///////////////////////////////////////////////////////////////////////////////////
/// OpenGL Mathematics (glm.g-truc.net)
///
/// Copyright (c) 2005 - 2015 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.
/// 
/// Restrictions:
///             By making use of the Software for military purposes, you choose to make
///             a Bunny unhappy.
/// 
/// 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>
        struct compute_dot<tquat, T, P>
        {
                static GLM_FUNC_QUALIFIER 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);
                }
        };
}//namespace detail

        //////////////////////////////////////
        // Component accesses

#       ifdef GLM_FORCE_SIZE_FUNC
                template <typename T, precision P>
                GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::size_type tquat<T, P>::size() const
                {
                        return 4;
                }

                template <typename T, precision P>
                GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::size_type i)
                {
                        assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
                        return (&x)[i];
                }

                template <typename T, precision P>
                GLM_FUNC_QUALIFIER T const & tquat<T, P>::operator[](typename tquat<T, P>::size_type i) const
                {
                        assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
                        return (&x)[i];
                }
#       else
                template <typename T, precision P>
                GLM_FUNC_QUALIFIER GLM_CONSTEXPR typename tquat<T, P>::length_type tquat<T, P>::length() const
                {
                        return 4;
                }

                template <typename T, precision P>
                GLM_FUNC_QUALIFIER T & tquat<T, P>::operator[](typename tquat<T, P>::length_type i)
                {
                        assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
                        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
                {
                        assert(i >= 0 && static_cast<detail::component_count_t>(i) < detail::component_count(*this));
                        return (&x)[i];
                }
#       endif//GLM_FORCE_SIZE_FUNC

        //////////////////////////////////////
        // Implicit basic constructors

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

        template <typename T, precision P>
        template <precision Q>
        GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<T, Q> 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 tquat<T, P>::tquat(ctor)
        {}

        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)
        {}

        //////////////////////////////////////////////////////////////
        // Conversions

        template <typename T, precision P>
        template <typename U, precision Q>
        GLM_FUNC_QUALIFIER tquat<T, P>::tquat(tquat<U, Q> 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 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(tvec3<T, P> const & u, tvec3<T, P> const & v)
        {
                tvec3<T, P> const LocalW(cross(u, v));
                T Dot = detail::compute_dot<tvec3, T, P>::call(u, v);
                tquat<T, P> q(T(1) + Dot, LocalW.x, LocalW.y, LocalW.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);
        }

#       if GLM_HAS_EXPLICIT_CONVERSION_OPERATORS
        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat3x3<T, P>()
        {
                return mat3_cast(*this);
        }
        
        template <typename T, precision P>      
        GLM_FUNC_QUALIFIER tquat<T, P>::operator tmat4x4<T, P>()
        {
                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)
        {
                return tquat<T, P>(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)
        {
                return conjugate(q) / dot(q, q);
        }

        //////////////////////////////////////////////////////////////
        // 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 operators

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

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

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

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

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

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tquat<T, P> operator/(tquat<T, P> const & q, T const & s)
        {
                return 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==(tquat<T, P> const & q1, 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!=(tquat<T, P> const & q1, 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 T length(tquat<T, P> 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)
        {
                T len = length(q);
                if(len <= T(0)) // Problem
                        return tquat<T, P>(1, 0, 0, 0);
                T oneOverLen = T(1) / len;
                return tquat<T, P>(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)
        {
                return 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 tquat<T, P> mix(tquat<T, P> const & x, 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);
                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 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 tquat<T, P> mix2
        (
                tquat<T, P> const & x, 
                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 tquat<T, P> mix(tquat<T, P> const & x, tquat<T, P> const & y, T 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 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 tquat<T, P> lerp(tquat<T, P> const & x, tquat<T, P> const & y, T 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 tquat<T, P> slerp(tquat<T, P> const & x,     tquat<T, P> const & y, T a)
        {
                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 tquat<T, P>(
                                mix(x.w, z.w, a),
                                mix(x.x, z.x, a),
                                mix(x.y, z.y, a),
                                mix(x.z, z.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 tquat<T, P> rotate(tquat<T, P> const & q, T const & angle, tvec3<T, P> const & v)
        {
                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;
                }

                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));
        }

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

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER T roll(tquat<T, P> 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));
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER T pitch(tquat<T, P> 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));
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER T yaw(tquat<T, P> const & q)
        {
                return asin(T(-2) * (q.x * q.z - q.w * q.y));
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tmat3x3<T, P> mat3_cast(tquat<T, P> const & q)
        {
                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 tmat4x4<T, P> mat4_cast(tquat<T, P> const & q)
        {
                return tmat4x4<T, P>(mat3_cast(q));
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tquat<T, P> quat_cast(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;

                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;
                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 tquat<T, P> quat_cast(tmat4x4<T, P> const & m4)
        {
                return quat_cast(tmat3x3<T, P>(m4));
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER T angle(tquat<T, P> const & x)
        {
                return acos(x.w) * T(2);
        }

        template <typename T, precision P>
        GLM_FUNC_QUALIFIER tvec3<T, P> axis(tquat<T, P> 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);
                T tmp2 = static_cast<T>(1) / sqrt(tmp1);
                return tvec3<T, P>(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)
        {
                tquat<T, P> Result(uninitialize);

                T const a(angle);
                T const s = glm::sin(a * static_cast<T>(0.5));

                Result.w = glm::cos(a * static_cast<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 tvec4<bool, P> lessThan(tquat<T, P> const & x, tquat<T, P> const & y)
        {
                tvec4<bool, P> Result(uninitialize);
                for(detail::component_count_t i = 0; i < detail::component_count(x); ++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)
        {
                tvec4<bool, P> Result(uninitialize);
                for(detail::component_count_t i = 0; i < detail::component_count(x); ++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)
        {
                tvec4<bool, P> Result(uninitialize);
                for(detail::component_count_t i = 0; i < detail::component_count(x); ++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)
        {
                tvec4<bool, P> Result(uninitialize);
                for(detail::component_count_t i = 0; i < detail::component_count(x); ++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)
        {
                tvec4<bool, P> Result(uninitialize);
                for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
                        Result[i] = 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)
        {
                tvec4<bool, P> Result(uninitialize);
                for(detail::component_count_t i = 0; i < detail::component_count(x); ++i)
                        Result[i] = x[i] != y[i];
                return Result;
        }
}//namespace glm