1 files changed, 273 insertions, 260 deletions

diff --git a/external/include/glm/gtc/quaternion.inl b/external/include/glm/gtc/quaternion.inl
index c9b2af7..df4a5f7 100644
--- a/external/include/glm/gtc/quaternion.inl
+++ b/external/include/glm/gtc/quaternion.inl
@@ -4,78 +4,80 @@
 #include "../trigonometric.hpp"
 #include "../geometric.hpp"
 #include "../exponential.hpp"
+#include "../detail/compute_vector_relational.hpp"
+#include "epsilon.hpp"
 #include <limits>
 
 namespace glm{
 namespace detail
 {
-	template <typename T, precision P, bool Aligned>
-	struct compute_dot<tquat, T, P, Aligned>
+	template<typename T, qualifier Q, bool Aligned>
+	struct compute_dot<tquat<T, Q>, T, Aligned>
 	{
-		static GLM_FUNC_QUALIFIER T call(tquat<T, P> const& x, tquat<T, P> const& y)
+		static GLM_FUNC_QUALIFIER T call(tquat<T, Q> const& a, tquat<T, Q> const& b)
 		{
-			tvec4<T, P> tmp(x.x * y.x, x.y * y.y, x.z * y.z, x.w * y.w);
+			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, precision P, bool Aligned>
+	template<typename T, qualifier Q, bool Aligned>
 	struct compute_quat_add
 	{
-		static tquat<T, P> call(tquat<T, P> const& q, tquat<T, P> const& p)
+		static tquat<T, Q> call(tquat<T, Q> const& q, tquat<T, Q> const& p)
 		{
-			return tquat<T, P>(q.w + p.w, q.x + p.x, q.y + p.y, q.z + p.z);
+			return tquat<T, Q>(q.w + p.w, q.x + p.x, q.y + p.y, q.z + p.z);
 		}
 	};
 
-	template <typename T, precision P, bool Aligned>
+	template<typename T, qualifier Q, bool Aligned>
 	struct compute_quat_sub
 	{
-		static tquat<T, P> call(tquat<T, P> const& q, tquat<T, P> const& p)
+		static tquat<T, Q> call(tquat<T, Q> const& q, tquat<T, Q> const& p)
 		{
-			return tquat<T, P>(q.w - p.w, q.x - p.x, q.y - p.y, q.z - p.z);
+			return tquat<T, Q>(q.w - p.w, q.x - p.x, q.y - p.y, q.z - p.z);
 		}
 	};
 
-	template <typename T, precision P, bool Aligned>
+	template<typename T, qualifier Q, bool Aligned>
 	struct compute_quat_mul_scalar
 	{
-		static tquat<T, P> call(tquat<T, P> const& q, T s)
+		static tquat<T, Q> call(tquat<T, Q> const& q, T s)
 		{
-			return tquat<T, P>(q.w * s, q.x * s, q.y * s, q.z * s);
+			return tquat<T, Q>(q.w * s, q.x * s, q.y * s, q.z * s);
 		}
 	};
 
-	template <typename T, precision P, bool Aligned>
+	template<typename T, qualifier Q, bool Aligned>
 	struct compute_quat_div_scalar
 	{
-		static tquat<T, P> call(tquat<T, P> const& q, T s)
+		static tquat<T, Q> call(tquat<T, Q> const& q, T s)
 		{
-			return tquat<T, P>(q.w / s, q.x / s, q.y / s, q.z / s);
+			return tquat<T, Q>(q.w / s, q.x / s, q.y / s, q.z / s);
 		}
 	};
 
-	template <typename T, precision P, bool Aligned>
+	template<typename T, qualifier Q, bool Aligned>
 	struct compute_quat_mul_vec4
 	{
-		static tvec4<T, P> call(tquat<T, P> const & q, tvec4<T, P> const & v)
+		static vec<4, T, Q> call(tquat<T, Q> const& q, vec<4, T, Q> const& v)
 		{
-			return tvec4<T, P>(q * tvec3<T, P>(v), v.w);
+			return vec<4, T, Q>(q * vec<3, T, Q>(v), v.w);
 		}
 	};
 }//namespace detail
 
 	// -- Component accesses --
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::length_type i)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T & tquat<T, Q>::operator[](typename tquat<T, Q>::length_type i)
 	{
 		assert(i >= 0 && i < this->length());
 		return (&x)[i];
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::length_type i) const
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T const& tquat<T, Q>::operator[](typename tquat<T, Q>::length_type i) const
 	{
 		assert(i >= 0 && i < this->length());
 		return (&x)[i];
@@ -83,129 +85,139 @@ namespace detail
 
 	// -- Implicit basic constructors --
 
-#	if !GLM_HAS_DEFAULTED_FUNCTIONS || !defined(GLM_FORCE_NO_CTOR_INIT)
-		template <typename T, precision P>
-		GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat()
-#			ifndef GLM_FORCE_NO_CTOR_INIT
-				: x(0), y(0), z(0), w(1)
+#	if !GLM_HAS_DEFAULTED_FUNCTIONS || defined(GLM_FORCE_CTOR_INIT)
+		template<typename T, qualifier Q>
+		GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat()
+#			ifdef GLM_FORCE_CTOR_INIT
+			: x(0), y(0), z(0), w(1)
 #			endif
 		{}
 #	endif
 
 #	if !GLM_HAS_DEFAULTED_FUNCTIONS
-		template <typename T, precision P>
-		GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(tquat<T, P> const & q)
+		template<typename T, qualifier Q>
+		GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(tquat<T, Q> const& q)
 			: x(q.x), y(q.y), z(q.z), w(q.w)
 		{}
 #	endif//!GLM_HAS_DEFAULTED_FUNCTIONS
 
-	template <typename T, precision P>
-	template <precision Q>
-	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(tquat<T, Q> const & q)
+	template<typename T, qualifier Q>
+	template<qualifier P>
+	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(tquat<T, P> const& q)
 		: x(q.x), y(q.y), z(q.z), w(q.w)
 	{}
 
 	// -- Explicit basic constructors --
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER GLM_CONSTEXPR_CTOR tquat<T, P>::tquat(ctor)
-	{}
-
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(T const & s, tvec3<T, P> const & v)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(T s, vec<3, T, Q> const& v)
 		: x(v.x), y(v.y), z(v.z), w(s)
 	{}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(T const & w, T const & x, T const & y, T const & z)
-		: x(x), y(y), z(z), w(w)
+	template <typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(T _w, T _x, T _y, T _z)
+		: x(_x), y(_y), z(_z), w(_w)
 	{}
 
 	// -- Conversion constructors --
 
-	template <typename T, precision P>
-	template <typename U, precision Q>
-	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, P>::tquat(tquat<U, Q> const & q)
+	template<typename T, qualifier Q>
+	template<typename U, qualifier P>
+	GLM_FUNC_QUALIFIER GLM_CONSTEXPR tquat<T, Q>::tquat(tquat<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> 
+	//template<typename valType>
 	//GLM_FUNC_QUALIFIER tquat<valType>::tquat
 	//(
-	//	valType const & pitch,
-	//	valType const & yaw,
-	//	valType const & roll
+	//	valType const& pitch,
+	//	valType const& yaw,
+	//	valType const& roll
 	//)
 	//{
-	//	tvec3<valType> eulerAngle(pitch * valType(0.5), yaw * valType(0.5), roll * valType(0.5));
-	//	tvec3<valType> c = glm::cos(eulerAngle * valType(0.5));
-	//	tvec3<valType> s = glm::sin(eulerAngle * valType(0.5));
-	//	
+	//	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, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const & u, tvec3<T, P> const & v)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(vec<3, T, Q> const& u, vec<3, T, Q> const& v)
 	{
-		tvec3<T, P> const LocalW(cross(u, v));
-		T Dot = detail::compute_dot<tvec3, T, P, detail::is_aligned<P>::value>::call(u, v);
-		tquat<T, P> q(T(1) + Dot, LocalW.x, LocalW.y, LocalW.z);
+		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(q);
+	    *this = normalize(tquat<T, Q>(real_part, t.x, t.y, t.z));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tvec3<T, P> const & eulerAngle)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(vec<3, T, Q> const& eulerAngle)
 	{
-		tvec3<T, P> c = glm::cos(eulerAngle * T(0.5));
-		tvec3<T, P> s = glm::sin(eulerAngle * T(0.5));
-		
+		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, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat3x3<T, P> const & m)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(mat<3, 3, T, Q> const& m)
 	{
 		*this = quat_cast(m);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tmat4x4<T, P> const & m)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q>::tquat(mat<4, 4, T, Q> const& m)
 	{
 		*this = quat_cast(m);
 	}
 
 #	if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat3x3<T, P>()
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q>::operator mat<3, 3, T, Q>()
 	{
 		return mat3_cast(*this);
 	}
-	
-	template <typename T, precision P>	
-	GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat4x4<T, P>()
+
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q>::operator mat<4, 4, T, Q>()
 	{
 		return mat4_cast(*this);
 	}
 #	endif//GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> conjugate(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> conjugate(tquat<T, Q> const& q)
 	{
-		return tquat<T, P>(q.w, -q.x, -q.y, -q.z);
+		return tquat<T, Q>(q.w, -q.x, -q.y, -q.z);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> inverse(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> inverse(tquat<T, Q> const& q)
 	{
 		return conjugate(q) / dot(q, q);
 	}
@@ -213,8 +225,8 @@ namespace detail
 	// -- Unary arithmetic operators --
 
 #	if !GLM_HAS_DEFAULTED_FUNCTIONS
-		template <typename T, precision P>
-		GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator=(tquat<T, P> const & q)
+		template<typename T, qualifier Q>
+		GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator=(tquat<T, Q> const& q)
 		{
 			this->w = q.w;
 			this->x = q.x;
@@ -224,9 +236,9 @@ namespace detail
 		}
 #	endif//!GLM_HAS_DEFAULTED_FUNCTIONS
 
-	template <typename T, precision P>
-	template <typename U>
-	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator=(tquat<U, P> const & q)
+	template<typename T, qualifier Q>
+	template<typename U>
+	GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator=(tquat<U, Q> const& q)
 	{
 		this->w = static_cast<T>(q.w);
 		this->x = static_cast<T>(q.x);
@@ -235,26 +247,26 @@ namespace detail
 		return *this;
 	}
 
-	template <typename T, precision P>
-	template <typename U>
-	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator+=(tquat<U, P> const& q)
+	template<typename T, qualifier Q>
+	template<typename U>
+	GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator+=(tquat<U, Q> const& q)
 	{
-		return (*this = detail::compute_quat_add<T, P, detail::is_aligned<P>::value>::call(*this, tquat<T, P>(q)));
+		return (*this = detail::compute_quat_add<T, Q, detail::is_aligned<Q>::value>::call(*this, tquat<T, Q>(q)));
 	}
 
-	template <typename T, precision P>
-	template <typename U>
-	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator-=(tquat<U, P> const& q)
+	template<typename T, qualifier Q>
+	template<typename U>
+	GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator-=(tquat<U, Q> const& q)
 	{
-		return (*this = detail::compute_quat_sub<T, P, detail::is_aligned<P>::value>::call(*this, tquat<T, P>(q)));
+		return (*this = detail::compute_quat_sub<T, Q, detail::is_aligned<Q>::value>::call(*this, tquat<T, Q>(q)));
 	}
 
-	template <typename T, precision P>
-	template <typename U>
-	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(tquat<U, P> const & r)
+	template<typename T, qualifier Q>
+	template<typename U>
+	GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator*=(tquat<U, Q> const& r)
 	{
-		tquat<T, P> const p(*this);
-		tquat<T, P> const q(r);
+		tquat<T, Q> const p(*this);
+		tquat<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;
@@ -263,132 +275,145 @@ namespace detail
 		return *this;
 	}
 
-	template <typename T, precision P>
-	template <typename U>
-	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator*=(U s)
+	template<typename T, qualifier Q>
+	template<typename U>
+	GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator*=(U s)
 	{
-		return (*this = detail::compute_quat_mul_scalar<T, P, detail::is_aligned<P>::value>::call(*this, static_cast<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, precision P>
-	template <typename U>
-	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator/=(U s)
+	template<typename T, qualifier Q>
+	template<typename U>
+	GLM_FUNC_QUALIFIER tquat<T, Q> & tquat<T, Q>::operator/=(U s)
 	{
-		return (*this = detail::compute_quat_div_scalar<T, P, detail::is_aligned<P>::value>::call(*this, static_cast<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, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> operator+(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator+(tquat<T, Q> const& q)
 	{
 		return q;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> operator-(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator-(tquat<T, Q> const& q)
 	{
-		return tquat<T, P>(-q.w, -q.x, -q.y, -q.z);
+		return tquat<T, Q>(-q.w, -q.x, -q.y, -q.z);
 	}
 
 	// -- Binary operators --
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> operator+(tquat<T, P> const & q,	tquat<T, P> const & p)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator+(tquat<T, Q> const& q, tquat<T, Q> const& p)
 	{
-		return tquat<T, P>(q) += p;
+		return tquat<T, Q>(q) += p;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const & q,	tquat<T, P> const & p)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator-(tquat<T, Q> const& q, tquat<T, Q> const& p)
 	{
-		return tquat<T, P>(q) *= p;
+		return tquat<T, Q>(q) -= p;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tquat<T, P> const & q,	tvec3<T, P> const & v)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator*(tquat<T, Q> const& q, tquat<T, Q> const& p)
 	{
-		tvec3<T, P> const QuatVector(q.x, q.y, q.z);
-		tvec3<T, P> const uv(glm::cross(QuatVector, v));
-		tvec3<T, P> const uuv(glm::cross(QuatVector, uv));
+		return tquat<T, Q>(q) *= p;
+	}
+
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(tquat<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, precision P>
-	GLM_FUNC_QUALIFIER tvec3<T, P> operator*(tvec3<T, P> const & v, tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<3, T, Q> operator*(vec<3, T, Q> const& v, tquat<T, Q> const& q)
 	{
 		return glm::inverse(q) * v;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tquat<T, P> const& q, tvec4<T, P> const& v)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(tquat<T, Q> const& q, vec<4, T, Q> const& v)
 	{
-		return detail::compute_quat_mul_vec4<T, P, detail::is_aligned<P>::value>::call(q, v);
+		return detail::compute_quat_mul_vec4<T, Q, detail::is_aligned<Q>::value>::call(q, v);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<T, P> operator*(tvec4<T, P> const & v, tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, T, Q> operator*(vec<4, T, Q> const& v, tquat<T, Q> const& q)
 	{
 		return glm::inverse(q) * v;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> operator*(tquat<T, P> const & q, T const & s)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator*(tquat<T, Q> const& q, T const& s)
 	{
-		return tquat<T, P>(
+		return tquat<T, Q>(
 			q.w * s, q.x * s, q.y * s, q.z * s);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> operator*(T const & s, tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator*(T const& s, tquat<T, Q> const& q)
 	{
 		return q * s;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> operator/(tquat<T, P> const & q, T const & s)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> operator/(tquat<T, Q> const& q, T const& s)
 	{
-		return tquat<T, P>(
+		return tquat<T, Q>(
 			q.w / s, q.x / s, q.y / s, q.z / s);
 	}
 
 	// -- Boolean operators --
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER bool operator==(tquat<T, P> const & q1, tquat<T, P> const & q2)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER bool operator==(tquat<T, Q> const& q1, tquat<T, Q> const& q2)
 	{
-		return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w);
+		return all(epsilonEqual(q1, q2, epsilon<T>()));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER bool operator!=(tquat<T, P> const & q1, tquat<T, P> const & q2)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER bool operator!=(tquat<T, Q> const& q1, tquat<T, Q> const& q2)
 	{
-		return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w);
+		return any(epsilonNotEqual(q1, q2, epsilon<T>()));
 	}
 
 	// -- Operations --
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER T length(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T dot(tquat<T, Q> const& x, tquat<T, Q> const& y)
+	{
+		GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'dot' accepts only floating-point inputs");
+		return detail::compute_dot<tquat<T, Q>, T, detail::is_aligned<Q>::value>::call(x, y);
+	}
+
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T length(tquat<T, Q> const& q)
 	{
 		return glm::sqrt(dot(q, q));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> normalize(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> normalize(tquat<T, Q> const& q)
 	{
 		T len = length(q);
 		if(len <= T(0)) // Problem
-			return tquat<T, P>(1, 0, 0, 0);
+			return tquat<T, Q>(static_cast<T>(1), static_cast<T>(0), static_cast<T>(0), static_cast<T>(0));
 		T oneOverLen = T(1) / len;
-		return tquat<T, P>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
+		return tquat<T, Q>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> cross(tquat<T, P> const & q1, tquat<T, P> const & q2)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> cross(tquat<T, Q> const& q1, tquat<T, Q> const& q2)
 	{
-		return tquat<T, P>(
+		return tquat<T, Q>(
 			q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z,
 			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,
@@ -396,14 +421,14 @@ namespace detail
 	}
 /*
 	// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle))
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> const & y, T const & a)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> mix(tquat<T, Q> const& x, tquat<T, Q> const& y, T const& a)
 	{
 		if(a <= T(0)) return x;
 		if(a >= T(1)) return y;
 
 		float fCos = dot(x, y);
-		tquat<T, P> y2(y); //BUG!!! tquat<T, P> y2;
+		tquat<T, Q> y2(y); //BUG!!! tquat<T, Q> y2;
 		if(fCos < T(0))
 		{
 			y2 = -y;
@@ -426,19 +451,19 @@ namespace detail
 			k1 = sin((T(0) + a) * fAngle) * fOneOverSin;
 		}
 
-		return tquat<T, P>(
+		return tquat<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, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> mix2
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> mix2
 	(
-		tquat<T, P> const & x, 
-		tquat<T, P> const & y, 
-		T const & a
+		tquat<T, Q> const& x,
+		tquat<T, Q> const& y,
+		T const& a
 	)
 	{
 		bool flip = false;
@@ -466,13 +491,13 @@ namespace detail
 
 		if(flip)
 			alpha = -alpha;
-		
+
 		return normalize(beta * x + alpha * y);
 	}
 */
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> const & y, T a)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> mix(tquat<T, Q> const& x, tquat<T, Q> const& y, T a)
 	{
 		T cosTheta = dot(x, y);
 
@@ -480,7 +505,7 @@ namespace detail
 		if(cosTheta > T(1) - epsilon<T>())
 		{
 			// Linear interpolation
-			return tquat<T, P>(
+			return tquat<T, Q>(
 				mix(x.w, y.w, a),
 				mix(x.x, y.x, a),
 				mix(x.y, y.y, a),
@@ -494,8 +519,8 @@ namespace detail
 		}
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> lerp(tquat<T, P> const & x, tquat<T, P> const & y, T a)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> lerp(tquat<T, Q> const& x, tquat<T, Q> const& y, T a)
 	{
 		// Lerp is only defined in [0, 1]
 		assert(a >= static_cast<T>(0));
@@ -504,14 +529,14 @@ namespace detail
 		return x * (T(1) - a) + (y * a);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> slerp(tquat<T, P> const & x,	tquat<T, P> const & y, T a)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> slerp(tquat<T, Q> const& x,	tquat<T, Q> const& y, T a)
 	{
-		tquat<T, P> z = y;
+		tquat<T, Q> z = y;
 
 		T cosTheta = dot(x, y);
 
-		// If cosTheta < 0, the interpolation will take the long way around the sphere. 
+		// If cosTheta < 0, the interpolation will take the long way around the sphere.
 		// To fix this, one quat must be negated.
 		if (cosTheta < T(0))
 		{
@@ -523,7 +548,7 @@ namespace detail
 		if(cosTheta > T(1) - epsilon<T>())
 		{
 			// Linear interpolation
-			return tquat<T, P>(
+			return tquat<T, Q>(
 				mix(x.w, z.w, a),
 				mix(x.x, z.x, a),
 				mix(x.y, z.y, a),
@@ -537,10 +562,10 @@ namespace detail
 		}
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> rotate(tquat<T, P> const & q, T const & angle, tvec3<T, P> const & v)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> rotate(tquat<T, Q> const& q, T const& angle, vec<3, T, Q> const& v)
 	{
-		tvec3<T, P> Tmp = v;
+		vec<3, T, Q> Tmp = v;
 
 		// Axis of rotation must be normalised
 		T len = glm::length(Tmp);
@@ -555,38 +580,45 @@ namespace detail
 		T const AngleRad(angle);
 		T const Sin = sin(AngleRad * T(0.5));
 
-		return q * tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
-		//return gtc::quaternion::cross(q, tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
+		return q * tquat<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
+		//return gtc::quaternion::cross(q, tquat<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec3<T, P> eulerAngles(tquat<T, P> const & x)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<3, T, Q> eulerAngles(tquat<T, Q> const& x)
 	{
-		return tvec3<T, P>(pitch(x), yaw(x), roll(x));
+		return vec<3, T, Q>(pitch(x), yaw(x), roll(x));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER T roll(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T roll(tquat<T, Q> const& q)
 	{
-		return T(atan(T(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z));
+		return static_cast<T>(atan(static_cast<T>(2) * (q.x * q.y + q.w * q.z), q.w * q.w + q.x * q.x - q.y * q.y - q.z * q.z));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER T pitch(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T pitch(tquat<T, Q> const& q)
 	{
-		return T(atan(T(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z));
+		//return T(atan(T(2) * (q.y * q.z + q.w * q.x), q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z));
+		const T y = static_cast<T>(2) * (q.y * q.z + q.w * q.x);
+		const T x = q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z;
+
+		if(detail::compute_equal<T>::call(y, static_cast<T>(0)) && detail::compute_equal<T>::call(x, static_cast<T>(0))) //avoid atan2(0,0) - handle singularity - Matiis
+			return static_cast<T>(static_cast<T>(2) * atan(q.x,q.w));
+
+		return static_cast<T>(atan(y,x));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER T yaw(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T yaw(tquat<T, Q> const& q)
 	{
-		return asin(clamp(T(-2) * (q.x * q.z - q.w * q.y), T(-1), T(1)));
+		return asin(clamp(static_cast<T>(-2) * (q.x * q.z - q.w * q.y), static_cast<T>(-1), static_cast<T>(1)));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tmat3x3<T, P> mat3_cast(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER mat<3, 3, T, Q> mat3_cast(tquat<T, Q> const& q)
 	{
-		tmat3x3<T, P> Result(T(1));
+		mat<3, 3, T, Q> Result(T(1));
 		T qxx(q.x * q.x);
 		T qyy(q.y * q.y);
 		T qzz(q.z * q.z);
@@ -611,14 +643,14 @@ namespace detail
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tmat4x4<T, P> mat4_cast(tquat<T, P> const & q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER mat<4, 4, T, Q> mat4_cast(tquat<T, Q> const& q)
 	{
-		return tmat4x4<T, P>(mat3_cast(q));
+		return mat<4, 4, T, Q>(mat3_cast(q));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(tmat3x3<T, P> const & m)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> quat_cast(mat<3, 3, T, Q> const& m)
 	{
 		T fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2];
 		T fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2];
@@ -643,70 +675,51 @@ namespace detail
 			biggestIndex = 3;
 		}
 
-		T biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5);
+		T biggestVal = sqrt(fourBiggestSquaredMinus1 + static_cast<T>(1)) * static_cast<T>(0.5);
 		T mult = static_cast<T>(0.25) / biggestVal;
 
-		tquat<T, P> Result(uninitialize);
 		switch(biggestIndex)
 		{
 		case 0:
-			Result.w = biggestVal;
-			Result.x = (m[1][2] - m[2][1]) * mult;
-			Result.y = (m[2][0] - m[0][2]) * mult;
-			Result.z = (m[0][1] - m[1][0]) * mult;
-			break;
+			return tquat<T, Q>(biggestVal, (m[1][2] - m[2][1]) * mult, (m[2][0] - m[0][2]) * mult, (m[0][1] - m[1][0]) * mult);
 		case 1:
-			Result.w = (m[1][2] - m[2][1]) * mult;
-			Result.x = biggestVal;
-			Result.y = (m[0][1] + m[1][0]) * mult;
-			Result.z = (m[2][0] + m[0][2]) * mult;
-			break;
+			return tquat<T, Q>((m[1][2] - m[2][1]) * mult, biggestVal, (m[0][1] + m[1][0]) * mult, (m[2][0] + m[0][2]) * mult);
 		case 2:
-			Result.w = (m[2][0] - m[0][2]) * mult;
-			Result.x = (m[0][1] + m[1][0]) * mult;
-			Result.y = biggestVal;
-			Result.z = (m[1][2] + m[2][1]) * mult;
-			break;
+			return tquat<T, Q>((m[2][0] - m[0][2]) * mult, (m[0][1] + m[1][0]) * mult, biggestVal, (m[1][2] + m[2][1]) * mult);
 		case 3:
-			Result.w = (m[0][1] - m[1][0]) * mult;
-			Result.x = (m[2][0] + m[0][2]) * mult;
-			Result.y = (m[1][2] + m[2][1]) * mult;
-			Result.z = biggestVal;
-			break;
-			
-		default:					// Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity.
+			return tquat<T, Q>((m[0][1] - m[1][0]) * mult, (m[2][0] + m[0][2]) * mult, (m[1][2] + m[2][1]) * mult, biggestVal);
+		default: // Silence a -Wswitch-default warning in GCC. Should never actually get here. Assert is just for sanity.
 			assert(false);
-			break;
+			return tquat<T, Q>(1, 0, 0, 0);
 		}
-		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(tmat4x4<T, P> const & m4)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> quat_cast(mat<4, 4, T, Q> const& m4)
 	{
-		return quat_cast(tmat3x3<T, P>(m4));
+		return quat_cast(mat<3, 3, T, Q>(m4));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER T angle(tquat<T, P> const & x)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER T angle(tquat<T, Q> const& x)
 	{
-		return acos(x.w) * T(2);
+		return acos(x.w) * static_cast<T>(2);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec3<T, P> axis(tquat<T, P> const & x)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<3, T, Q> axis(tquat<T, Q> const& x)
 	{
 		T tmp1 = static_cast<T>(1) - x.w * x.w;
 		if(tmp1 <= static_cast<T>(0))
-			return tvec3<T, P>(0, 0, 1);
+			return vec<3, T, Q>(0, 0, 1);
 		T tmp2 = static_cast<T>(1) / sqrt(tmp1);
-		return tvec3<T, P>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
+		return vec<3, T, Q>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tquat<T, P> angleAxis(T const & angle, tvec3<T, P> const & v)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER tquat<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& v)
 	{
-		tquat<T, P> Result(uninitialize);
+		tquat<T, Q> Result;
 
 		T const a(angle);
 		T const s = glm::sin(a * static_cast<T>(0.5));
@@ -718,74 +731,74 @@ namespace detail
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> lessThan(tquat<T, P> const & x, tquat<T, P> const & y)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThan(tquat<T, Q> const& x, tquat<T, Q> const& y)
 	{
-		tvec4<bool, P> Result(uninitialize);
+		vec<4, bool, Q> Result;
 		for(length_t i = 0; i < x.length(); ++i)
 			Result[i] = x[i] < y[i];
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> lessThanEqual(tquat<T, P> const & x, tquat<T, P> const & y)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThanEqual(tquat<T, Q> const& x, tquat<T, Q> const& y)
 	{
-		tvec4<bool, P> Result(uninitialize);
+		vec<4, bool, Q> Result;
 		for(length_t i = 0; i < x.length(); ++i)
 			Result[i] = x[i] <= y[i];
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThan(tquat<T, P> const & x, tquat<T, P> const & y)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThan(tquat<T, Q> const& x, tquat<T, Q> const& y)
 	{
-		tvec4<bool, P> Result(uninitialize);
+		vec<4, bool, Q> Result;
 		for(length_t i = 0; i < x.length(); ++i)
 			Result[i] = x[i] > y[i];
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> greaterThanEqual(tquat<T, P> const & x, tquat<T, P> const & y)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThanEqual(tquat<T, Q> const& x, tquat<T, Q> const& y)
 	{
-		tvec4<bool, P> Result(uninitialize);
+		vec<4, bool, Q> Result;
 		for(length_t i = 0; i < x.length(); ++i)
 			Result[i] = x[i] >= y[i];
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> equal(tquat<T, P> const & x, tquat<T, P> const & y)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> equal(tquat<T, Q> const& x, tquat<T, Q> const& y)
 	{
-		tvec4<bool, P> Result(uninitialize);
+		vec<4, bool, Q> Result;
 		for(length_t i = 0; i < x.length(); ++i)
-			Result[i] = x[i] == y[i];
+			Result[i] = detail::compute_equal<T>::call(x[i], y[i]);
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> notEqual(tquat<T, P> const & x, tquat<T, P> const & y)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> notEqual(tquat<T, Q> const& x, tquat<T, Q> const& y)
 	{
-		tvec4<bool, P> Result(uninitialize);
+		vec<4, bool, Q> Result;
 		for(length_t i = 0; i < x.length(); ++i)
-			Result[i] = x[i] != y[i];
+			Result[i] = !detail::compute_equal<T>::call(x[i], y[i]);
 		return Result;
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> isnan(tquat<T, P> const& q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(tquat<T, Q> const& q)
 	{
 		GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs");
 
-		return tvec4<bool, P>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
+		return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
 	}
 
-	template <typename T, precision P>
-	GLM_FUNC_QUALIFIER tvec4<bool, P> isinf(tquat<T, P> const& q)
+	template<typename T, qualifier Q>
+	GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(tquat<T, Q> const& q)
 	{
 		GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");
 
-		return tvec4<bool, P>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
+		return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
 	}
 }//namespace glm