text: /*
  Copyright (c) 2003-2013 Gino van den Bergen / Erwin Coumans  http://bulletphysics.org
  
  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 B3_SIMD__QUATERNION_H_
  #define B3_SIMD__QUATERNION_H_
  
  #include "b3Vector3.h"
  #include "b3QuadWord.h"
  
  #ifdef B3_USE_SSE
  
  const __m128 B3_ATTRIBUTE_ALIGNED16(b3vOnes) = {1.0f, 1.0f, 1.0f, 1.0f};
  
  #endif
  
  #if defined(B3_USE_SSE) || defined(B3_USE_NEON)
  
  const b3SimdFloat4 B3_ATTRIBUTE_ALIGNED16(b3vQInv) = {-0.0f, -0.0f, -0.0f, +0.0f};
  const b3SimdFloat4 B3_ATTRIBUTE_ALIGNED16(b3vPPPM) = {+0.0f, +0.0f, +0.0f, -0.0f};
  
  #endif
  
  /**@brief The b3Quaternion implements quaternion to perform linear algebra rotations in combination with b3Matrix3x3, b3Vector3 and b3Transform. */
  class b3Quaternion : public b3QuadWord
  {
  public:
  	/**@brief No initialization constructor */
  	b3Quaternion() {}
  
  #if (defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)) || defined(B3_USE_NEON)
  	// Set Vector
  	B3_FORCE_INLINE b3Quaternion(const b3SimdFloat4 vec)
  	{
  		mVec128 = vec;
  	}
  
  	// Copy constructor
  	B3_FORCE_INLINE b3Quaternion(const b3Quaternion& rhs)
  	{
  		mVec128 = rhs.mVec128;
  	}
  
  	// Assignment Operator
  	B3_FORCE_INLINE b3Quaternion&
  	operator=(const b3Quaternion& v)
  	{
  		mVec128 = v.mVec128;
  
  		return *this;
  	}
  
  #endif
  
  	//		template <typename b3Scalar>
  	//		explicit Quaternion(const b3Scalar *v) : Tuple4<b3Scalar>(v) {}
  	/**@brief Constructor from scalars */
  	b3Quaternion(const b3Scalar& _x, const b3Scalar& _y, const b3Scalar& _z, const b3Scalar& _w)
  		: b3QuadWord(_x, _y, _z, _w)
  	{
  		//b3Assert(!((_x==1.f) && (_y==0.f) && (_z==0.f) && (_w==0.f)));
  	}
  	/**@brief Axis angle Constructor
     * @param axis The axis which the rotation is around
     * @param angle The magnitude of the rotation around the angle (Radians) */
  	b3Quaternion(const b3Vector3& _axis, const b3Scalar& _angle)
  	{
  		setRotation(_axis, _angle);
  	}
  	/**@brief Constructor from Euler angles
     * @param yaw Angle around Y unless B3_EULER_DEFAULT_ZYX defined then Z
     * @param pitch Angle around X unless B3_EULER_DEFAULT_ZYX defined then Y
     * @param roll Angle around Z unless B3_EULER_DEFAULT_ZYX defined then X */
  	b3Quaternion(const b3Scalar& yaw, const b3Scalar& pitch, const b3Scalar& roll)
  	{
  #ifndef B3_EULER_DEFAULT_ZYX
  		setEuler(yaw, pitch, roll);
  #else
  		setEulerZYX(yaw, pitch, roll);
  #endif
  	}
  	/**@brief Set the rotation using axis angle notation 
     * @param axis The axis around which to rotate
     * @param angle The magnitude of the rotation in Radians */
  	void setRotation(const b3Vector3& axis1, const b3Scalar& _angle)
  	{
  		b3Vector3 axis = axis1;
  		axis.safeNormalize();
  
  		b3Scalar d = axis.length();
  		b3Assert(d != b3Scalar(0.0));
  		if (d < B3_EPSILON)
  		{
  			setValue(0, 0, 0, 1);
  		}
  		else
  		{
  			b3Scalar s = b3Sin(_angle * b3Scalar(0.5)) / d;
  			setValue(axis.getX() * s, axis.getY() * s, axis.getZ() * s,
  					 b3Cos(_angle * b3Scalar(0.5)));
  		}
  	}
  	/**@brief Set the quaternion using Euler angles
     * @param yaw Angle around Y
     * @param pitch Angle around X
     * @param roll Angle around Z */
  	void setEuler(const b3Scalar& yaw, const b3Scalar& pitch, const b3Scalar& roll)
  	{
  		b3Scalar halfYaw = b3Scalar(yaw) * b3Scalar(0.5);
  		b3Scalar halfPitch = b3Scalar(pitch) * b3Scalar(0.5);
  		b3Scalar halfRoll = b3Scalar(roll) * b3Scalar(0.5);
  		b3Scalar cosYaw = b3Cos(halfYaw);
  		b3Scalar sinYaw = b3Sin(halfYaw);
  		b3Scalar cosPitch = b3Cos(halfPitch);
  		b3Scalar sinPitch = b3Sin(halfPitch);
  		b3Scalar cosRoll = b3Cos(halfRoll);
  		b3Scalar sinRoll = b3Sin(halfRoll);
  		setValue(cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw,
  				 cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw,
  				 sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw,
  				 cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw);
  	}
  
  	/**@brief Set the quaternion using euler angles 
     * @param yaw Angle around Z
     * @param pitch Angle around Y
     * @param roll Angle around X */
  	void setEulerZYX(const b3Scalar& yawZ, const b3Scalar& pitchY, const b3Scalar& rollX)
  	{
  		b3Scalar halfYaw = b3Scalar(yawZ) * b3Scalar(0.5);
  		b3Scalar halfPitch = b3Scalar(pitchY) * b3Scalar(0.5);
  		b3Scalar halfRoll = b3Scalar(rollX) * b3Scalar(0.5);
  		b3Scalar cosYaw = b3Cos(halfYaw);
  		b3Scalar sinYaw = b3Sin(halfYaw);
  		b3Scalar cosPitch = b3Cos(halfPitch);
  		b3Scalar sinPitch = b3Sin(halfPitch);
  		b3Scalar cosRoll = b3Cos(halfRoll);
  		b3Scalar sinRoll = b3Sin(halfRoll);
  		setValue(sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw,   //x
  				 cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw,   //y
  				 cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw,   //z
  				 cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw);  //formerly yzx
  		normalize();
  	}
  
  	/**@brief Get the euler angles from this quaternion
  	   * @param yaw Angle around Z
  	   * @param pitch Angle around Y
  	   * @param roll Angle around X */
  	void getEulerZYX(b3Scalar& yawZ, b3Scalar& pitchY, b3Scalar& rollX) const
  	{
  		b3Scalar squ;
  		b3Scalar sqx;
  		b3Scalar sqy;
  		b3Scalar sqz;
  		b3Scalar sarg;
  		sqx = m_floats[0] * m_floats[0];
  		sqy = m_floats[1] * m_floats[1];
  		sqz = m_floats[2] * m_floats[2];
  		squ = m_floats[3] * m_floats[3];
  		rollX = b3Atan2(2 * (m_floats[1] * m_floats[2] + m_floats[3] * m_floats[0]), squ - sqx - sqy + sqz);
  		sarg = b3Scalar(-2.) * (m_floats[0] * m_floats[2] - m_floats[3] * m_floats[1]);
  		pitchY = sarg <= b3Scalar(-1.0) ? b3Scalar(-0.5) * B3_PI : (sarg >= b3Scalar(1.0) ? b3Scalar(0.5) * B3_PI : b3Asin(sarg));
  		yawZ = b3Atan2(2 * (m_floats[0] * m_floats[1] + m_floats[3] * m_floats[2]), squ + sqx - sqy - sqz);
  	}
  
  	/**@brief Add two quaternions
     * @param q The quaternion to add to this one */
  	B3_FORCE_INLINE b3Quaternion& operator+=(const b3Quaternion& q)
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		mVec128 = _mm_add_ps(mVec128, q.mVec128);
  #elif defined(B3_USE_NEON)
  		mVec128 = vaddq_f32(mVec128, q.mVec128);
  #else
  		m_floats[0] += q.getX();
  		m_floats[1] += q.getY();
  		m_floats[2] += q.getZ();
  		m_floats[3] += q.m_floats[3];
  #endif
  		return *this;
  	}
  
  	/**@brief Subtract out a quaternion
     * @param q The quaternion to subtract from this one */
  	b3Quaternion& operator-=(const b3Quaternion& q)
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		mVec128 = _mm_sub_ps(mVec128, q.mVec128);
  #elif defined(B3_USE_NEON)
  		mVec128 = vsubq_f32(mVec128, q.mVec128);
  #else
  		m_floats[0] -= q.getX();
  		m_floats[1] -= q.getY();
  		m_floats[2] -= q.getZ();
  		m_floats[3] -= q.m_floats[3];
  #endif
  		return *this;
  	}
  
  	/**@brief Scale this quaternion
     * @param s The scalar to scale by */
  	b3Quaternion& operator*=(const b3Scalar& s)
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		__m128 vs = _mm_load_ss(&s);  //	(S 0 0 0)
  		vs = b3_pshufd_ps(vs, 0);     //	(S S S S)
  		mVec128 = _mm_mul_ps(mVec128, vs);
  #elif defined(B3_USE_NEON)
  		mVec128 = vmulq_n_f32(mVec128, s);
  #else
  		m_floats[0] *= s;
  		m_floats[1] *= s;
  		m_floats[2] *= s;
  		m_floats[3] *= s;
  #endif
  		return *this;
  	}
  
  	/**@brief Multiply this quaternion by q on the right
     * @param q The other quaternion 
     * Equivilant to this = this * q */
  	b3Quaternion& operator*=(const b3Quaternion& q)
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		__m128 vQ2 = q.get128();
  
  		__m128 A1 = b3_pshufd_ps(mVec128, B3_SHUFFLE(0, 1, 2, 0));
  		__m128 B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(3, 3, 3, 0));
  
  		A1 = A1 * B1;
  
  		__m128 A2 = b3_pshufd_ps(mVec128, B3_SHUFFLE(1, 2, 0, 1));
  		__m128 B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1));
  
  		A2 = A2 * B2;
  
  		B1 = b3_pshufd_ps(mVec128, B3_SHUFFLE(2, 0, 1, 2));
  		B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2));
  
  		B1 = B1 * B2;  //	A3 *= B3
  
  		mVec128 = b3_splat_ps(mVec128, 3);  //	A0
  		mVec128 = mVec128 * vQ2;            //	A0 * B0
  
  		A1 = A1 + A2;                  //	AB12
  		mVec128 = mVec128 - B1;        //	AB03 = AB0 - AB3
  		A1 = _mm_xor_ps(A1, b3vPPPM);  //	change sign of the last element
  		mVec128 = mVec128 + A1;        //	AB03 + AB12
  
  #elif defined(B3_USE_NEON)
  
  		float32x4_t vQ1 = mVec128;
  		float32x4_t vQ2 = q.get128();
  		float32x4_t A0, A1, B1, A2, B2, A3, B3;
  		float32x2_t vQ1zx, vQ2wx, vQ1yz, vQ2zx, vQ2yz, vQ2xz;
  
  		{
  			float32x2x2_t tmp;
  			tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1));  // {z x}, {w y}
  			vQ1zx = tmp.val[0];
  
  			tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2));  // {z x}, {w y}
  			vQ2zx = tmp.val[0];
  		}
  		vQ2wx = vext_f32(vget_high_f32(vQ2), vget_low_f32(vQ2), 1);
  
  		vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
  
  		vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
  		vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
  
  		A1 = vcombine_f32(vget_low_f32(vQ1), vQ1zx);                     // X Y  z x
  		B1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ2), 1), vQ2wx);  // W W  W X
  
  		A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
  		B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
  
  		A3 = vcombine_f32(vQ1zx, vQ1yz);  // Z X Y Z
  		B3 = vcombine_f32(vQ2yz, vQ2xz);  // Y Z x z
  
  		A1 = vmulq_f32(A1, B1);
  		A2 = vmulq_f32(A2, B2);
  		A3 = vmulq_f32(A3, B3);                           //	A3 *= B3
  		A0 = vmulq_lane_f32(vQ2, vget_high_f32(vQ1), 1);  //	A0 * B0
  
  		A1 = vaddq_f32(A1, A2);  //	AB12 = AB1 + AB2
  		A0 = vsubq_f32(A0, A3);  //	AB03 = AB0 - AB3
  
  		//	change the sign of the last element
  		A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
  		A0 = vaddq_f32(A0, A1);  //	AB03 + AB12
  
  		mVec128 = A0;
  #else
  		setValue(
  			m_floats[3] * q.getX() + m_floats[0] * q.m_floats[3] + m_floats[1] * q.getZ() - m_floats[2] * q.getY(),
  			m_floats[3] * q.getY() + m_floats[1] * q.m_floats[3] + m_floats[2] * q.getX() - m_floats[0] * q.getZ(),
  			m_floats[3] * q.getZ() + m_floats[2] * q.m_floats[3] + m_floats[0] * q.getY() - m_floats[1] * q.getX(),
  			m_floats[3] * q.m_floats[3] - m_floats[0] * q.getX() - m_floats[1] * q.getY() - m_floats[2] * q.getZ());
  #endif
  		return *this;
  	}
  	/**@brief Return the dot product between this quaternion and another
     * @param q The other quaternion */
  	b3Scalar dot(const b3Quaternion& q) const
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		__m128 vd;
  
  		vd = _mm_mul_ps(mVec128, q.mVec128);
  
  		__m128 t = _mm_movehl_ps(vd, vd);
  		vd = _mm_add_ps(vd, t);
  		t = _mm_shuffle_ps(vd, vd, 0x55);
  		vd = _mm_add_ss(vd, t);
  
  		return _mm_cvtss_f32(vd);
  #elif defined(B3_USE_NEON)
  		float32x4_t vd = vmulq_f32(mVec128, q.mVec128);
  		float32x2_t x = vpadd_f32(vget_low_f32(vd), vget_high_f32(vd));
  		x = vpadd_f32(x, x);
  		return vget_lane_f32(x, 0);
  #else
  		return m_floats[0] * q.getX() +
  			   m_floats[1] * q.getY() +
  			   m_floats[2] * q.getZ() +
  			   m_floats[3] * q.m_floats[3];
  #endif
  	}
  
  	/**@brief Return the length squared of the quaternion */
  	b3Scalar length2() const
  	{
  		return dot(*this);
  	}
  
  	/**@brief Return the length of the quaternion */
  	b3Scalar length() const
  	{
  		return b3Sqrt(length2());
  	}
  
  	/**@brief Normalize the quaternion 
     * Such that x^2 + y^2 + z^2 +w^2 = 1 */
  	b3Quaternion& normalize()
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		__m128 vd;
  
  		vd = _mm_mul_ps(mVec128, mVec128);
  
  		__m128 t = _mm_movehl_ps(vd, vd);
  		vd = _mm_add_ps(vd, t);
  		t = _mm_shuffle_ps(vd, vd, 0x55);
  		vd = _mm_add_ss(vd, t);
  
  		vd = _mm_sqrt_ss(vd);
  		vd = _mm_div_ss(b3vOnes, vd);
  		vd = b3_pshufd_ps(vd, 0);  // splat
  		mVec128 = _mm_mul_ps(mVec128, vd);
  
  		return *this;
  #else
  		return *this /= length();
  #endif
  	}
  
  	/**@brief Return a scaled version of this quaternion
     * @param s The scale factor */
  	B3_FORCE_INLINE b3Quaternion
  	operator*(const b3Scalar& s) const
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		__m128 vs = _mm_load_ss(&s);  //	(S 0 0 0)
  		vs = b3_pshufd_ps(vs, 0x00);  //	(S S S S)
  
  		return b3Quaternion(_mm_mul_ps(mVec128, vs));
  #elif defined(B3_USE_NEON)
  		return b3Quaternion(vmulq_n_f32(mVec128, s));
  #else
  		return b3Quaternion(getX() * s, getY() * s, getZ() * s, m_floats[3] * s);
  #endif
  	}
  
  	/**@brief Return an inversely scaled versionof this quaternion
     * @param s The inverse scale factor */
  	b3Quaternion operator/(const b3Scalar& s) const
  	{
  		b3Assert(s != b3Scalar(0.0));
  		return *this * (b3Scalar(1.0) / s);
  	}
  
  	/**@brief Inversely scale this quaternion
     * @param s The scale factor */
  	b3Quaternion& operator/=(const b3Scalar& s)
  	{
  		b3Assert(s != b3Scalar(0.0));
  		return *this *= b3Scalar(1.0) / s;
  	}
  
  	/**@brief Return a normalized version of this quaternion */
  	b3Quaternion normalized() const
  	{
  		return *this / length();
  	}
  	/**@brief Return the angle between this quaternion and the other 
     * @param q The other quaternion */
  	b3Scalar angle(const b3Quaternion& q) const
  	{
  		b3Scalar s = b3Sqrt(length2() * q.length2());
  		b3Assert(s != b3Scalar(0.0));
  		return b3Acos(dot(q) / s);
  	}
  	/**@brief Return the angle of rotation represented by this quaternion */
  	b3Scalar getAngle() const
  	{
  		b3Scalar s = b3Scalar(2.) * b3Acos(m_floats[3]);
  		return s;
  	}
  
  	/**@brief Return the axis of the rotation represented by this quaternion */
  	b3Vector3 getAxis() const
  	{
  		b3Scalar s_squared = 1.f - m_floats[3] * m_floats[3];
  
  		if (s_squared < b3Scalar(10.) * B3_EPSILON)  //Check for divide by zero
  			return b3MakeVector3(1.0, 0.0, 0.0);     // Arbitrary
  		b3Scalar s = 1.f / b3Sqrt(s_squared);
  		return b3MakeVector3(m_floats[0] * s, m_floats[1] * s, m_floats[2] * s);
  	}
  
  	/**@brief Return the inverse of this quaternion */
  	b3Quaternion inverse() const
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		return b3Quaternion(_mm_xor_ps(mVec128, b3vQInv));
  #elif defined(B3_USE_NEON)
  		return b3Quaternion((b3SimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)b3vQInv));
  #else
  		return b3Quaternion(-m_floats[0], -m_floats[1], -m_floats[2], m_floats[3]);
  #endif
  	}
  
  	/**@brief Return the sum of this quaternion and the other 
     * @param q2 The other quaternion */
  	B3_FORCE_INLINE b3Quaternion
  	operator+(const b3Quaternion& q2) const
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		return b3Quaternion(_mm_add_ps(mVec128, q2.mVec128));
  #elif defined(B3_USE_NEON)
  		return b3Quaternion(vaddq_f32(mVec128, q2.mVec128));
  #else
  		const b3Quaternion& q1 = *this;
  		return b3Quaternion(q1.getX() + q2.getX(), q1.getY() + q2.getY(), q1.getZ() + q2.getZ(), q1.m_floats[3] + q2.m_floats[3]);
  #endif
  	}
  
  	/**@brief Return the difference between this quaternion and the other 
     * @param q2 The other quaternion */
  	B3_FORCE_INLINE b3Quaternion
  	operator-(const b3Quaternion& q2) const
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		return b3Quaternion(_mm_sub_ps(mVec128, q2.mVec128));
  #elif defined(B3_USE_NEON)
  		return b3Quaternion(vsubq_f32(mVec128, q2.mVec128));
  #else
  		const b3Quaternion& q1 = *this;
  		return b3Quaternion(q1.getX() - q2.getX(), q1.getY() - q2.getY(), q1.getZ() - q2.getZ(), q1.m_floats[3] - q2.m_floats[3]);
  #endif
  	}
  
  	/**@brief Return the negative of this quaternion 
     * This simply negates each element */
  	B3_FORCE_INLINE b3Quaternion operator-() const
  	{
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  		return b3Quaternion(_mm_xor_ps(mVec128, b3vMzeroMask));
  #elif defined(B3_USE_NEON)
  		return b3Quaternion((b3SimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)b3vMzeroMask));
  #else
  		const b3Quaternion& q2 = *this;
  		return b3Quaternion(-q2.getX(), -q2.getY(), -q2.getZ(), -q2.m_floats[3]);
  #endif
  	}
  	/**@todo document this and it's use */
  	B3_FORCE_INLINE b3Quaternion farthest(const b3Quaternion& qd) const
  	{
  		b3Quaternion diff, sum;
  		diff = *this - qd;
  		sum = *this + qd;
  		if (diff.dot(diff) > sum.dot(sum))
  			return qd;
  		return (-qd);
  	}
  
  	/**@todo document this and it's use */
  	B3_FORCE_INLINE b3Quaternion nearest(const b3Quaternion& qd) const
  	{
  		b3Quaternion diff, sum;
  		diff = *this - qd;
  		sum = *this + qd;
  		if (diff.dot(diff) < sum.dot(sum))
  			return qd;
  		return (-qd);
  	}
  
  	/**@brief Return the quaternion which is the result of Spherical Linear Interpolation between this and the other quaternion
     * @param q The other quaternion to interpolate with 
     * @param t The ratio between this and q to interpolate.  If t = 0 the result is this, if t=1 the result is q.
     * Slerp interpolates assuming constant velocity.  */
  	b3Quaternion slerp(const b3Quaternion& q, const b3Scalar& t) const
  	{
  		b3Scalar magnitude = b3Sqrt(length2() * q.length2());
  		b3Assert(magnitude > b3Scalar(0));
  
  		b3Scalar product = dot(q) / magnitude;
  		if (b3Fabs(product) < b3Scalar(1))
  		{
  			// Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
  			const b3Scalar sign = (product < 0) ? b3Scalar(-1) : b3Scalar(1);
  
  			const b3Scalar theta = b3Acos(sign * product);
  			const b3Scalar s1 = b3Sin(sign * t * theta);
  			const b3Scalar d = b3Scalar(1.0) / b3Sin(theta);
  			const b3Scalar s0 = b3Sin((b3Scalar(1.0) - t) * theta);
  
  			return b3Quaternion(
  				(m_floats[0] * s0 + q.getX() * s1) * d,
  				(m_floats[1] * s0 + q.getY() * s1) * d,
  				(m_floats[2] * s0 + q.getZ() * s1) * d,
  				(m_floats[3] * s0 + q.m_floats[3] * s1) * d);
  		}
  		else
  		{
  			return *this;
  		}
  	}
  
  	static const b3Quaternion& getIdentity()
  	{
  		static const b3Quaternion identityQuat(b3Scalar(0.), b3Scalar(0.), b3Scalar(0.), b3Scalar(1.));
  		return identityQuat;
  	}
  
  	B3_FORCE_INLINE const b3Scalar& getW() const { return m_floats[3]; }
  };
  
  /**@brief Return the product of two quaternions */
  B3_FORCE_INLINE b3Quaternion
  operator*(const b3Quaternion& q1, const b3Quaternion& q2)
  {
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  	__m128 vQ1 = q1.get128();
  	__m128 vQ2 = q2.get128();
  	__m128 A0, A1, B1, A2, B2;
  
  	A1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(0, 1, 2, 0));  // X Y  z x     //      vtrn
  	B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(3, 3, 3, 0));  // W W  W X     // vdup vext
  
  	A1 = A1 * B1;
  
  	A2 = b3_pshufd_ps(vQ1, B3_SHUFFLE(1, 2, 0, 1));  // Y Z  X Y     // vext
  	B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1));  // z x  Y Y     // vtrn vdup
  
  	A2 = A2 * B2;
  
  	B1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(2, 0, 1, 2));  // z x Y Z      // vtrn vext
  	B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2));  // Y Z x z      // vext vtrn
  
  	B1 = B1 * B2;  //	A3 *= B3
  
  	A0 = b3_splat_ps(vQ1, 3);  //	A0
  	A0 = A0 * vQ2;             //	A0 * B0
  
  	A1 = A1 + A2;  //	AB12
  	A0 = A0 - B1;  //	AB03 = AB0 - AB3
  
  	A1 = _mm_xor_ps(A1, b3vPPPM);  //	change sign of the last element
  	A0 = A0 + A1;                  //	AB03 + AB12
  
  	return b3Quaternion(A0);
  
  #elif defined(B3_USE_NEON)
  
  	float32x4_t vQ1 = q1.get128();
  	float32x4_t vQ2 = q2.get128();
  	float32x4_t A0, A1, B1, A2, B2, A3, B3;
  	float32x2_t vQ1zx, vQ2wx, vQ1yz, vQ2zx, vQ2yz, vQ2xz;
  
  	{
  		float32x2x2_t tmp;
  		tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1));  // {z x}, {w y}
  		vQ1zx = tmp.val[0];
  
  		tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2));  // {z x}, {w y}
  		vQ2zx = tmp.val[0];
  	}
  	vQ2wx = vext_f32(vget_high_f32(vQ2), vget_low_f32(vQ2), 1);
  
  	vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
  
  	vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
  	vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
  
  	A1 = vcombine_f32(vget_low_f32(vQ1), vQ1zx);                     // X Y  z x
  	B1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ2), 1), vQ2wx);  // W W  W X
  
  	A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
  	B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
  
  	A3 = vcombine_f32(vQ1zx, vQ1yz);  // Z X Y Z
  	B3 = vcombine_f32(vQ2yz, vQ2xz);  // Y Z x z
  
  	A1 = vmulq_f32(A1, B1);
  	A2 = vmulq_f32(A2, B2);
  	A3 = vmulq_f32(A3, B3);                           //	A3 *= B3
  	A0 = vmulq_lane_f32(vQ2, vget_high_f32(vQ1), 1);  //	A0 * B0
  
  	A1 = vaddq_f32(A1, A2);  //	AB12 = AB1 + AB2
  	A0 = vsubq_f32(A0, A3);  //	AB03 = AB0 - AB3
  
  	//	change the sign of the last element
  	A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
  	A0 = vaddq_f32(A0, A1);  //	AB03 + AB12
  
  	return b3Quaternion(A0);
  
  #else
  	return b3Quaternion(
  		q1.getW() * q2.getX() + q1.getX() * q2.getW() + q1.getY() * q2.getZ() - q1.getZ() * q2.getY(),
  		q1.getW() * q2.getY() + q1.getY() * q2.getW() + q1.getZ() * q2.getX() - q1.getX() * q2.getZ(),
  		q1.getW() * q2.getZ() + q1.getZ() * q2.getW() + q1.getX() * q2.getY() - q1.getY() * q2.getX(),
  		q1.getW() * q2.getW() - q1.getX() * q2.getX() - q1.getY() * q2.getY() - q1.getZ() * q2.getZ());
  #endif
  }
  
  B3_FORCE_INLINE b3Quaternion
  operator*(const b3Quaternion& q, const b3Vector3& w)
  {
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  	__m128 vQ1 = q.get128();
  	__m128 vQ2 = w.get128();
  	__m128 A1, B1, A2, B2, A3, B3;
  
  	A1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(3, 3, 3, 0));
  	B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(0, 1, 2, 0));
  
  	A1 = A1 * B1;
  
  	A2 = b3_pshufd_ps(vQ1, B3_SHUFFLE(1, 2, 0, 1));
  	B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1));
  
  	A2 = A2 * B2;
  
  	A3 = b3_pshufd_ps(vQ1, B3_SHUFFLE(2, 0, 1, 2));
  	B3 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2));
  
  	A3 = A3 * B3;  //	A3 *= B3
  
  	A1 = A1 + A2;                  //	AB12
  	A1 = _mm_xor_ps(A1, b3vPPPM);  //	change sign of the last element
  	A1 = A1 - A3;                  //	AB123 = AB12 - AB3
  
  	return b3Quaternion(A1);
  
  #elif defined(B3_USE_NEON)
  
  	float32x4_t vQ1 = q.get128();
  	float32x4_t vQ2 = w.get128();
  	float32x4_t A1, B1, A2, B2, A3, B3;
  	float32x2_t vQ1wx, vQ2zx, vQ1yz, vQ2yz, vQ1zx, vQ2xz;
  
  	vQ1wx = vext_f32(vget_high_f32(vQ1), vget_low_f32(vQ1), 1);
  	{
  		float32x2x2_t tmp;
  
  		tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2));  // {z x}, {w y}
  		vQ2zx = tmp.val[0];
  
  		tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1));  // {z x}, {w y}
  		vQ1zx = tmp.val[0];
  	}
  
  	vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
  
  	vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
  	vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
  
  	A1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ1), 1), vQ1wx);  // W W  W X
  	B1 = vcombine_f32(vget_low_f32(vQ2), vQ2zx);                     // X Y  z x
  
  	A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
  	B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
  
  	A3 = vcombine_f32(vQ1zx, vQ1yz);  // Z X Y Z
  	B3 = vcombine_f32(vQ2yz, vQ2xz);  // Y Z x z
  
  	A1 = vmulq_f32(A1, B1);
  	A2 = vmulq_f32(A2, B2);
  	A3 = vmulq_f32(A3, B3);  //	A3 *= B3
  
  	A1 = vaddq_f32(A1, A2);  //	AB12 = AB1 + AB2
  
  	//	change the sign of the last element
  	A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
  
  	A1 = vsubq_f32(A1, A3);  //	AB123 = AB12 - AB3
  
  	return b3Quaternion(A1);
  
  #else
  	return b3Quaternion(
  		q.getW() * w.getX() + q.getY() * w.getZ() - q.getZ() * w.getY(),
  		q.getW() * w.getY() + q.getZ() * w.getX() - q.getX() * w.getZ(),
  		q.getW() * w.getZ() + q.getX() * w.getY() - q.getY() * w.getX(),
  		-q.getX() * w.getX() - q.getY() * w.getY() - q.getZ() * w.getZ());
  #endif
  }
  
  B3_FORCE_INLINE b3Quaternion
  operator*(const b3Vector3& w, const b3Quaternion& q)
  {
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  	__m128 vQ1 = w.get128();
  	__m128 vQ2 = q.get128();
  	__m128 A1, B1, A2, B2, A3, B3;
  
  	A1 = b3_pshufd_ps(vQ1, B3_SHUFFLE(0, 1, 2, 0));  // X Y  z x
  	B1 = b3_pshufd_ps(vQ2, B3_SHUFFLE(3, 3, 3, 0));  // W W  W X
  
  	A1 = A1 * B1;
  
  	A2 = b3_pshufd_ps(vQ1, B3_SHUFFLE(1, 2, 0, 1));
  	B2 = b3_pshufd_ps(vQ2, B3_SHUFFLE(2, 0, 1, 1));
  
  	A2 = A2 * B2;
  
  	A3 = b3_pshufd_ps(vQ1, B3_SHUFFLE(2, 0, 1, 2));
  	B3 = b3_pshufd_ps(vQ2, B3_SHUFFLE(1, 2, 0, 2));
  
  	A3 = A3 * B3;  //	A3 *= B3
  
  	A1 = A1 + A2;                  //	AB12
  	A1 = _mm_xor_ps(A1, b3vPPPM);  //	change sign of the last element
  	A1 = A1 - A3;                  //	AB123 = AB12 - AB3
  
  	return b3Quaternion(A1);
  
  #elif defined(B3_USE_NEON)
  
  	float32x4_t vQ1 = w.get128();
  	float32x4_t vQ2 = q.get128();
  	float32x4_t A1, B1, A2, B2, A3, B3;
  	float32x2_t vQ1zx, vQ2wx, vQ1yz, vQ2zx, vQ2yz, vQ2xz;
  
  	{
  		float32x2x2_t tmp;
  
  		tmp = vtrn_f32(vget_high_f32(vQ1), vget_low_f32(vQ1));  // {z x}, {w y}
  		vQ1zx = tmp.val[0];
  
  		tmp = vtrn_f32(vget_high_f32(vQ2), vget_low_f32(vQ2));  // {z x}, {w y}
  		vQ2zx = tmp.val[0];
  	}
  	vQ2wx = vext_f32(vget_high_f32(vQ2), vget_low_f32(vQ2), 1);
  
  	vQ1yz = vext_f32(vget_low_f32(vQ1), vget_high_f32(vQ1), 1);
  
  	vQ2yz = vext_f32(vget_low_f32(vQ2), vget_high_f32(vQ2), 1);
  	vQ2xz = vext_f32(vQ2zx, vQ2zx, 1);
  
  	A1 = vcombine_f32(vget_low_f32(vQ1), vQ1zx);                     // X Y  z x
  	B1 = vcombine_f32(vdup_lane_f32(vget_high_f32(vQ2), 1), vQ2wx);  // W W  W X
  
  	A2 = vcombine_f32(vQ1yz, vget_low_f32(vQ1));
  	B2 = vcombine_f32(vQ2zx, vdup_lane_f32(vget_low_f32(vQ2), 1));
  
  	A3 = vcombine_f32(vQ1zx, vQ1yz);  // Z X Y Z
  	B3 = vcombine_f32(vQ2yz, vQ2xz);  // Y Z x z
  
  	A1 = vmulq_f32(A1, B1);
  	A2 = vmulq_f32(A2, B2);
  	A3 = vmulq_f32(A3, B3);  //	A3 *= B3
  
  	A1 = vaddq_f32(A1, A2);  //	AB12 = AB1 + AB2
  
  	//	change the sign of the last element
  	A1 = (b3SimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)b3vPPPM);
  
  	A1 = vsubq_f32(A1, A3);  //	AB123 = AB12 - AB3
  
  	return b3Quaternion(A1);
  
  #else
  	return b3Quaternion(
  		+w.getX() * q.getW() + w.getY() * q.getZ() - w.getZ() * q.getY(),
  		+w.getY() * q.getW() + w.getZ() * q.getX() - w.getX() * q.getZ(),
  		+w.getZ() * q.getW() + w.getX() * q.getY() - w.getY() * q.getX(),
  		-w.getX() * q.getX() - w.getY() * q.getY() - w.getZ() * q.getZ());
  #endif
  }
  
  /**@brief Calculate the dot product between two quaternions */
  B3_FORCE_INLINE b3Scalar
  b3Dot(const b3Quaternion& q1, const b3Quaternion& q2)
  {
  	return q1.dot(q2);
  }
  
  /**@brief Return the length of a quaternion */
  B3_FORCE_INLINE b3Scalar
  b3Length(const b3Quaternion& q)
  {
  	return q.length();
  }
  
  /**@brief Return the angle between two quaternions*/
  B3_FORCE_INLINE b3Scalar
  b3Angle(const b3Quaternion& q1, const b3Quaternion& q2)
  {
  	return q1.angle(q2);
  }
  
  /**@brief Return the inverse of a quaternion*/
  B3_FORCE_INLINE b3Quaternion
  b3Inverse(const b3Quaternion& q)
  {
  	return q.inverse();
  }
  
  /**@brief Return the result of spherical linear interpolation betwen two quaternions 
   * @param q1 The first quaternion
   * @param q2 The second quaternion 
   * @param t The ration between q1 and q2.  t = 0 return q1, t=1 returns q2 
   * Slerp assumes constant velocity between positions. */
  B3_FORCE_INLINE b3Quaternion
  b3Slerp(const b3Quaternion& q1, const b3Quaternion& q2, const b3Scalar& t)
  {
  	return q1.slerp(q2, t);
  }
  
  B3_FORCE_INLINE b3Quaternion
  b3QuatMul(const b3Quaternion& rot0, const b3Quaternion& rot1)
  {
  	return rot0 * rot1;
  }
  
  B3_FORCE_INLINE b3Quaternion
  b3QuatNormalized(const b3Quaternion& orn)
  {
  	return orn.normalized();
  }
  
  B3_FORCE_INLINE b3Vector3
  b3QuatRotate(const b3Quaternion& rotation, const b3Vector3& v)
  {
  	b3Quaternion q = rotation * v;
  	q *= rotation.inverse();
  #if defined(B3_USE_SSE_IN_API) && defined(B3_USE_SSE)
  	return b3MakeVector3(_mm_and_ps(q.get128(), b3vFFF0fMask));
  #elif defined(B3_USE_NEON)
  	return b3MakeVector3((float32x4_t)vandq_s32((int32x4_t)q.get128(), b3vFFF0Mask));
  #else
  	return b3MakeVector3(q.getX(), q.getY(), q.getZ());
  #endif
  }
  
  B3_FORCE_INLINE b3Quaternion
  b3ShortestArcQuat(const b3Vector3& v0, const b3Vector3& v1)  // Game Programming Gems 2.10. make sure v0,v1 are normalized
  {
  	b3Vector3 c = v0.cross(v1);
  	b3Scalar d = v0.dot(v1);
  
  	if (d < -1.0 + B3_EPSILON)
  	{
  		b3Vector3 n, unused;
  		b3PlaneSpace1(v0, n, unused);
  		return b3Quaternion(n.getX(), n.getY(), n.getZ(), 0.0f);  // just pick any vector that is orthogonal to v0
  	}
  
  	b3Scalar s = b3Sqrt((1.0f + d) * 2.0f);
  	b3Scalar rs = 1.0f / s;
  
  	return b3Quaternion(c.getX() * rs, c.getY() * rs, c.getZ() * rs, s * 0.5f);
  }
  
  B3_FORCE_INLINE b3Quaternion
  b3ShortestArcQuatNormalize2(b3Vector3& v0, b3Vector3& v1)
  {
  	v0.normalize();
  	v1.normalize();
  	return b3ShortestArcQuat(v0, v1);
  }
  
  #endif  //B3_SIMD__QUATERNION_H_
  