h, g_XMSix );

    XMVECTOR i = XMVectorFloor( h6 );
    XMVECTOR f = XMVectorSubtract( h6, i );

    // p = v* (1-s)
    XMVECTOR p = XMVectorMultiply( v, XMVectorSubtract( g_XMOne, s ) );

    // q = v*(1-f*s)
    XMVECTOR q = XMVectorMultiply( v, XMVectorSubtract( g_XMOne, XMVectorMultiply( f, s ) ) );

    // t = v*(1 - (1-f)*s)
    XMVECTOR t = XMVectorMultiply( v, XMVectorSubtract( g_XMOne, XMVectorMultiply( XMVectorSubtract( g_XMOne, f ), s ) ) );

    int ii = static_cast<int>( XMVectorGetX( XMVectorMod( i, g_XMSix ) ) );

    XMVECTOR _rgb;

    switch (ii)
    {
    case 0: // rgb = vtp
        {
            XMVECTOR vt = XMVectorSelect( t, v, g_XMSelect1000 );
            _rgb = XMVectorSelect( p, vt, g_XMSelect1100 );
        }
        break;
    case 1: // rgb = qvp
        {
            XMVECTOR qv = XMVectorSelect( v, q, g_XMSelect1000 );
            _rgb = XMVectorSelect( p, qv, g_XMSelect1100 );
        }
        break;
    case 2: // rgb = pvt
        {
            XMVECTOR pv = XMVectorSelect( v, p, g_XMSelect1000 );
            _rgb = XMVectorSelect( t, pv, g_XMSelect1100 );
        }
        break;
    case 3: // rgb = pqv
        {
            XMVECTOR pq = XMVectorSelect( q, p, g_XMSelect1000 );
            _rgb = XMVectorSelect( v, pq, g_XMSelect1100 );
        }
        break;
    case 4: // rgb = tpv
        {
            XMVECTOR tp = XMVectorSelect( p, t, g_XMSelect1000 );
            _rgb = XMVectorSelect( v, tp, g_XMSelect1100 );
        }
        break;
    default: // rgb = vpq
        {
            XMVECTOR vp = XMVectorSelect( p, v, g_XMSelect1000 );
            _rgb = XMVectorSelect( q, vp, g_XMSelect1100 );
        }
        break;
    }

    return XMVectorSelect( hsv, _rgb, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorRGBToYUV( FXMVECTOR rgb )
{
    static const XMVECTORF32 Scale0 = { { { 0.299f, -0.147f, 0.615f, 0.0f } } };
    static const XMVECTORF32 Scale1 = { { { 0.587f, -0.289f, -0.515f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { 0.114f, 0.436f, -0.100f, 0.0f } } };

    XMMATRIX M( Scale0, Scale1, Scale2, g_XMZero );
    XMVECTOR clr = XMVector3Transform( rgb, M );

    return XMVectorSelect( rgb, clr, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorYUVToRGB( FXMVECTOR yuv )
{
    static const XMVECTORF32 Scale1 = { { { 0.0f, -0.395f, 2.032f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { 1.140f, -0.581f, 0.0f, 0.0f } } };

    XMMATRIX M( g_XMOne, Scale1, Scale2, g_XMZero );
    XMVECTOR clr = XMVector3Transform( yuv, M );

    return XMVectorSelect( yuv, clr, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorRGBToYUV_HD( FXMVECTOR rgb )
{
    static const XMVECTORF32 Scale0 = { { { 0.2126f, -0.0997f, 0.6150f, 0.0f } } };
    static const XMVECTORF32 Scale1 = { { { 0.7152f, -0.3354f, -0.5586f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { 0.0722f, 0.4351f, -0.0564f, 0.0f } } };

    XMMATRIX M( Scale0, Scale1, Scale2, g_XMZero );
    XMVECTOR clr = XMVector3Transform( rgb, M );

    return XMVectorSelect( rgb, clr, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorYUVToRGB_HD( FXMVECTOR yuv )
{
    static const XMVECTORF32 Scale1 = { { { 0.0f, -0.2153f, 2.1324f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { 1.2803f, -0.3806f, 0.0f, 0.0f } } };
        
    XMMATRIX M( g_XMOne, Scale1, Scale2, g_XMZero );
    XMVECTOR clr = XMVector3Transform( yuv, M );

    return XMVectorSelect( yuv, clr, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorRGBToXYZ( FXMVECTOR rgb )
{
    static const XMVECTORF32 Scale0 = { { { 0.4887180f, 0.1762044f, 0.0000000f, 0.0f } } };
    static const XMVECTORF32 Scale1 = { { { 0.3106803f, 0.8129847f, 0.0102048f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { 0.2006017f, 0.0108109f, 0.9897952f, 0.0f } } };
    static const XMVECTORF32 Scale  = { { { 1.f / 0.17697f, 1.f / 0.17697f, 1.f / 0.17697f, 0.0f } } };

    XMMATRIX M( Scale0, Scale1, Scale2, g_XMZero );
    XMVECTOR clr = XMVectorMultiply( XMVector3Transform( rgb, M ), Scale );

    return XMVectorSelect( rgb, clr, g_XMSelect1110 );
}

inline XMVECTOR XM_CALLCONV XMColorXYZToRGB( FXMVECTOR xyz )
{
    static const XMVECTORF32 Scale0 = { { { 2.3706743f, -0.5138850f, 0.0052982f, 0.0f } } };
    static const XMVECTORF32 Scale1 = { { { -0.9000405f, 1.4253036f, -0.0146949f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { -0.4706338f, 0.0885814f, 1.0093968f, 0.0f } } };
    static const XMVECTORF32 Scale  = { { { 0.17697f, 0.17697f, 0.17697f, 0.0f } } };

    XMMATRIX M( Scale0, Scale1, Scale2, g_XMZero );
    XMVECTOR clr = XMVector3Transform( XMVectorMultiply( xyz, Scale ), M );

    return XMVectorSelect( xyz, clr, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorXYZToSRGB( FXMVECTOR xyz )
{
    static const XMVECTORF32 Scale0 = { { { 3.2406f, -0.9689f, 0.0557f, 0.0f } } };
    static const XMVECTORF32 Scale1 = { { { -1.5372f, 1.8758f, -0.2040f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { -0.4986f, 0.0415f, 1.0570f, 0.0f } } };
    static const XMVECTORF32 Cutoff = { { { 0.0031308f, 0.0031308f, 0.0031308f, 0.0f } } };
    static const XMVECTORF32 Exp    = { { { 1.0f / 2.4f, 1.0f / 2.4f, 1.0f / 2.4f, 1.0f } } };

    XMMATRIX M( Scale0, Scale1, Scale2, g_XMZero );
    XMVECTOR lclr = XMVector3Transform( xyz, M );

    XMVECTOR sel = XMVectorGreater( lclr, Cutoff );

    // clr = 12.92 * lclr for lclr <= 0.0031308f
    XMVECTOR smallC = XMVectorMultiply( lclr, g_XMsrgbScale );

    // clr = (1+a)*pow(lclr, 1/2.4) - a for lclr > 0.0031308 (where a = 0.055)
    XMVECTOR largeC = XMVectorSubtract( XMVectorMultiply( g_XMsrgbA1, XMVectorPow( lclr, Exp ) ), g_XMsrgbA );

    XMVECTOR clr = XMVectorSelect( smallC, largeC, sel );

    return XMVectorSelect( xyz, clr, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorSRGBToXYZ( FXMVECTOR srgb )
{
    static const XMVECTORF32 Scale0 = { { { 0.4124f, 0.2126f, 0.0193f, 0.0f } } };
    static const XMVECTORF32 Scale1 = { { { 0.3576f, 0.7152f, 0.1192f, 0.0f } } };
    static const XMVECTORF32 Scale2 = { { { 0.1805f, 0.0722f, 0.9505f, 0.0f } } };
    static const XMVECTORF32 Cutoff = { { { 0.04045f, 0.04045f, 0.04045f, 0.0f } } };
    static const XMVECTORF32 Exp    = { { { 2.4f, 2.4f, 2.4f, 1.0f } } };

    XMVECTOR sel = XMVectorGreater( srgb, Cutoff );

    // lclr = clr / 12.92
    XMVECTOR smallC = XMVectorDivide( srgb, g_XMsrgbScale );

    // lclr = pow( (clr + a) / (1+a), 2.4 )
    XMVECTOR largeC = XMVectorPow( XMVectorDivide( XMVectorAdd( srgb, g_XMsrgbA ), g_XMsrgbA1 ), Exp );

    XMVECTOR lclr = XMVectorSelect( smallC, largeC, sel );

    XMMATRIX M( Scale0, Scale1, Scale2, g_XMZero );
    XMVECTOR clr = XMVector3Transform( lclr, M );

    return XMVectorSelect( srgb, clr, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorRGBToSRGB( FXMVECTOR rgb )
{
    static const XMVECTORF32 Cutoff   = { { { 0.0031308f, 0.0031308f, 0.0031308f, 1.f } } };
    static const XMVECTORF32 Linear   = { { { 12.92f, 12.92f, 12.92f, 1.f } } };
    static const XMVECTORF32 Scale    = { { { 1.055f, 1.055f, 1.055f, 1.f } } };
    static const XMVECTORF32 Bias     = { { { 0.055f, 0.055f, 0.055f, 0.f } } };
    static const XMVECTORF32 InvGamma = { { { 1.0f / 2.4f, 1.0f / 2.4f, 1.0f / 2.4f, 1.f } } };

    XMVECTOR V = XMVectorSaturate(rgb);
    XMVECTOR V0 = XMVectorMultiply( V, Linear );
    XMVECTOR V1 = XMVectorSubtract( XMVectorMultiply( Scale, XMVectorPow( V, InvGamma ) ), Bias );
    XMVECTOR select = XMVectorLess( V, Cutoff );
    V = XMVectorSelect( V1, V0, select );
    return XMVectorSelect( rgb, V, g_XMSelect1110 );
}

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

inline XMVECTOR XM_CALLCONV XMColorSRGBToRGB( FXMVECTOR srgb )
{
    static const XMVECTORF32 Cutoff  = { { { 0.04045f, 0.04045f, 0.04045f, 1.f } } };
    static const XMVECTORF32 ILinear = { { { 1.f / 12.92f, 1.f / 12.92f, 1.f / 12.92f, 1.f } } };
    static const XMVECTORF32 Scale   = { { { 1.f / 1.055f, 1.f / 1.055f, 1.f / 1.055f, 1.f } } };
    static const XMVECTORF32 Bias    = { { { 0.055f, 0.055f, 0.055f, 0.f } } };
    static const XMVECTORF32 Gamma   = { { { 2.4f, 2.4f, 2.4f, 1.f } } };

    XMVECTOR V = XMVectorSaturate(srgb);
    XMVECTOR V0 = XMVectorMultiply( V, ILinear );
    XMVECTOR V1 = XMVectorPow( XMVectorMultiply( XMVectorAdd( V, Bias ), Scale ), Gamma );
    XMVECTOR select = XMVectorGreater( V, Cutoff );
    V = XMVectorSelect( V0, V1, select );
    return XMVectorSelect( srgb, V, g_XMSelect1110 );
}

/****************************************************************************
 *
 * Miscellaneous
 *
 ****************************************************************************/

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

inline bool XMVerifyCPUSupport()
{
#if defined(_XM_SSE_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
    int CPUInfo[4] = { -1 };
    __cpuid(CPUInfo, 0);

#ifdef __AVX2__
    if (CPUInfo[0] < 7)
        return false;
#else
    if (CPUInfo[0] < 1)
        return false;
#endif

    __cpuid(CPUInfo, 1);

#if defined(__AVX2__) || defined(_XM_AVX2_INTRINSICS_)
    // The compiler can emit FMA3 instructions even without explicit intrinsics use
    if ((CPUInfo[2] & 0x38081001) != 0x38081001)
        return false; // No F16C/AVX/OSXSAVE/SSE4.1/FMA3/SSE3 support
#elif defined(_XM_FMA3_INTRINSICS_) && defined(_XM_F16C_INTRINSICS_)
    if ((CPUInfo[2] & 0x38081001) != 0x38081001)
        return false; // No F16C/AVX/OSXSAVE/SSE4.1/FMA3/SSE3 support
#elif defined(_XM_FMA3_INTRINSICS_)
    if ((CPUInfo[2] & 0x18081001) != 0x18081001)
        return false; // No AVX/OSXSAVE/SSE4.1/FMA3/SSE3 support
#elif defined(_XM_F16C_INTRINSICS_)
    if ((CPUInfo[2] & 0x38080001) != 0x38080001)
        return false; // No F16C/AVX/OSXSAVE/SSE4.1/SSE3 support
#elif defined(__AVX__) || defined(_XM_AVX_INTRINSICS_)
    if ((CPUInfo[2] & 0x18080001) != 0x18080001)
        return false; // No AVX/OSXSAVE/SSE4.1/SSE3 support
#elif defined(_XM_SSE4_INTRINSICS_)
    if ((CPUInfo[2] & 0x80001) != 0x80001)
        return false; // No SSE3/SSE4.1 support
#elif defined(_XM_SSE3_INTRINSICS_)
    if (!(CPUInfo[2] & 0x1))
        return false; // No SSE3 support  
#endif

    // The x64 processor model requires SSE2 support, but no harm in checking
    if ((CPUInfo[3] & 0x6000000) != 0x6000000)
        return false; // No SSE2/SSE support

#if defined(__AVX2__) || defined(_XM_AVX2_INTRINSICS_)
    __cpuidex(CPUInfo, 7, 0);
    if (!(CPUInfo[1] & 0x20))
        return false; // No AVX2 support
#endif

    return true;
#elif defined(_XM_ARM_NEON_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
    // ARM-NEON support is required for the Windows on ARM platform
    return true;
#else
    // No intrinsics path always supported
    return true;
#endif
}

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

inline XMVECTOR XM_CALLCONV XMFresnelTerm
(
    FXMVECTOR CosIncidentAngle,
    FXMVECTOR RefractionIndex
)
{
    assert(!XMVector4IsInfinite(CosIncidentAngle));

    // Result = 0.5f * (g - c)^2 / (g + c)^2 * ((c * (g + c) - 1)^2 / (c * (g - c) + 1)^2 + 1) where
    // c = CosIncidentAngle
    // g = sqrt(c^2 + RefractionIndex^2 - 1)

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

    XMVECTOR G = XMVectorMultiplyAdd(RefractionIndex, RefractionIndex, g_XMNegativeOne.v);
    G = XMVectorMultiplyAdd(CosIncidentAngle, CosIncidentAngle, G);
    G = XMVectorAbs(G);
    G = XMVectorSqrt(G);

    XMVECTOR S = XMVectorAdd(G, CosIncidentAngle);
    XMVECTOR D = XMVectorSubtract(G, CosIncidentAngle);

    XMVECTOR V0 = XMVectorMultiply(D, D);
    XMVECTOR V1 = XMVectorMultiply(S, S);
    V1 = XMVectorReciprocal(V1);
    V0 = XMVectorMultiply(g_XMOneHalf.v, V0);
    V0 = XMVectorMultiply(V0, V1);

    XMVECTOR V2 = XMVectorMultiplyAdd(CosIncidentAngle, S, g_XMNegativeOne.v);
    XMVECTOR V3 = XMVectorMultiplyAdd(CosIncidentAngle, D, g_XMOne.v);
    V2 = XMVectorMultiply(V2, V2);
    V3 = XMVectorMultiply(V3, V3);
    V3 = XMVectorReciprocal(V3);
    V2 = XMVectorMultiplyAdd(V2, V3, g_XMOne.v);

    XMVECTOR Result = XMVectorMultiply(V0, V2);

    Result = XMVectorSaturate(Result);

    return Result;

#elif defined(_XM_SSE_INTRINSICS_)
    // G = sqrt(abs((RefractionIndex^2-1) + CosIncidentAngle^2))
    XMVECTOR G = _mm_mul_ps(RefractionIndex,RefractionIndex);
    XMVECTOR vTemp = _mm_mul_ps(CosIncidentAngle,CosIncidentAngle);
    G = _mm_sub_ps(G,g_XMOne);
    vTemp = _mm_add_ps(vTemp,G);
    // max((0-vTemp),vTemp) == abs(vTemp)
    // The abs is needed to deal with refraction and cosine being zero
    G = _mm_setzero_ps();
    G = _mm_sub_ps(G,vTemp);
    G = _mm_max_ps(G,vTemp);
    // Last operation, the sqrt()
    G = _mm_sqrt_ps(G);

    // Calc G-C and G+C
    XMVECTOR GAddC = _mm_add_ps(G,CosIncidentAngle);
    XMVECTOR GSubC = _mm_sub_ps(G,CosIncidentAngle);
    // Perform the term (0.5f *(g - c)^2) / (g + c)^2 
    XMVECTOR vResult = _mm_mul_ps(GSubC,GSubC);
    vTemp = _mm_mul_ps(GAddC,GAddC);
    vResult = _mm_mul_ps(vResult,g_XMOneHalf);
    vResult = _mm_div_ps(vResult,vTemp);
    // Perform the term ((c * (g + c) - 1)^2 / (c * (g - c) + 1)^2 + 1)
    GAddC = _mm_mul_ps(GAddC,CosIncidentAngle);
    GSubC = _mm_mul_ps(GSubC,CosIncidentAngle);
    GAddC = _mm_sub_ps(GAddC,g_XMOne);
    GSubC = _mm_add_ps(GSubC,g_XMOne);
    GAddC = _mm_mul_ps(GAddC,GAddC);
    GSubC = _mm_mul_ps(GSubC,GSubC);
    GAddC = _mm_div_ps(GAddC,GSubC);
    GAddC = _mm_add_ps(GAddC,g_XMOne);
    // Multiply the two term parts
    vResult = _mm_mul_ps(vResult,GAddC);
    // Clamp to 0.0 - 1.0f
    vResult = _mm_max_ps(vResult,g_XMZero);
    vResult = _mm_min_ps(vResult,g_XMOne);
    return vResult;
#endif
}

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

inline bool XMScalarNearEqual
(
    float S1,
    float S2,
    float Epsilon
)
{
    float Delta = S1 - S2;
    return (fabsf(Delta) <= Epsilon);
}

//------------------------------------------------------------------------------
// Modulo the range of the given angle such that -XM_PI <= Angle < XM_PI
inline float XMScalarModAngle
(
    float Angle
)
{
    // Note: The modulo is performed with unsigned math only to work
    // around a precision error on numbers that are close to PI

    // Normalize the range from 0.0f to XM_2PI
    Angle = Angle + XM_PI;
    // Perform the modulo, unsigned
    float fTemp = fabsf(Angle);
    fTemp = fTemp - (XM_2PI * (float)((int32_t)(fTemp/XM_2PI)));
    // Restore the number to the range of -XM_PI to XM_PI-epsilon
    fTemp = fTemp - XM_PI;
    // If the modulo'd value was negative, restore negation
    if (Angle<0.0f) {
        fTemp = -fTemp;
    }
    return fTemp;
}

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

inline float XMScalarSin
(
    float Value
)
{
    // Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
    float quotient = XM_1DIV2PI*Value;
    if (Value >= 0.0f)
    {
        quotient = (float)((int)(quotient + 0.5f));
    }
    else
    {
        quotient = (float)((int)(quotient - 0.5f));
    }
    float y = Value - XM_2PI*quotient;

    // Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
    if (y > XM_PIDIV2)
    {
        y = XM_PI - y;
    }
    else if (y < -XM_PIDIV2)
    {
        y = -XM_PI - y;
    }

    // 11-degree minimax approximation
    float y2 = y * y;
    return ( ( ( ( (-2.3889859e-08f * y2 + 2.7525562e-06f) * y2 - 0.00019840874f ) * y2 + 0.0083333310f ) * y2 - 0.16666667f ) * y2 + 1.0f ) * y;
}

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

inline float XMScalarSinEst
(
    float Value
)
{
    // Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
    float quotient = XM_1DIV2PI*Value;
    if (Value >= 0.0f)
    {
        quotient = (float)((int)(quotient + 0.5f));
    }
    else
    {
        quotient = (float)((int)(quotient - 0.5f));
    }
    float y = Value - XM_2PI*quotient;

    // Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
    if (y > XM_PIDIV2)
    {
        y = XM_PI - y;
    }
    else if (y < -XM_PIDIV2)
    {
        y = -XM_PI - y;
    }

    // 7-degree minimax approximation
    float y2 = y * y;
    return ( ( ( -0.00018524670f * y2 + 0.0083139502f ) * y2 - 0.16665852f ) * y2 + 1.0f ) * y;
}

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

inline float XMScalarCos
(
    float Value
)
{
    // Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
    float quotient = XM_1DIV2PI*Value;
    if (Value >= 0.0f)
    {
        quotient = (float)((int)(quotient + 0.5f));
    }
    else
    {
        quotient = (float)((int)(quotient - 0.5f));
    }
    float y = Value - XM_2PI*quotient;

    // Map y to [-pi/2,pi/2] with cos(y) = sign*cos(x).
    float sign;
    if (y > XM_PIDIV2)
    {
        y = XM_PI - y;
        sign = -1.0f;
    }
    else if (y < -XM_PIDIV2)
    {
        y = -XM_PI - y;
        sign = -1.0f;
    }
    else
    {
        sign = +1.0f;
    }

    // 10-degree minimax approximation
    float y2 = y*y;
    float p = ( ( ( ( -2.6051615e-07f * y2 + 2.4760495e-05f ) * y2 - 0.0013888378f ) * y2 + 0.041666638f ) * y2 - 0.5f ) * y2 + 1.0f;
    return sign*p;
}

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

inline float XMScalarCosEst
(
    float Value
)
{
    // Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
    float quotient = XM_1DIV2PI*Value;
    if (Value >= 0.0f)
    {
        quotient = (float)((int)(quotient + 0.5f));
    }
    else
    {
        quotient = (float)((int)(quotient - 0.5f));
    }
    float y = Value - XM_2PI*quotient;

    // Map y to [-pi/2,pi/2] with cos(y) = sign*cos(x).
    float sign;
    if (y > XM_PIDIV2)
    {
        y = XM_PI - y;
        sign = -1.0f;
    }
    else if (y < -XM_PIDIV2)
    {
        y = -XM_PI - y;
        sign = -1.0f;
    }
    else
    {
        sign = +1.0f;
    }

    // 6-degree minimax approximation
    float y2 = y * y;
    float p = ( ( -0.0012712436f * y2 + 0.041493919f ) * y2 - 0.49992746f ) * y2 + 1.0f;
    return sign*p;
}

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

_Use_decl_annotations_
inline void XMScalarSinCos
(
    float* pSin,
    float* pCos,
    float  Value
)
{
    assert(pSin);
    assert(pCos);

    // Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
    float quotient = XM_1DIV2PI*Value;
    if (Value >= 0.0f)
    {
        quotient = (float)((int)(quotient + 0.5f));
    }
    else
    {
        quotient = (float)((int)(quotient - 0.5f));
    }
    float y = Value - XM_2PI*quotient;

    // Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
    float sign;
    if (y > XM_PIDIV2)
    {
        y = XM_PI - y;
        sign = -1.0f;
    }
    else if (y < -XM_PIDIV2)
    {
        y = -XM_PI - y;
        sign = -1.0f;
    }
    else
    {
        sign = +1.0f;
    }

    float y2 = y * y;

    // 11-degree minimax approximation
    *pSin = ( ( ( ( (-2.3889859e-08f * y2 + 2.7525562e-06f) * y2 - 0.00019840874f ) * y2 + 0.0083333310f ) * y2 - 0.16666667f ) * y2 + 1.0f ) * y;

    // 10-degree minimax approximation
    float p = ( ( ( ( -2.6051615e-07f * y2 + 2.4760495e-05f ) * y2 - 0.0013888378f ) * y2 + 0.041666638f ) * y2 - 0.5f ) * y2 + 1.0f;
    *pCos = sign*p;
}

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

_Use_decl_annotations_
inline void XMScalarSinCosEst
(
    float* pSin,
    float* pCos,
    float  Value
)
{
    assert(pSin);
    assert(pCos);

    // Map Value to y in [-pi,pi], x = 2*pi*quotient + remainder.
    float quotient = XM_1DIV2PI*Value;
    if (Value >= 0.0f)
    {
        quotient = (float)((int)(quotient + 0.5f));
    }
    else
    {
        quotient = (float)((int)(quotient - 0.5f));
    }
    float y = Value - XM_2PI*quotient;

    // Map y to [-pi/2,pi/2] with sin(y) = sin(Value).
    float sign;
    if (y > XM_PIDIV2)
    {
        y = XM_PI - y;
        sign = -1.0f;
    }
    else if (y < -XM_PIDIV2)
    {
        y = -XM_PI - y;
        sign = -1.0f;
    }
    else
    {
        sign = +1.0f;
    }

    float y2 = y * y;

    // 7-degree minimax approximation
    *pSin = ( ( ( -0.00018524670f * y2 + 0.0083139502f ) * y2 - 0.16665852f ) * y2 + 1.0f ) * y;

    // 6-degree minimax approximation
    float p = ( ( -0.0012712436f * y2 + 0.041493919f ) * y2 - 0.49992746f ) * y2 + 1.0f;
    *pCos = sign*p;
}

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

inline float XMScalarASin
(
    float Value
)
{
    // Clamp input to [-1,1].
    bool nonnegative = (Value >= 0.0f);
    float x = fabsf(Value);
    float omx = 1.0f - x;
    if (omx < 0.0f)
    {
        omx = 0.0f;
    }
    float root = sqrtf(omx);

    // 7-degree minimax approximation
    float result = ( ( ( ( ( ( -0.0012624911f * x + 0.0066700901f ) * x - 0.0170881256f ) * x + 0.0308918810f ) * x - 0.0501743046f ) * x + 0.0889789874f ) * x - 0.2145988016f ) * x + 1.5707963050f;
    result *= root;  // acos(|x|)

    // acos(x) = pi - acos(-x) when x < 0, asin(x) = pi/2 - acos(x)
    return (nonnegative ? XM_PIDIV2 - result : result - XM_PIDIV2);
}

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

inline float XMScalarASinEst
(
    float Value
)
{
    // Clamp input to [-1,1].
    bool nonnegative = (Value >= 0.0f);
    float x = fabsf(Value);
    float omx = 1.0f - x;
    if (omx < 0.0f)
    {
        omx = 0.0f;
    }
    float root = sqrtf(omx);

    // 3-degree minimax approximation
    float result = ((-0.0187293f*x+0.0742610f)*x-0.2121144f)*x+1.5707288f;
    result *= root;  // acos(|x|)

    // acos(x) = pi - acos(-x) when x < 0, asin(x) = pi/2 - acos(x)
    return (nonnegative ? XM_PIDIV2 - result : result - XM_PIDIV2);
}

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

inline float XMScalarACos
(
    float Value
)
{
    // Clamp input to [-1,1].
    bool nonnegative = (Value >= 0.0f);
    float x = fabsf(Value);
    float omx = 1.0f - x;
    if (omx < 0.0f)
    {
        omx = 0.0f;
    }
    float root = sqrtf(omx);

    // 7-degree minimax approximation
    float result = ( ( ( ( ( ( -0.0012624911f * x + 0.0066700901f ) * x - 0.0170881256f ) * x + 0.0308918810f ) * x - 0.0501743046f ) * x + 0.0889789874f ) * x - 0.2145988016f ) * x + 1.5707963050f;
    result *= root;

    // acos(x) = pi - acos(-x) when x < 0
    return (nonnegative ? result : XM_PI - result);
}

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

inline float XMScalarACosEst
(
    float Value
)
{
    // Clamp input to [-1,1].
    bool nonnegative = (Value >= 0.0f);
    float x = fabsf(Value);
    float omx = 1.0f - x;
    if (omx < 0.0f)
    {
        omx = 0.0f;
    }
    float root = sqrtf(omx);

    // 3-degree minimax approximation
    float result = ( ( -0.0187293f * x + 0.0742610f ) * x - 0.2121144f ) * x + 1.5707288f;
    result *= root;

    // acos(x) = pi - acos(-x) when x < 0
    return (nonnegative ? result : XM_PI - result);
}