btMatrix3x3.h

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/*
Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans  http://continuousphysics.com/Bullet/

This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose, 
including commercial applications, and to alter it and redistribute it freely, 
subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/


#ifndef BT_MATRIX3x3_H
#define BT_MATRIX3x3_H

#include "btVector3.h"
#include "btQuaternion.h"
#include <stdio.h>

#ifdef BT_USE_SSE
//const __m128 ATTRIBUTE_ALIGNED16(v2220) = {2.0f, 2.0f, 2.0f, 0.0f};
//const __m128 ATTRIBUTE_ALIGNED16(vMPPP) = {-0.0f, +0.0f, +0.0f, +0.0f};
#define vMPPP (_mm_set_ps (+0.0f, +0.0f, +0.0f, -0.0f))
#endif

#if defined(BT_USE_SSE)
#define v1000 (_mm_set_ps(0.0f,0.0f,0.0f,1.0f))
#define v0100 (_mm_set_ps(0.0f,0.0f,1.0f,0.0f))
#define v0010 (_mm_set_ps(0.0f,1.0f,0.0f,0.0f))
#elif defined(BT_USE_NEON)
const btSimdFloat4 ATTRIBUTE_ALIGNED16(v1000) = {1.0f, 0.0f, 0.0f, 0.0f};
const btSimdFloat4 ATTRIBUTE_ALIGNED16(v0100) = {0.0f, 1.0f, 0.0f, 0.0f};
const btSimdFloat4 ATTRIBUTE_ALIGNED16(v0010) = {0.0f, 0.0f, 1.0f, 0.0f};
#endif

#ifdef BT_USE_DOUBLE_PRECISION
#define btMatrix3x3Data btMatrix3x3DoubleData 
#else
#define btMatrix3x3Data btMatrix3x3FloatData
#endif //BT_USE_DOUBLE_PRECISION


ATTRIBUTE_ALIGNED16(class) btMatrix3x3 {

        btVector3 m_el[3];

public:
        btMatrix3x3 () {}

        //              explicit btMatrix3x3(const btScalar *m) { setFromOpenGLSubMatrix(m); }

        explicit btMatrix3x3(const btQuaternion& q) { setRotation(q); }
        /*
        template <typename btScalar>
        Matrix3x3(const btScalar& yaw, const btScalar& pitch, const btScalar& roll)
        { 
        setEulerYPR(yaw, pitch, roll);
        }
        */
        btMatrix3x3(const btScalar& xx, const btScalar& xy, const btScalar& xz,
                const btScalar& yx, const btScalar& yy, const btScalar& yz,
                const btScalar& zx, const btScalar& zy, const btScalar& zz)
        { 
                setValue(xx, xy, xz, 
                        yx, yy, yz, 
                        zx, zy, zz);
        }

#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
        SIMD_FORCE_INLINE btMatrix3x3 (const btSimdFloat4 v0, const btSimdFloat4 v1, const btSimdFloat4 v2 ) 
        {
        m_el[0].mVec128 = v0;
        m_el[1].mVec128 = v1;
        m_el[2].mVec128 = v2;
        }

        SIMD_FORCE_INLINE btMatrix3x3 (const btVector3& v0, const btVector3& v1, const btVector3& v2 ) 
        {
        m_el[0] = v0;
        m_el[1] = v1;
        m_el[2] = v2;
        }

        // Copy constructor
        SIMD_FORCE_INLINE btMatrix3x3(const btMatrix3x3& rhs)
        {
                m_el[0].mVec128 = rhs.m_el[0].mVec128;
                m_el[1].mVec128 = rhs.m_el[1].mVec128;
                m_el[2].mVec128 = rhs.m_el[2].mVec128;
        }

        // Assignment Operator
        SIMD_FORCE_INLINE btMatrix3x3& operator=(const btMatrix3x3& m) 
        {
                m_el[0].mVec128 = m.m_el[0].mVec128;
                m_el[1].mVec128 = m.m_el[1].mVec128;
                m_el[2].mVec128 = m.m_el[2].mVec128;
                
                return *this;
        }

#else

        SIMD_FORCE_INLINE btMatrix3x3 (const btMatrix3x3& other)
        {
                m_el[0] = other.m_el[0];
                m_el[1] = other.m_el[1];
                m_el[2] = other.m_el[2];
        }
    
        SIMD_FORCE_INLINE btMatrix3x3& operator=(const btMatrix3x3& other)
        {
                m_el[0] = other.m_el[0];
                m_el[1] = other.m_el[1];
                m_el[2] = other.m_el[2];
                return *this;
        }

#endif

        SIMD_FORCE_INLINE btVector3 getColumn(int i) const
        {
                return btVector3(m_el[0][i],m_el[1][i],m_el[2][i]);
        }


        SIMD_FORCE_INLINE const btVector3& getRow(int i) const
        {
                btFullAssert(0 <= i && i < 3);
                return m_el[i];
        }

        SIMD_FORCE_INLINE btVector3&  operator[](int i)
        { 
                btFullAssert(0 <= i && i < 3);
                return m_el[i]; 
        }

        SIMD_FORCE_INLINE const btVector3& operator[](int i) const
        {
                btFullAssert(0 <= i && i < 3);
                return m_el[i]; 
        }

        btMatrix3x3& operator*=(const btMatrix3x3& m); 

        btMatrix3x3& operator+=(const btMatrix3x3& m); 

        btMatrix3x3& operator-=(const btMatrix3x3& m); 

        void setFromOpenGLSubMatrix(const btScalar *m)
        {
                m_el[0].setValue(m[0],m[4],m[8]);
                m_el[1].setValue(m[1],m[5],m[9]);
                m_el[2].setValue(m[2],m[6],m[10]);

        }
        void setValue(const btScalar& xx, const btScalar& xy, const btScalar& xz, 
                const btScalar& yx, const btScalar& yy, const btScalar& yz, 
                const btScalar& zx, const btScalar& zy, const btScalar& zz)
        {
                m_el[0].setValue(xx,xy,xz);
                m_el[1].setValue(yx,yy,yz);
                m_el[2].setValue(zx,zy,zz);
        }

        void setRotation(const btQuaternion& q) 
        {
                btScalar d = q.length2();
                btFullAssert(d != btScalar(0.0));
                btScalar s = btScalar(2.0) / d;
    
    #if defined BT_USE_SIMD_VECTOR3 && defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE)
        __m128  vs, Q = q.get128();
                __m128i Qi = btCastfTo128i(Q);
        __m128  Y, Z;
        __m128  V1, V2, V3;
        __m128  V11, V21, V31;
        __m128  NQ = _mm_xor_ps(Q, btvMzeroMask);
                __m128i NQi = btCastfTo128i(NQ);
        
        V1 = btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(1,0,2,3)));        // Y X Z W
                V2 = _mm_shuffle_ps(NQ, Q, BT_SHUFFLE(0,0,1,3));     // -X -X  Y  W
        V3 = btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(2,1,0,3)));        // Z Y X W
        V1 = _mm_xor_ps(V1, vMPPP);     //      change the sign of the first element
                        
        V11     = btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(1,1,0,3)));   // Y Y X W
                V21 = _mm_unpackhi_ps(Q, Q);                    //  Z  Z  W  W
                V31 = _mm_shuffle_ps(Q, NQ, BT_SHUFFLE(0,2,0,3));       //  X  Z -X -W

                V2 = V2 * V1;   //
                V1 = V1 * V11;  //
                V3 = V3 * V31;  //

        V11 = _mm_shuffle_ps(NQ, Q, BT_SHUFFLE(2,3,1,3));       //      -Z -W  Y  W
                V11 = V11 * V21;        //
        V21 = _mm_xor_ps(V21, vMPPP);   //      change the sign of the first element
                V31 = _mm_shuffle_ps(Q, NQ, BT_SHUFFLE(3,3,1,3));       //       W  W -Y -W
        V31 = _mm_xor_ps(V31, vMPPP);   //      change the sign of the first element
                Y = btCastiTo128f(_mm_shuffle_epi32 (NQi, BT_SHUFFLE(3,2,0,3)));        // -W -Z -X -W
                Z = btCastiTo128f(_mm_shuffle_epi32 (Qi, BT_SHUFFLE(1,0,1,3))); //  Y  X  Y  W

                vs = _mm_load_ss(&s);
                V21 = V21 * Y;
                V31 = V31 * Z;

                V1 = V1 + V11;
        V2 = V2 + V21;
        V3 = V3 + V31;

        vs = bt_splat3_ps(vs, 0);
            //  s ready
        V1 = V1 * vs;
        V2 = V2 * vs;
        V3 = V3 * vs;
        
        V1 = V1 + v1000;
        V2 = V2 + v0100;
        V3 = V3 + v0010;
        
        m_el[0] = V1; 
        m_el[1] = V2;
        m_el[2] = V3;
    #else    
                btScalar xs = q.x() * s,   ys = q.y() * s,   zs = q.z() * s;
                btScalar wx = q.w() * xs,  wy = q.w() * ys,  wz = q.w() * zs;
                btScalar xx = q.x() * xs,  xy = q.x() * ys,  xz = q.x() * zs;
                btScalar yy = q.y() * ys,  yz = q.y() * zs,  zz = q.z() * zs;
                setValue(
            btScalar(1.0) - (yy + zz), xy - wz, xz + wy,
                        xy + wz, btScalar(1.0) - (xx + zz), yz - wx,
                        xz - wy, yz + wx, btScalar(1.0) - (xx + yy));
        #endif
    }


        void setEulerYPR(const btScalar& yaw, const btScalar& pitch, const btScalar& roll) 
        {
                setEulerZYX(roll, pitch, yaw);
        }

        void setEulerZYX(btScalar eulerX,btScalar eulerY,btScalar eulerZ) { 
                btScalar ci ( btCos(eulerX)); 
                btScalar cj ( btCos(eulerY)); 
                btScalar ch ( btCos(eulerZ)); 
                btScalar si ( btSin(eulerX)); 
                btScalar sj ( btSin(eulerY)); 
                btScalar sh ( btSin(eulerZ)); 
                btScalar cc = ci * ch; 
                btScalar cs = ci * sh; 
                btScalar sc = si * ch; 
                btScalar ss = si * sh;

                setValue(cj * ch, sj * sc - cs, sj * cc + ss,
                        cj * sh, sj * ss + cc, sj * cs - sc, 
                        -sj,      cj * si,      cj * ci);
        }

        void setIdentity()
        { 
#if (defined(BT_USE_SSE_IN_API)&& defined (BT_USE_SSE)) || defined(BT_USE_NEON)
                        m_el[0] = v1000; 
                        m_el[1] = v0100;
                        m_el[2] = v0010;
#else
                setValue(btScalar(1.0), btScalar(0.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(1.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(0.0), btScalar(1.0)); 
#endif
        }

        static const btMatrix3x3&       getIdentity()
        {
#if (defined(BT_USE_SSE_IN_API)&& defined (BT_USE_SSE)) || defined(BT_USE_NEON)
        static const btMatrix3x3 
        identityMatrix(v1000, v0100, v0010);
#else
                static const btMatrix3x3 
        identityMatrix(
            btScalar(1.0), btScalar(0.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(1.0), btScalar(0.0), 
                        btScalar(0.0), btScalar(0.0), btScalar(1.0));
#endif
                return identityMatrix;
        }

        void getOpenGLSubMatrix(btScalar *m) const 
        {
#if defined BT_USE_SIMD_VECTOR3 && defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE)
        __m128 v0 = m_el[0].mVec128;
        __m128 v1 = m_el[1].mVec128;
        __m128 v2 = m_el[2].mVec128;    //  x2 y2 z2 w2
        __m128 *vm = (__m128 *)m;
        __m128 vT;
        
        v2 = _mm_and_ps(v2, btvFFF0fMask);  //  x2 y2 z2 0
        
        vT = _mm_unpackhi_ps(v0, v1);   //      z0 z1 * *
        v0 = _mm_unpacklo_ps(v0, v1);   //      x0 x1 y0 y1

        v1 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(2, 3, 1, 3) );   // y0 y1 y2 0
        v0 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(0, 1, 0, 3) );   // x0 x1 x2 0
        v2 = btCastdTo128f(_mm_move_sd(btCastfTo128d(v2), btCastfTo128d(vT)));  // z0 z1 z2 0

        vm[0] = v0;
        vm[1] = v1;
        vm[2] = v2;
#elif defined(BT_USE_NEON)
        // note: zeros the w channel. We can preserve it at the cost of two more vtrn instructions.
        static const uint32x2_t zMask = (const uint32x2_t) {static_cast<uint32_t>(-1), 0 };
        float32x4_t *vm = (float32x4_t *)m;
        float32x4x2_t top = vtrnq_f32( m_el[0].mVec128, m_el[1].mVec128 );  // {x0 x1 z0 z1}, {y0 y1 w0 w1}
        float32x2x2_t bl = vtrn_f32( vget_low_f32(m_el[2].mVec128), vdup_n_f32(0.0f) );       // {x2  0 }, {y2 0}
        float32x4_t v0 = vcombine_f32( vget_low_f32(top.val[0]), bl.val[0] );
        float32x4_t v1 = vcombine_f32( vget_low_f32(top.val[1]), bl.val[1] );
        float32x2_t q = (float32x2_t) vand_u32( (uint32x2_t) vget_high_f32( m_el[2].mVec128), zMask );
        float32x4_t v2 = vcombine_f32( vget_high_f32(top.val[0]), q );       // z0 z1 z2  0

        vm[0] = v0;
        vm[1] = v1;
        vm[2] = v2;
#else
                m[0]  = btScalar(m_el[0].x()); 
                m[1]  = btScalar(m_el[1].x());
                m[2]  = btScalar(m_el[2].x());
                m[3]  = btScalar(0.0); 
                m[4]  = btScalar(m_el[0].y());
                m[5]  = btScalar(m_el[1].y());
                m[6]  = btScalar(m_el[2].y());
                m[7]  = btScalar(0.0); 
                m[8]  = btScalar(m_el[0].z()); 
                m[9]  = btScalar(m_el[1].z());
                m[10] = btScalar(m_el[2].z());
                m[11] = btScalar(0.0); 
#endif
        }

        void getRotation(btQuaternion& q) const
        {
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
        btScalar trace = m_el[0].x() + m_el[1].y() + m_el[2].z();
        btScalar s, x;
        
        union {
            btSimdFloat4 vec;
            btScalar f[4];
        } temp;
        
        if (trace > btScalar(0.0)) 
        {
            x = trace + btScalar(1.0);

            temp.f[0]=m_el[2].y() - m_el[1].z();
            temp.f[1]=m_el[0].z() - m_el[2].x();
            temp.f[2]=m_el[1].x() - m_el[0].y();
            temp.f[3]=x;
            //temp.f[3]= s * btScalar(0.5);
        } 
        else 
        {
            int i, j, k;
            if(m_el[0].x() < m_el[1].y()) 
            { 
                if( m_el[1].y() < m_el[2].z() )
                    { i = 2; j = 0; k = 1; }
                else
                    { i = 1; j = 2; k = 0; }
            }
            else
            {
                if( m_el[0].x() < m_el[2].z())
                    { i = 2; j = 0; k = 1; }
                else
                    { i = 0; j = 1; k = 2; }
            }

            x = m_el[i][i] - m_el[j][j] - m_el[k][k] + btScalar(1.0);

            temp.f[3] = (m_el[k][j] - m_el[j][k]);
            temp.f[j] = (m_el[j][i] + m_el[i][j]);
            temp.f[k] = (m_el[k][i] + m_el[i][k]);
            temp.f[i] = x;
            //temp.f[i] = s * btScalar(0.5);
        }

        s = btSqrt(x);
        q.set128(temp.vec);
        s = btScalar(0.5) / s;

        q *= s;
#else    
                btScalar trace = m_el[0].x() + m_el[1].y() + m_el[2].z();

                btScalar temp[4];

                if (trace > btScalar(0.0)) 
                {
                        btScalar s = btSqrt(trace + btScalar(1.0));
                        temp[3]=(s * btScalar(0.5));
                        s = btScalar(0.5) / s;

                        temp[0]=((m_el[2].y() - m_el[1].z()) * s);
                        temp[1]=((m_el[0].z() - m_el[2].x()) * s);
                        temp[2]=((m_el[1].x() - m_el[0].y()) * s);
                } 
                else 
                {
                        int i = m_el[0].x() < m_el[1].y() ? 
                                (m_el[1].y() < m_el[2].z() ? 2 : 1) :
                                (m_el[0].x() < m_el[2].z() ? 2 : 0); 
                        int j = (i + 1) % 3;  
                        int k = (i + 2) % 3;

                        btScalar s = btSqrt(m_el[i][i] - m_el[j][j] - m_el[k][k] + btScalar(1.0));
                        temp[i] = s * btScalar(0.5);
                        s = btScalar(0.5) / s;

                        temp[3] = (m_el[k][j] - m_el[j][k]) * s;
                        temp[j] = (m_el[j][i] + m_el[i][j]) * s;
                        temp[k] = (m_el[k][i] + m_el[i][k]) * s;
                }
                q.setValue(temp[0],temp[1],temp[2],temp[3]);
#endif
        }

        void getEulerYPR(btScalar& yaw, btScalar& pitch, btScalar& roll) const
        {

                // first use the normal calculus
                yaw = btScalar(btAtan2(m_el[1].x(), m_el[0].x()));
                pitch = btScalar(btAsin(-m_el[2].x()));
                roll = btScalar(btAtan2(m_el[2].y(), m_el[2].z()));

                // on pitch = +/-HalfPI
                if (btFabs(pitch)==SIMD_HALF_PI)
                {
                        if (yaw>0)
                                yaw-=SIMD_PI;
                        else
                                yaw+=SIMD_PI;

                        if (roll>0)
                                roll-=SIMD_PI;
                        else
                                roll+=SIMD_PI;
                }
        };


        void getEulerZYX(btScalar& yaw, btScalar& pitch, btScalar& roll, unsigned int solution_number = 1) const
        {
                struct Euler
                {
                        btScalar yaw;
                        btScalar pitch;
                        btScalar roll;
                };

                Euler euler_out;
                Euler euler_out2; //second solution
                //get the pointer to the raw data

                // Check that pitch is not at a singularity
                if (btFabs(m_el[2].x()) >= 1)
                {
                        euler_out.yaw = 0;
                        euler_out2.yaw = 0;

                        // From difference of angles formula
                        btScalar delta = btAtan2(m_el[0].x(),m_el[0].z());
                        if (m_el[2].x() > 0)  //gimbal locked up
                        {
                                euler_out.pitch = SIMD_PI / btScalar(2.0);
                                euler_out2.pitch = SIMD_PI / btScalar(2.0);
                                euler_out.roll = euler_out.pitch + delta;
                                euler_out2.roll = euler_out.pitch + delta;
                        }
                        else // gimbal locked down
                        {
                                euler_out.pitch = -SIMD_PI / btScalar(2.0);
                                euler_out2.pitch = -SIMD_PI / btScalar(2.0);
                                euler_out.roll = -euler_out.pitch + delta;
                                euler_out2.roll = -euler_out.pitch + delta;
                        }
                }
                else
                {
                        euler_out.pitch = - btAsin(m_el[2].x());
                        euler_out2.pitch = SIMD_PI - euler_out.pitch;

                        euler_out.roll = btAtan2(m_el[2].y()/btCos(euler_out.pitch), 
                                m_el[2].z()/btCos(euler_out.pitch));
                        euler_out2.roll = btAtan2(m_el[2].y()/btCos(euler_out2.pitch), 
                                m_el[2].z()/btCos(euler_out2.pitch));

                        euler_out.yaw = btAtan2(m_el[1].x()/btCos(euler_out.pitch), 
                                m_el[0].x()/btCos(euler_out.pitch));
                        euler_out2.yaw = btAtan2(m_el[1].x()/btCos(euler_out2.pitch), 
                                m_el[0].x()/btCos(euler_out2.pitch));
                }

                if (solution_number == 1)
                { 
                        yaw = euler_out.yaw; 
                        pitch = euler_out.pitch;
                        roll = euler_out.roll;
                }
                else
                { 
                        yaw = euler_out2.yaw; 
                        pitch = euler_out2.pitch;
                        roll = euler_out2.roll;
                }
        }

        btMatrix3x3 scaled(const btVector3& s) const
        {
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
                return btMatrix3x3(m_el[0] * s, m_el[1] * s, m_el[2] * s);
#else           
                return btMatrix3x3(
            m_el[0].x() * s.x(), m_el[0].y() * s.y(), m_el[0].z() * s.z(),
                        m_el[1].x() * s.x(), m_el[1].y() * s.y(), m_el[1].z() * s.z(),
                        m_el[2].x() * s.x(), m_el[2].y() * s.y(), m_el[2].z() * s.z());
#endif
        }

        btScalar            determinant() const;
        btMatrix3x3 adjoint() const;
        btMatrix3x3 absolute() const;
        btMatrix3x3 transpose() const;
        btMatrix3x3 inverse() const; 

        btVector3 solve33(const btVector3& b) const
        {
                btVector3 col1 = getColumn(0);
                btVector3 col2 = getColumn(1);
                btVector3 col3 = getColumn(2);
                
                btScalar det = btDot(col1, btCross(col2, col3));
                if (btFabs(det)>SIMD_EPSILON)
                {
                        det = 1.0f / det;
                }
                btVector3 x;
                x[0] = det * btDot(b, btCross(col2, col3));
                x[1] = det * btDot(col1, btCross(b, col3));
                x[2] = det * btDot(col1, btCross(col2, b));
                return x;
        }

        btMatrix3x3 transposeTimes(const btMatrix3x3& m) const;
        btMatrix3x3 timesTranspose(const btMatrix3x3& m) const;

        SIMD_FORCE_INLINE btScalar tdotx(const btVector3& v) const 
        {
                return m_el[0].x() * v.x() + m_el[1].x() * v.y() + m_el[2].x() * v.z();
        }
        SIMD_FORCE_INLINE btScalar tdoty(const btVector3& v) const 
        {
                return m_el[0].y() * v.x() + m_el[1].y() * v.y() + m_el[2].y() * v.z();
        }
        SIMD_FORCE_INLINE btScalar tdotz(const btVector3& v) const 
        {
                return m_el[0].z() * v.x() + m_el[1].z() * v.y() + m_el[2].z() * v.z();
        }

        SIMD_FORCE_INLINE void extractRotation(btQuaternion &q,btScalar tolerance = 1.0e-9, int maxIter=100)
        {
                int iter =0;
                btScalar w;
                const btMatrix3x3& A=*this;
                for(iter = 0; iter < maxIter; iter++)
                {
                        btMatrix3x3 R(q);
                        btVector3 omega = (R.getColumn(0).cross(A.getColumn(0)) + R.getColumn(1).cross(A.getColumn(1)) 
                                + R.getColumn(2).cross(A.getColumn(2))
                                ) * (btScalar(1.0) / btFabs(R.getColumn(0).dot(A.getColumn(0)) + R.getColumn
                                (1).dot(A.getColumn(1)) + R.getColumn(2).dot(A.getColumn(2))) +
                                        tolerance);
                        w = omega.norm();
                        if(w < tolerance)
                                break;
                        q = btQuaternion(btVector3((btScalar(1.0) / w) * omega),w) *
                                q;
                        q.normalize();
                }
        }




        void diagonalize(btMatrix3x3& rot, btScalar threshold, int maxSteps)
        {
                rot.setIdentity();
                for (int step = maxSteps; step > 0; step--)
                {
                        // find off-diagonal element [p][q] with largest magnitude
                        int p = 0;
                        int q = 1;
                        int r = 2;
                        btScalar max = btFabs(m_el[0][1]);
                        btScalar v = btFabs(m_el[0][2]);
                        if (v > max)
                        {
                                q = 2;
                                r = 1;
                                max = v;
                        }
                        v = btFabs(m_el[1][2]);
                        if (v > max)
                        {
                                p = 1;
                                q = 2;
                                r = 0;
                                max = v;
                        }

                        btScalar t = threshold * (btFabs(m_el[0][0]) + btFabs(m_el[1][1]) + btFabs(m_el[2][2]));
                        if (max <= t)
                        {
                                if (max <= SIMD_EPSILON * t)
                                {
                                        return;
                                }
                                step = 1;
                        }

                        // compute Jacobi rotation J which leads to a zero for element [p][q] 
                        btScalar mpq = m_el[p][q];
                        btScalar theta = (m_el[q][q] - m_el[p][p]) / (2 * mpq);
                        btScalar theta2 = theta * theta;
                        btScalar cos;
                        btScalar sin;
                        if (theta2 * theta2 < btScalar(10 / SIMD_EPSILON))
                        {
                                t = (theta >= 0) ? 1 / (theta + btSqrt(1 + theta2))
                                        : 1 / (theta - btSqrt(1 + theta2));
                                cos = 1 / btSqrt(1 + t * t);
                                sin = cos * t;
                        }
                        else
                        {
                                // approximation for large theta-value, i.e., a nearly diagonal matrix
                                t = 1 / (theta * (2 + btScalar(0.5) / theta2));
                                cos = 1 - btScalar(0.5) * t * t;
                                sin = cos * t;
                        }

                        // apply rotation to matrix (this = J^T * this * J)
                        m_el[p][q] = m_el[q][p] = 0;
                        m_el[p][p] -= t * mpq;
                        m_el[q][q] += t * mpq;
                        btScalar mrp = m_el[r][p];
                        btScalar mrq = m_el[r][q];
                        m_el[r][p] = m_el[p][r] = cos * mrp - sin * mrq;
                        m_el[r][q] = m_el[q][r] = cos * mrq + sin * mrp;

                        // apply rotation to rot (rot = rot * J)
                        for (int i = 0; i < 3; i++)
                        {
                                btVector3& row = rot[i];
                                mrp = row[p];
                                mrq = row[q];
                                row[p] = cos * mrp - sin * mrq;
                                row[q] = cos * mrq + sin * mrp;
                        }
                }
        }



        btScalar cofac(int r1, int c1, int r2, int c2) const 
        {
                return m_el[r1][c1] * m_el[r2][c2] - m_el[r1][c2] * m_el[r2][c1];
        }

        void    serialize(struct        btMatrix3x3Data& dataOut) const;

        void    serializeFloat(struct   btMatrix3x3FloatData& dataOut) const;

        void    deSerialize(const struct        btMatrix3x3Data& dataIn);

        void    deSerializeFloat(const struct   btMatrix3x3FloatData& dataIn);

        void    deSerializeDouble(const struct  btMatrix3x3DoubleData& dataIn);

};


SIMD_FORCE_INLINE btMatrix3x3& 
btMatrix3x3::operator*=(const btMatrix3x3& m)
{
#if defined BT_USE_SIMD_VECTOR3 && defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE)
    __m128 rv00, rv01, rv02;
    __m128 rv10, rv11, rv12;
    __m128 rv20, rv21, rv22;
    __m128 mv0, mv1, mv2;

    rv02 = m_el[0].mVec128;
    rv12 = m_el[1].mVec128;
    rv22 = m_el[2].mVec128;

    mv0 = _mm_and_ps(m[0].mVec128, btvFFF0fMask); 
    mv1 = _mm_and_ps(m[1].mVec128, btvFFF0fMask); 
    mv2 = _mm_and_ps(m[2].mVec128, btvFFF0fMask); 
    
    // rv0
    rv00 = bt_splat_ps(rv02, 0);
    rv01 = bt_splat_ps(rv02, 1);
    rv02 = bt_splat_ps(rv02, 2);
    
    rv00 = _mm_mul_ps(rv00, mv0);
    rv01 = _mm_mul_ps(rv01, mv1);
    rv02 = _mm_mul_ps(rv02, mv2);
    
    // rv1
    rv10 = bt_splat_ps(rv12, 0);
    rv11 = bt_splat_ps(rv12, 1);
    rv12 = bt_splat_ps(rv12, 2);
    
    rv10 = _mm_mul_ps(rv10, mv0);
    rv11 = _mm_mul_ps(rv11, mv1);
    rv12 = _mm_mul_ps(rv12, mv2);
    
    // rv2
    rv20 = bt_splat_ps(rv22, 0);
    rv21 = bt_splat_ps(rv22, 1);
    rv22 = bt_splat_ps(rv22, 2);
    
    rv20 = _mm_mul_ps(rv20, mv0);
    rv21 = _mm_mul_ps(rv21, mv1);
    rv22 = _mm_mul_ps(rv22, mv2);

    rv00 = _mm_add_ps(rv00, rv01);
    rv10 = _mm_add_ps(rv10, rv11);
    rv20 = _mm_add_ps(rv20, rv21);

    m_el[0].mVec128 = _mm_add_ps(rv00, rv02);
    m_el[1].mVec128 = _mm_add_ps(rv10, rv12);
    m_el[2].mVec128 = _mm_add_ps(rv20, rv22);

#elif defined(BT_USE_NEON)

    float32x4_t rv0, rv1, rv2;
    float32x4_t v0, v1, v2;
    float32x4_t mv0, mv1, mv2;

    v0 = m_el[0].mVec128;
    v1 = m_el[1].mVec128;
    v2 = m_el[2].mVec128;

    mv0 = (float32x4_t) vandq_s32((int32x4_t)m[0].mVec128, btvFFF0Mask); 
    mv1 = (float32x4_t) vandq_s32((int32x4_t)m[1].mVec128, btvFFF0Mask); 
    mv2 = (float32x4_t) vandq_s32((int32x4_t)m[2].mVec128, btvFFF0Mask); 
    
    rv0 = vmulq_lane_f32(mv0, vget_low_f32(v0), 0);
    rv1 = vmulq_lane_f32(mv0, vget_low_f32(v1), 0);
    rv2 = vmulq_lane_f32(mv0, vget_low_f32(v2), 0);
    
    rv0 = vmlaq_lane_f32(rv0, mv1, vget_low_f32(v0), 1);
    rv1 = vmlaq_lane_f32(rv1, mv1, vget_low_f32(v1), 1);
    rv2 = vmlaq_lane_f32(rv2, mv1, vget_low_f32(v2), 1);
    
    rv0 = vmlaq_lane_f32(rv0, mv2, vget_high_f32(v0), 0);
    rv1 = vmlaq_lane_f32(rv1, mv2, vget_high_f32(v1), 0);
    rv2 = vmlaq_lane_f32(rv2, mv2, vget_high_f32(v2), 0);

    m_el[0].mVec128 = rv0;
    m_el[1].mVec128 = rv1;
    m_el[2].mVec128 = rv2;
#else    
        setValue(
        m.tdotx(m_el[0]), m.tdoty(m_el[0]), m.tdotz(m_el[0]),
                m.tdotx(m_el[1]), m.tdoty(m_el[1]), m.tdotz(m_el[1]),
                m.tdotx(m_el[2]), m.tdoty(m_el[2]), m.tdotz(m_el[2]));
#endif
        return *this;
}

SIMD_FORCE_INLINE btMatrix3x3& 
btMatrix3x3::operator+=(const btMatrix3x3& m)
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
    m_el[0].mVec128 = m_el[0].mVec128 + m.m_el[0].mVec128;
    m_el[1].mVec128 = m_el[1].mVec128 + m.m_el[1].mVec128;
    m_el[2].mVec128 = m_el[2].mVec128 + m.m_el[2].mVec128;
#else
        setValue(
                m_el[0][0]+m.m_el[0][0], 
                m_el[0][1]+m.m_el[0][1],
                m_el[0][2]+m.m_el[0][2],
                m_el[1][0]+m.m_el[1][0], 
                m_el[1][1]+m.m_el[1][1],
                m_el[1][2]+m.m_el[1][2],
                m_el[2][0]+m.m_el[2][0], 
                m_el[2][1]+m.m_el[2][1],
                m_el[2][2]+m.m_el[2][2]);
#endif
        return *this;
}

SIMD_FORCE_INLINE btMatrix3x3
operator*(const btMatrix3x3& m, const btScalar & k)
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
    __m128 vk = bt_splat_ps(_mm_load_ss((float *)&k), 0x80);
    return btMatrix3x3(
                _mm_mul_ps(m[0].mVec128, vk), 
                _mm_mul_ps(m[1].mVec128, vk), 
                _mm_mul_ps(m[2].mVec128, vk)); 
#elif defined(BT_USE_NEON)
    return btMatrix3x3(
                vmulq_n_f32(m[0].mVec128, k),
                vmulq_n_f32(m[1].mVec128, k),
                vmulq_n_f32(m[2].mVec128, k)); 
#else
        return btMatrix3x3(
                m[0].x()*k,m[0].y()*k,m[0].z()*k,
                m[1].x()*k,m[1].y()*k,m[1].z()*k,
                m[2].x()*k,m[2].y()*k,m[2].z()*k);
#endif
}

SIMD_FORCE_INLINE btMatrix3x3 
operator+(const btMatrix3x3& m1, const btMatrix3x3& m2)
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
        return btMatrix3x3(
        m1[0].mVec128 + m2[0].mVec128,
        m1[1].mVec128 + m2[1].mVec128,
        m1[2].mVec128 + m2[2].mVec128);
#else
        return btMatrix3x3(
        m1[0][0]+m2[0][0], 
        m1[0][1]+m2[0][1],
        m1[0][2]+m2[0][2],
        
        m1[1][0]+m2[1][0], 
        m1[1][1]+m2[1][1],
        m1[1][2]+m2[1][2],
        
        m1[2][0]+m2[2][0], 
        m1[2][1]+m2[2][1],
        m1[2][2]+m2[2][2]);
#endif    
}

SIMD_FORCE_INLINE btMatrix3x3 
operator-(const btMatrix3x3& m1, const btMatrix3x3& m2)
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
        return btMatrix3x3(
        m1[0].mVec128 - m2[0].mVec128,
        m1[1].mVec128 - m2[1].mVec128,
        m1[2].mVec128 - m2[2].mVec128);
#else
        return btMatrix3x3(
        m1[0][0]-m2[0][0], 
        m1[0][1]-m2[0][1],
        m1[0][2]-m2[0][2],
        
        m1[1][0]-m2[1][0], 
        m1[1][1]-m2[1][1],
        m1[1][2]-m2[1][2],
        
        m1[2][0]-m2[2][0], 
        m1[2][1]-m2[2][1],
        m1[2][2]-m2[2][2]);
#endif
}


SIMD_FORCE_INLINE btMatrix3x3& 
btMatrix3x3::operator-=(const btMatrix3x3& m)
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
    m_el[0].mVec128 = m_el[0].mVec128 - m.m_el[0].mVec128;
    m_el[1].mVec128 = m_el[1].mVec128 - m.m_el[1].mVec128;
    m_el[2].mVec128 = m_el[2].mVec128 - m.m_el[2].mVec128;
#else
        setValue(
        m_el[0][0]-m.m_el[0][0], 
        m_el[0][1]-m.m_el[0][1],
        m_el[0][2]-m.m_el[0][2],
        m_el[1][0]-m.m_el[1][0], 
        m_el[1][1]-m.m_el[1][1],
        m_el[1][2]-m.m_el[1][2],
        m_el[2][0]-m.m_el[2][0], 
        m_el[2][1]-m.m_el[2][1],
        m_el[2][2]-m.m_el[2][2]);
#endif
        return *this;
}


SIMD_FORCE_INLINE btScalar 
btMatrix3x3::determinant() const
{ 
        return btTriple((*this)[0], (*this)[1], (*this)[2]);
}


SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::absolute() const
{
#if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
    return btMatrix3x3(
            _mm_and_ps(m_el[0].mVec128, btvAbsfMask),
            _mm_and_ps(m_el[1].mVec128, btvAbsfMask),
            _mm_and_ps(m_el[2].mVec128, btvAbsfMask));
#elif defined(BT_USE_NEON)
    return btMatrix3x3(
            (float32x4_t)vandq_s32((int32x4_t)m_el[0].mVec128, btv3AbsMask),
            (float32x4_t)vandq_s32((int32x4_t)m_el[1].mVec128, btv3AbsMask),
            (float32x4_t)vandq_s32((int32x4_t)m_el[2].mVec128, btv3AbsMask));
#else   
        return btMatrix3x3(
            btFabs(m_el[0].x()), btFabs(m_el[0].y()), btFabs(m_el[0].z()),
            btFabs(m_el[1].x()), btFabs(m_el[1].y()), btFabs(m_el[1].z()),
            btFabs(m_el[2].x()), btFabs(m_el[2].y()), btFabs(m_el[2].z()));
#endif
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::transpose() const 
{
#if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
    __m128 v0 = m_el[0].mVec128;
    __m128 v1 = m_el[1].mVec128;
    __m128 v2 = m_el[2].mVec128;    //  x2 y2 z2 w2
    __m128 vT;
    
    v2 = _mm_and_ps(v2, btvFFF0fMask);  //  x2 y2 z2 0
    
    vT = _mm_unpackhi_ps(v0, v1);       //      z0 z1 * *
    v0 = _mm_unpacklo_ps(v0, v1);       //      x0 x1 y0 y1

    v1 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(2, 3, 1, 3) );       // y0 y1 y2 0
    v0 = _mm_shuffle_ps(v0, v2, BT_SHUFFLE(0, 1, 0, 3) );       // x0 x1 x2 0
    v2 = btCastdTo128f(_mm_move_sd(btCastfTo128d(v2), btCastfTo128d(vT)));      // z0 z1 z2 0


    return btMatrix3x3( v0, v1, v2 );
#elif defined(BT_USE_NEON)
    // note: zeros the w channel. We can preserve it at the cost of two more vtrn instructions.
    static const uint32x2_t zMask = (const uint32x2_t) {static_cast<uint32_t>(-1), 0 };
    float32x4x2_t top = vtrnq_f32( m_el[0].mVec128, m_el[1].mVec128 );  // {x0 x1 z0 z1}, {y0 y1 w0 w1}
    float32x2x2_t bl = vtrn_f32( vget_low_f32(m_el[2].mVec128), vdup_n_f32(0.0f) );       // {x2  0 }, {y2 0}
    float32x4_t v0 = vcombine_f32( vget_low_f32(top.val[0]), bl.val[0] );
    float32x4_t v1 = vcombine_f32( vget_low_f32(top.val[1]), bl.val[1] );
    float32x2_t q = (float32x2_t) vand_u32( (uint32x2_t) vget_high_f32( m_el[2].mVec128), zMask );
    float32x4_t v2 = vcombine_f32( vget_high_f32(top.val[0]), q );       // z0 z1 z2  0
    return btMatrix3x3( v0, v1, v2 ); 
#else
        return btMatrix3x3( m_el[0].x(), m_el[1].x(), m_el[2].x(),
                        m_el[0].y(), m_el[1].y(), m_el[2].y(),
                        m_el[0].z(), m_el[1].z(), m_el[2].z());
#endif
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::adjoint() const 
{
        return btMatrix3x3(cofac(1, 1, 2, 2), cofac(0, 2, 2, 1), cofac(0, 1, 1, 2),
                cofac(1, 2, 2, 0), cofac(0, 0, 2, 2), cofac(0, 2, 1, 0),
                cofac(1, 0, 2, 1), cofac(0, 1, 2, 0), cofac(0, 0, 1, 1));
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::inverse() const
{
        btVector3 co(cofac(1, 1, 2, 2), cofac(1, 2, 2, 0), cofac(1, 0, 2, 1));
        btScalar det = (*this)[0].dot(co);
        //btFullAssert(det != btScalar(0.0));
        btAssert(det != btScalar(0.0));
        btScalar s = btScalar(1.0) / det;
        return btMatrix3x3(co.x() * s, cofac(0, 2, 2, 1) * s, cofac(0, 1, 1, 2) * s,
                co.y() * s, cofac(0, 0, 2, 2) * s, cofac(0, 2, 1, 0) * s,
                co.z() * s, cofac(0, 1, 2, 0) * s, cofac(0, 0, 1, 1) * s);
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::transposeTimes(const btMatrix3x3& m) const
{
#if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
    // zeros w
//    static const __m128i xyzMask = (const __m128i){ -1ULL, 0xffffffffULL };
    __m128 row = m_el[0].mVec128;
    __m128 m0 = _mm_and_ps( m.getRow(0).mVec128, btvFFF0fMask );
    __m128 m1 = _mm_and_ps( m.getRow(1).mVec128, btvFFF0fMask);
    __m128 m2 = _mm_and_ps( m.getRow(2).mVec128, btvFFF0fMask );
    __m128 r0 = _mm_mul_ps(m0, _mm_shuffle_ps(row, row, 0));
    __m128 r1 = _mm_mul_ps(m0, _mm_shuffle_ps(row, row, 0x55));
    __m128 r2 = _mm_mul_ps(m0, _mm_shuffle_ps(row, row, 0xaa));
    row = m_el[1].mVec128;
    r0 = _mm_add_ps( r0, _mm_mul_ps(m1, _mm_shuffle_ps(row, row, 0)));
    r1 = _mm_add_ps( r1, _mm_mul_ps(m1, _mm_shuffle_ps(row, row, 0x55)));
    r2 = _mm_add_ps( r2, _mm_mul_ps(m1, _mm_shuffle_ps(row, row, 0xaa)));
    row = m_el[2].mVec128;
    r0 = _mm_add_ps( r0, _mm_mul_ps(m2, _mm_shuffle_ps(row, row, 0)));
    r1 = _mm_add_ps( r1, _mm_mul_ps(m2, _mm_shuffle_ps(row, row, 0x55)));
    r2 = _mm_add_ps( r2, _mm_mul_ps(m2, _mm_shuffle_ps(row, row, 0xaa)));
    return btMatrix3x3( r0, r1, r2 );

#elif defined BT_USE_NEON
    // zeros w
    static const uint32x4_t xyzMask = (const uint32x4_t){ static_cast<uint32_t>(-1), static_cast<uint32_t>(-1), static_cast<uint32_t>(-1), 0 };
    float32x4_t m0 = (float32x4_t) vandq_u32( (uint32x4_t) m.getRow(0).mVec128, xyzMask );
    float32x4_t m1 = (float32x4_t) vandq_u32( (uint32x4_t) m.getRow(1).mVec128, xyzMask );
    float32x4_t m2 = (float32x4_t) vandq_u32( (uint32x4_t) m.getRow(2).mVec128, xyzMask );
    float32x4_t row = m_el[0].mVec128;
    float32x4_t r0 = vmulq_lane_f32( m0, vget_low_f32(row), 0);
    float32x4_t r1 = vmulq_lane_f32( m0, vget_low_f32(row), 1);
    float32x4_t r2 = vmulq_lane_f32( m0, vget_high_f32(row), 0);
    row = m_el[1].mVec128;
    r0 = vmlaq_lane_f32( r0, m1, vget_low_f32(row), 0);
    r1 = vmlaq_lane_f32( r1, m1, vget_low_f32(row), 1);
    r2 = vmlaq_lane_f32( r2, m1, vget_high_f32(row), 0);
    row = m_el[2].mVec128;
    r0 = vmlaq_lane_f32( r0, m2, vget_low_f32(row), 0);
    r1 = vmlaq_lane_f32( r1, m2, vget_low_f32(row), 1);
    r2 = vmlaq_lane_f32( r2, m2, vget_high_f32(row), 0);
    return btMatrix3x3( r0, r1, r2 );
#else
    return btMatrix3x3(
                m_el[0].x() * m[0].x() + m_el[1].x() * m[1].x() + m_el[2].x() * m[2].x(),
                m_el[0].x() * m[0].y() + m_el[1].x() * m[1].y() + m_el[2].x() * m[2].y(),
                m_el[0].x() * m[0].z() + m_el[1].x() * m[1].z() + m_el[2].x() * m[2].z(),
                m_el[0].y() * m[0].x() + m_el[1].y() * m[1].x() + m_el[2].y() * m[2].x(),
                m_el[0].y() * m[0].y() + m_el[1].y() * m[1].y() + m_el[2].y() * m[2].y(),
                m_el[0].y() * m[0].z() + m_el[1].y() * m[1].z() + m_el[2].y() * m[2].z(),
                m_el[0].z() * m[0].x() + m_el[1].z() * m[1].x() + m_el[2].z() * m[2].x(),
                m_el[0].z() * m[0].y() + m_el[1].z() * m[1].y() + m_el[2].z() * m[2].y(),
                m_el[0].z() * m[0].z() + m_el[1].z() * m[1].z() + m_el[2].z() * m[2].z());
#endif
}

SIMD_FORCE_INLINE btMatrix3x3 
btMatrix3x3::timesTranspose(const btMatrix3x3& m) const
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))
    __m128 a0 = m_el[0].mVec128;
    __m128 a1 = m_el[1].mVec128;
    __m128 a2 = m_el[2].mVec128;
    
    btMatrix3x3 mT = m.transpose(); // we rely on transpose() zeroing w channel so that we don't have to do it here
    __m128 mx = mT[0].mVec128;
    __m128 my = mT[1].mVec128;
    __m128 mz = mT[2].mVec128;
    
    __m128 r0 = _mm_mul_ps(mx, _mm_shuffle_ps(a0, a0, 0x00));
    __m128 r1 = _mm_mul_ps(mx, _mm_shuffle_ps(a1, a1, 0x00));
    __m128 r2 = _mm_mul_ps(mx, _mm_shuffle_ps(a2, a2, 0x00));
    r0 = _mm_add_ps(r0, _mm_mul_ps(my, _mm_shuffle_ps(a0, a0, 0x55)));
    r1 = _mm_add_ps(r1, _mm_mul_ps(my, _mm_shuffle_ps(a1, a1, 0x55)));
    r2 = _mm_add_ps(r2, _mm_mul_ps(my, _mm_shuffle_ps(a2, a2, 0x55)));
    r0 = _mm_add_ps(r0, _mm_mul_ps(mz, _mm_shuffle_ps(a0, a0, 0xaa)));
    r1 = _mm_add_ps(r1, _mm_mul_ps(mz, _mm_shuffle_ps(a1, a1, 0xaa)));
    r2 = _mm_add_ps(r2, _mm_mul_ps(mz, _mm_shuffle_ps(a2, a2, 0xaa)));
    return btMatrix3x3( r0, r1, r2);
            
#elif defined BT_USE_NEON
    float32x4_t a0 = m_el[0].mVec128;
    float32x4_t a1 = m_el[1].mVec128;
    float32x4_t a2 = m_el[2].mVec128;
    
    btMatrix3x3 mT = m.transpose(); // we rely on transpose() zeroing w channel so that we don't have to do it here
    float32x4_t mx = mT[0].mVec128;
    float32x4_t my = mT[1].mVec128;
    float32x4_t mz = mT[2].mVec128;
    
    float32x4_t r0 = vmulq_lane_f32( mx, vget_low_f32(a0), 0);
    float32x4_t r1 = vmulq_lane_f32( mx, vget_low_f32(a1), 0);
    float32x4_t r2 = vmulq_lane_f32( mx, vget_low_f32(a2), 0);
    r0 = vmlaq_lane_f32( r0, my, vget_low_f32(a0), 1);
    r1 = vmlaq_lane_f32( r1, my, vget_low_f32(a1), 1);
    r2 = vmlaq_lane_f32( r2, my, vget_low_f32(a2), 1);
    r0 = vmlaq_lane_f32( r0, mz, vget_high_f32(a0), 0);
    r1 = vmlaq_lane_f32( r1, mz, vget_high_f32(a1), 0);
    r2 = vmlaq_lane_f32( r2, mz, vget_high_f32(a2), 0);
    return btMatrix3x3( r0, r1, r2 );
    
#else
        return btMatrix3x3(
                m_el[0].dot(m[0]), m_el[0].dot(m[1]), m_el[0].dot(m[2]),
                m_el[1].dot(m[0]), m_el[1].dot(m[1]), m_el[1].dot(m[2]),
                m_el[2].dot(m[0]), m_el[2].dot(m[1]), m_el[2].dot(m[2]));
#endif
}

SIMD_FORCE_INLINE btVector3 
operator*(const btMatrix3x3& m, const btVector3& v) 
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))|| defined (BT_USE_NEON)
    return v.dot3(m[0], m[1], m[2]);
#else
        return btVector3(m[0].dot(v), m[1].dot(v), m[2].dot(v));
#endif
}


SIMD_FORCE_INLINE btVector3
operator*(const btVector3& v, const btMatrix3x3& m)
{
#if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))

    const __m128 vv = v.mVec128;

    __m128 c0 = bt_splat_ps( vv, 0);
    __m128 c1 = bt_splat_ps( vv, 1);
    __m128 c2 = bt_splat_ps( vv, 2);

    c0 = _mm_mul_ps(c0, _mm_and_ps(m[0].mVec128, btvFFF0fMask) );
    c1 = _mm_mul_ps(c1, _mm_and_ps(m[1].mVec128, btvFFF0fMask) );
    c0 = _mm_add_ps(c0, c1);
    c2 = _mm_mul_ps(c2, _mm_and_ps(m[2].mVec128, btvFFF0fMask) );
    
    return btVector3(_mm_add_ps(c0, c2));
#elif defined(BT_USE_NEON)
    const float32x4_t vv = v.mVec128;
    const float32x2_t vlo = vget_low_f32(vv);
    const float32x2_t vhi = vget_high_f32(vv);

    float32x4_t c0, c1, c2;

    c0 = (float32x4_t) vandq_s32((int32x4_t)m[0].mVec128, btvFFF0Mask);
    c1 = (float32x4_t) vandq_s32((int32x4_t)m[1].mVec128, btvFFF0Mask);
    c2 = (float32x4_t) vandq_s32((int32x4_t)m[2].mVec128, btvFFF0Mask);

    c0 = vmulq_lane_f32(c0, vlo, 0);
    c1 = vmulq_lane_f32(c1, vlo, 1);
    c2 = vmulq_lane_f32(c2, vhi, 0);
    c0 = vaddq_f32(c0, c1);
    c0 = vaddq_f32(c0, c2);
    
    return btVector3(c0);
#else
        return btVector3(m.tdotx(v), m.tdoty(v), m.tdotz(v));
#endif
}

SIMD_FORCE_INLINE btMatrix3x3 
operator*(const btMatrix3x3& m1, const btMatrix3x3& m2)
{
#if defined BT_USE_SIMD_VECTOR3 && (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))

    __m128 m10 = m1[0].mVec128;  
    __m128 m11 = m1[1].mVec128;
    __m128 m12 = m1[2].mVec128;
    
    __m128 m2v = _mm_and_ps(m2[0].mVec128, btvFFF0fMask);
    
    __m128 c0 = bt_splat_ps( m10, 0);
    __m128 c1 = bt_splat_ps( m11, 0);
    __m128 c2 = bt_splat_ps( m12, 0);
    
    c0 = _mm_mul_ps(c0, m2v);
    c1 = _mm_mul_ps(c1, m2v);
    c2 = _mm_mul_ps(c2, m2v);
    
    m2v = _mm_and_ps(m2[1].mVec128, btvFFF0fMask);
    
    __m128 c0_1 = bt_splat_ps( m10, 1);
    __m128 c1_1 = bt_splat_ps( m11, 1);
    __m128 c2_1 = bt_splat_ps( m12, 1);
    
    c0_1 = _mm_mul_ps(c0_1, m2v);
    c1_1 = _mm_mul_ps(c1_1, m2v);
    c2_1 = _mm_mul_ps(c2_1, m2v);
    
    m2v = _mm_and_ps(m2[2].mVec128, btvFFF0fMask);
    
    c0 = _mm_add_ps(c0, c0_1);
    c1 = _mm_add_ps(c1, c1_1);
    c2 = _mm_add_ps(c2, c2_1);
    
    m10 = bt_splat_ps( m10, 2);
    m11 = bt_splat_ps( m11, 2);
    m12 = bt_splat_ps( m12, 2);
    
    m10 = _mm_mul_ps(m10, m2v);
    m11 = _mm_mul_ps(m11, m2v);
    m12 = _mm_mul_ps(m12, m2v);
    
    c0 = _mm_add_ps(c0, m10);
    c1 = _mm_add_ps(c1, m11);
    c2 = _mm_add_ps(c2, m12);
    
    return btMatrix3x3(c0, c1, c2);

#elif defined(BT_USE_NEON)

    float32x4_t rv0, rv1, rv2;
    float32x4_t v0, v1, v2;
    float32x4_t mv0, mv1, mv2;

    v0 = m1[0].mVec128;
    v1 = m1[1].mVec128;
    v2 = m1[2].mVec128;

    mv0 = (float32x4_t) vandq_s32((int32x4_t)m2[0].mVec128, btvFFF0Mask); 
    mv1 = (float32x4_t) vandq_s32((int32x4_t)m2[1].mVec128, btvFFF0Mask); 
    mv2 = (float32x4_t) vandq_s32((int32x4_t)m2[2].mVec128, btvFFF0Mask); 
    
    rv0 = vmulq_lane_f32(mv0, vget_low_f32(v0), 0);
    rv1 = vmulq_lane_f32(mv0, vget_low_f32(v1), 0);
    rv2 = vmulq_lane_f32(mv0, vget_low_f32(v2), 0);
    
    rv0 = vmlaq_lane_f32(rv0, mv1, vget_low_f32(v0), 1);
    rv1 = vmlaq_lane_f32(rv1, mv1, vget_low_f32(v1), 1);
    rv2 = vmlaq_lane_f32(rv2, mv1, vget_low_f32(v2), 1);
    
    rv0 = vmlaq_lane_f32(rv0, mv2, vget_high_f32(v0), 0);
    rv1 = vmlaq_lane_f32(rv1, mv2, vget_high_f32(v1), 0);
    rv2 = vmlaq_lane_f32(rv2, mv2, vget_high_f32(v2), 0);

        return btMatrix3x3(rv0, rv1, rv2);
        
#else   
        return btMatrix3x3(
                m2.tdotx( m1[0]), m2.tdoty( m1[0]), m2.tdotz( m1[0]),
                m2.tdotx( m1[1]), m2.tdoty( m1[1]), m2.tdotz( m1[1]),
                m2.tdotx( m1[2]), m2.tdoty( m1[2]), m2.tdotz( m1[2]));
#endif
}

/*
SIMD_FORCE_INLINE btMatrix3x3 btMultTransposeLeft(const btMatrix3x3& m1, const btMatrix3x3& m2) {
return btMatrix3x3(
m1[0][0] * m2[0][0] + m1[1][0] * m2[1][0] + m1[2][0] * m2[2][0],
m1[0][0] * m2[0][1] + m1[1][0] * m2[1][1] + m1[2][0] * m2[2][1],
m1[0][0] * m2[0][2] + m1[1][0] * m2[1][2] + m1[2][0] * m2[2][2],
m1[0][1] * m2[0][0] + m1[1][1] * m2[1][0] + m1[2][1] * m2[2][0],
m1[0][1] * m2[0][1] + m1[1][1] * m2[1][1] + m1[2][1] * m2[2][1],
m1[0][1] * m2[0][2] + m1[1][1] * m2[1][2] + m1[2][1] * m2[2][2],
m1[0][2] * m2[0][0] + m1[1][2] * m2[1][0] + m1[2][2] * m2[2][0],
m1[0][2] * m2[0][1] + m1[1][2] * m2[1][1] + m1[2][2] * m2[2][1],
m1[0][2] * m2[0][2] + m1[1][2] * m2[1][2] + m1[2][2] * m2[2][2]);
}
*/

SIMD_FORCE_INLINE bool operator==(const btMatrix3x3& m1, const btMatrix3x3& m2)
{
#if (defined (BT_USE_SSE_IN_API) && defined (BT_USE_SSE))

    __m128 c0, c1, c2;

    c0 = _mm_cmpeq_ps(m1[0].mVec128, m2[0].mVec128);
    c1 = _mm_cmpeq_ps(m1[1].mVec128, m2[1].mVec128);
    c2 = _mm_cmpeq_ps(m1[2].mVec128, m2[2].mVec128);
    
    c0 = _mm_and_ps(c0, c1);
    c0 = _mm_and_ps(c0, c2);

        int m = _mm_movemask_ps((__m128)c0);
        return (0x7 == (m & 0x7));
        
#else 
        return 
    (   m1[0][0] == m2[0][0] && m1[1][0] == m2[1][0] && m1[2][0] == m2[2][0] &&
                m1[0][1] == m2[0][1] && m1[1][1] == m2[1][1] && m1[2][1] == m2[2][1] &&
                m1[0][2] == m2[0][2] && m1[1][2] == m2[1][2] && m1[2][2] == m2[2][2] );
#endif
}

struct  btMatrix3x3FloatData
{
        btVector3FloatData m_el[3];
};

struct  btMatrix3x3DoubleData
{
        btVector3DoubleData m_el[3];
};


        

SIMD_FORCE_INLINE       void    btMatrix3x3::serialize(struct   btMatrix3x3Data& dataOut) const
{
        for (int i=0;i<3;i++)
                m_el[i].serialize(dataOut.m_el[i]);
}

SIMD_FORCE_INLINE       void    btMatrix3x3::serializeFloat(struct      btMatrix3x3FloatData& dataOut) const
{
        for (int i=0;i<3;i++)
                m_el[i].serializeFloat(dataOut.m_el[i]);
}


SIMD_FORCE_INLINE       void    btMatrix3x3::deSerialize(const struct   btMatrix3x3Data& dataIn)
{
        for (int i=0;i<3;i++)
                m_el[i].deSerialize(dataIn.m_el[i]);
}

SIMD_FORCE_INLINE       void    btMatrix3x3::deSerializeFloat(const struct      btMatrix3x3FloatData& dataIn)
{
        for (int i=0;i<3;i++)
                m_el[i].deSerializeFloat(dataIn.m_el[i]);
}

SIMD_FORCE_INLINE       void    btMatrix3x3::deSerializeDouble(const struct     btMatrix3x3DoubleData& dataIn)
{
        for (int i=0;i<3;i++)
                m_el[i].deSerializeDouble(dataIn.m_el[i]);
}

#endif //BT_MATRIX3x3_H