godot/thirdparty/bullet/LinearMath/btQuaternion.h

/*
Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans  https://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 BT_SIMD__QUATERNION_H_
#define BT_SIMD__QUATERNION_H_

#include "btVector3.h"
#include "btQuadWord.h"

#ifdef BT_USE_DOUBLE_PRECISION
#define btQuaternionData btQuaternionDoubleData
#define btQuaternionDataName "btQuaternionDoubleData"
#else
#define btQuaternionData btQuaternionFloatData
#define btQuaternionDataName "btQuaternionFloatData"
#endif  //BT_USE_DOUBLE_PRECISION

#ifdef BT_USE_SSE

//const __m128 ATTRIBUTE_ALIGNED16(vOnes) = {1.0f, 1.0f, 1.0f, 1.0f};
#define vOnes (_mm_set_ps(1.0f, 1.0f, 1.0f, 1.0f))

#endif

#if defined(BT_USE_SSE)

#define vQInv (_mm_set_ps(+0.0f, -0.0f, -0.0f, -0.0f))
#define vPPPM (_mm_set_ps(-0.0f, +0.0f, +0.0f, +0.0f))

#elif defined(BT_USE_NEON)

const btSimdFloat4 ATTRIBUTE_ALIGNED16(vQInv) = {-0.0f, -0.0f, -0.0f, +0.0f};
const btSimdFloat4 ATTRIBUTE_ALIGNED16(vPPPM) = {+0.0f, +0.0f, +0.0f, -0.0f};

#endif

/**@brief The btQuaternion implements quaternion to perform linear algebra rotations in combination with btMatrix3x3, btVector3 and btTransform. */
class btQuaternion : public btQuadWord
{
public:
	/**@brief No initialization constructor */
	btQuaternion() {}

#if (defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)) || defined(BT_USE_NEON)
	// Set Vector
	SIMD_FORCE_INLINE btQuaternion(const btSimdFloat4 vec)
	{
		mVec128 = vec;
	}

	// Copy constructor
	SIMD_FORCE_INLINE btQuaternion(const btQuaternion& rhs)
	{
		mVec128 = rhs.mVec128;
	}

	// Assignment Operator
	SIMD_FORCE_INLINE btQuaternion&
	operator=(const btQuaternion& v)
	{
		mVec128 = v.mVec128;

		return *this;
	}

#endif

	//		template <typename btScalar>
	//		explicit Quaternion(const btScalar *v) : Tuple4<btScalar>(v) {}
	/**@brief Constructor from scalars */
	btQuaternion(const btScalar& _x, const btScalar& _y, const btScalar& _z, const btScalar& _w)
		: btQuadWord(_x, _y, _z, _w)
	{
	}
	/**@brief Axis angle Constructor
   * @param axis The axis which the rotation is around
   * @param angle The magnitude of the rotation around the angle (Radians) */
	btQuaternion(const btVector3& _axis, const btScalar& _angle)
	{
		setRotation(_axis, _angle);
	}
	/**@brief Constructor from Euler angles
   * @param yaw Angle around Y unless BT_EULER_DEFAULT_ZYX defined then Z
   * @param pitch Angle around X unless BT_EULER_DEFAULT_ZYX defined then Y
   * @param roll Angle around Z unless BT_EULER_DEFAULT_ZYX defined then X */
	btQuaternion(const btScalar& yaw, const btScalar& pitch, const btScalar& roll)
	{
#ifndef BT_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 btVector3& axis, const btScalar& _angle)
	{
		btScalar d = axis.length();
		btAssert(d != btScalar(0.0));
		btScalar s = btSin(_angle * btScalar(0.5)) / d;
		setValue(axis.x() * s, axis.y() * s, axis.z() * s,
				 btCos(_angle * btScalar(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 btScalar& yaw, const btScalar& pitch, const btScalar& roll)
	{
		btScalar halfYaw = btScalar(yaw) * btScalar(0.5);
		btScalar halfPitch = btScalar(pitch) * btScalar(0.5);
		btScalar halfRoll = btScalar(roll) * btScalar(0.5);
		btScalar cosYaw = btCos(halfYaw);
		btScalar sinYaw = btSin(halfYaw);
		btScalar cosPitch = btCos(halfPitch);
		btScalar sinPitch = btSin(halfPitch);
		btScalar cosRoll = btCos(halfRoll);
		btScalar sinRoll = btSin(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 btScalar& yawZ, const btScalar& pitchY, const btScalar& rollX)
	{
		btScalar halfYaw = btScalar(yawZ) * btScalar(0.5);
		btScalar halfPitch = btScalar(pitchY) * btScalar(0.5);
		btScalar halfRoll = btScalar(rollX) * btScalar(0.5);
		btScalar cosYaw = btCos(halfYaw);
		btScalar sinYaw = btSin(halfYaw);
		btScalar cosPitch = btCos(halfPitch);
		btScalar sinPitch = btSin(halfPitch);
		btScalar cosRoll = btCos(halfRoll);
		btScalar sinRoll = btSin(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
	}

	/**@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(btScalar& yawZ, btScalar& pitchY, btScalar& rollX) const
	{
		btScalar squ;
		btScalar sqx;
		btScalar sqy;
		btScalar sqz;
		btScalar 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];
		sarg = btScalar(-2.) * (m_floats[0] * m_floats[2] - m_floats[3] * m_floats[1]);

		// If the pitch angle is PI/2 or -PI/2, we can only compute
		// the sum roll + yaw.  However, any combination that gives
		// the right sum will produce the correct orientation, so we
		// set rollX = 0 and compute yawZ.
		if (sarg <= -btScalar(0.99999))
		{
			pitchY = btScalar(-0.5) * SIMD_PI;
			rollX = 0;
			yawZ = btScalar(2) * btAtan2(m_floats[0], -m_floats[1]);
		}
		else if (sarg >= btScalar(0.99999))
		{
			pitchY = btScalar(0.5) * SIMD_PI;
			rollX = 0;
			yawZ = btScalar(2) * btAtan2(-m_floats[0], m_floats[1]);
		}
		else
		{
			pitchY = btAsin(sarg);
			rollX = btAtan2(2 * (m_floats[1] * m_floats[2] + m_floats[3] * m_floats[0]), squ - sqx - sqy + sqz);
			yawZ = btAtan2(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 */
	SIMD_FORCE_INLINE btQuaternion& operator+=(const btQuaternion& q)
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		mVec128 = _mm_add_ps(mVec128, q.mVec128);
#elif defined(BT_USE_NEON)
		mVec128 = vaddq_f32(mVec128, q.mVec128);
#else
		m_floats[0] += q.x();
		m_floats[1] += q.y();
		m_floats[2] += q.z();
		m_floats[3] += q.m_floats[3];
#endif
		return *this;
	}

	/**@brief Subtract out a quaternion
   * @param q The quaternion to subtract from this one */
	btQuaternion& operator-=(const btQuaternion& q)
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		mVec128 = _mm_sub_ps(mVec128, q.mVec128);
#elif defined(BT_USE_NEON)
		mVec128 = vsubq_f32(mVec128, q.mVec128);
#else
		m_floats[0] -= q.x();
		m_floats[1] -= q.y();
		m_floats[2] -= q.z();
		m_floats[3] -= q.m_floats[3];
#endif
		return *this;
	}

	/**@brief Scale this quaternion
   * @param s The scalar to scale by */
	btQuaternion& operator*=(const btScalar& s)
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		__m128 vs = _mm_load_ss(&s);  //	(S 0 0 0)
		vs = bt_pshufd_ps(vs, 0);     //	(S S S S)
		mVec128 = _mm_mul_ps(mVec128, vs);
#elif defined(BT_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 */
	btQuaternion& operator*=(const btQuaternion& q)
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		__m128 vQ2 = q.get128();

		__m128 A1 = bt_pshufd_ps(mVec128, BT_SHUFFLE(0, 1, 2, 0));
		__m128 B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(3, 3, 3, 0));

		A1 = A1 * B1;

		__m128 A2 = bt_pshufd_ps(mVec128, BT_SHUFFLE(1, 2, 0, 1));
		__m128 B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1));

		A2 = A2 * B2;

		B1 = bt_pshufd_ps(mVec128, BT_SHUFFLE(2, 0, 1, 2));
		B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2));

		B1 = B1 * B2;  //	A3 *= B3

		mVec128 = bt_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, vPPPM);  //	change sign of the last element
		mVec128 = mVec128 + A1;      //	AB03 + AB12

#elif defined(BT_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 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);
		A0 = vaddq_f32(A0, A1);  //	AB03 + AB12

		mVec128 = A0;
#else
		setValue(
			m_floats[3] * q.x() + m_floats[0] * q.m_floats[3] + m_floats[1] * q.z() - m_floats[2] * q.y(),
			m_floats[3] * q.y() + m_floats[1] * q.m_floats[3] + m_floats[2] * q.x() - m_floats[0] * q.z(),
			m_floats[3] * q.z() + m_floats[2] * q.m_floats[3] + m_floats[0] * q.y() - m_floats[1] * q.x(),
			m_floats[3] * q.m_floats[3] - m_floats[0] * q.x() - m_floats[1] * q.y() - m_floats[2] * q.z());
#endif
		return *this;
	}
	/**@brief Return the dot product between this quaternion and another
   * @param q The other quaternion */
	btScalar dot(const btQuaternion& q) const
	{
#if defined BT_USE_SIMD_VECTOR3 && defined(BT_USE_SSE_IN_API) && defined(BT_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(BT_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.x() +
			   m_floats[1] * q.y() +
			   m_floats[2] * q.z() +
			   m_floats[3] * q.m_floats[3];
#endif
	}

	/**@brief Return the length squared of the quaternion */
	btScalar length2() const
	{
		return dot(*this);
	}

	/**@brief Return the length of the quaternion */
	btScalar length() const
	{
		return btSqrt(length2());
	}
	btQuaternion& safeNormalize()
	{
		btScalar l2 = length2();
		if (l2 > SIMD_EPSILON)
		{
			normalize();
		}
		return *this;
	}
	/**@brief Normalize the quaternion 
   * Such that x^2 + y^2 + z^2 +w^2 = 1 */
	btQuaternion& normalize()
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_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(vOnes, vd);
		vd = bt_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 */
	SIMD_FORCE_INLINE btQuaternion
	operator*(const btScalar& s) const
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		__m128 vs = _mm_load_ss(&s);  //	(S 0 0 0)
		vs = bt_pshufd_ps(vs, 0x00);  //	(S S S S)

		return btQuaternion(_mm_mul_ps(mVec128, vs));
#elif defined(BT_USE_NEON)
		return btQuaternion(vmulq_n_f32(mVec128, s));
#else
		return btQuaternion(x() * s, y() * s, z() * s, m_floats[3] * s);
#endif
	}

	/**@brief Return an inversely scaled versionof this quaternion
   * @param s The inverse scale factor */
	btQuaternion operator/(const btScalar& s) const
	{
		btAssert(s != btScalar(0.0));
		return *this * (btScalar(1.0) / s);
	}

	/**@brief Inversely scale this quaternion
   * @param s The scale factor */
	btQuaternion& operator/=(const btScalar& s)
	{
		btAssert(s != btScalar(0.0));
		return *this *= btScalar(1.0) / s;
	}

	/**@brief Return a normalized version of this quaternion */
	btQuaternion normalized() const
	{
		return *this / length();
	}
	/**@brief Return the ***half*** angle between this quaternion and the other
   * @param q The other quaternion */
	btScalar angle(const btQuaternion& q) const
	{
		btScalar s = btSqrt(length2() * q.length2());
		btAssert(s != btScalar(0.0));
		return btAcos(dot(q) / s);
	}

	/**@brief Return the angle between this quaternion and the other along the shortest path
	* @param q The other quaternion */
	btScalar angleShortestPath(const btQuaternion& q) const
	{
		btScalar s = btSqrt(length2() * q.length2());
		btAssert(s != btScalar(0.0));
		if (dot(q) < 0)  // Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
			return btAcos(dot(-q) / s) * btScalar(2.0);
		else
			return btAcos(dot(q) / s) * btScalar(2.0);
	}

	/**@brief Return the angle [0, 2Pi] of rotation represented by this quaternion */
	btScalar getAngle() const
	{
		btScalar s = btScalar(2.) * btAcos(m_floats[3]);
		return s;
	}

	/**@brief Return the angle [0, Pi] of rotation represented by this quaternion along the shortest path */
	btScalar getAngleShortestPath() const
	{
		btScalar s;
		if (m_floats[3] >= 0)
			s = btScalar(2.) * btAcos(m_floats[3]);
		else
			s = btScalar(2.) * btAcos(-m_floats[3]);
		return s;
	}

	/**@brief Return the axis of the rotation represented by this quaternion */
	btVector3 getAxis() const
	{
		btScalar s_squared = 1.f - m_floats[3] * m_floats[3];

		if (s_squared < btScalar(10.) * SIMD_EPSILON)  //Check for divide by zero
			return btVector3(1.0, 0.0, 0.0);           // Arbitrary
		btScalar s = 1.f / btSqrt(s_squared);
		return btVector3(m_floats[0] * s, m_floats[1] * s, m_floats[2] * s);
	}

	/**@brief Return the inverse of this quaternion */
	btQuaternion inverse() const
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		return btQuaternion(_mm_xor_ps(mVec128, vQInv));
#elif defined(BT_USE_NEON)
		return btQuaternion((btSimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)vQInv));
#else
		return btQuaternion(-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 */
	SIMD_FORCE_INLINE btQuaternion
	operator+(const btQuaternion& q2) const
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		return btQuaternion(_mm_add_ps(mVec128, q2.mVec128));
#elif defined(BT_USE_NEON)
		return btQuaternion(vaddq_f32(mVec128, q2.mVec128));
#else
		const btQuaternion& q1 = *this;
		return btQuaternion(q1.x() + q2.x(), q1.y() + q2.y(), q1.z() + q2.z(), q1.m_floats[3] + q2.m_floats[3]);
#endif
	}

	/**@brief Return the difference between this quaternion and the other 
   * @param q2 The other quaternion */
	SIMD_FORCE_INLINE btQuaternion
	operator-(const btQuaternion& q2) const
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		return btQuaternion(_mm_sub_ps(mVec128, q2.mVec128));
#elif defined(BT_USE_NEON)
		return btQuaternion(vsubq_f32(mVec128, q2.mVec128));
#else
		const btQuaternion& q1 = *this;
		return btQuaternion(q1.x() - q2.x(), q1.y() - q2.y(), q1.z() - q2.z(), q1.m_floats[3] - q2.m_floats[3]);
#endif
	}

	/**@brief Return the negative of this quaternion 
   * This simply negates each element */
	SIMD_FORCE_INLINE btQuaternion operator-() const
	{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
		return btQuaternion(_mm_xor_ps(mVec128, btvMzeroMask));
#elif defined(BT_USE_NEON)
		return btQuaternion((btSimdFloat4)veorq_s32((int32x4_t)mVec128, (int32x4_t)btvMzeroMask));
#else
		const btQuaternion& q2 = *this;
		return btQuaternion(-q2.x(), -q2.y(), -q2.z(), -q2.m_floats[3]);
#endif
	}
	/**@todo document this and it's use */
	SIMD_FORCE_INLINE btQuaternion farthest(const btQuaternion& qd) const
	{
		btQuaternion 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 */
	SIMD_FORCE_INLINE btQuaternion nearest(const btQuaternion& qd) const
	{
		btQuaternion 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.  */
	btQuaternion slerp(const btQuaternion& q, const btScalar& t) const
	{
		const btScalar magnitude = btSqrt(length2() * q.length2());
		btAssert(magnitude > btScalar(0));

		const btScalar product = dot(q) / magnitude;
		const btScalar absproduct = btFabs(product);

		if (absproduct < btScalar(1.0 - SIMD_EPSILON))
		{
			// Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
			const btScalar theta = btAcos(absproduct);
			const btScalar d = btSin(theta);
			btAssert(d > btScalar(0));

			const btScalar sign = (product < 0) ? btScalar(-1) : btScalar(1);
			const btScalar s0 = btSin((btScalar(1.0) - t) * theta) / d;
			const btScalar s1 = btSin(sign * t * theta) / d;

			return btQuaternion(
				(m_floats[0] * s0 + q.x() * s1),
				(m_floats[1] * s0 + q.y() * s1),
				(m_floats[2] * s0 + q.z() * s1),
				(m_floats[3] * s0 + q.w() * s1));
		}
		else
		{
			return *this;
		}
	}

	static const btQuaternion& getIdentity()
	{
		static const btQuaternion identityQuat(btScalar(0.), btScalar(0.), btScalar(0.), btScalar(1.));
		return identityQuat;
	}

	SIMD_FORCE_INLINE const btScalar& getW() const { return m_floats[3]; }

	SIMD_FORCE_INLINE void serialize(struct btQuaternionData& dataOut) const;

	SIMD_FORCE_INLINE void deSerialize(const struct btQuaternionFloatData& dataIn);

	SIMD_FORCE_INLINE void deSerialize(const struct btQuaternionDoubleData& dataIn);

	SIMD_FORCE_INLINE void serializeFloat(struct btQuaternionFloatData& dataOut) const;

	SIMD_FORCE_INLINE void deSerializeFloat(const struct btQuaternionFloatData& dataIn);

	SIMD_FORCE_INLINE void serializeDouble(struct btQuaternionDoubleData& dataOut) const;

	SIMD_FORCE_INLINE void deSerializeDouble(const struct btQuaternionDoubleData& dataIn);
};

/**@brief Return the product of two quaternions */
SIMD_FORCE_INLINE btQuaternion
operator*(const btQuaternion& q1, const btQuaternion& q2)
{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
	__m128 vQ1 = q1.get128();
	__m128 vQ2 = q2.get128();
	__m128 A0, A1, B1, A2, B2;

	A1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(0, 1, 2, 0));  // X Y  z x     //      vtrn
	B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(3, 3, 3, 0));  // W W  W X     // vdup vext

	A1 = A1 * B1;

	A2 = bt_pshufd_ps(vQ1, BT_SHUFFLE(1, 2, 0, 1));  // Y Z  X Y     // vext
	B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1));  // z x  Y Y     // vtrn vdup

	A2 = A2 * B2;

	B1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(2, 0, 1, 2));  // z x Y Z      // vtrn vext
	B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2));  // Y Z x z      // vext vtrn

	B1 = B1 * B2;  //	A3 *= B3

	A0 = bt_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, vPPPM);  //	change sign of the last element
	A0 = A0 + A1;                //	AB03 + AB12

	return btQuaternion(A0);

#elif defined(BT_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 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);
	A0 = vaddq_f32(A0, A1);  //	AB03 + AB12

	return btQuaternion(A0);

#else
	return btQuaternion(
		q1.w() * q2.x() + q1.x() * q2.w() + q1.y() * q2.z() - q1.z() * q2.y(),
		q1.w() * q2.y() + q1.y() * q2.w() + q1.z() * q2.x() - q1.x() * q2.z(),
		q1.w() * q2.z() + q1.z() * q2.w() + q1.x() * q2.y() - q1.y() * q2.x(),
		q1.w() * q2.w() - q1.x() * q2.x() - q1.y() * q2.y() - q1.z() * q2.z());
#endif
}

SIMD_FORCE_INLINE btQuaternion
operator*(const btQuaternion& q, const btVector3& w)
{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
	__m128 vQ1 = q.get128();
	__m128 vQ2 = w.get128();
	__m128 A1, B1, A2, B2, A3, B3;

	A1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(3, 3, 3, 0));
	B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(0, 1, 2, 0));

	A1 = A1 * B1;

	A2 = bt_pshufd_ps(vQ1, BT_SHUFFLE(1, 2, 0, 1));
	B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1));

	A2 = A2 * B2;

	A3 = bt_pshufd_ps(vQ1, BT_SHUFFLE(2, 0, 1, 2));
	B3 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2));

	A3 = A3 * B3;  //	A3 *= B3

	A1 = A1 + A2;                //	AB12
	A1 = _mm_xor_ps(A1, vPPPM);  //	change sign of the last element
	A1 = A1 - A3;                //	AB123 = AB12 - AB3

	return btQuaternion(A1);

#elif defined(BT_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 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);

	A1 = vsubq_f32(A1, A3);  //	AB123 = AB12 - AB3

	return btQuaternion(A1);

#else
	return btQuaternion(
		q.w() * w.x() + q.y() * w.z() - q.z() * w.y(),
		q.w() * w.y() + q.z() * w.x() - q.x() * w.z(),
		q.w() * w.z() + q.x() * w.y() - q.y() * w.x(),
		-q.x() * w.x() - q.y() * w.y() - q.z() * w.z());
#endif
}

SIMD_FORCE_INLINE btQuaternion
operator*(const btVector3& w, const btQuaternion& q)
{
#if defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
	__m128 vQ1 = w.get128();
	__m128 vQ2 = q.get128();
	__m128 A1, B1, A2, B2, A3, B3;

	A1 = bt_pshufd_ps(vQ1, BT_SHUFFLE(0, 1, 2, 0));  // X Y  z x
	B1 = bt_pshufd_ps(vQ2, BT_SHUFFLE(3, 3, 3, 0));  // W W  W X

	A1 = A1 * B1;

	A2 = bt_pshufd_ps(vQ1, BT_SHUFFLE(1, 2, 0, 1));
	B2 = bt_pshufd_ps(vQ2, BT_SHUFFLE(2, 0, 1, 1));

	A2 = A2 * B2;

	A3 = bt_pshufd_ps(vQ1, BT_SHUFFLE(2, 0, 1, 2));
	B3 = bt_pshufd_ps(vQ2, BT_SHUFFLE(1, 2, 0, 2));

	A3 = A3 * B3;  //	A3 *= B3

	A1 = A1 + A2;                //	AB12
	A1 = _mm_xor_ps(A1, vPPPM);  //	change sign of the last element
	A1 = A1 - A3;                //	AB123 = AB12 - AB3

	return btQuaternion(A1);

#elif defined(BT_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 = (btSimdFloat4)veorq_s32((int32x4_t)A1, (int32x4_t)vPPPM);

	A1 = vsubq_f32(A1, A3);  //	AB123 = AB12 - AB3

	return btQuaternion(A1);

#else
	return btQuaternion(
		+w.x() * q.w() + w.y() * q.z() - w.z() * q.y(),
		+w.y() * q.w() + w.z() * q.x() - w.x() * q.z(),
		+w.z() * q.w() + w.x() * q.y() - w.y() * q.x(),
		-w.x() * q.x() - w.y() * q.y() - w.z() * q.z());
#endif
}

/**@brief Calculate the dot product between two quaternions */
SIMD_FORCE_INLINE btScalar
dot(const btQuaternion& q1, const btQuaternion& q2)
{
	return q1.dot(q2);
}

/**@brief Return the length of a quaternion */
SIMD_FORCE_INLINE btScalar
length(const btQuaternion& q)
{
	return q.length();
}

/**@brief Return the angle between two quaternions*/
SIMD_FORCE_INLINE btScalar
btAngle(const btQuaternion& q1, const btQuaternion& q2)
{
	return q1.angle(q2);
}

/**@brief Return the inverse of a quaternion*/
SIMD_FORCE_INLINE btQuaternion
inverse(const btQuaternion& 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. */
SIMD_FORCE_INLINE btQuaternion
slerp(const btQuaternion& q1, const btQuaternion& q2, const btScalar& t)
{
	return q1.slerp(q2, t);
}

SIMD_FORCE_INLINE btVector3
quatRotate(const btQuaternion& rotation, const btVector3& v)
{
	btQuaternion q = rotation * v;
	q *= rotation.inverse();
#if defined BT_USE_SIMD_VECTOR3 && defined(BT_USE_SSE_IN_API) && defined(BT_USE_SSE)
	return btVector3(_mm_and_ps(q.get128(), btvFFF0fMask));
#elif defined(BT_USE_NEON)
	return btVector3((float32x4_t)vandq_s32((int32x4_t)q.get128(), btvFFF0Mask));
#else
	return btVector3(q.getX(), q.getY(), q.getZ());
#endif
}

SIMD_FORCE_INLINE btQuaternion
shortestArcQuat(const btVector3& v0, const btVector3& v1)  // Game Programming Gems 2.10. make sure v0,v1 are normalized
{
	btVector3 c = v0.cross(v1);
	btScalar d = v0.dot(v1);

	if (d < -1.0 + SIMD_EPSILON)
	{
		btVector3 n, unused;
		btPlaneSpace1(v0, n, unused);
		return btQuaternion(n.x(), n.y(), n.z(), 0.0f);  // just pick any vector that is orthogonal to v0
	}

	btScalar s = btSqrt((1.0f + d) * 2.0f);
	btScalar rs = 1.0f / s;

	return btQuaternion(c.getX() * rs, c.getY() * rs, c.getZ() * rs, s * 0.5f);
}

SIMD_FORCE_INLINE btQuaternion
shortestArcQuatNormalize2(btVector3& v0, btVector3& v1)
{
	v0.normalize();
	v1.normalize();
	return shortestArcQuat(v0, v1);
}

struct btQuaternionFloatData
{
	float m_floats[4];
};

struct btQuaternionDoubleData
{
	double m_floats[4];
};

SIMD_FORCE_INLINE void btQuaternion::serializeFloat(struct btQuaternionFloatData& dataOut) const
{
	///could also do a memcpy, check if it is worth it
	for (int i = 0; i < 4; i++)
		dataOut.m_floats[i] = float(m_floats[i]);
}

SIMD_FORCE_INLINE void btQuaternion::deSerializeFloat(const struct btQuaternionFloatData& dataIn)
{
	for (int i = 0; i < 4; i++)
		m_floats[i] = btScalar(dataIn.m_floats[i]);
}

SIMD_FORCE_INLINE void btQuaternion::serializeDouble(struct btQuaternionDoubleData& dataOut) const
{
	///could also do a memcpy, check if it is worth it
	for (int i = 0; i < 4; i++)
		dataOut.m_floats[i] = double(m_floats[i]);
}

SIMD_FORCE_INLINE void btQuaternion::deSerializeDouble(const struct btQuaternionDoubleData& dataIn)
{
	for (int i = 0; i < 4; i++)
		m_floats[i] = btScalar(dataIn.m_floats[i]);
}

SIMD_FORCE_INLINE void btQuaternion::serialize(struct btQuaternionData& dataOut) const
{
	///could also do a memcpy, check if it is worth it
	for (int i = 0; i < 4; i++)
		dataOut.m_floats[i] = m_floats[i];
}

SIMD_FORCE_INLINE void btQuaternion::deSerialize(const struct btQuaternionFloatData& dataIn)
{
	for (int i = 0; i < 4; i++)
		m_floats[i] = (btScalar)dataIn.m_floats[i];
}

SIMD_FORCE_INLINE void btQuaternion::deSerialize(const struct btQuaternionDoubleData& dataIn)
{
	for (int i = 0; i < 4; i++)
		m_floats[i] = (btScalar)dataIn.m_floats[i];
}

#endif  //BT_SIMD__QUATERNION_H_