sources/third_party/vulkan/src/libs/glm/gtc/quaternion.inl

///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2014 G-Truc Creation (www.g-truc.net)
/// Permission is hereby granted, free of charge, to any person obtaining a copy
/// of this software and associated documentation files (the "Software"), to deal
/// in the Software without restriction, including without limitation the rights
/// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
/// copies of the Software, and to permit persons to whom the Software is
/// furnished to do so, subject to the following conditions:
/// 
/// The above copyright notice and this permission notice shall be included in
/// all copies or substantial portions of the Software.
/// 
/// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
/// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
/// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
/// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
/// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
/// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
/// THE SOFTWARE.
///
/// @ref gtc_quaternion
/// @file glm/gtc/quaternion.inl
/// @date 2009-05-21 / 2011-06-15
/// @author Christophe Riccio
///////////////////////////////////////////////////////////////////////////////////

#include "../trigonometric.hpp"
#include "../geometric.hpp"
#include "../exponential.hpp"
#include <limits>

namespace glm{
namespace detail
{
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER GLM_CONSTEXPR length_t tquat<T, P>::length() const
	{
		return 4;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P>::tquat() :
		x(0),
		y(0),
		z(0),
		w(1)
	{}

	template <typename T, precision P>
	template <typename U, precision Q>
	GLM_FUNC_QUALIFIER tquat<T, P>::tquat
	(
		tquat<U, Q> const & q
	) :
		x(q.x),
		y(q.y),
		z(q.z),
		w(q.w)
	{}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P>::tquat
	(
		T const & s,
		tvec3<T, P> const & v
	) :
		x(v.x),
		y(v.y),
		z(v.z),
		w(s)
	{}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P>::tquat
	(
		T const & w,
		T const & x,
		T const & y,
		T const & z
	) :
		x(x),
		y(y),
		z(z),
		w(w)
	{}

	//////////////////////////////////////////////////////////////
	// tquat conversions

	//template <typename valType> 
	//GLM_FUNC_QUALIFIER tquat<valType>::tquat
	//(
	//	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));
	//	
	//	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
	(
		detail::tvec3<T, P> const & u,
		detail::tvec3<T, P> const & v
	)
	{
		detail::tvec3<T, P> w = cross(u, v);
		T Dot = detail::compute_dot<detail::tvec3, T, P>::call(u, v);
		detail::tquat<T, P> q(T(1) + Dot, w.x, w.y, w.z);

		*this = normalize(q);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P>::tquat
	(
		tvec3<T, P> const & eulerAngle
	)
	{
		tvec3<T, P> c = glm::cos(eulerAngle * T(0.5));
		tvec3<T, P> 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
	)
	{
		*this = quat_cast(m);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P>::tquat
	(
		tmat4x4<T, P> const & m
	)
	{
		*this = quat_cast(m);
	}

	//////////////////////////////////////////////////////////////
	// tquat<T, P> accesses

	template <typename T, precision P> 
	GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[] (length_t i)
	{
		assert(i >= 0 && i < this->length());
		return (&x)[i];
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[] (length_t i) const
	{
		assert(i >= 0 && i < this->length());
		return (&x)[i];
	}
}//namespace detail

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> conjugate
	(
		detail::tquat<T, P> const & q
	)
	{
		return detail::tquat<T, P>(q.w, -q.x, -q.y, -q.z);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> inverse
	(
		detail::tquat<T, P> const & q
	)
	{
		return conjugate(q) / dot(q, q);
	}

namespace detail
{
	//////////////////////////////////////////////////////////////
	// tquat<valType> operators

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator +=
	(
		tquat<T, P> const & q
	)
	{
		this->w += q.w;
		this->x += q.x;
		this->y += q.y;
		this->z += q.z;
		return *this;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator *=
	(
		tquat<T, P> const & q
	)
	{
		tquat<T, P> const p(*this);

		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, precision P> 
	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator *=
	(
		T const & s
	)
	{
		this->w *= s;
		this->x *= s;
		this->y *= s;
		this->z *= s;
		return *this;
	}

	template <typename T, precision P> 
	GLM_FUNC_QUALIFIER tquat<T, P> & tquat<T, P>::operator /=
	(
		T const & s
	)
	{
		this->w /= s;
		this->x /= s;
		this->y /= s;
		this->z /= s;
		return *this;
	}

	//////////////////////////////////////////////////////////////
	// tquat<T, P> external functions

	template <typename T, precision P>
	struct compute_dot<tquat, T, P>
	{
		static T call(tquat<T, P> const & x, tquat<T, P> const & y)
		{
			tvec4<T, P> tmp(x.x * y.x, x.y * y.y, x.z * y.z, x.w * y.w);
			return (tmp.x + tmp.y) + (tmp.z + tmp.w);
		}
	};

	//////////////////////////////////////////////////////////////
	// tquat<T, P> external operators

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> operator-
	(
		detail::tquat<T, P> const & q
	)
	{
		return detail::tquat<T, P>(-q.w, -q.x, -q.y, -q.z);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> operator+
	(
		detail::tquat<T, P> const & q,
		detail::tquat<T, P> const & p
	)
	{
		return detail::tquat<T, P>(q) += p;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> operator*
	(
		detail::tquat<T, P> const & q,
		detail::tquat<T, P> const & p
	)
	{
		return detail::tquat<T, P>(q) *= p;
	}

	// Transformation
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator*
	(
		detail::tquat<T, P> const & q,
		detail::tvec3<T, P> const & v
	)
	{
		T Two(2);

		detail::tvec3<T, P> uv, uuv;
		detail::tvec3<T, P> QuatVector(q.x, q.y, q.z);
		uv = glm::cross(QuatVector, v);
		uuv = glm::cross(QuatVector, uv);
		uv *= (Two * q.w);
		uuv *= Two;

		return v + uv + uuv;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tvec3<T, P> operator*
	(
		detail::tvec3<T, P> const & v,
		detail::tquat<T, P> const & q
	)
	{
		return glm::inverse(q) * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator*
	(
		detail::tquat<T, P> const & q,
		detail::tvec4<T, P> const & v
	)
	{
		return detail::tvec4<T, P>(q * detail::tvec3<T, P>(v), v.w);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tvec4<T, P> operator*
	(
		detail::tvec4<T, P> const & v,
		detail::tquat<T, P> const & q
	)
	{
		return glm::inverse(q) * v;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> operator*
	(
		detail::tquat<T, P> const & q,
		T const & s
	)
	{
		return detail::tquat<T, P>(
			q.w * s, q.x * s, q.y * s, q.z * s);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> operator*
	(
		T const & s,
		detail::tquat<T, P> const & q
	)
	{
		return q * s;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> operator/
	(
		detail::tquat<T, P> const & q,
		T const & s
	)
	{
		return detail::tquat<T, P>(
			q.w / s, q.x / s, q.y / s, q.z / s);
	}

	//////////////////////////////////////
	// Boolean operators

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER bool operator==
	(
		detail::tquat<T, P> const & q1,
		detail::tquat<T, P> const & q2
	)
	{
		return (q1.x == q2.x) && (q1.y == q2.y) && (q1.z == q2.z) && (q1.w == q2.w);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER bool operator!=
	(
		detail::tquat<T, P> const & q1,
		detail::tquat<T, P> const & q2
	)
	{
		return (q1.x != q2.x) || (q1.y != q2.y) || (q1.z != q2.z) || (q1.w != q2.w);
	}

}//namespace detail

	////////////////////////////////////////////////////////
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T length
	(
		detail::tquat<T, P> const & q
	)
	{
		return glm::sqrt(dot(q, q));
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> normalize
	(
		detail::tquat<T, P> const & q
	)
	{
		T len = length(q);
		if(len <= T(0)) // Problem
			return detail::tquat<T, P>(1, 0, 0, 0);
		T oneOverLen = T(1) / len;
		return detail::tquat<T, P>(q.w * oneOverLen, q.x * oneOverLen, q.y * oneOverLen, q.z * oneOverLen);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> cross
	(
		detail::tquat<T, P> const & q1,
		detail::tquat<T, P> const & q2
	)
	{
		return detail::tquat<T, P>(
			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,
			q1.w * q2.z + q1.z * q2.w + q1.x * q2.y - q1.y * q2.x);
	}
/*
	// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle))
	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> mix
	(
		detail::tquat<T, P> const & x, 
		detail::tquat<T, P> const & y, 
		T const & a
	)
	{
		if(a <= T(0)) return x;
		if(a >= T(1)) return y;

		float fCos = dot(x, y);
		detail::tquat<T, P> y2(y); //BUG!!! tquat<T, P> y2;
		if(fCos < T(0))
		{
			y2 = -y;
			fCos = -fCos;
		}

		//if(fCos > 1.0f) // problem
		float k0, k1;
		if(fCos > T(0.9999))
		{
			k0 = T(1) - a;
			k1 = 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((T(1) - a) * fAngle) * fOneOverSin;
			k1 = sin((T(0) + a) * fAngle) * fOneOverSin;
		}

		return detail::tquat<T, P>(
			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 detail::tquat<T, P> mix2
	(
		detail::tquat<T, P> const & x, 
		detail::tquat<T, P> const & y, 
		T const & a
	)
	{
		bool flip = false;
		if(a <= static_cast<T>(0)) return x;
		if(a >= static_cast<T>(1)) return y;

		T cos_t = dot(x, y);
		if(cos_t < T(0))
		{
			cos_t = -cos_t;
			flip = true;
		}

		T alpha(0), beta(0);

		if(T(1) - cos_t < 1e-7)
			beta = static_cast<T>(1) - alpha;
		else
		{
			T theta = acos(cos_t);
			T sin_t = sin(theta);
			beta = sin(theta * (T(1) - alpha)) / sin_t;
			alpha = sin(alpha * theta) / sin_t;
		}

		if(flip)
			alpha = -alpha;
		
		return normalize(beta * x + alpha * y);
	}
*/

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> mix
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y,
		T const & a
	)
	{
		T cosTheta = dot(x, y);

		// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
		if(cosTheta > T(1) - epsilon<T>())
		{
			// Linear interpolation
			return detail::tquat<T, P>(
				mix(x.w, y.w, a),
				mix(x.x, y.x, a),
				mix(x.y, y.y, a),
				mix(x.z, y.z, a));
		}
		else
		{
			// Essential Mathematics, page 467
			T angle = acos(cosTheta);
			return (sin((T(1) - a) * angle) * x + sin(a * angle) * y) / sin(angle);
		}
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> lerp
	(
		detail::tquat<T, P> const & x, 
		detail::tquat<T, P> const & y, 
		T const & a
	)
	{
		// Lerp is only defined in [0, 1]
		assert(a >= static_cast<T>(0));
		assert(a <= static_cast<T>(1));

		return x * (T(1) - a) + (y * a);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> slerp
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y,
		T const & a
	)
	{
		detail::tquat<T, P> z = y;

		T cosTheta = dot(x, y);

		// 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))
		{
			z        = -y;
			cosTheta = -cosTheta;
		}

		// Perform a linear interpolation when cosTheta is close to 1 to avoid side effect of sin(angle) becoming a zero denominator
		if(cosTheta > T(1) - epsilon<T>())
		{
			// Linear interpolation
			return detail::tquat<T, P>(
				mix(x.w, y.w, a),
				mix(x.x, y.x, a),
				mix(x.y, y.y, a),
				mix(x.z, y.z, a));
		}
		else
		{
			// Essential Mathematics, page 467
			T angle = acos(cosTheta);
			return (sin((T(1) - a) * angle) * x + sin(a * angle) * z) / sin(angle);
		}
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> rotate
	(
		detail::tquat<T, P> const & q,
		T const & angle,
		detail::tvec3<T, P> const & v
	)
	{
		detail::tvec3<T, P> Tmp = v;

		// Axis of rotation must be normalised
		T len = glm::length(Tmp);
		if(abs(len - T(1)) > T(0.001))
		{
			T oneOverLen = static_cast<T>(1) / len;
			Tmp.x *= oneOverLen;
			Tmp.y *= oneOverLen;
			Tmp.z *= oneOverLen;
		}

#ifdef GLM_FORCE_RADIANS
		T const AngleRad(angle);
#else
#		pragma message("GLM: rotate function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
		T const AngleRad = radians(angle);
#endif
		T const Sin = sin(AngleRad * T(0.5));

		return q * detail::tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
		//return gtc::quaternion::cross(q, detail::tquat<T, P>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tvec3<T, P> eulerAngles
	(
		detail::tquat<T, P> const & x
	)
	{
		return detail::tvec3<T, P>(pitch(x), yaw(x), roll(x));
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T roll
	(
		detail::tquat<T, P> const & q
	)
	{
#ifdef GLM_FORCE_RADIANS
		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));
#else
#		pragma message("GLM: roll function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
		return glm::degrees(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));
#endif
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T pitch
	(
		detail::tquat<T, P> const & q
	)
	{
#ifdef GLM_FORCE_RADIANS
		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));
#else
#		pragma message("GLM: pitch function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
		return glm::degrees(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));
#endif
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T yaw
	(
		detail::tquat<T, P> const & q
	)
	{
#ifdef GLM_FORCE_RADIANS
		return asin(T(-2) * (q.x * q.z - q.w * q.y));
#else
#		pragma message("GLM: yaw function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
		return glm::degrees(asin(T(-2) * (q.x * q.z - q.w * q.y)));
#endif
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tmat3x3<T, P> mat3_cast
	(
		detail::tquat<T, P> const & q
	)
	{
		detail::tmat3x3<T, P> Result(T(1));
		T qxx(q.x * q.x);
		T qyy(q.y * q.y);
		T qzz(q.z * q.z);
		T qxz(q.x * q.z);
		T qxy(q.x * q.y);
		T qyz(q.y * q.z);
		T qwx(q.w * q.x);
		T qwy(q.w * q.y);
		T qwz(q.w * q.z);

		Result[0][0] = 1 - 2 * (qyy +  qzz);
		Result[0][1] = 2 * (qxy + qwz);
		Result[0][2] = 2 * (qxz - qwy);

		Result[1][0] = 2 * (qxy - qwz);
		Result[1][1] = 1 - 2 * (qxx +  qzz);
		Result[1][2] = 2 * (qyz + qwx);

		Result[2][0] = 2 * (qxz + qwy);
		Result[2][1] = 2 * (qyz - qwx);
		Result[2][2] = 1 - 2 * (qxx +  qyy);
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tmat4x4<T, P> mat4_cast
	(
		detail::tquat<T, P> const & q
	)
	{
		return detail::tmat4x4<T, P>(mat3_cast(q));
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> quat_cast
	(
		detail::tmat3x3<T, P> const & m
	)
	{
		T fourXSquaredMinus1 = m[0][0] - m[1][1] - m[2][2];
		T fourYSquaredMinus1 = m[1][1] - m[0][0] - m[2][2];
		T fourZSquaredMinus1 = m[2][2] - m[0][0] - m[1][1];
		T fourWSquaredMinus1 = m[0][0] + m[1][1] + m[2][2];

		int biggestIndex = 0;
		T fourBiggestSquaredMinus1 = fourWSquaredMinus1;
		if(fourXSquaredMinus1 > fourBiggestSquaredMinus1)
		{
			fourBiggestSquaredMinus1 = fourXSquaredMinus1;
			biggestIndex = 1;
		}
		if(fourYSquaredMinus1 > fourBiggestSquaredMinus1)
		{
			fourBiggestSquaredMinus1 = fourYSquaredMinus1;
			biggestIndex = 2;
		}
		if(fourZSquaredMinus1 > fourBiggestSquaredMinus1)
		{
			fourBiggestSquaredMinus1 = fourZSquaredMinus1;
			biggestIndex = 3;
		}

		T biggestVal = sqrt(fourBiggestSquaredMinus1 + T(1)) * T(0.5);
		T mult = static_cast<T>(0.25) / biggestVal;

		detail::tquat<T, P> Result;
		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;
		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;
		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;
		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.
			assert(false);
			break;
		}
		return Result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> quat_cast
	(
		detail::tmat4x4<T, P> const & m4
	)
	{
		return quat_cast(detail::tmat3x3<T, P>(m4));
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER T angle
	(
		detail::tquat<T, P> const & x
	)
	{
#ifdef GLM_FORCE_RADIANS
		return acos(x.w) * T(2);
#else
#		pragma message("GLM: angle function returning degrees is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
		return glm::degrees(acos(x.w) * T(2));
#endif
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tvec3<T, P> axis
	(
		detail::tquat<T, P> const & x
	)
	{
		T tmp1 = static_cast<T>(1) - x.w * x.w;
		if(tmp1 <= static_cast<T>(0))
			return detail::tvec3<T, P>(0, 0, 1);
		T tmp2 = static_cast<T>(1) / sqrt(tmp1);
		return detail::tvec3<T, P>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tquat<T, P> angleAxis
	(
		T const & angle,
		detail::tvec3<T, P> const & v
	)
	{
		detail::tquat<T, P> result;

#ifdef GLM_FORCE_RADIANS
		T const a(angle);
#else
#		pragma message("GLM: angleAxis function taking degrees as a parameter is deprecated. #define GLM_FORCE_RADIANS before including GLM headers to remove this message.")
		T const a(glm::radians(angle));
#endif
		T s = glm::sin(a * T(0.5));

		result.w = glm::cos(a * T(0.5));
		result.x = v.x * s;
		result.y = v.y * s;
		result.z = v.z * s;
		return result;
	}

	template <typename T, precision P>
	GLM_FUNC_QUALIFIER detail::tvec4<bool, P> lessThan
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y
	)
	{
		detail::tvec4<bool, P> 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 detail::tvec4<bool, P> lessThanEqual
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y
	)
	{
		detail::tvec4<bool, P> 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 detail::tvec4<bool, P> greaterThan
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y
	)
	{
		detail::tvec4<bool, P> 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 detail::tvec4<bool, P> greaterThanEqual
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y
	)
	{
		detail::tvec4<bool, P> 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 detail::tvec4<bool, P> equal
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y
	)
	{
		detail::tvec4<bool, P> 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 detail::tvec4<bool, P>  notEqual
	(
		detail::tquat<T, P> const & x,
		detail::tquat<T, P> const & y
	)
	{
		detail::tvec4<bool, P> Result;
		for(length_t i = 0; i < x.length(); ++i)
			Result[i] = x[i] != y[i];
		return Result;
	}
}//namespace glm