text: /// @ref gtx_quaternion
  
  #include <limits>
  #include "glm-0.9.9.8/glm/gtc/constants.hpp"
  
  namespace glm
  {
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q> quat_identity()
  	{
  		return qua<T, Q>(static_cast<T>(1), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<3, T, Q> cross(vec<3, T, Q> const& v, qua<T, Q> const& q)
  	{
  		return inverse(q) * v;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<3, T, Q> cross(qua<T, Q> const& q, vec<3, T, Q> const& v)
  	{
  		return q * v;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> squad
  	(
  		qua<T, Q> const& q1,
  		qua<T, Q> const& q2,
  		qua<T, Q> const& s1,
  		qua<T, Q> const& s2,
  		T const& h)
  	{
  		return mix(mix(q1, q2, h), mix(s1, s2, h), static_cast<T>(2) * (static_cast<T>(1) - h) * h);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> intermediate
  	(
  		qua<T, Q> const& prev,
  		qua<T, Q> const& curr,
  		qua<T, Q> const& next
  	)
  	{
  		qua<T, Q> invQuat = inverse(curr);
  		return exp((log(next * invQuat) + log(prev * invQuat)) / static_cast<T>(-4)) * curr;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<3, T, Q> rotate(qua<T, Q> const& q, vec<3, T, Q> const& v)
  	{
  		return q * v;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<4, T, Q> rotate(qua<T, Q> const& q, vec<4, T, Q> const& v)
  	{
  		return q * v;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER T extractRealComponent(qua<T, Q> const& q)
  	{
  		T w = static_cast<T>(1) - q.x * q.x - q.y * q.y - q.z * q.z;
  		if(w < T(0))
  			return T(0);
  		else
  			return -sqrt(w);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR T length2(qua<T, Q> const& q)
  	{
  		return q.x * q.x + q.y * q.y + q.z * q.z + q.w * q.w;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> shortMix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
  	{
  		if(a <= static_cast<T>(0)) return x;
  		if(a >= static_cast<T>(1)) return y;
  
  		T fCos = dot(x, y);
  		qua<T, Q> y2(y); //BUG!!! qua<T> y2;
  		if(fCos < static_cast<T>(0))
  		{
  			y2 = -y;
  			fCos = -fCos;
  		}
  
  		//if(fCos > 1.0f) // problem
  		T k0, k1;
  		if(fCos > (static_cast<T>(1) - epsilon<T>()))
  		{
  			k0 = static_cast<T>(1) - a;
  			k1 = static_cast<T>(0) + a; //BUG!!! 1.0f + a;
  		}
  		else
  		{
  			T fSin = sqrt(T(1) - fCos * fCos);
  			T fAngle = atan(fSin, fCos);
  			T fOneOverSin = static_cast<T>(1) / fSin;
  			k0 = sin((static_cast<T>(1) - a) * fAngle) * fOneOverSin;
  			k1 = sin((static_cast<T>(0) + a) * fAngle) * fOneOverSin;
  		}
  
  		return qua<T, Q>(
  			k0 * x.w + k1 * y2.w,
  			k0 * x.x + k1 * y2.x,
  			k0 * x.y + k1 * y2.y,
  			k0 * x.z + k1 * y2.z);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> fastMix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
  	{
  		return glm::normalize(x * (static_cast<T>(1) - a) + (y * a));
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> rotation(vec<3, T, Q> const& orig, vec<3, T, Q> const& dest)
  	{
  		T cosTheta = dot(orig, dest);
  		vec<3, T, Q> rotationAxis;
  
  		if(cosTheta >= static_cast<T>(1) - epsilon<T>()) {
  			// orig and dest point in the same direction
  			return quat_identity<T,Q>();
  		}
  
  		if(cosTheta < static_cast<T>(-1) + epsilon<T>())
  		{
  			// special case when vectors in opposite directions :
  			// there is no "ideal" rotation axis
  			// So guess one; any will do as long as it's perpendicular to start
  			// This implementation favors a rotation around the Up axis (Y),
  			// since it's often what you want to do.
  			rotationAxis = cross(vec<3, T, Q>(0, 0, 1), orig);
  			if(length2(rotationAxis) < epsilon<T>()) // bad luck, they were parallel, try again!
  				rotationAxis = cross(vec<3, T, Q>(1, 0, 0), orig);
  
  			rotationAxis = normalize(rotationAxis);
  			return angleAxis(pi<T>(), rotationAxis);
  		}
  
  		// Implementation from Stan Melax's Game Programming Gems 1 article
  		rotationAxis = cross(orig, dest);
  
  		T s = sqrt((T(1) + cosTheta) * static_cast<T>(2));
  		T invs = static_cast<T>(1) / s;
  
  		return qua<T, Q>(
  			s * static_cast<T>(0.5f),
  			rotationAxis.x * invs,
  			rotationAxis.y * invs,
  			rotationAxis.z * invs);
  	}
  }//namespace glm
  