path: root/Minecraft.Client/PS3/PS3Extras/DirectX/DirectXMath.h

//-------------------------------------------------------------------------------------
// DirectXMath.h -- 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.
//-------------------------------------------------------------------------------------


// MGH -------------------
#define _XM_BIGENDIAN_
#define _XM_NO_INTRINSICS_
// -----------------------

#ifdef _MSC_VER
#pragma once
#endif

#ifndef __cplusplus
#error DirectX Math requires C++
#endif

#define DIRECTX_MATH_VERSION 303

#if !defined(_XM_BIGENDIAN_) && !defined(_XM_LITTLEENDIAN_)
#if defined(_M_AMD64) || defined(_M_IX86) || defined(_M_ARM)
#define _XM_LITTLEENDIAN_
#elif defined(_M_PPCBE)
#define _XM_BIGENDIAN_
#else
#error DirectX Math does not support this target
#endif
#endif // !_XM_BIGENDIAN_ && !_XM_LITTLEENDIAN_



#if !defined(_XM_ARM_NEON_INTRINSICS_) && !defined(_XM_SSE_INTRINSICS_) && !defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
#if defined(_M_IX86) || defined(_M_AMD64)
#define _XM_SSE_INTRINSICS_
#elif defined(_M_PPCBE)
#define _XM_VMX128_INTRINSICS_
#elif defined(_M_ARM)
#define _XM_ARM_NEON_INTRINSICS_
#elif !defined(_XM_NO_INTRINSICS_)
#error DirectX Math does not support this target
#endif
#endif // !_XM_ARM_NEON_INTRINSICS_ && !_XM_SSE_INTRINSICS_ && !_XM_VMX128_INTRINSICS_ && !_XM_NO_INTRINSICS_

#pragma warning(push)
#pragma warning(disable:4514 4820 4985)
#include <cmath>
#include <float.h>
// MGH - #include <malloc.h>
#pragma warning(pop)


#if defined(_XM_SSE_INTRINSICS_)
#ifndef _XM_NO_INTRINSICS_
#include <xmmintrin.h>
#include <emmintrin.h>
#endif
#elif defined(_XM_VMX128_INTRINSICS_)
#error This version of DirectX Math does not support Xbox 360
#elif defined(_XM_ARM_NEON_INTRINSICS_)
#ifndef _XM_NO_INTRINSICS_
#include <arm_neon.h>
#endif
#endif



#include <DirectX/no_sal2.h>
#include <assert.h>


#pragma warning(push)
#pragma warning(disable : 4005 4668)
#include <stdint.h>
#pragma warning(pop)


namespace DirectX
{

/****************************************************************************
 *
 * Constant definitions
 *
 ****************************************************************************/

#if defined(__XNAMATH_H__) && defined(XM_PI)
#undef XM_PI
#undef XM_2PI
#undef XM_1DIVPI
#undef XM_1DIV2PI
#undef XM_PIDIV2
#undef XM_PIDIV4
#undef XM_SELECT_0
#undef XM_SELECT_1
#undef XM_PERMUTE_0X
#undef XM_PERMUTE_0Y
#undef XM_PERMUTE_0Z
#undef XM_PERMUTE_0W
#undef XM_PERMUTE_1X
#undef XM_PERMUTE_1Y
#undef XM_PERMUTE_1Z
#undef XM_PERMUTE_1W
#undef XM_CRMASK_CR6
#undef XM_CRMASK_CR6TRUE
#undef XM_CRMASK_CR6FALSE
#undef XM_CRMASK_CR6BOUNDS
#undef XM_CACHE_LINE_SIZE
#endif

const float XM_PI           = 3.141592654f;
const float XM_2PI          = 6.283185307f;
const float XM_1DIVPI       = 0.318309886f;
const float XM_1DIV2PI      = 0.159154943f;
const float XM_PIDIV2       = 1.570796327f;
const float XM_PIDIV4       = 0.785398163f;

const uint32_t XM_SELECT_0          = 0x00000000;
const uint32_t XM_SELECT_1          = 0xFFFFFFFF;

const uint32_t XM_PERMUTE_0X        = 0;
const uint32_t XM_PERMUTE_0Y        = 1;
const uint32_t XM_PERMUTE_0Z        = 2;
const uint32_t XM_PERMUTE_0W        = 3;
const uint32_t XM_PERMUTE_1X        = 4;
const uint32_t XM_PERMUTE_1Y        = 5;
const uint32_t XM_PERMUTE_1Z        = 6;
const uint32_t XM_PERMUTE_1W        = 7;

const uint32_t XM_SWIZZLE_X         = 0;
const uint32_t XM_SWIZZLE_Y         = 1;
const uint32_t XM_SWIZZLE_Z         = 2;
const uint32_t XM_SWIZZLE_W         = 3;

const uint32_t XM_CRMASK_CR6        = 0x000000F0;
const uint32_t XM_CRMASK_CR6TRUE    = 0x00000080;
const uint32_t XM_CRMASK_CR6FALSE   = 0x00000020;
const uint32_t XM_CRMASK_CR6BOUNDS  = XM_CRMASK_CR6FALSE;



/****************************************************************************
 *
 * Macros
 *
 ****************************************************************************/

#if defined(__XNAMATH_H__) && defined(XMComparisonAllTrue)
#undef XMComparisonAllTrue
#undef XMComparisonAnyTrue
#undef XMComparisonAllFalse
#undef XMComparisonAnyFalse
#undef XMComparisonMixed
#undef XMComparisonAllInBounds
#undef XMComparisonAnyOutOfBounds
#endif

// Unit conversion

inline float XMConvertToRadians(float fDegrees) { return fDegrees * (XM_PI / 180.0f); }
inline float XMConvertToDegrees(float fRadians) { return fRadians * (180.0f / XM_PI); }

// Condition register evaluation proceeding a recording (R) comparison

inline bool XMComparisonAllTrue(uint32_t CR) { return (((CR) & XM_CRMASK_CR6TRUE) == XM_CRMASK_CR6TRUE); }
inline bool XMComparisonAnyTrue(uint32_t CR) { return (((CR) & XM_CRMASK_CR6FALSE) != XM_CRMASK_CR6FALSE); }
inline bool XMComparisonAllFalse(uint32_t CR) { return (((CR) & XM_CRMASK_CR6FALSE) == XM_CRMASK_CR6FALSE); }
inline bool XMComparisonAnyFalse(uint32_t CR) { return (((CR) & XM_CRMASK_CR6TRUE) != XM_CRMASK_CR6TRUE); }
inline bool XMComparisonMixed(uint32_t CR) { return (((CR) & XM_CRMASK_CR6) == 0); }
inline bool XMComparisonAllInBounds(uint32_t CR) { return (((CR) & XM_CRMASK_CR6BOUNDS) == XM_CRMASK_CR6BOUNDS); }
inline bool XMComparisonAnyOutOfBounds(uint32_t CR) { return (((CR) & XM_CRMASK_CR6BOUNDS) != XM_CRMASK_CR6BOUNDS); }


/****************************************************************************
 *
 * Data types
 *
 ****************************************************************************/

#pragma warning(push)
#pragma warning(disable:4068 4201 4365 4324 4820)

#pragma prefast(push)
#pragma prefast(disable : 25000, "FXMVECTOR is 16 bytes")

#ifdef _XM_BIGENDIAN_
#pragma bitfield_order(push)
#pragma bitfield_order(lsb_to_msb)
#endif

//------------------------------------------------------------------------------
#if defined(_XM_NO_INTRINSICS_) && !defined(_M_PPCBE)
// The __vector4 structure is an intrinsic on Xbox but must be separately defined
// for x86/x64
struct __vector4
{
    union
    {
        float       vector4_f32[4];
        uint32_t    vector4_u32[4];
		// MGH - added to match 360 version
//----------------------
struct
		{
			float x;
			float y;
			float z;
			float w;
		};
		float v[4];
		uint32_t  u[4];
//----------------------

    };
};
#endif // _XM_NO_INTRINSICS_

//------------------------------------------------------------------------------
#if (defined (_M_IX86) || defined(_M_AMD64) || defined(_M_ARM)) && defined(_XM_NO_INTRINSICS_)
typedef uint32_t __vector4i[4];
#else
typedef __declspec(align(16)) uint32_t __vector4i[4];
#endif

//------------------------------------------------------------------------------
// Vector intrinsic: Four 32 bit floating point components aligned on a 16 byte 
// boundary and mapped to hardware vector registers
#if defined(_XM_SSE_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
typedef __m128 XMVECTOR;
#elif defined(_XM_ARM_NEON_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
typedef __n128 XMVECTOR;
#else
typedef __vector4 XMVECTOR;
#endif

// Fix-up for (1st-3rd) XMVECTOR parameters that are pass-in-register for x86, ARM, and Xbox 360; by reference otherwise
#if ( defined(_M_IX86) || defined(_M_ARM) || defined(_XM_VMX128_INTRINSICS_) ) && !defined(_XM_NO_INTRINSICS_)
typedef const XMVECTOR FXMVECTOR;
#else
typedef const XMVECTOR& FXMVECTOR;
#endif

// Fix-up for (4th) XMVECTOR parameter to pass in-register for ARM and Xbox 360; by reference otherwise
#if ( defined(_M_ARM) || defined(_XM_VMX128_INTRINSICS_) ) && !defined(_XM_NO_INTRINSICS_)
typedef const XMVECTOR GXMVECTOR;
#else
typedef const XMVECTOR& GXMVECTOR;
#endif

// Fix-up for (5th+) XMVECTOR parameters to pass in-register for Xbox 360 and by reference otherwise
#if defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
typedef const XMVECTOR CXMVECTOR;
#else
typedef const XMVECTOR& CXMVECTOR;
#endif

//------------------------------------------------------------------------------
// Conversion types for constants
__declspec(align(16)) struct XMVECTORF32
{
    union
    {
        float f[4];
        XMVECTOR v;
    };

    inline operator XMVECTOR() const { return v; }
    inline operator const float*() const { return f; }
#if !defined(_XM_NO_INTRINSICS_) && defined(_XM_SSE_INTRINSICS_)
    inline operator __m128i() const { return _mm_castps_si128(v); }
    inline operator __m128d() const { return _mm_castps_pd(v); }
#endif
};

__declspec(align(16)) struct XMVECTORI32
{
    union
    {
        int32_t i[4];
        XMVECTOR v;
    };

    inline operator XMVECTOR() const { return v; }
#if !defined(_XM_NO_INTRINSICS_) && defined(_XM_SSE_INTRINSICS_)
    inline operator __m128i() const { return _mm_castps_si128(v); }
    inline operator __m128d() const { return _mm_castps_pd(v); }
#endif
};

__declspec(align(16)) struct XMVECTORU8
{
    union
    {
        uint8_t u[16];
        XMVECTOR v;
    };

    inline operator XMVECTOR() const { return v; }
#if !defined(_XM_NO_INTRINSICS_) && defined(_XM_SSE_INTRINSICS_)
    inline operator __m128i() const { return _mm_castps_si128(v); }
    inline operator __m128d() const { return _mm_castps_pd(v); }
#endif
};

__declspec(align(16)) struct XMVECTORU32
{
    union
    {
        uint32_t u[4];
        XMVECTOR v;
    };

    inline operator XMVECTOR() const { return v; }
#if !defined(_XM_NO_INTRINSICS_) && defined(_XM_SSE_INTRINSICS_)
    inline operator __m128i() const { return _mm_castps_si128(v); }
    inline operator __m128d() const { return _mm_castps_pd(v); }
#endif
};

//------------------------------------------------------------------------------
// Vector operators
XMVECTOR    operator+ (FXMVECTOR V);
XMVECTOR    operator- (FXMVECTOR V);

XMVECTOR&   operator+= (XMVECTOR& V1, FXMVECTOR V2);
XMVECTOR&   operator-= (XMVECTOR& V1, FXMVECTOR V2);
XMVECTOR&   operator*= (XMVECTOR& V1, FXMVECTOR V2);
XMVECTOR&   operator/= (XMVECTOR& V1, FXMVECTOR V2);
XMVECTOR&   operator*= (XMVECTOR& V, float S);
XMVECTOR&   operator/= (XMVECTOR& V, float S);

XMVECTOR    operator+ (FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR    operator- (FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR    operator* (FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR    operator/ (FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR    operator* (FXMVECTOR V, float S);
XMVECTOR    operator* (float S, FXMVECTOR V);
XMVECTOR    operator/ (FXMVECTOR V, float S);

//------------------------------------------------------------------------------
// Matrix type: Sixteen 32 bit floating point components aligned on a
// 16 byte boundary and mapped to four hardware vector registers

struct XMMATRIX;

// Fix-up for XMMATRIX parameters to pass in-register on Xbox 360, by reference otherwise
#if defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
typedef const XMMATRIX CXMMATRIX;
#else
typedef const XMMATRIX& CXMMATRIX;
#endif

#if (defined(_M_IX86) || defined(_M_AMD64) || defined(_M_ARM)) && defined(_XM_NO_INTRINSICS_)
struct XMMATRIX
#else
__declspec(align(16)) struct XMMATRIX
#endif
{
#ifdef _XM_NO_INTRINSICS_
    union
    {
        XMVECTOR r[4];
        struct
        {
            float _11, _12, _13, _14;
            float _21, _22, _23, _24;
            float _31, _32, _33, _34;
            float _41, _42, _43, _44;
        };
        float m[4][4];
    };
#else
    XMVECTOR r[4];
#endif

    XMMATRIX() {}
    XMMATRIX(FXMVECTOR R0, FXMVECTOR R1, FXMVECTOR R2, GXMVECTOR R3) { r[0] = R0; r[1] = R1; r[2] = R2; r[3] = R3; }
    XMMATRIX(float m00, float m01, float m02, float m03,
             float m10, float m11, float m12, float m13,
             float m20, float m21, float m22, float m23,
             float m30, float m31, float m32, float m33);
    explicit XMMATRIX(_In_reads_(16) const float *pArray);

#ifdef _XM_NO_INTRINSICS_
    float       operator() (size_t Row, size_t Column) const { return m[Row][Column]; }
    float&      operator() (size_t Row, size_t Column) { return m[Row][Column]; }
#endif

    XMMATRIX&   operator= (const XMMATRIX& M) { r[0] = M.r[0]; r[1] = M.r[1]; r[2] = M.r[2]; r[3] = M.r[3]; return *this; }

    XMMATRIX    operator+ () const { return *this; }
    XMMATRIX    operator- () const;

    XMMATRIX&   operator+= (CXMMATRIX M);
    XMMATRIX&   operator-= (CXMMATRIX M);
    XMMATRIX&   operator*= (CXMMATRIX M);
    XMMATRIX&   operator*= (float S);
    XMMATRIX&   operator/= (float S);

    XMMATRIX    operator+ (CXMMATRIX M) const;
    XMMATRIX    operator- (CXMMATRIX M) const;
    XMMATRIX    operator* (CXMMATRIX M) const;
    XMMATRIX    operator* (float S) const;
    XMMATRIX    operator/ (float S) const;

    friend XMMATRIX operator* (float S, CXMMATRIX M);
};

//------------------------------------------------------------------------------
// 2D Vector; 32 bit floating point components
struct XMFLOAT2
{
    float x;
    float y;

    XMFLOAT2() {}
    XMFLOAT2(float _x, float _y) : x(_x), y(_y) {}
    explicit XMFLOAT2(_In_reads_(2) const float *pArray) : x(pArray[0]), y(pArray[1]) {}

    XMFLOAT2& operator= (const XMFLOAT2& Float2) { x = Float2.x; y = Float2.y; return *this; }
};

// 2D Vector; 32 bit floating point components aligned on a 16 byte boundary
__declspec(align(16)) struct XMFLOAT2A : public XMFLOAT2
{
    XMFLOAT2A() : XMFLOAT2() {}
    XMFLOAT2A(float _x, float _y) : XMFLOAT2(_x, _y) {}
    explicit XMFLOAT2A(_In_reads_(2) const float *pArray) : XMFLOAT2(pArray) {}

    XMFLOAT2A& operator= (const XMFLOAT2A& Float2) { x = Float2.x; y = Float2.y; return *this; }
};

//------------------------------------------------------------------------------
// 2D Vector; 32 bit signed integer components
struct XMINT2
{
    int32_t x;
    int32_t y;

    XMINT2() {}
    XMINT2(int32_t _x, int32_t _y) : x(_x), y(_y) {}
    explicit XMINT2(_In_reads_(2) const int32_t *pArray) : x(pArray[0]), y(pArray[1]) {}

    XMINT2& operator= (const XMINT2& Int2) { x = Int2.x; y = Int2.y; return *this; }
};

// 2D Vector; 32 bit unsigned integer components
struct XMUINT2
{
    uint32_t x;
    uint32_t y;

    XMUINT2() {}
    XMUINT2(uint32_t _x, uint32_t _y) : x(_x), y(_y) {}
    explicit XMUINT2(_In_reads_(2) const uint32_t *pArray) : x(pArray[0]), y(pArray[1]) {}

    XMUINT2& operator= (const XMUINT2& UInt2) { x = UInt2.x; y = UInt2.y; return *this; }
};

//------------------------------------------------------------------------------
// 3D Vector; 32 bit floating point components
struct XMFLOAT3
{
    float x;
    float y;
    float z;

    XMFLOAT3() {}
    XMFLOAT3(float _x, float _y, float _z) : x(_x), y(_y), z(_z) {}
    explicit XMFLOAT3(_In_reads_(3) const float *pArray) : x(pArray[0]), y(pArray[1]), z(pArray[2]) {}

    XMFLOAT3& operator= (const XMFLOAT3& Float3) { x = Float3.x; y = Float3.y; z = Float3.z; return *this; }
};

// 3D Vector; 32 bit floating point components aligned on a 16 byte boundary
__declspec(align(16)) struct XMFLOAT3A : public XMFLOAT3
{
    XMFLOAT3A() : XMFLOAT3() {}
    XMFLOAT3A(float _x, float _y, float _z) : XMFLOAT3(_x, _y, _z) {}
    explicit XMFLOAT3A(_In_reads_(3) const float *pArray) : XMFLOAT3(pArray) {}

    XMFLOAT3A& operator= (const XMFLOAT3A& Float3) { x = Float3.x; y = Float3.y; z = Float3.z; return *this; }
};

//------------------------------------------------------------------------------
// 3D Vector; 32 bit signed integer components
struct XMINT3
{
    int32_t x;
    int32_t y;
    int32_t z;

    XMINT3() {}
    XMINT3(int32_t _x, int32_t _y, int32_t _z) : x(_x), y(_y), z(_z) {}
    explicit XMINT3(_In_reads_(3) const int32_t *pArray) : x(pArray[0]), y(pArray[1]), z(pArray[2]) {}

    XMINT3& operator= (const XMINT3& i3) { x = i3.x; y = i3.y; z = i3.z; return *this; }
};

// 3D Vector; 32 bit unsigned integer components
struct XMUINT3
{
    uint32_t x;
    uint32_t y;
    uint32_t z;

    XMUINT3() {}
    XMUINT3(uint32_t _x, uint32_t _y, uint32_t _z) : x(_x), y(_y), z(_z) {}
    explicit XMUINT3(_In_reads_(3) const uint32_t *pArray) : x(pArray[0]), y(pArray[1]), z(pArray[2]) {}

    XMUINT3& operator= (const XMUINT3& u3) { x = u3.x; y = u3.y; z = u3.z; return *this; }
};

//------------------------------------------------------------------------------
// 4D Vector; 32 bit floating point components
struct XMFLOAT4
{
    float x;
    float y;
    float z;
    float w;

    XMFLOAT4() {}
    XMFLOAT4(float _x, float _y, float _z, float _w) : x(_x), y(_y), z(_z), w(_w) {}
    explicit XMFLOAT4(_In_reads_(4) const float *pArray) : x(pArray[0]), y(pArray[1]), z(pArray[2]), w(pArray[3]) {}

    XMFLOAT4& operator= (const XMFLOAT4& Float4) { x = Float4.x; y = Float4.y; z = Float4.z; w = Float4.w; return *this; }
};

// 4D Vector; 32 bit floating point components aligned on a 16 byte boundary
__declspec(align(16)) struct XMFLOAT4A : public XMFLOAT4
{
    XMFLOAT4A() : XMFLOAT4() {}
    XMFLOAT4A(float _x, float _y, float _z, float _w) : XMFLOAT4(_x, _y, _z, _w) {}
    explicit XMFLOAT4A(_In_reads_(4) const float *pArray) : XMFLOAT4(pArray) {}

    XMFLOAT4A& operator= (const XMFLOAT4A& Float4) { x = Float4.x; y = Float4.y; z = Float4.z; w = Float4.w; return *this; }
};

//------------------------------------------------------------------------------
// 4D Vector; 32 bit signed integer components
struct XMINT4
{
    int32_t x;
    int32_t y;
    int32_t z;
    int32_t w;

    XMINT4() {}
    XMINT4(int32_t _x, int32_t _y, int32_t _z, int32_t _w) : x(_x), y(_y), z(_z), w(_w) {}
    explicit XMINT4(_In_reads_(4) const int32_t *pArray) : x(pArray[0]), y(pArray[1]), z(pArray[2]), w(pArray[3]) {}

    XMINT4& operator= (const XMINT4& Int4) { x = Int4.x; y = Int4.y; z = Int4.z; w = Int4.w; return *this; }
};

// 4D Vector; 32 bit unsigned integer components
struct XMUINT4
{
    uint32_t x;
    uint32_t y;
    uint32_t z;
    uint32_t w;

    XMUINT4() {}
    XMUINT4(uint32_t _x, uint32_t _y, uint32_t _z, uint32_t _w) : x(_x), y(_y), z(_z), w(_w) {}
    explicit XMUINT4(_In_reads_(4) const uint32_t *pArray) : x(pArray[0]), y(pArray[1]), z(pArray[2]), w(pArray[3]) {}

    XMUINT4& operator= (const XMUINT4& UInt4) { x = UInt4.x; y = UInt4.y; z = UInt4.z; w = UInt4.w; return *this; }
};

//------------------------------------------------------------------------------
// 3x3 Matrix: 32 bit floating point components
struct XMFLOAT3X3
{
    union
    {
        struct
        {
            float _11, _12, _13;
            float _21, _22, _23;
            float _31, _32, _33;
        };
        float m[3][3];
    };

    XMFLOAT3X3() {}
    XMFLOAT3X3(float m00, float m01, float m02,
                float m10, float m11, float m12,
                float m20, float m21, float m22);
    explicit XMFLOAT3X3(_In_reads_(9) const float *pArray);

    float       operator() (size_t Row, size_t Column) const { return m[Row][Column]; }
    float&      operator() (size_t Row, size_t Column) { return m[Row][Column]; }

    XMFLOAT3X3& operator= (const XMFLOAT3X3& Float3x3);
};

//------------------------------------------------------------------------------
// 4x3 Matrix: 32 bit floating point components
struct XMFLOAT4X3
{
    union
    {
        struct
        {
            float _11, _12, _13;
            float _21, _22, _23;
            float _31, _32, _33;
            float _41, _42, _43;
        };
        float m[4][3];
    };

    XMFLOAT4X3() {}
    XMFLOAT4X3(float m00, float m01, float m02,
                float m10, float m11, float m12,
                float m20, float m21, float m22,
                float m30, float m31, float m32);
    explicit XMFLOAT4X3(_In_reads_(12) const float *pArray);

    float       operator() (size_t Row, size_t Column) const { return m[Row][Column]; }
    float&      operator() (size_t Row, size_t Column) { return m[Row][Column]; }

    XMFLOAT4X3& operator= (const XMFLOAT4X3& Float4x3);

};

// 4x3 Matrix: 32 bit floating point components aligned on a 16 byte boundary
__declspec(align(16)) struct XMFLOAT4X3A : public XMFLOAT4X3
{
    XMFLOAT4X3A() : XMFLOAT4X3() {}
    XMFLOAT4X3A(float m00, float m01, float m02,
                float m10, float m11, float m12,
                float m20, float m21, float m22,
                float m30, float m31, float m32) :
        XMFLOAT4X3(m00,m01,m02,m10,m11,m12,m20,m21,m22,m30,m31,m32) {}
    explicit XMFLOAT4X3A(_In_reads_(12) const float *pArray) : XMFLOAT4X3(pArray) {}

    float       operator() (size_t Row, size_t Column) const { return m[Row][Column]; }
    float&      operator() (size_t Row, size_t Column) { return m[Row][Column]; }

    XMFLOAT4X3A& operator= (const XMFLOAT4X3A& Float4x3);
};

//------------------------------------------------------------------------------
// 4x4 Matrix: 32 bit floating point components
struct XMFLOAT4X4
{
    union
    {
        struct
        {
            float _11, _12, _13, _14;
            float _21, _22, _23, _24;
            float _31, _32, _33, _34;
            float _41, _42, _43, _44;
        };
        float m[4][4];
    };

    XMFLOAT4X4() {}
    XMFLOAT4X4(float m00, float m01, float m02, float m03,
                float m10, float m11, float m12, float m13,
                float m20, float m21, float m22, float m23,
                float m30, float m31, float m32, float m33);
    explicit XMFLOAT4X4(_In_reads_(16) const float *pArray);

    float       operator() (size_t Row, size_t Column) const { return m[Row][Column]; }
    float&      operator() (size_t Row, size_t Column) { return m[Row][Column]; }

    XMFLOAT4X4& operator= (const XMFLOAT4X4& Float4x4);
};

// 4x4 Matrix: 32 bit floating point components aligned on a 16 byte boundary
__declspec(align(16)) struct XMFLOAT4X4A : public XMFLOAT4X4
{
    XMFLOAT4X4A() : XMFLOAT4X4() {}
    XMFLOAT4X4A(float m00, float m01, float m02, float m03,
                float m10, float m11, float m12, float m13,
                float m20, float m21, float m22, float m23,
                float m30, float m31, float m32, float m33)
        : XMFLOAT4X4(m00,m01,m02,m03,m10,m11,m12,m13,m20,m21,m22,m23,m30,m31,m32,m33) {}
    explicit XMFLOAT4X4A(_In_reads_(16) const float *pArray) : XMFLOAT4X4(pArray) {}

    float       operator() (size_t Row, size_t Column) const { return m[Row][Column]; }
    float&      operator() (size_t Row, size_t Column) { return m[Row][Column]; }

    XMFLOAT4X4A& operator= (const XMFLOAT4X4A& Float4x4);
};

////////////////////////////////////////////////////////////////////////////////


#ifdef _XM_BIGENDIAN_
#pragma bitfield_order(pop)
#endif

#pragma prefast(pop)
#pragma warning(pop)

/****************************************************************************
 *
 * Data conversion operations
 *
 ****************************************************************************/

#if !defined(_XM_NO_INTRINSICS_) && defined(_XM_VMX128_INTRINSICS_)
#else
XMVECTOR        XMConvertVectorIntToFloat(FXMVECTOR VInt, uint32_t DivExponent);
XMVECTOR        XMConvertVectorFloatToInt(FXMVECTOR VFloat, uint32_t MulExponent);
XMVECTOR        XMConvertVectorUIntToFloat(FXMVECTOR VUInt, uint32_t DivExponent);
XMVECTOR        XMConvertVectorFloatToUInt(FXMVECTOR VFloat, uint32_t MulExponent);
#endif

#if !defined(_XM_NO_INTRINSICS_) && defined(_XM_VMX128_INTRINSICS_)
#else

#if defined(__XNAMATH_H__) && defined(XMVectorSetBinaryConstant)
#undef XMVectorSetBinaryConstant
#undef XMVectorSplatConstant
#undef XMVectorSplatConstantInt
#endif

XMVECTOR XMVectorSetBinaryConstant(uint32_t C0, uint32_t C1, uint32_t C2, uint32_t C3);
XMVECTOR XMVectorSplatConstant(int32_t IntConstant, uint32_t DivExponent);
XMVECTOR XMVectorSplatConstantInt(int32_t IntConstant);
#endif

/****************************************************************************
 *
 * Load operations
 *
 ****************************************************************************/

XMVECTOR        XMLoadInt(_In_ const uint32_t* pSource);
XMVECTOR        XMLoadFloat(_In_ const float* pSource);

XMVECTOR        XMLoadInt2(_In_reads_(2) const uint32_t* pSource);
XMVECTOR        XMLoadInt2A(_In_reads_(2) const uint32_t* PSource);
XMVECTOR        XMLoadFloat2(_In_ const XMFLOAT2* pSource);
XMVECTOR        XMLoadFloat2A(_In_ const XMFLOAT2A* pSource);
XMVECTOR        XMLoadSInt2(_In_ const XMINT2* pSource);
XMVECTOR        XMLoadUInt2(_In_ const XMUINT2* pSource);

XMVECTOR        XMLoadInt3(_In_reads_(3) const uint32_t* pSource);
XMVECTOR        XMLoadInt3A(_In_reads_(3) const uint32_t* pSource);
XMVECTOR        XMLoadFloat3(_In_ const XMFLOAT3* pSource);
XMVECTOR        XMLoadFloat3A(_In_ const XMFLOAT3A* pSource);
XMVECTOR        XMLoadSInt3(_In_ const XMINT3* pSource);
XMVECTOR        XMLoadUInt3(_In_ const XMUINT3* pSource);

XMVECTOR        XMLoadInt4(_In_reads_(4) const uint32_t* pSource);
XMVECTOR        XMLoadInt4A(_In_reads_(4) const uint32_t* pSource);
XMVECTOR        XMLoadFloat4(_In_ const XMFLOAT4* pSource);
XMVECTOR        XMLoadFloat4A(_In_ const XMFLOAT4A* pSource);
XMVECTOR        XMLoadSInt4(_In_ const XMINT4* pSource);
XMVECTOR        XMLoadUInt4(_In_ const XMUINT4* pSource);

XMMATRIX        XMLoadFloat3x3(_In_ const XMFLOAT3X3* pSource);
XMMATRIX        XMLoadFloat4x3(_In_ const XMFLOAT4X3* pSource);
XMMATRIX        XMLoadFloat4x3A(_In_ const XMFLOAT4X3A* pSource);
XMMATRIX        XMLoadFloat4x4(_In_ const XMFLOAT4X4* pSource);
XMMATRIX        XMLoadFloat4x4A(_In_ const XMFLOAT4X4A* pSource);

/****************************************************************************
 *
 * Store operations
 *
 ****************************************************************************/

void            XMStoreInt(_Out_ uint32_t* pDestination, _In_ FXMVECTOR V);
void            XMStoreFloat(_Out_ float* pDestination, _In_ FXMVECTOR V);

void            XMStoreInt2(_Out_writes_(2) uint32_t* pDestination, _In_ FXMVECTOR V);
void            XMStoreInt2A(_Out_writes_(2) uint32_t* pDestination, _In_ FXMVECTOR V);
void            XMStoreFloat2(_Out_ XMFLOAT2* pDestination, _In_ FXMVECTOR V);
void            XMStoreFloat2A(_Out_ XMFLOAT2A* pDestination, _In_ FXMVECTOR V);
void            XMStoreSInt2(_Out_ XMINT2* pDestination, _In_ FXMVECTOR V);
void            XMStoreUInt2(_Out_ XMUINT2* pDestination, _In_ FXMVECTOR V);

void            XMStoreInt3(_Out_writes_(3) uint32_t* pDestination, _In_ FXMVECTOR V);
void            XMStoreInt3A(_Out_writes_(3) uint32_t* pDestination, _In_ FXMVECTOR V);
void            XMStoreFloat3(_Out_ XMFLOAT3* pDestination, _In_ FXMVECTOR V);
void            XMStoreFloat3A(_Out_ XMFLOAT3A* pDestination, _In_ FXMVECTOR V);
void            XMStoreSInt3(_Out_ XMINT3* pDestination, _In_ FXMVECTOR V);
void            XMStoreUInt3(_Out_ XMUINT3* pDestination, _In_ FXMVECTOR V);

void            XMStoreInt4(_Out_writes_(4) uint32_t* pDestination, _In_ FXMVECTOR V);
void            XMStoreInt4A(_Out_writes_(4) uint32_t* pDestination, _In_ FXMVECTOR V);
void            XMStoreFloat4(_Out_ XMFLOAT4* pDestination, _In_ FXMVECTOR V);
void            XMStoreFloat4A(_Out_ XMFLOAT4A* pDestination, _In_ FXMVECTOR V);
void            XMStoreSInt4(_Out_ XMINT4* pDestination, _In_ FXMVECTOR V);
void            XMStoreUInt4(_Out_ XMUINT4* pDestination, _In_ FXMVECTOR V);

void            XMStoreFloat3x3(_Out_ XMFLOAT3X3* pDestination, _In_ CXMMATRIX M);
void            XMStoreFloat4x3(_Out_ XMFLOAT4X3* pDestination, _In_ CXMMATRIX M);
void            XMStoreFloat4x3A(_Out_ XMFLOAT4X3A* pDestination, _In_ CXMMATRIX M);
void            XMStoreFloat4x4(_Out_ XMFLOAT4X4* pDestination, _In_ CXMMATRIX M);
void            XMStoreFloat4x4A(_Out_ XMFLOAT4X4A* pDestination, _In_ CXMMATRIX M);

/****************************************************************************
 *
 * General vector operations
 *
 ****************************************************************************/

XMVECTOR        XMVectorZero();
XMVECTOR        XMVectorSet(float x, float y, float z, float w);
XMVECTOR        XMVectorSetInt(uint32_t x, uint32_t y, uint32_t z, uint32_t w);
XMVECTOR        XMVectorReplicate(float Value);
XMVECTOR        XMVectorReplicatePtr(_In_ const float *pValue);
XMVECTOR        XMVectorReplicateInt(uint32_t Value);
XMVECTOR        XMVectorReplicateIntPtr(_In_ const uint32_t *pValue);
XMVECTOR        XMVectorTrueInt();
XMVECTOR        XMVectorFalseInt();
XMVECTOR        XMVectorSplatX(FXMVECTOR V);
XMVECTOR        XMVectorSplatY(FXMVECTOR V);
XMVECTOR        XMVectorSplatZ(FXMVECTOR V);
XMVECTOR        XMVectorSplatW(FXMVECTOR V);
XMVECTOR        XMVectorSplatOne();
XMVECTOR        XMVectorSplatInfinity();
XMVECTOR        XMVectorSplatQNaN();
XMVECTOR        XMVectorSplatEpsilon();
XMVECTOR        XMVectorSplatSignMask();

float           XMVectorGetByIndex(FXMVECTOR V, size_t i);
float           XMVectorGetX(FXMVECTOR V);
float           XMVectorGetY(FXMVECTOR V);
float           XMVectorGetZ(FXMVECTOR V);
float           XMVectorGetW(FXMVECTOR V);

void            XMVectorGetByIndexPtr(_Out_ float *f, _In_ FXMVECTOR V, _In_ size_t i);
void            XMVectorGetXPtr(_Out_ float *x, _In_ FXMVECTOR V);
void            XMVectorGetYPtr(_Out_ float *y, _In_ FXMVECTOR V);
void            XMVectorGetZPtr(_Out_ float *z, _In_ FXMVECTOR V);
void            XMVectorGetWPtr(_Out_ float *w, _In_ FXMVECTOR V);

uint32_t        XMVectorGetIntByIndex(FXMVECTOR V, size_t i);
uint32_t        XMVectorGetIntX(FXMVECTOR V);
uint32_t        XMVectorGetIntY(FXMVECTOR V);
uint32_t        XMVectorGetIntZ(FXMVECTOR V);
uint32_t        XMVectorGetIntW(FXMVECTOR V);

void            XMVectorGetIntByIndexPtr(_Out_ uint32_t *x, _In_ FXMVECTOR V, _In_ size_t i);
void            XMVectorGetIntXPtr(_Out_ uint32_t *x, _In_ FXMVECTOR V);
void            XMVectorGetIntYPtr(_Out_ uint32_t *y, _In_ FXMVECTOR V);
void            XMVectorGetIntZPtr(_Out_ uint32_t *z, _In_ FXMVECTOR V);
void            XMVectorGetIntWPtr(_Out_ uint32_t *w, _In_ FXMVECTOR V);

XMVECTOR        XMVectorSetByIndex(FXMVECTOR V,float f, size_t i);
XMVECTOR        XMVectorSetX(FXMVECTOR V, float x);
XMVECTOR        XMVectorSetY(FXMVECTOR V, float y);
XMVECTOR        XMVectorSetZ(FXMVECTOR V, float z);
XMVECTOR        XMVectorSetW(FXMVECTOR V, float w);

XMVECTOR        XMVectorSetByIndexPtr(_In_ FXMVECTOR V, _In_ const float *f, _In_ size_t i);
XMVECTOR        XMVectorSetXPtr(_In_ FXMVECTOR V, _In_ const float *x);
XMVECTOR        XMVectorSetYPtr(_In_ FXMVECTOR V, _In_ const float *y);
XMVECTOR        XMVectorSetZPtr(_In_ FXMVECTOR V, _In_ const float *z);
XMVECTOR        XMVectorSetWPtr(_In_ FXMVECTOR V, _In_ const float *w);

XMVECTOR        XMVectorSetIntByIndex(FXMVECTOR V, uint32_t x, size_t i);
XMVECTOR        XMVectorSetIntX(FXMVECTOR V, uint32_t x);
XMVECTOR        XMVectorSetIntY(FXMVECTOR V, uint32_t y);
XMVECTOR        XMVectorSetIntZ(FXMVECTOR V, uint32_t z);
XMVECTOR        XMVectorSetIntW(FXMVECTOR V, uint32_t w);

XMVECTOR        XMVectorSetIntByIndexPtr(_In_ FXMVECTOR V, _In_ const uint32_t *x, _In_ size_t i);
XMVECTOR        XMVectorSetIntXPtr(_In_ FXMVECTOR V, _In_ const uint32_t *x);
XMVECTOR        XMVectorSetIntYPtr(_In_ FXMVECTOR V, _In_ const uint32_t *y);
XMVECTOR        XMVectorSetIntZPtr(_In_ FXMVECTOR V, _In_ const uint32_t *z);
XMVECTOR        XMVectorSetIntWPtr(_In_ FXMVECTOR V, _In_ const uint32_t *w);

#if defined(__XNAMATH_H__) && defined(XMVectorSwizzle)
#undef XMVectorSwizzle
#endif

XMVECTOR        XMVectorSwizzle(FXMVECTOR V, uint32_t E0, uint32_t E1, uint32_t E2, uint32_t E3);
XMVECTOR        XMVectorPermute(FXMVECTOR V1, FXMVECTOR V2, uint32_t PermuteX, uint32_t PermuteY, uint32_t PermuteZ, uint32_t PermuteW);
XMVECTOR        XMVectorSelectControl(uint32_t VectorIndex0, uint32_t VectorIndex1, uint32_t VectorIndex2, uint32_t VectorIndex3);
XMVECTOR        XMVectorSelect(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR Control);
XMVECTOR        XMVectorMergeXY(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorMergeZW(FXMVECTOR V1, FXMVECTOR V2);

#if defined(__XNAMATH_H__) && defined(XMVectorShiftLeft)
#undef XMVectorShiftLeft
#undef XMVectorRotateLeft
#undef XMVectorRotateRight
#undef XMVectorInsert
#endif

XMVECTOR XMVectorShiftLeft(FXMVECTOR V1, FXMVECTOR V2, uint32_t Elements);
XMVECTOR XMVectorRotateLeft(FXMVECTOR V, uint32_t Elements);
XMVECTOR XMVectorRotateRight(FXMVECTOR V, uint32_t Elements);
XMVECTOR XMVectorInsert(FXMVECTOR VD, FXMVECTOR VS, uint32_t VSLeftRotateElements,
                        uint32_t Select0, uint32_t Select1, uint32_t Select2, uint32_t Select3);

XMVECTOR        XMVectorEqual(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorEqualR(_Out_ uint32_t* pCR, _In_ FXMVECTOR V1, _In_ FXMVECTOR V2);
XMVECTOR        XMVectorEqualInt(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorEqualIntR(_Out_ uint32_t* pCR, _In_ FXMVECTOR V, _In_ FXMVECTOR V2);
XMVECTOR        XMVectorNearEqual(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR Epsilon);
XMVECTOR        XMVectorNotEqual(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorNotEqualInt(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorGreater(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorGreaterR(_Out_ uint32_t* pCR, _In_ FXMVECTOR V1, _In_ FXMVECTOR V2);
XMVECTOR        XMVectorGreaterOrEqual(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorGreaterOrEqualR(_Out_ uint32_t* pCR, _In_ FXMVECTOR V1, _In_ FXMVECTOR V2);
XMVECTOR        XMVectorLess(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorLessOrEqual(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorInBounds(FXMVECTOR V, FXMVECTOR Bounds);
XMVECTOR        XMVectorInBoundsR(_Out_ uint32_t* pCR, _In_ FXMVECTOR V, _In_ FXMVECTOR Bounds);

XMVECTOR        XMVectorIsNaN(FXMVECTOR V);
XMVECTOR        XMVectorIsInfinite(FXMVECTOR V);

XMVECTOR        XMVectorMin(FXMVECTOR V1,FXMVECTOR V2);
XMVECTOR        XMVectorMax(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorRound(FXMVECTOR V);
XMVECTOR        XMVectorTruncate(FXMVECTOR V);
XMVECTOR        XMVectorFloor(FXMVECTOR V);
XMVECTOR        XMVectorCeiling(FXMVECTOR V);
XMVECTOR        XMVectorClamp(FXMVECTOR V, FXMVECTOR Min, FXMVECTOR Max);
XMVECTOR        XMVectorSaturate(FXMVECTOR V);

XMVECTOR        XMVectorAndInt(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorAndCInt(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorOrInt(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorNorInt(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorXorInt(FXMVECTOR V1, FXMVECTOR V2);

XMVECTOR        XMVectorNegate(FXMVECTOR V);
XMVECTOR        XMVectorAdd(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorAddAngles(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorSubtract(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorSubtractAngles(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorMultiply(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorMultiplyAdd(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR V3);
XMVECTOR        XMVectorDivide(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorNegativeMultiplySubtract(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR V3);
XMVECTOR        XMVectorScale(FXMVECTOR V, float ScaleFactor);
XMVECTOR        XMVectorReciprocalEst(FXMVECTOR V);
XMVECTOR        XMVectorReciprocal(FXMVECTOR V);
XMVECTOR        XMVectorSqrtEst(FXMVECTOR V);
XMVECTOR        XMVectorSqrt(FXMVECTOR V);
XMVECTOR        XMVectorReciprocalSqrtEst(FXMVECTOR V);
XMVECTOR        XMVectorReciprocalSqrt(FXMVECTOR V);
XMVECTOR        XMVectorExp(FXMVECTOR V);
XMVECTOR        XMVectorLog(FXMVECTOR V);
XMVECTOR        XMVectorPow(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorAbs(FXMVECTOR V);
XMVECTOR        XMVectorMod(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVectorModAngles(FXMVECTOR Angles);
XMVECTOR        XMVectorSin(FXMVECTOR V);
XMVECTOR        XMVectorSinEst(FXMVECTOR V);
XMVECTOR        XMVectorCos(FXMVECTOR V);
XMVECTOR        XMVectorCosEst(FXMVECTOR V);
void            XMVectorSinCos(_Out_ XMVECTOR* pSin, _Out_ XMVECTOR* pCos, _In_ FXMVECTOR V);
void            XMVectorSinCosEst(_Out_ XMVECTOR* pSin, _Out_ XMVECTOR* pCos, _In_ FXMVECTOR V);
XMVECTOR        XMVectorTan(FXMVECTOR V);
XMVECTOR        XMVectorTanEst(FXMVECTOR V);
XMVECTOR        XMVectorSinH(FXMVECTOR V);
XMVECTOR        XMVectorCosH(FXMVECTOR V);
XMVECTOR        XMVectorTanH(FXMVECTOR V);
XMVECTOR        XMVectorASin(FXMVECTOR V);
XMVECTOR        XMVectorASinEst(FXMVECTOR V);
XMVECTOR        XMVectorACos(FXMVECTOR V);
XMVECTOR        XMVectorACosEst(FXMVECTOR V);
XMVECTOR        XMVectorATan(FXMVECTOR V);
XMVECTOR        XMVectorATanEst(FXMVECTOR V);
XMVECTOR        XMVectorATan2(FXMVECTOR Y, FXMVECTOR X);
XMVECTOR        XMVectorATan2Est(FXMVECTOR Y, FXMVECTOR X);
XMVECTOR        XMVectorLerp(FXMVECTOR V0, FXMVECTOR V1, float t);
XMVECTOR        XMVectorLerpV(FXMVECTOR V0, FXMVECTOR V1, FXMVECTOR T);
XMVECTOR        XMVectorHermite(FXMVECTOR Position0, FXMVECTOR Tangent0, FXMVECTOR Position1, GXMVECTOR Tangent1, float t);
XMVECTOR        XMVectorHermiteV(FXMVECTOR Position0, FXMVECTOR Tangent0, FXMVECTOR Position1, GXMVECTOR Tangent1, CXMVECTOR T);
XMVECTOR        XMVectorCatmullRom(FXMVECTOR Position0, FXMVECTOR Position1, FXMVECTOR Position2, GXMVECTOR Position3, float t);
XMVECTOR        XMVectorCatmullRomV(FXMVECTOR Position0, FXMVECTOR Position1, FXMVECTOR Position2, GXMVECTOR Position3, CXMVECTOR T);
XMVECTOR        XMVectorBaryCentric(FXMVECTOR Position0, FXMVECTOR Position1, FXMVECTOR Position2, float f, float g);
XMVECTOR        XMVectorBaryCentricV(FXMVECTOR Position0, FXMVECTOR Position1, FXMVECTOR Position2, GXMVECTOR F, CXMVECTOR G);

/****************************************************************************
 *
 * 2D vector operations
 *
 ****************************************************************************/

bool            XMVector2Equal(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector2EqualR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2EqualInt(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector2EqualIntR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2NearEqual(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR Epsilon);
bool            XMVector2NotEqual(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2NotEqualInt(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2Greater(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector2GreaterR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2GreaterOrEqual(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector2GreaterOrEqualR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2Less(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2LessOrEqual(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector2InBounds(FXMVECTOR V, FXMVECTOR Bounds);

bool            XMVector2IsNaN(FXMVECTOR V);
bool            XMVector2IsInfinite(FXMVECTOR V);

XMVECTOR        XMVector2Dot(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector2Cross(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector2LengthSq(FXMVECTOR V);
XMVECTOR        XMVector2ReciprocalLengthEst(FXMVECTOR V);
XMVECTOR        XMVector2ReciprocalLength(FXMVECTOR V);
XMVECTOR        XMVector2LengthEst(FXMVECTOR V);
XMVECTOR        XMVector2Length(FXMVECTOR V);
XMVECTOR        XMVector2NormalizeEst(FXMVECTOR V);
XMVECTOR        XMVector2Normalize(FXMVECTOR V);
XMVECTOR        XMVector2ClampLength(FXMVECTOR V, float LengthMin, float LengthMax);
XMVECTOR        XMVector2ClampLengthV(FXMVECTOR V, FXMVECTOR LengthMin, FXMVECTOR LengthMax);
XMVECTOR        XMVector2Reflect(FXMVECTOR Incident, FXMVECTOR Normal);
XMVECTOR        XMVector2Refract(FXMVECTOR Incident, FXMVECTOR Normal, float RefractionIndex);
XMVECTOR        XMVector2RefractV(FXMVECTOR Incident, FXMVECTOR Normal, FXMVECTOR RefractionIndex);
XMVECTOR        XMVector2Orthogonal(FXMVECTOR V);
XMVECTOR        XMVector2AngleBetweenNormalsEst(FXMVECTOR N1, FXMVECTOR N2);
XMVECTOR        XMVector2AngleBetweenNormals(FXMVECTOR N1, FXMVECTOR N2);
XMVECTOR        XMVector2AngleBetweenVectors(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector2LinePointDistance(FXMVECTOR LinePoint1, FXMVECTOR LinePoint2, FXMVECTOR Point);
XMVECTOR        XMVector2IntersectLine(FXMVECTOR Line1Point1, FXMVECTOR Line1Point2, FXMVECTOR Line2Point1, GXMVECTOR Line2Point2);
XMVECTOR        XMVector2Transform(FXMVECTOR V, CXMMATRIX M);
XMFLOAT4*       XMVector2TransformStream(_Out_writes_bytes_(sizeof(XMFLOAT4)+OutputStride*(VectorCount-1)) XMFLOAT4* pOutputStream,
                                         _In_ size_t OutputStride,
                                         _In_reads_bytes_(sizeof(XMFLOAT2)+InputStride*(VectorCount-1)) const XMFLOAT2* pInputStream,
                                         _In_ size_t InputStride, _In_ size_t VectorCount, _In_ CXMMATRIX M);
XMVECTOR        XMVector2TransformCoord(FXMVECTOR V, CXMMATRIX M);
XMFLOAT2*       XMVector2TransformCoordStream(_Out_writes_bytes_(sizeof(XMFLOAT2)+OutputStride*(VectorCount-1)) XMFLOAT2* pOutputStream,
                                              _In_ size_t OutputStride,
                                              _In_reads_bytes_(sizeof(XMFLOAT2)+InputStride*(VectorCount-1)) const XMFLOAT2* pInputStream,
                                              _In_ size_t InputStride, _In_ size_t VectorCount, _In_ CXMMATRIX M);
XMVECTOR        XMVector2TransformNormal(FXMVECTOR V, CXMMATRIX M);
XMFLOAT2*       XMVector2TransformNormalStream(_Out_writes_bytes_(sizeof(XMFLOAT2)+OutputStride*(VectorCount-1)) XMFLOAT2* pOutputStream,
                                               _In_ size_t OutputStride,
                                               _In_reads_bytes_(sizeof(XMFLOAT2)+InputStride*(VectorCount-1)) const XMFLOAT2* pInputStream,
                                               _In_ size_t InputStride, _In_ size_t VectorCount, _In_ CXMMATRIX M);

/****************************************************************************
 *
 * 3D vector operations
 *
 ****************************************************************************/

bool            XMVector3Equal(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector3EqualR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3EqualInt(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector3EqualIntR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3NearEqual(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR Epsilon);
bool            XMVector3NotEqual(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3NotEqualInt(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3Greater(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector3GreaterR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3GreaterOrEqual(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector3GreaterOrEqualR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3Less(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3LessOrEqual(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector3InBounds(FXMVECTOR V, FXMVECTOR Bounds);

bool            XMVector3IsNaN(FXMVECTOR V);
bool            XMVector3IsInfinite(FXMVECTOR V);

XMVECTOR        XMVector3Dot(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector3Cross(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector3LengthSq(FXMVECTOR V);
XMVECTOR        XMVector3ReciprocalLengthEst(FXMVECTOR V);
XMVECTOR        XMVector3ReciprocalLength(FXMVECTOR V);
XMVECTOR        XMVector3LengthEst(FXMVECTOR V);
XMVECTOR        XMVector3Length(FXMVECTOR V);
XMVECTOR        XMVector3NormalizeEst(FXMVECTOR V);
XMVECTOR        XMVector3Normalize(FXMVECTOR V);
XMVECTOR        XMVector3ClampLength(FXMVECTOR V, float LengthMin, float LengthMax);
XMVECTOR        XMVector3ClampLengthV(FXMVECTOR V, FXMVECTOR LengthMin, FXMVECTOR LengthMax);
XMVECTOR        XMVector3Reflect(FXMVECTOR Incident, FXMVECTOR Normal);
XMVECTOR        XMVector3Refract(FXMVECTOR Incident, FXMVECTOR Normal, float RefractionIndex);
XMVECTOR        XMVector3RefractV(FXMVECTOR Incident, FXMVECTOR Normal, FXMVECTOR RefractionIndex);
XMVECTOR        XMVector3Orthogonal(FXMVECTOR V);
XMVECTOR        XMVector3AngleBetweenNormalsEst(FXMVECTOR N1, FXMVECTOR N2);
XMVECTOR        XMVector3AngleBetweenNormals(FXMVECTOR N1, FXMVECTOR N2);
XMVECTOR        XMVector3AngleBetweenVectors(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector3LinePointDistance(FXMVECTOR LinePoint1, FXMVECTOR LinePoint2, FXMVECTOR Point);
void            XMVector3ComponentsFromNormal(_Out_ XMVECTOR* pParallel, _Out_ XMVECTOR* pPerpendicular, _In_ FXMVECTOR V, _In_ FXMVECTOR Normal);
XMVECTOR        XMVector3Rotate(FXMVECTOR V, FXMVECTOR RotationQuaternion);
XMVECTOR        XMVector3InverseRotate(FXMVECTOR V, FXMVECTOR RotationQuaternion);
XMVECTOR        XMVector3Transform(FXMVECTOR V, CXMMATRIX M);
XMFLOAT4*       XMVector3TransformStream(_Out_writes_bytes_(sizeof(XMFLOAT4)+OutputStride*(VectorCount-1)) XMFLOAT4* pOutputStream,
                                         _In_ size_t OutputStride,
                                         _In_reads_bytes_(sizeof(XMFLOAT3)+InputStride*(VectorCount-1)) const XMFLOAT3* pInputStream,
                                         _In_ size_t InputStride, _In_ size_t VectorCount, _In_ CXMMATRIX M);
XMVECTOR        XMVector3TransformCoord(FXMVECTOR V, CXMMATRIX M);
XMFLOAT3*       XMVector3TransformCoordStream(_Out_writes_bytes_(sizeof(XMFLOAT3)+OutputStride*(VectorCount-1)) XMFLOAT3* pOutputStream,
                                              _In_ size_t OutputStride,
                                              _In_reads_bytes_(sizeof(XMFLOAT3)+InputStride*(VectorCount-1)) const XMFLOAT3* pInputStream,
                                              _In_ size_t InputStride, _In_ size_t VectorCount, _In_ CXMMATRIX M);
XMVECTOR        XMVector3TransformNormal(FXMVECTOR V, CXMMATRIX M);
XMFLOAT3*       XMVector3TransformNormalStream(_Out_writes_bytes_(sizeof(XMFLOAT3)+OutputStride*(VectorCount-1)) XMFLOAT3* pOutputStream,
                                               _In_ size_t OutputStride,
                                               _In_reads_bytes_(sizeof(XMFLOAT3)+InputStride*(VectorCount-1)) const XMFLOAT3* pInputStream,
                                               _In_ size_t InputStride, _In_ size_t VectorCount, _In_ CXMMATRIX M);
XMVECTOR        XMVector3Project(FXMVECTOR V, float ViewportX, float ViewportY, float ViewportWidth, float ViewportHeight, float ViewportMinZ, float ViewportMaxZ, 
                                 CXMMATRIX Projection, CXMMATRIX View, CXMMATRIX World);
XMFLOAT3*       XMVector3ProjectStream(_Out_writes_bytes_(sizeof(XMFLOAT3)+OutputStride*(VectorCount-1)) XMFLOAT3* pOutputStream,
                                       _In_ size_t OutputStride,
                                       _In_reads_bytes_(sizeof(XMFLOAT3)+InputStride*(VectorCount-1)) const XMFLOAT3* pInputStream,
                                       _In_ size_t InputStride, _In_ size_t VectorCount, 
                                       _In_ float ViewportX, _In_ float ViewportY, _In_ float ViewportWidth, _In_ float ViewportHeight, _In_ float ViewportMinZ, _In_ float ViewportMaxZ, 
                                       _In_ CXMMATRIX Projection, _In_ CXMMATRIX View, _In_ CXMMATRIX World);
XMVECTOR        XMVector3Unproject(FXMVECTOR V, float ViewportX, float ViewportY, float ViewportWidth, float ViewportHeight, float ViewportMinZ, float ViewportMaxZ, 
                                   CXMMATRIX Projection, CXMMATRIX View, CXMMATRIX World);
XMFLOAT3*       XMVector3UnprojectStream(_Out_writes_bytes_(sizeof(XMFLOAT3)+OutputStride*(VectorCount-1)) XMFLOAT3* pOutputStream,
                                         _In_ size_t OutputStride,
                                         _In_reads_bytes_(sizeof(XMFLOAT3)+InputStride*(VectorCount-1)) const XMFLOAT3* pInputStream,
                                         _In_ size_t InputStride, _In_ size_t VectorCount, 
                                         _In_ float ViewportX, _In_ float ViewportY, _In_ float ViewportWidth, _In_ float ViewportHeight, _In_ float ViewportMinZ, _In_ float ViewportMaxZ, 
                                         _In_ CXMMATRIX Projection, _In_ CXMMATRIX View, _In_ CXMMATRIX World);

/****************************************************************************
 *
 * 4D vector operations
 *
 ****************************************************************************/

bool            XMVector4Equal(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector4EqualR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4EqualInt(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector4EqualIntR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4NearEqual(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR Epsilon);
bool            XMVector4NotEqual(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4NotEqualInt(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4Greater(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector4GreaterR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4GreaterOrEqual(FXMVECTOR V1, FXMVECTOR V2);
uint32_t        XMVector4GreaterOrEqualR(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4Less(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4LessOrEqual(FXMVECTOR V1, FXMVECTOR V2);
bool            XMVector4InBounds(FXMVECTOR V, FXMVECTOR Bounds);

bool            XMVector4IsNaN(FXMVECTOR V);
bool            XMVector4IsInfinite(FXMVECTOR V);

XMVECTOR        XMVector4Dot(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector4Cross(FXMVECTOR V1, FXMVECTOR V2, FXMVECTOR V3);
XMVECTOR        XMVector4LengthSq(FXMVECTOR V);
XMVECTOR        XMVector4ReciprocalLengthEst(FXMVECTOR V);
XMVECTOR        XMVector4ReciprocalLength(FXMVECTOR V);
XMVECTOR        XMVector4LengthEst(FXMVECTOR V);
XMVECTOR        XMVector4Length(FXMVECTOR V);
XMVECTOR        XMVector4NormalizeEst(FXMVECTOR V);
XMVECTOR        XMVector4Normalize(FXMVECTOR V);
XMVECTOR        XMVector4ClampLength(FXMVECTOR V, float LengthMin, float LengthMax);
XMVECTOR        XMVector4ClampLengthV(FXMVECTOR V, FXMVECTOR LengthMin, FXMVECTOR LengthMax);
XMVECTOR        XMVector4Reflect(FXMVECTOR Incident, FXMVECTOR Normal);
XMVECTOR        XMVector4Refract(FXMVECTOR Incident, FXMVECTOR Normal, float RefractionIndex);
XMVECTOR        XMVector4RefractV(FXMVECTOR Incident, FXMVECTOR Normal, FXMVECTOR RefractionIndex);
XMVECTOR        XMVector4Orthogonal(FXMVECTOR V);
XMVECTOR        XMVector4AngleBetweenNormalsEst(FXMVECTOR N1, FXMVECTOR N2);
XMVECTOR        XMVector4AngleBetweenNormals(FXMVECTOR N1, FXMVECTOR N2);
XMVECTOR        XMVector4AngleBetweenVectors(FXMVECTOR V1, FXMVECTOR V2);
XMVECTOR        XMVector4Transform(FXMVECTOR V, CXMMATRIX M);
XMFLOAT4*       XMVector4TransformStream(_Out_writes_bytes_(sizeof(XMFLOAT4)+OutputStride*(VectorCount-1)) XMFLOAT4* pOutputStream,
                                         _In_ size_t OutputStride,
                                         _In_reads_bytes_(sizeof(XMFLOAT4)+InputStride*(VectorCount-1)) const XMFLOAT4* pInputStream,
                                         _In_ size_t InputStride, _In_ size_t VectorCount, _In_ CXMMATRIX M);

/****************************************************************************
 *
 * Matrix operations
 *
 ****************************************************************************/

bool            XMMatrixIsNaN(CXMMATRIX M);
bool            XMMatrixIsInfinite(CXMMATRIX M);
bool            XMMatrixIsIdentity(CXMMATRIX M);

XMMATRIX        XMMatrixMultiply(CXMMATRIX M1, CXMMATRIX M2);
XMMATRIX        XMMatrixMultiplyTranspose(CXMMATRIX M1, CXMMATRIX M2);
XMMATRIX        XMMatrixTranspose(CXMMATRIX M);
XMMATRIX        XMMatrixInverse(_Out_opt_ XMVECTOR* pDeterminant, _In_ CXMMATRIX M);
XMVECTOR        XMMatrixDeterminant(CXMMATRIX M);
_Success_(return)
bool            XMMatrixDecompose(_Out_ XMVECTOR *outScale, _Out_ XMVECTOR *outRotQuat, _Out_ XMVECTOR *outTrans, _In_ CXMMATRIX M);

XMMATRIX        XMMatrixIdentity();
XMMATRIX        XMMatrixSet(float m00, float m01, float m02, float m03,
                            float m10, float m11, float m12, float m13,
                            float m20, float m21, float m22, float m23,
                            float m30, float m31, float m32, float m33);
XMMATRIX        XMMatrixTranslation(float OffsetX, float OffsetY, float OffsetZ);
XMMATRIX        XMMatrixTranslationFromVector(FXMVECTOR Offset);
XMMATRIX        XMMatrixScaling(float ScaleX, float ScaleY, float ScaleZ);
XMMATRIX        XMMatrixScalingFromVector(FXMVECTOR Scale);
XMMATRIX        XMMatrixRotationX(float Angle);
XMMATRIX        XMMatrixRotationY(float Angle);
XMMATRIX        XMMatrixRotationZ(float Angle);
XMMATRIX        XMMatrixRotationRollPitchYaw(float Pitch, float Yaw, float Roll);
XMMATRIX        XMMatrixRotationRollPitchYawFromVector(FXMVECTOR Angles);
XMMATRIX        XMMatrixRotationNormal(FXMVECTOR NormalAxis, float Angle);
XMMATRIX        XMMatrixRotationAxis(FXMVECTOR Axis, float Angle);
XMMATRIX        XMMatrixRotationQuaternion(FXMVECTOR Quaternion);
XMMATRIX        XMMatrixTransformation2D(FXMVECTOR ScalingOrigin, float ScalingOrientation, FXMVECTOR Scaling, 
                                         FXMVECTOR RotationOrigin, float Rotation, GXMVECTOR Translation);
XMMATRIX        XMMatrixTransformation(FXMVECTOR ScalingOrigin, FXMVECTOR ScalingOrientationQuaternion, FXMVECTOR Scaling, 
                                       GXMVECTOR RotationOrigin, CXMVECTOR RotationQuaternion, CXMVECTOR Translation);
XMMATRIX        XMMatrixAffineTransformation2D(FXMVECTOR Scaling, FXMVECTOR RotationOrigin, float Rotation, FXMVECTOR Translation);
XMMATRIX        XMMatrixAffineTransformation(FXMVECTOR Scaling, FXMVECTOR RotationOrigin, FXMVECTOR RotationQuaternion, GXMVECTOR Translation);
XMMATRIX        XMMatrixReflect(FXMVECTOR ReflectionPlane);
XMMATRIX        XMMatrixShadow(FXMVECTOR ShadowPlane, FXMVECTOR LightPosition);

XMMATRIX        XMMatrixLookAtLH(FXMVECTOR EyePosition, FXMVECTOR FocusPosition, FXMVECTOR UpDirection);
XMMATRIX        XMMatrixLookAtRH(FXMVECTOR EyePosition, FXMVECTOR FocusPosition, FXMVECTOR UpDirection);
XMMATRIX        XMMatrixLookToLH(FXMVECTOR EyePosition, FXMVECTOR EyeDirection, FXMVECTOR UpDirection);
XMMATRIX        XMMatrixLookToRH(FXMVECTOR EyePosition, FXMVECTOR EyeDirection, FXMVECTOR UpDirection);
XMMATRIX        XMMatrixPerspectiveLH(float ViewWidth, float ViewHeight, float NearZ, float FarZ);
XMMATRIX        XMMatrixPerspectiveRH(float ViewWidth, float ViewHeight, float NearZ, float FarZ);
XMMATRIX        XMMatrixPerspectiveFovLH(float FovAngleY, float AspectHByW, float NearZ, float FarZ);
XMMATRIX        XMMatrixPerspectiveFovRH(float FovAngleY, float AspectHByW, float NearZ, float FarZ);
XMMATRIX        XMMatrixPerspectiveOffCenterLH(float ViewLeft, float ViewRight, float ViewBottom, float ViewTop, float NearZ, float FarZ);
XMMATRIX        XMMatrixPerspectiveOffCenterRH(float ViewLeft, float ViewRight, float ViewBottom, float ViewTop, float NearZ, float FarZ);
XMMATRIX        XMMatrixOrthographicLH(float ViewWidth, float ViewHeight, float NearZ, float FarZ);
XMMATRIX        XMMatrixOrthographicRH(float ViewWidth, float ViewHeight, float NearZ, float FarZ);
XMMATRIX        XMMatrixOrthographicOffCenterLH(float ViewLeft, float ViewRight, float ViewBottom, float ViewTop, float NearZ, float FarZ);
XMMATRIX        XMMatrixOrthographicOffCenterRH(float ViewLeft, float ViewRight, float ViewBottom, float ViewTop, float NearZ, float FarZ);


/****************************************************************************
 *
 * Quaternion operations
 *
 ****************************************************************************/

bool            XMQuaternionEqual(FXMVECTOR Q1, FXMVECTOR Q2);
bool            XMQuaternionNotEqual(FXMVECTOR Q1, FXMVECTOR Q2);

bool            XMQuaternionIsNaN(FXMVECTOR Q);
bool            XMQuaternionIsInfinite(FXMVECTOR Q);
bool            XMQuaternionIsIdentity(FXMVECTOR Q);

XMVECTOR        XMQuaternionDot(FXMVECTOR Q1, FXMVECTOR Q2);
XMVECTOR        XMQuaternionMultiply(FXMVECTOR Q1, FXMVECTOR Q2);
XMVECTOR        XMQuaternionLengthSq(FXMVECTOR Q);
XMVECTOR        XMQuaternionReciprocalLength(FXMVECTOR Q);
XMVECTOR        XMQuaternionLength(FXMVECTOR Q);
XMVECTOR        XMQuaternionNormalizeEst(FXMVECTOR Q);
XMVECTOR        XMQuaternionNormalize(FXMVECTOR Q);
XMVECTOR        XMQuaternionConjugate(FXMVECTOR Q);
XMVECTOR        XMQuaternionInverse(FXMVECTOR Q);
XMVECTOR        XMQuaternionLn(FXMVECTOR Q);
XMVECTOR        XMQuaternionExp(FXMVECTOR Q);
XMVECTOR        XMQuaternionSlerp(FXMVECTOR Q0, FXMVECTOR Q1, float t);
XMVECTOR        XMQuaternionSlerpV(FXMVECTOR Q0, FXMVECTOR Q1, FXMVECTOR T);
XMVECTOR        XMQuaternionSquad(FXMVECTOR Q0, FXMVECTOR Q1, FXMVECTOR Q2, GXMVECTOR Q3, float t);
XMVECTOR        XMQuaternionSquadV(FXMVECTOR Q0, FXMVECTOR Q1, FXMVECTOR Q2, GXMVECTOR Q3, CXMVECTOR T);
void            XMQuaternionSquadSetup(_Out_ XMVECTOR* pA, _Out_ XMVECTOR* pB, _Out_ XMVECTOR* pC, _In_ FXMVECTOR Q0, _In_ FXMVECTOR Q1, _In_ FXMVECTOR Q2, _In_ GXMVECTOR Q3);
XMVECTOR        XMQuaternionBaryCentric(FXMVECTOR Q0, FXMVECTOR Q1, FXMVECTOR Q2, float f, float g);
XMVECTOR        XMQuaternionBaryCentricV(FXMVECTOR Q0, FXMVECTOR Q1, FXMVECTOR Q2, GXMVECTOR F, CXMVECTOR G);

XMVECTOR        XMQuaternionIdentity();
XMVECTOR        XMQuaternionRotationRollPitchYaw(float Pitch, float Yaw, float Roll);
XMVECTOR        XMQuaternionRotationRollPitchYawFromVector(FXMVECTOR Angles);
XMVECTOR        XMQuaternionRotationNormal(FXMVECTOR NormalAxis, float Angle);
XMVECTOR        XMQuaternionRotationAxis(FXMVECTOR Axis, float Angle);
XMVECTOR        XMQuaternionRotationMatrix(CXMMATRIX M);

void            XMQuaternionToAxisAngle(_Out_ XMVECTOR* pAxis, _Out_ float* pAngle, _In_ FXMVECTOR Q);

/****************************************************************************
 *
 * Plane operations
 *
 ****************************************************************************/

bool            XMPlaneEqual(FXMVECTOR P1, FXMVECTOR P2);
bool            XMPlaneNearEqual(FXMVECTOR P1, FXMVECTOR P2, FXMVECTOR Epsilon);
bool            XMPlaneNotEqual(FXMVECTOR P1, FXMVECTOR P2);

bool            XMPlaneIsNaN(FXMVECTOR P);
bool            XMPlaneIsInfinite(FXMVECTOR P);

XMVECTOR        XMPlaneDot(FXMVECTOR P, FXMVECTOR V);
XMVECTOR        XMPlaneDotCoord(FXMVECTOR P, FXMVECTOR V);
XMVECTOR        XMPlaneDotNormal(FXMVECTOR P, FXMVECTOR V);
XMVECTOR        XMPlaneNormalizeEst(FXMVECTOR P);
XMVECTOR        XMPlaneNormalize(FXMVECTOR P);
XMVECTOR        XMPlaneIntersectLine(FXMVECTOR P, FXMVECTOR LinePoint1, FXMVECTOR LinePoint2);
void            XMPlaneIntersectPlane(_Out_ XMVECTOR* pLinePoint1, _Out_ XMVECTOR* pLinePoint2, _In_ FXMVECTOR P1, _In_ FXMVECTOR P2);
XMVECTOR        XMPlaneTransform(FXMVECTOR P, CXMMATRIX M);
XMFLOAT4*       XMPlaneTransformStream(_Out_writes_bytes_(sizeof(XMFLOAT4)+OutputStride*(PlaneCount-1)) XMFLOAT4* pOutputStream,
                                       _In_ size_t OutputStride,
                                       _In_reads_bytes_(sizeof(XMFLOAT4)+InputStride*(PlaneCount-1)) const XMFLOAT4* pInputStream,
                                       _In_ size_t InputStride, _In_ size_t PlaneCount, _In_ CXMMATRIX M);

XMVECTOR        XMPlaneFromPointNormal(FXMVECTOR Point, FXMVECTOR Normal);
XMVECTOR        XMPlaneFromPoints(FXMVECTOR Point1, FXMVECTOR Point2, FXMVECTOR Point3);

/****************************************************************************
 *
 * Color operations
 *
 ****************************************************************************/

bool            XMColorEqual(FXMVECTOR C1, FXMVECTOR C2);
bool            XMColorNotEqual(FXMVECTOR C1, FXMVECTOR C2);
bool            XMColorGreater(FXMVECTOR C1, FXMVECTOR C2);
bool            XMColorGreaterOrEqual(FXMVECTOR C1, FXMVECTOR C2);
bool            XMColorLess(FXMVECTOR C1, FXMVECTOR C2);
bool            XMColorLessOrEqual(FXMVECTOR C1, FXMVECTOR C2);

bool            XMColorIsNaN(FXMVECTOR C);
bool            XMColorIsInfinite(FXMVECTOR C);

XMVECTOR        XMColorNegative(FXMVECTOR C);
XMVECTOR        XMColorModulate(FXMVECTOR C1, FXMVECTOR C2);
XMVECTOR        XMColorAdjustSaturation(FXMVECTOR C, float Saturation);
XMVECTOR        XMColorAdjustContrast(FXMVECTOR C, float Contrast);

XMVECTOR        XMColorRGBToHSL( FXMVECTOR rgb );
XMVECTOR        XMColorHSLToRGB( FXMVECTOR hsl );

XMVECTOR        XMColorRGBToHSV( FXMVECTOR rgb );
XMVECTOR        XMColorHSVToRGB( FXMVECTOR hsv );

XMVECTOR        XMColorRGBToYUV( FXMVECTOR rgb );
XMVECTOR        XMColorYUVToRGB( FXMVECTOR yuv );

XMVECTOR        XMColorRGBToYUV_HD( FXMVECTOR rgb );
XMVECTOR        XMColorYUVToRGB_HD( FXMVECTOR yuv );

XMVECTOR        XMColorRGBToXYZ( FXMVECTOR rgb );
XMVECTOR        XMColorXYZToRGB( FXMVECTOR xyz );

XMVECTOR        XMColorXYZToSRGB( FXMVECTOR xyz );
XMVECTOR        XMColorSRGBToXYZ( FXMVECTOR srgb );

/****************************************************************************
 *
 * Miscellaneous operations
 *
 ****************************************************************************/

bool            XMVerifyCPUSupport();

XMVECTOR        XMFresnelTerm(FXMVECTOR CosIncidentAngle, FXMVECTOR RefractionIndex);

bool            XMScalarNearEqual(float S1, float S2, float Epsilon);
float           XMScalarModAngle(float Value);

float           XMScalarSin(float Value);
float           XMScalarSinEst(float Value);

float           XMScalarCos(float Value);
float           XMScalarCosEst(float Value);

void            XMScalarSinCos(_Out_ float* pSin, _Out_ float* pCos, float Value);
void            XMScalarSinCosEst(_Out_ float* pSin, _Out_ float* pCos, float Value);

float           XMScalarASin(float Value);
float           XMScalarASinEst(float Value);

float           XMScalarACos(float Value);
float           XMScalarACosEst(float Value);

/****************************************************************************
 *
 * Templates
 *
 ****************************************************************************/

#if defined(__XNAMATH_H__) && defined(XMMin)
#undef XMMin
#undef XMMax
#endif

template<class T> inline T XMMin(T a, T b) { return (a < b) ? a : b; }
template<class T> inline T XMMax(T a, T b) { return (a > b) ? a : b; }

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

#if defined(_XM_SSE_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)

#define XM_PERMUTE_PS( v, c ) _mm_shuffle_ps( v, v, c )

// PermuteHelper internal template (SSE only)
namespace Internal
{
    // Slow path fallback for permutes that do not map to a single SSE shuffle opcode.
    template<uint32_t Shuffle, bool WhichX, bool WhichY, bool WhichZ, bool WhichW> struct PermuteHelper
    {
        static XMVECTOR Permute(FXMVECTOR v1, FXMVECTOR v2)
        {
            static const XMVECTORU32 selectMask =
            {
                WhichX ? 0xFFFFFFFF : 0,
                WhichY ? 0xFFFFFFFF : 0,
                WhichZ ? 0xFFFFFFFF : 0,
                WhichW ? 0xFFFFFFFF : 0,
            };

            XMVECTOR shuffled1 = XM_PERMUTE_PS(v1, Shuffle);
            XMVECTOR shuffled2 = XM_PERMUTE_PS(v2, Shuffle);

            XMVECTOR masked1 = _mm_andnot_ps(selectMask, shuffled1);
            XMVECTOR masked2 = _mm_and_ps(selectMask, shuffled2);

            return _mm_or_ps(masked1, masked2);
        }
    };

    // Fast path for permutes that only read from the first vector.
    template<uint32_t Shuffle> struct PermuteHelper<Shuffle, false, false, false, false>
    {
        static XMVECTOR Permute(FXMVECTOR v1, FXMVECTOR v2) { (v2); return XM_PERMUTE_PS(v1, Shuffle); }
    };

    // Fast path for permutes that only read from the second vector.
    template<uint32_t Shuffle> struct PermuteHelper<Shuffle, true, true, true, true>
    {
        static XMVECTOR Permute(FXMVECTOR v1, FXMVECTOR v2){ (v1); return XM_PERMUTE_PS(v2, Shuffle); }
    };

    // Fast path for permutes that read XY from the first vector, ZW from the second.
    template<uint32_t Shuffle> struct PermuteHelper<Shuffle, false, false, true, true>
    {
        static XMVECTOR Permute(FXMVECTOR v1, FXMVECTOR v2) { return _mm_shuffle_ps(v1, v2, Shuffle); }
    };

    // Fast path for permutes that read XY from the second vector, ZW from the first.
    template<uint32_t Shuffle> struct PermuteHelper<Shuffle, true, true, false, false>
    {
        static XMVECTOR Permute(FXMVECTOR v1, FXMVECTOR v2) { return _mm_shuffle_ps(v2, v1, Shuffle); }
    };
};

#endif // _XM_SSE_INTRINSICS_ && !_XM_NO_INTRINSICS_

// General permute template
template<uint32_t PermuteX, uint32_t PermuteY, uint32_t PermuteZ, uint32_t PermuteW>
    inline XMVECTOR XMVectorPermute(FXMVECTOR V1, FXMVECTOR V2)
{
    static_assert(PermuteX <= 7, "PermuteX template parameter out of range");
    static_assert(PermuteY <= 7, "PermuteY template parameter out of range");
    static_assert(PermuteZ <= 7, "PermuteZ template parameter out of range");
    static_assert(PermuteW <= 7, "PermuteW template parameter out of range");

#if defined(_XM_SSE_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
    const uint32_t Shuffle = _MM_SHUFFLE(PermuteW & 3, PermuteZ & 3, PermuteY & 3, PermuteX & 3);

    const bool WhichX = PermuteX > 3;
    const bool WhichY = PermuteY > 3;
    const bool WhichZ = PermuteZ > 3;
    const bool WhichW = PermuteW > 3;

    return Internal::PermuteHelper<Shuffle, WhichX, WhichY, WhichZ, WhichW>::Permute(V1, V2);
#else

    return XMVectorPermute( V1, V2, PermuteX, PermuteY, PermuteZ, PermuteW );

#endif
}

// Special-case permute templates
template<> inline XMVECTOR XMVectorPermute<0,1,2,3>(FXMVECTOR V1, FXMVECTOR V2) { (V2); return V1; }
template<> inline XMVECTOR XMVectorPermute<4,5,6,7>(FXMVECTOR V1, FXMVECTOR V2) { (V1); return V2; }

#if defined(_XM_ARM_NEON_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)

// If the indices are all in the range 0-3 or 4-7, then use XMVectorSwizzle instead
// The mirror cases are not spelled out here as the programmer can always swap the arguments
// (i.e. prefer permutes where the X element comes from the V1 vector instead of the V2 vector)

template<> inline XMVECTOR XMVectorPermute<0,1,4,5>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vget_low_f32(V1), vget_low_f32(V2) ); }
template<> inline XMVECTOR XMVectorPermute<1,0,4,5>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_low_f32(V1) ), vget_low_f32(V2) ); }
template<> inline XMVECTOR XMVectorPermute<0,1,5,4>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vget_low_f32(V1), vrev64_f32( vget_low_f32(V2) ) ); }
template<> inline XMVECTOR XMVectorPermute<1,0,5,4>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_low_f32(V1) ), vrev64_f32( vget_low_f32(V2) ) ); }

template<> inline XMVECTOR XMVectorPermute<2,3,6,7>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vget_high_f32(V1), vget_high_f32(V2) ); }
template<> inline XMVECTOR XMVectorPermute<3,2,6,7>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_high_f32(V1) ), vget_high_f32(V2) ); }
template<> inline XMVECTOR XMVectorPermute<2,3,7,6>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vget_high_f32(V1), vrev64_f32( vget_high_f32(V2) ) ); }
template<> inline XMVECTOR XMVectorPermute<3,2,7,6>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_high_f32(V1) ), vrev64_f32( vget_high_f32(V2) ) ); }

template<> inline XMVECTOR XMVectorPermute<0,1,6,7>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vget_low_f32(V1), vget_high_f32(V2) ); }
template<> inline XMVECTOR XMVectorPermute<1,0,6,7>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_low_f32(V1) ), vget_high_f32(V2) ); }
template<> inline XMVECTOR XMVectorPermute<0,1,7,6>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vget_low_f32(V1), vrev64_f32( vget_high_f32(V2) ) ); }
template<> inline XMVECTOR XMVectorPermute<1,0,7,6>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_low_f32(V1) ), vrev64_f32( vget_high_f32(V2) ) ); }

template<> inline XMVECTOR XMVectorPermute<3,2,4,5>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_high_f32(V1) ), vget_low_f32(V2) ); }
template<> inline XMVECTOR XMVectorPermute<2,3,5,4>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vget_high_f32(V1), vrev64_f32( vget_low_f32(V2) ) ); }
template<> inline XMVECTOR XMVectorPermute<3,2,5,4>(FXMVECTOR V1, FXMVECTOR V2) { return vcombine_f32( vrev64_f32( vget_high_f32(V1) ), vrev64_f32( vget_low_f32(V2) ) ); }

template<> inline XMVECTOR XMVectorPermute<0,4,2,6>(FXMVECTOR V1, FXMVECTOR V2) { return vtrnq_f32(V1,V2).val[0]; }
template<> inline XMVECTOR XMVectorPermute<1,5,3,7>(FXMVECTOR V1, FXMVECTOR V2) { return vtrnq_f32(V1,V2).val[1]; }

template<> inline XMVECTOR XMVectorPermute<0,4,1,5>(FXMVECTOR V1, FXMVECTOR V2) { return vzipq_f32(V1,V2).val[0]; }
template<> inline XMVECTOR XMVectorPermute<2,6,3,7>(FXMVECTOR V1, FXMVECTOR V2) { return vzipq_f32(V1,V2).val[1]; }

template<> inline XMVECTOR XMVectorPermute<0,2,4,6>(FXMVECTOR V1, FXMVECTOR V2) { return vuzpq_f32(V1,V2).val[0]; }
template<> inline XMVECTOR XMVectorPermute<1,3,5,7>(FXMVECTOR V1, FXMVECTOR V2) { return vuzpq_f32(V1,V2).val[1]; }

template<> inline XMVECTOR XMVectorPermute<1,2,3,4>(FXMVECTOR V1, FXMVECTOR V2) { return vextq_f32(V1, V2, 1); }
template<> inline XMVECTOR XMVectorPermute<2,3,4,5>(FXMVECTOR V1, FXMVECTOR V2) { return vextq_f32(V1, V2, 2); }
template<> inline XMVECTOR XMVectorPermute<3,4,5,6>(FXMVECTOR V1, FXMVECTOR V2) { return vextq_f32(V1, V2, 3); }

#endif // _XM_ARM_NEON_INTRINSICS_ && !_XM_NO_INTRINSICS_

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

// General swizzle template
template<uint32_t SwizzleX, uint32_t SwizzleY, uint32_t SwizzleZ, uint32_t SwizzleW>
    inline XMVECTOR XMVectorSwizzle(FXMVECTOR V)
{
    static_assert(SwizzleX <= 3, "SwizzleX template parameter out of range");
    static_assert(SwizzleY <= 3, "SwizzleY template parameter out of range");
    static_assert(SwizzleZ <= 3, "SwizzleZ template parameter out of range");
    static_assert(SwizzleW <= 3, "SwizzleW template parameter out of range");

#if defined(_XM_SSE_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
    return XM_PERMUTE_PS( V, _MM_SHUFFLE( SwizzleW, SwizzleZ, SwizzleY, SwizzleX ) );
#elif defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
    return __vpermwi(V, ((SwizzleX & 3) << 6) | ((SwizzleY & 3) << 4) | ((SwizzleZ & 3) << 2) | (SwizzleW & 3) );
#else

    return XMVectorSwizzle( V, SwizzleX, SwizzleY, SwizzleZ, SwizzleW );

#endif
}

// Specialized swizzles
template<> inline XMVECTOR XMVectorSwizzle<0,1,2,3>(FXMVECTOR V) { return V; }


#if defined(_XM_ARM_NEON_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)

template<> inline XMVECTOR XMVectorSwizzle<0,0,0,0>(FXMVECTOR V) { return vdupq_lane_f32( vget_low_f32(V), 0); }
template<> inline XMVECTOR XMVectorSwizzle<1,1,1,1>(FXMVECTOR V) { return vdupq_lane_f32( vget_low_f32(V), 1); }
template<> inline XMVECTOR XMVectorSwizzle<2,2,2,2>(FXMVECTOR V) { return vdupq_lane_f32( vget_high_f32(V), 0); }
template<> inline XMVECTOR XMVectorSwizzle<3,3,3,3>(FXMVECTOR V) { return vdupq_lane_f32( vget_high_f32(V), 1); }

template<> inline XMVECTOR XMVectorSwizzle<1,0,3,2>(FXMVECTOR V) { return vrev64q_f32(V); }

template<> inline XMVECTOR XMVectorSwizzle<0,1,0,1>(FXMVECTOR V) { __n64 vt = vget_low_f32(V); return vcombine_f32( vt, vt ); }
template<> inline XMVECTOR XMVectorSwizzle<2,3,2,3>(FXMVECTOR V) { __n64 vt = vget_high_f32(V); return vcombine_f32( vt, vt ); }
template<> inline XMVECTOR XMVectorSwizzle<1,0,1,0>(FXMVECTOR V) { __n64 vt = vrev64_f32( vget_low_f32(V) ); return vcombine_f32( vt, vt ); }
template<> inline XMVECTOR XMVectorSwizzle<3,2,3,2>(FXMVECTOR V) { __n64 vt = vrev64_f32( vget_high_f32(V) ); return vcombine_f32( vt, vt ); }

template<> inline XMVECTOR XMVectorSwizzle<0,1,3,2>(FXMVECTOR V) { return vcombine_f32( vget_low_f32(V), vrev64_f32( vget_high_f32(V) ) ); }
template<> inline XMVECTOR XMVectorSwizzle<1,0,2,3>(FXMVECTOR V) { return vcombine_f32( vrev64_f32( vget_low_f32(V) ), vget_high_f32(V) ); }
template<> inline XMVECTOR XMVectorSwizzle<2,3,1,0>(FXMVECTOR V) { return vcombine_f32( vget_high_f32(V), vrev64_f32( vget_low_f32(V) ) ); }
template<> inline XMVECTOR XMVectorSwizzle<3,2,0,1>(FXMVECTOR V) { return vcombine_f32( vrev64_f32( vget_high_f32(V) ), vget_low_f32(V) ); }
template<> inline XMVECTOR XMVectorSwizzle<3,2,1,0>(FXMVECTOR V) { return vcombine_f32( vrev64_f32( vget_high_f32(V) ), vrev64_f32( vget_low_f32(V) ) ); }

template<> inline XMVECTOR XMVectorSwizzle<0,0,2,2>(FXMVECTOR V) { return vtrnq_f32(V,V).val[0]; }
template<> inline XMVECTOR XMVectorSwizzle<1,1,3,3>(FXMVECTOR V) { return vtrnq_f32(V,V).val[1]; }

template<> inline XMVECTOR XMVectorSwizzle<0,0,1,1>(FXMVECTOR V) { return vzipq_f32(V,V).val[0]; }
template<> inline XMVECTOR XMVectorSwizzle<2,2,3,3>(FXMVECTOR V) { return vzipq_f32(V,V).val[1]; }

template<> inline XMVECTOR XMVectorSwizzle<0,2,0,2>(FXMVECTOR V) { return vuzpq_f32(V,V).val[0]; }
template<> inline XMVECTOR XMVectorSwizzle<1,3,1,3>(FXMVECTOR V) { return vuzpq_f32(V,V).val[1]; }

template<> inline XMVECTOR XMVectorSwizzle<1,2,3,0>(FXMVECTOR V) { return vextq_f32(V, V, 1); }
template<> inline XMVECTOR XMVectorSwizzle<2,3,0,1>(FXMVECTOR V) { return vextq_f32(V, V, 2); }
template<> inline XMVECTOR XMVectorSwizzle<3,0,1,2>(FXMVECTOR V) { return vextq_f32(V, V, 3); }

#endif // _XM_ARM_NEON_INTRINSICS_ && !_XM_NO_INTRINSICS_

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

template<uint32_t Elements>
    inline XMVECTOR XMVectorShiftLeft(FXMVECTOR V1, FXMVECTOR V2)
{
    static_assert( Elements < 4, "Elements template parameter out of range" );
#if defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
#else
    return XMVectorPermute<Elements, (Elements + 1), (Elements + 2), (Elements + 3)>(V1, V2);
#endif
}

template<uint32_t Elements>
    inline XMVECTOR XMVectorRotateLeft(FXMVECTOR V)
{
    static_assert( Elements < 4, "Elements template parameter out of range" );
#if defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
#else
    return XMVectorSwizzle<Elements & 3, (Elements + 1) & 3, (Elements + 2) & 3, (Elements + 3) & 3>(V);
#endif
}

template<uint32_t Elements>
    inline XMVECTOR XMVectorRotateRight(FXMVECTOR V)
{
    static_assert( Elements < 4, "Elements template parameter out of range" );
#if defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
#else
    return XMVectorSwizzle<(4 - Elements) & 3, (5 - Elements) & 3, (6 - Elements) & 3, (7 - Elements) & 3>(V);
#endif
}

template<uint32_t VSLeftRotateElements, uint32_t Select0, uint32_t Select1, uint32_t Select2, uint32_t Select3>
    inline XMVECTOR XMVectorInsert(FXMVECTOR VD, FXMVECTOR VS)
{
#if defined(_XM_VMX128_INTRINSICS_) && !defined(_XM_NO_INTRINSICS_)
#else
    XMVECTOR Control = XMVectorSelectControl(Select0&1, Select1&1, Select2&1, Select3&1);
    return XMVectorSelect( VD, XMVectorRotateLeft<VSLeftRotateElements>(VS), Control );
#endif
}

/****************************************************************************
 *
 * Globals
 *
 ****************************************************************************/

// The purpose of the following global constants is to prevent redundant 
// reloading of the constants when they are referenced by more than one
// separate inline math routine called within the same function.  Declaring
// a constant locally within a routine is sufficient to prevent redundant
// reloads of that constant when that single routine is called multiple
// times in a function, but if the constant is used (and declared) in a 
// separate math routine it would be reloaded.

#ifndef XMGLOBALCONST
#define XMGLOBALCONST	static const // extern const // MGH - __declspec(selectany)
#endif

XMGLOBALCONST XMVECTORF32 g_XMSinCoefficients0    = {-0.16666667f, +0.0083333310f, -0.00019840874f, +2.7525562e-06f};
XMGLOBALCONST XMVECTORF32 g_XMSinCoefficients1    = {-2.3889859e-08f, -0.16665852f /*Est1*/, +0.0083139502f /*Est2*/, -0.00018524670f /*Est3*/};
XMGLOBALCONST XMVECTORF32 g_XMCosCoefficients0    = {-0.5f, +0.041666638f, -0.0013888378f, +2.4760495e-05f};
XMGLOBALCONST XMVECTORF32 g_XMCosCoefficients1    = {-2.6051615e-07f, -0.49992746f /*Est1*/, +0.041493919f /*Est2*/, -0.0012712436f /*Est3*/};
XMGLOBALCONST XMVECTORF32 g_XMTanCoefficients0    = {1.0f, 0.333333333f, 0.133333333f, 5.396825397e-2f};
XMGLOBALCONST XMVECTORF32 g_XMTanCoefficients1    = {2.186948854e-2f, 8.863235530e-3f, 3.592128167e-3f, 1.455834485e-3f};
XMGLOBALCONST XMVECTORF32 g_XMTanCoefficients2    = {5.900274264e-4f, 2.391290764e-4f, 9.691537707e-5f, 3.927832950e-5f};
XMGLOBALCONST XMVECTORF32 g_XMArcCoefficients0    = {+1.5707963050f, -0.2145988016f, +0.0889789874f, -0.0501743046f};
XMGLOBALCONST XMVECTORF32 g_XMArcCoefficients1    = {+0.0308918810f, -0.0170881256f, +0.0066700901f, -0.0012624911f};
XMGLOBALCONST XMVECTORF32 g_XMATanCoefficients0   = {-0.3333314528f, +0.1999355085f, -0.1420889944f, +0.1065626393f};
XMGLOBALCONST XMVECTORF32 g_XMATanCoefficients1   = {-0.0752896400f, +0.0429096138f, -0.0161657367f, +0.0028662257f};
XMGLOBALCONST XMVECTORF32 g_XMATanEstCoefficients0 = {+0.999866f, +0.999866f, +0.999866f, +0.999866f};
XMGLOBALCONST XMVECTORF32 g_XMATanEstCoefficients1 = {-0.3302995f, +0.180141f, -0.085133f, +0.0208351f};
XMGLOBALCONST XMVECTORF32 g_XMTanEstCoefficients  = {2.484f, -1.954923183e-1f, 2.467401101f, XM_1DIVPI};
XMGLOBALCONST XMVECTORF32 g_XMArcEstCoefficients  = {+1.5707288f,-0.2121144f,+0.0742610f,-0.0187293f};
XMGLOBALCONST XMVECTORF32 g_XMPiConstants0        = {XM_PI, XM_2PI, XM_1DIVPI, XM_1DIV2PI};
XMGLOBALCONST XMVECTORF32 g_XMIdentityR0          = {1.0f, 0.0f, 0.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMIdentityR1          = {0.0f, 1.0f, 0.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMIdentityR2          = {0.0f, 0.0f, 1.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMIdentityR3          = {0.0f, 0.0f, 0.0f, 1.0f};
XMGLOBALCONST XMVECTORF32 g_XMNegIdentityR0       = {-1.0f,0.0f, 0.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMNegIdentityR1       = {0.0f,-1.0f, 0.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMNegIdentityR2       = {0.0f, 0.0f,-1.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMNegIdentityR3       = {0.0f, 0.0f, 0.0f,-1.0f};
XMGLOBALCONST XMVECTORI32 g_XMNegativeZero      = {0x80000000, 0x80000000, 0x80000000, 0x80000000};
XMGLOBALCONST XMVECTORI32 g_XMNegate3           = {0x80000000, 0x80000000, 0x80000000, 0x00000000};
XMGLOBALCONST XMVECTORI32 g_XMMask3             = {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0x00000000};
XMGLOBALCONST XMVECTORI32 g_XMMaskX             = {0xFFFFFFFF, 0x00000000, 0x00000000, 0x00000000};
XMGLOBALCONST XMVECTORI32 g_XMMaskY             = {0x00000000, 0xFFFFFFFF, 0x00000000, 0x00000000};
XMGLOBALCONST XMVECTORI32 g_XMMaskZ             = {0x00000000, 0x00000000, 0xFFFFFFFF, 0x00000000};
XMGLOBALCONST XMVECTORI32 g_XMMaskW             = {0x00000000, 0x00000000, 0x00000000, 0xFFFFFFFF};
XMGLOBALCONST XMVECTORF32 g_XMOne               = { 1.0f, 1.0f, 1.0f, 1.0f};
XMGLOBALCONST XMVECTORF32 g_XMOne3              = { 1.0f, 1.0f, 1.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMZero              = { 0.0f, 0.0f, 0.0f, 0.0f};
XMGLOBALCONST XMVECTORF32 g_XMTwo               = { 2.f, 2.f, 2.f, 2.f };
XMGLOBALCONST XMVECTORF32 g_XMFour              = { 4.f, 4.f, 4.f, 4.f };
XMGLOBALCONST XMVECTORF32 g_XMSix               = { 6.f, 6.f, 6.f, 6.f };
XMGLOBALCONST XMVECTORF32 g_XMNegativeOne       = {-1.0f,-1.0f,-1.0f,-1.0f};
XMGLOBALCONST XMVECTORF32 g_XMOneHalf           = { 0.5f, 0.5f, 0.5f, 0.5f};
XMGLOBALCONST XMVECTORF32 g_XMNegativeOneHalf   = {-0.5f,-0.5f,-0.5f,-0.5f};
XMGLOBALCONST XMVECTORF32 g_XMNegativeTwoPi     = {-XM_2PI, -XM_2PI, -XM_2PI, -XM_2PI};
XMGLOBALCONST XMVECTORF32 g_XMNegativePi        = {-XM_PI, -XM_PI, -XM_PI, -XM_PI};
XMGLOBALCONST XMVECTORF32 g_XMHalfPi            = {XM_PIDIV2, XM_PIDIV2, XM_PIDIV2, XM_PIDIV2};
XMGLOBALCONST XMVECTORF32 g_XMPi                = {XM_PI, XM_PI, XM_PI, XM_PI};
XMGLOBALCONST XMVECTORF32 g_XMReciprocalPi      = {XM_1DIVPI, XM_1DIVPI, XM_1DIVPI, XM_1DIVPI};
XMGLOBALCONST XMVECTORF32 g_XMTwoPi             = {XM_2PI, XM_2PI, XM_2PI, XM_2PI};
XMGLOBALCONST XMVECTORF32 g_XMReciprocalTwoPi   = {XM_1DIV2PI, XM_1DIV2PI, XM_1DIV2PI, XM_1DIV2PI};
XMGLOBALCONST XMVECTORF32 g_XMEpsilon           = {1.192092896e-7f, 1.192092896e-7f, 1.192092896e-7f, 1.192092896e-7f};
XMGLOBALCONST XMVECTORI32 g_XMInfinity          = {0x7F800000, 0x7F800000, 0x7F800000, 0x7F800000};
XMGLOBALCONST XMVECTORI32 g_XMQNaN              = {0x7FC00000, 0x7FC00000, 0x7FC00000, 0x7FC00000};
XMGLOBALCONST XMVECTORI32 g_XMQNaNTest          = {0x007FFFFF, 0x007FFFFF, 0x007FFFFF, 0x007FFFFF};
XMGLOBALCONST XMVECTORI32 g_XMAbsMask           = {0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF};
XMGLOBALCONST XMVECTORI32 g_XMFltMin            = {0x00800000, 0x00800000, 0x00800000, 0x00800000};
XMGLOBALCONST XMVECTORI32 g_XMFltMax            = {0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF, 0x7F7FFFFF};
XMGLOBALCONST XMVECTORI32 g_XMNegOneMask        = {0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF, 0xFFFFFFFF};
XMGLOBALCONST XMVECTORI32 g_XMMaskA8R8G8B8      = {0x00FF0000, 0x0000FF00, 0x000000FF, 0xFF000000};
XMGLOBALCONST XMVECTORI32 g_XMFlipA8R8G8B8      = {0x00000000, 0x00000000, 0x00000000, 0x80000000};
XMGLOBALCONST XMVECTORF32 g_XMFixAA8R8G8B8      = {0.0f,0.0f,0.0f,(float)(0x80000000U)};
XMGLOBALCONST XMVECTORF32 g_XMNormalizeA8R8G8B8 = {1.0f/(255.0f*(float)(0x10000)),1.0f/(255.0f*(float)(0x100)),1.0f/255.0f,1.0f/(255.0f*(float)(0x1000000))};
XMGLOBALCONST XMVECTORI32 g_XMMaskA2B10G10R10   = {0x000003FF, 0x000FFC00, 0x3FF00000, 0xC0000000};
XMGLOBALCONST XMVECTORI32 g_XMFlipA2B10G10R10   = {0x00000200, 0x00080000, 0x20000000, 0x80000000};
XMGLOBALCONST XMVECTORF32 g_XMFixAA2B10G10R10   = {-512.0f,-512.0f*(float)(0x400),-512.0f*(float)(0x100000),(float)(0x80000000U)};
XMGLOBALCONST XMVECTORF32 g_XMNormalizeA2B10G10R10 = {1.0f/511.0f,1.0f/(511.0f*(float)(0x400)),1.0f/(511.0f*(float)(0x100000)),1.0f/(3.0f*(float)(0x40000000))};
XMGLOBALCONST XMVECTORI32 g_XMMaskX16Y16        = {0x0000FFFF, 0xFFFF0000, 0x00000000, 0x00000000};
XMGLOBALCONST XMVECTORI32 g_XMFlipX16Y16        = {0x00008000, 0x00000000, 0x00000000, 0x00000000};
XMGLOBALCONST XMVECTORF32 g_XMFixX16Y16         = {-32768.0f,0.0f,0.0f,0.0f};
XMGLOBALCONST XMVECTORF32 g_XMNormalizeX16Y16   = {1.0f/32767.0f,1.0f/(32767.0f*65536.0f),0.0f,0.0f};
XMGLOBALCONST XMVECTORI32 g_XMMaskX16Y16Z16W16  = {0x0000FFFF, 0x0000FFFF, 0xFFFF0000, 0xFFFF0000};
XMGLOBALCONST XMVECTORI32 g_XMFlipX16Y16Z16W16  = {0x00008000, 0x00008000, 0x00000000, 0x00000000};
XMGLOBALCONST XMVECTORF32 g_XMFixX16Y16Z16W16   = {-32768.0f,-32768.0f,0.0f,0.0f};
XMGLOBALCONST XMVECTORF32 g_XMNormalizeX16Y16Z16W16 = {1.0f/32767.0f,1.0f/32767.0f,1.0f/(32767.0f*65536.0f),1.0f/(32767.0f*65536.0f)};
XMGLOBALCONST XMVECTORF32 g_XMNoFraction        = {8388608.0f,8388608.0f,8388608.0f,8388608.0f};
XMGLOBALCONST XMVECTORI32 g_XMMaskByte          = {0x000000FF, 0x000000FF, 0x000000FF, 0x000000FF};
XMGLOBALCONST XMVECTORF32 g_XMNegateX           = {-1.0f, 1.0f, 1.0f, 1.0f};
XMGLOBALCONST XMVECTORF32 g_XMNegateY           = { 1.0f,-1.0f, 1.0f, 1.0f};
XMGLOBALCONST XMVECTORF32 g_XMNegateZ           = { 1.0f, 1.0f,-1.0f, 1.0f};
XMGLOBALCONST XMVECTORF32 g_XMNegateW           = { 1.0f, 1.0f, 1.0f,-1.0f};
XMGLOBALCONST XMVECTORI32 g_XMSelect0101        = {XM_SELECT_0, XM_SELECT_1, XM_SELECT_0, XM_SELECT_1};
XMGLOBALCONST XMVECTORI32 g_XMSelect1010        = {XM_SELECT_1, XM_SELECT_0, XM_SELECT_1, XM_SELECT_0};
XMGLOBALCONST XMVECTORI32 g_XMOneHalfMinusEpsilon = { 0x3EFFFFFD, 0x3EFFFFFD, 0x3EFFFFFD, 0x3EFFFFFD};
XMGLOBALCONST XMVECTORI32 g_XMSelect1000        = {XM_SELECT_1, XM_SELECT_0, XM_SELECT_0, XM_SELECT_0};
XMGLOBALCONST XMVECTORI32 g_XMSelect1100        = {XM_SELECT_1, XM_SELECT_1, XM_SELECT_0, XM_SELECT_0};
XMGLOBALCONST XMVECTORI32 g_XMSelect1110        = {XM_SELECT_1, XM_SELECT_1, XM_SELECT_1, XM_SELECT_0};
XMGLOBALCONST XMVECTORI32 g_XMSelect1011          = { XM_SELECT_1, XM_SELECT_0, XM_SELECT_1, XM_SELECT_1 };
XMGLOBALCONST XMVECTORF32 g_XMFixupY16          = {1.0f,1.0f/65536.0f,0.0f,0.0f};
XMGLOBALCONST XMVECTORF32 g_XMFixupY16W16       = {1.0f,1.0f,1.0f/65536.0f,1.0f/65536.0f};
XMGLOBALCONST XMVECTORI32 g_XMFlipY             = {0,0x80000000,0,0};
XMGLOBALCONST XMVECTORI32 g_XMFlipZ             = {0,0,0x80000000,0};
XMGLOBALCONST XMVECTORI32 g_XMFlipW             = {0,0,0,0x80000000};
XMGLOBALCONST XMVECTORI32 g_XMFlipYZ            = {0,0x80000000,0x80000000,0};
XMGLOBALCONST XMVECTORI32 g_XMFlipZW            = {0,0,0x80000000,0x80000000};
XMGLOBALCONST XMVECTORI32 g_XMFlipYW            = {0,0x80000000,0,0x80000000};
XMGLOBALCONST XMVECTORI32 g_XMMaskDec4          = {0x3FF,0x3FF<<10,0x3FF<<20,0x3<<30};
XMGLOBALCONST XMVECTORI32 g_XMXorDec4           = {0x200,0x200<<10,0x200<<20,0};
XMGLOBALCONST XMVECTORF32 g_XMAddUDec4          = {0,0,0,32768.0f*65536.0f};
XMGLOBALCONST XMVECTORF32 g_XMAddDec4           = {-512.0f,-512.0f*1024.0f,-512.0f*1024.0f*1024.0f,0};
XMGLOBALCONST XMVECTORF32 g_XMMulDec4           = {1.0f,1.0f/1024.0f,1.0f/(1024.0f*1024.0f),1.0f/(1024.0f*1024.0f*1024.0f)};
XMGLOBALCONST XMVECTORI32 g_XMMaskByte4         = {0xFF,0xFF00,0xFF0000,0xFF000000};
XMGLOBALCONST XMVECTORI32 g_XMXorByte4          = {0x80,0x8000,0x800000,0x00000000};
XMGLOBALCONST XMVECTORF32 g_XMAddByte4          = {-128.0f,-128.0f*256.0f,-128.0f*65536.0f,0};
XMGLOBALCONST XMVECTORF32 g_XMFixUnsigned       = {32768.0f*65536.0f,32768.0f*65536.0f,32768.0f*65536.0f,32768.0f*65536.0f};
XMGLOBALCONST XMVECTORF32 g_XMMaxInt            = {65536.0f*32768.0f-128.0f,65536.0f*32768.0f-128.0f,65536.0f*32768.0f-128.0f,65536.0f*32768.0f-128.0f};
XMGLOBALCONST XMVECTORF32 g_XMMaxUInt           = {65536.0f*65536.0f-256.0f,65536.0f*65536.0f-256.0f,65536.0f*65536.0f-256.0f,65536.0f*65536.0f-256.0f};
XMGLOBALCONST XMVECTORF32 g_XMUnsignedFix       = {32768.0f*65536.0f,32768.0f*65536.0f,32768.0f*65536.0f,32768.0f*65536.0f};
XMGLOBALCONST XMVECTORF32 g_XMsrgbScale         = { 12.92f, 12.92f, 12.92f, 1.0f };
XMGLOBALCONST XMVECTORF32 g_XMsrgbA             = { 0.055f, 0.055f, 0.055f, 0.0f };
XMGLOBALCONST XMVECTORF32 g_XMsrgbA1            = { 1.055f, 1.055f, 1.055f, 1.0f };

/****************************************************************************
 *
 * Implementation
 *
 ****************************************************************************/

#pragma warning(push)
#pragma warning(disable:4068 4214 4204 4365 4616 4640 6001)

#pragma prefast(push)
#pragma prefast(disable : 25000, "FXMVECTOR is 16 bytes")

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

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

inline XMVECTOR XMVectorSetBinaryConstant(uint32_t C0, uint32_t C1, uint32_t C2, uint32_t C3)
{
#if defined(_XM_NO_INTRINSICS_)
    XMVECTORU32 vResult;
    vResult.u[0] = (0-(C0&1)) & 0x3F800000;
    vResult.u[1] = (0-(C1&1)) & 0x3F800000;
    vResult.u[2] = (0-(C2&1)) & 0x3F800000;
    vResult.u[3] = (0-(C3&1)) & 0x3F800000;
    return vResult.v;
#elif defined(_XM_ARM_NEON_INTRINSICS_)
    XMVECTORU32 vResult;
    vResult.u[0] = (0-(C0&1)) & 0x3F800000;
    vResult.u[1] = (0-(C1&1)) & 0x3F800000;
    vResult.u[2] = (0-(C2&1)) & 0x3F800000;
    vResult.u[3] = (0-(C3&1)) & 0x3F800000;
    return vResult.v;
#else // XM_SSE_INTRINSICS_
    static const XMVECTORU32 g_vMask1 = {1,1,1,1};
    // Move the parms to a vector
    __m128i vTemp = _mm_set_epi32(C3,C2,C1,C0);
    // Mask off the low bits
    vTemp = _mm_and_si128(vTemp,g_vMask1);
    // 0xFFFFFFFF on true bits
    vTemp = _mm_cmpeq_epi32(vTemp,g_vMask1);
    // 0xFFFFFFFF -> 1.0f, 0x00000000 -> 0.0f
    vTemp = _mm_and_si128(vTemp,g_XMOne);
    return _mm_castsi128_ps(vTemp);
#endif
}

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

inline XMVECTOR XMVectorSplatConstant(int32_t IntConstant, uint32_t DivExponent)
{
    assert( IntConstant >= -16 && IntConstant <= 15 );
    assert( DivExponent < 32 );
#if defined(_XM_NO_INTRINSICS_)

    using DirectX::XMConvertVectorIntToFloat;

    XMVECTORI32 V = { IntConstant, IntConstant, IntConstant, IntConstant };
    return XMConvertVectorIntToFloat( V.v, DivExponent);

#elif defined(_XM_ARM_NEON_INTRINSICS_)
    // Splat the int
    int32x4_t vScale = vdupq_n_s32(IntConstant);
    // Convert to a float
    XMVECTOR vResult = vcvtq_f32_s32(vScale);
    // Convert DivExponent into 1.0f/(1<<DivExponent)
    uint32_t uScale = 0x3F800000U - (DivExponent << 23);
    // Splat the scalar value (It's really a float)
    vScale = vdupq_n_s32(uScale);
    // Multiply by the reciprocal (Perform a right shift by DivExponent)
    vResult = vmulq_f32(vResult,reinterpret_cast<const float32x4_t *>(&vScale)[0]);
    return vResult;
#else // XM_SSE_INTRINSICS_
    // Splat the int
    __m128i vScale = _mm_set1_epi32(IntConstant);
    // Convert to a float
    XMVECTOR vResult = _mm_cvtepi32_ps(vScale);
    // Convert DivExponent into 1.0f/(1<<DivExponent)
    uint32_t uScale = 0x3F800000U - (DivExponent << 23);
    // Splat the scalar value (It's really a float)
    vScale = _mm_set1_epi32(uScale);
    // Multiply by the reciprocal (Perform a right shift by DivExponent)
    vResult = _mm_mul_ps(vResult,_mm_castsi128_ps(vScale));
    return vResult;
#endif
}

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

inline XMVECTOR XMVectorSplatConstantInt(int32_t IntConstant)
{
    assert( IntConstant >= -16 && IntConstant <= 15 );
#if defined(_XM_NO_INTRINSICS_)

    XMVECTORI32 V = { IntConstant, IntConstant, IntConstant, IntConstant };
    return V.v;

#elif defined(_XM_ARM_NEON_INTRINSICS_)
    int32x4_t V = vdupq_n_s32( IntConstant );
    return reinterpret_cast<float32x4_t *>(&V)[0];
#else // XM_SSE_INTRINSICS_
    __m128i V = _mm_set1_epi32( IntConstant );
    return reinterpret_cast<__m128 *>(&V)[0];
#endif
}

// Implemented for VMX128 intrinsics as #defines aboves
#endif // _XM_NO_INTRINSICS_ || _XM_SSE_INTRINSICS_ || _XM_ARM_NEON_INTRINSICS_

#include "DirectXMathConvert.inl"
#include "DirectXMathVector.inl"
#include "DirectXMathMatrix.inl"
#include "DirectXMathMisc.inl"


#pragma prefast(pop)
#pragma warning(pop)

}; // namespace DirectX