text: #include "glm/trigonometric.hpp"
  #include "glm/exponential.hpp"
  #include "glm/ext/quaternion_geometric.hpp"
  #include <limits>
  
  namespace glm{
  namespace detail
  {
  	template <typename T>
  	struct genTypeTrait<qua<T> >
  	{
  		static const genTypeEnum GENTYPE = GENTYPE_QUAT;
  	};
  
  	template<typename T, qualifier Q, bool Aligned>
  	struct compute_dot<qua<T, Q>, T, Aligned>
  	{
  		static GLM_FUNC_QUALIFIER T call(qua<T, Q> const& a, qua<T, Q> const& b)
  		{
  			vec<4, T, Q> tmp(a.x * b.x, a.y * b.y, a.z * b.z, a.w * b.w);
  			return (tmp.x + tmp.y) + (tmp.z + tmp.w);
  		}
  	};
  
  	template<typename T, qualifier Q, bool Aligned>
  	struct compute_quat_add
  	{
  		static qua<T, Q> call(qua<T, Q> const& q, qua<T, Q> const& p)
  		{
  			return qua<T, Q>(q.w + p.w, q.x + p.x, q.y + p.y, q.z + p.z);
  		}
  	};
  
  	template<typename T, qualifier Q, bool Aligned>
  	struct compute_quat_sub
  	{
  		static qua<T, Q> call(qua<T, Q> const& q, qua<T, Q> const& p)
  		{
  			return qua<T, Q>(q.w - p.w, q.x - p.x, q.y - p.y, q.z - p.z);
  		}
  	};
  
  	template<typename T, qualifier Q, bool Aligned>
  	struct compute_quat_mul_scalar
  	{
  		static qua<T, Q> call(qua<T, Q> const& q, T s)
  		{
  			return qua<T, Q>(q.w * s, q.x * s, q.y * s, q.z * s);
  		}
  	};
  
  	template<typename T, qualifier Q, bool Aligned>
  	struct compute_quat_div_scalar
  	{
  		static qua<T, Q> call(qua<T, Q> const& q, T s)
  		{
  			return qua<T, Q>(q.w / s, q.x / s, q.y / s, q.z / s);
  		}
  	};
  
  	template<typename T, qualifier Q, bool Aligned>
  	struct compute_quat_mul_vec4
  	{
  		static vec<4, T, Q> call(qua<T, Q> const& q, vec<4, T, Q> const& v)
  		{
  			return vec<4, T, Q>(q * vec<3, T, Q>(v), v.w);
  		}
  	};
  }//namespace detail
  
  	// -- Component accesses --
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR T & qua<T, Q>::operator[](typename qua<T, Q>::length_type i)
  	{
  		assert(i >= 0 && i < this->length());
  		return (&x)[i];
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR T const& qua<T, Q>::operator[](typename qua<T, Q>::length_type i) const
  	{
  		assert(i >= 0 && i < this->length());
  		return (&x)[i];
  	}
  
  	// -- Implicit basic constructors --
  
  #	if GLM_CONFIG_DEFAULTED_FUNCTIONS == GLM_DISABLE
  		template<typename T, qualifier Q>
  		GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q>::qua()
  #			if GLM_CONFIG_DEFAULTED_FUNCTIONS != GLM_DISABLE
  			: x(0), y(0), z(0), w(1)
  #			endif
  		{}
  
  		template<typename T, qualifier Q>
  		GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q>::qua(qua<T, Q> const& q)
  			: x(q.x), y(q.y), z(q.z), w(q.w)
  		{}
  #	endif
  
  	template<typename T, qualifier Q>
  	template<qualifier P>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q>::qua(qua<T, P> const& q)
  		: x(q.x), y(q.y), z(q.z), w(q.w)
  	{}
  
  	// -- Explicit basic constructors --
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q>::qua(T s, vec<3, T, Q> const& v)
  		: x(v.x), y(v.y), z(v.z), w(s)
  	{}
  
  	template <typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q>::qua(T _w, T _x, T _y, T _z)
  		: x(_x), y(_y), z(_z), w(_w)
  	{}
  
  	// -- Conversion constructors --
  
  	template<typename T, qualifier Q>
  	template<typename U, qualifier P>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR qua<T, Q>::qua(qua<U, P> const& q)
  		: x(static_cast<T>(q.x))
  		, y(static_cast<T>(q.y))
  		, z(static_cast<T>(q.z))
  		, w(static_cast<T>(q.w))
  	{}
  
  	//template<typename valType>
  	//GLM_FUNC_QUALIFIER qua<valType>::qua
  	//(
  	//	valType const& pitch,
  	//	valType const& yaw,
  	//	valType const& roll
  	//)
  	//{
  	//	vec<3, valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5));
  	//	vec<3, valType> c = glm::cos(eulerAngle * valType(0.5));
  	//	vec<3, valType> s = glm::sin(eulerAngle * valType(0.5));
  	//
  	//	this->w = c.x * c.y * c.z + s.x * s.y * s.z;
  	//	this->x = s.x * c.y * c.z - c.x * s.y * s.z;
  	//	this->y = c.x * s.y * c.z + s.x * c.y * s.z;
  	//	this->z = c.x * c.y * s.z - s.x * s.y * c.z;
  	//}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q>::qua(vec<3, T, Q> const& u, vec<3, T, Q> const& v)
  	{
  		T norm_u_norm_v = sqrt(dot(u, u) * dot(v, v));
  		T real_part = norm_u_norm_v + dot(u, v);
  		vec<3, T, Q> t;
  
  		if(real_part < static_cast<T>(1.e-6f) * norm_u_norm_v)
  		{
  			// If u and v are exactly opposite, rotate 180 degrees
  			// around an arbitrary orthogonal axis. Axis normalisation
  			// can happen later, when we normalise the quaternion.
  			real_part = static_cast<T>(0);
  			t = abs(u.x) > abs(u.z) ? vec<3, T, Q>(-u.y, u.x, static_cast<T>(0)) : vec<3, T, Q>(static_cast<T>(0), -u.z, u.y);
  		}
  		else
  		{
  			// Otherwise, build quaternion the standard way.
  			t = cross(u, v);
  		}
  
  		*this = normalize(qua<T, Q>(real_part, t.x, t.y, t.z));
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q>::qua(vec<3, T, Q> const& eulerAngle)
  	{
  		vec<3, T, Q> c = glm::cos(eulerAngle * T(0.5));
  		vec<3, T, Q> s = glm::sin(eulerAngle * T(0.5));
  
  		this->w = c.x * c.y * c.z + s.x * s.y * s.z;
  		this->x = s.x * c.y * c.z - c.x * s.y * s.z;
  		this->y = c.x * s.y * c.z + s.x * c.y * s.z;
  		this->z = c.x * c.y * s.z - s.x * s.y * c.z;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q>::qua(mat<3, 3, T, Q> const& m)
  	{
  		*this = quat_cast(m);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q>::qua(mat<4, 4, T, Q> const& m)
  	{
  		*this = quat_cast(m);
  	}
  
  #	if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q>::operator mat<3, 3, T, Q>()
  	{
  		return mat3_cast(*this);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q>::operator mat<4, 4, T, Q>()
  	{
  		return mat4_cast(*this);
  	}
  #	endif//GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
  
  	// -- Unary arithmetic operators --
  
  #	if GLM_CONFIG_DEFAULTED_FUNCTIONS == GLM_DISABLE
  		template<typename T, qualifier Q>
  		GLM_FUNC_QUALIFIER qua<T, Q> & qua<T, Q>::operator=(qua<T, Q> const& q)
  		{
  			this->w = q.w;
  			this->x = q.x;
  			this->y = q.y;
  			this->z = q.z;
  			return *this;
  		}
  #	endif
  
  	template<typename T, qualifier Q>
  	template<typename U>
  	GLM_FUNC_QUALIFIER qua<T, Q> & qua<T, Q>::operator=(qua<U, Q> const& q)
  	{
  		this->w = static_cast<T>(q.w);
  		this->x = static_cast<T>(q.x);
  		this->y = static_cast<T>(q.y);
  		this->z = static_cast<T>(q.z);
  		return *this;
  	}
  
  	template<typename T, qualifier Q>
  	template<typename U>
  	GLM_FUNC_QUALIFIER qua<T, Q> & qua<T, Q>::operator+=(qua<U, Q> const& q)
  	{
  		return (*this = detail::compute_quat_add<T, Q, detail::is_aligned<Q>::value>::call(*this, qua<T, Q>(q)));
  	}
  
  	template<typename T, qualifier Q>
  	template<typename U>
  	GLM_FUNC_QUALIFIER qua<T, Q> & qua<T, Q>::operator-=(qua<U, Q> const& q)
  	{
  		return (*this = detail::compute_quat_sub<T, Q, detail::is_aligned<Q>::value>::call(*this, qua<T, Q>(q)));
  	}
  
  	template<typename T, qualifier Q>
  	template<typename U>
  	GLM_FUNC_QUALIFIER qua<T, Q> & qua<T, Q>::operator*=(qua<U, Q> const& r)
  	{
  		qua<T, Q> const p(*this);
  		qua<T, Q> const q(r);
  
  		this->w = p.w * q.w - p.x * q.x - p.y * q.y - p.z * q.z;
  		this->x = p.w * q.x + p.x * q.w + p.y * q.z - p.z * q.y;
  		this->y = p.w * q.y + p.y * q.w + p.z * q.x - p.x * q.z;
  		this->z = p.w * q.z + p.z * q.w + p.x * q.y - p.y * q.x;
  		return *this;
  	}
  
  	template<typename T, qualifier Q>
  	template<typename U>
  	GLM_FUNC_QUALIFIER qua<T, Q> & qua<T, Q>::operator*=(U s)
  	{
  		return (*this = detail::compute_quat_mul_scalar<T, Q, detail::is_aligned<Q>::value>::call(*this, static_cast<U>(s)));
  	}
  
  	template<typename T, qualifier Q>
  	template<typename U>
  	GLM_FUNC_QUALIFIER qua<T, Q> & qua<T, Q>::operator/=(U s)
  	{
  		return (*this = detail::compute_quat_div_scalar<T, Q, detail::is_aligned<Q>::value>::call(*this, static_cast<U>(s)));
  	}
  
  	// -- Unary bit operators --
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator+(qua<T, Q> const& q)
  	{
  		return q;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator-(qua<T, Q> const& q)
  	{
  		return qua<T, Q>(-q.w, -q.x, -q.y, -q.z);
  	}
  
  	// -- Binary operators --
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator+(qua<T, Q> const& q, qua<T, Q> const& p)
  	{
  		return qua<T, Q>(q) += p;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator-(qua<T, Q> const& q, qua<T, Q> const& p)
  	{
  		return qua<T, Q>(q) -= p;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator*(qua<T, Q> const& q, qua<T, Q> const& p)
  	{
  		return qua<T, Q>(q) *= p;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(qua<T, Q> const& q, vec<3, T, Q> const& v)
  	{
  		vec<3, T, Q> const QuatVector(q.x, q.y, q.z);
  		vec<3, T, Q> const uv(glm::cross(QuatVector, v));
  		vec<3, T, Q> const uuv(glm::cross(QuatVector, uv));
  
  		return v + ((uv * q.w) + uuv) * static_cast<T>(2);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(vec<3, T, Q> const& v, qua<T, Q> const& q)
  	{
  		return glm::inverse(q) * v;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(qua<T, Q> const& q, vec<4, T, Q> const& v)
  	{
  		return detail::compute_quat_mul_vec4<T, Q, detail::is_aligned<Q>::value>::call(q, v);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(vec<4, T, Q> const& v, qua<T, Q> const& q)
  	{
  		return glm::inverse(q) * v;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator*(qua<T, Q> const& q, T const& s)
  	{
  		return qua<T, Q>(
  			q.w * s, q.x * s, q.y * s, q.z * s);
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator*(T const& s, qua<T, Q> const& q)
  	{
  		return q * s;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER qua<T, Q> operator/(qua<T, Q> const& q, T const& s)
  	{
  		return qua<T, Q>(
  			q.w / s, q.x / s, q.y / s, q.z / s);
  	}
  
  	// -- Boolean operators --
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR bool operator==(qua<T, Q> const& q1, qua<T, Q> const& q2)
  	{
  		return q1.x == q2.x && q1.y == q2.y && q1.z == q2.z && q1.w == q2.w;
  	}
  
  	template<typename T, qualifier Q>
  	GLM_FUNC_QUALIFIER GLM_CONSTEXPR bool operator!=(qua<T, Q> const& q1, qua<T, Q> const& q2)
  	{
  		return q1.x != q2.x || q1.y != q2.y || q1.z != q2.z || q1.w != q2.w;
  	}
  }//namespace glm
  
  #if GLM_CONFIG_SIMD == GLM_ENABLE
  #	include "type_quat_simd.inl"
  #endif
  
  