/// @ref gtc_quaternion

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

namespace glm
{
	// -- Operations --
/*
	// (x * sin(1 - a) * angle / sin(angle)) + (y * sin(a) * angle / sin(angle))
	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> const& y, T const& a)
	{
		if(a <= T(0)) return x;
		if(a >= T(1)) return y;

		float fCos = dot(x, y);
		qua<T, Q> y2(y); //BUG!!! qua<T, Q> 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 qua<T, Q>(
			k0 * x.w + k1 * y2.w,
			k0 * x.x + k1 * y2.x,
			k0 * x.y + k1 * y2.y,
			k0 * x.z + k1 * y2.z);
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> mix2
	(
		qua<T, Q> const& x,
		qua<T, Q> 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, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> mix(qua<T, Q> const& x, qua<T, Q> 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 qua<T, Q>(
				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, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> lerp(qua<T, Q> const& x, qua<T, Q> 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, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> slerp(qua<T, Q> const& x,	qua<T, Q> const& y, T a)
	{
		qua<T, Q> 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 qua<T, Q>(
				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, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> rotate(qua<T, Q> const& q, T const& angle, vec<3, T, Q> const& v)
	{
		vec<3, T, Q> 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 * qua<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * Sin, Tmp.y * Sin, Tmp.z * Sin);
		//return gtc::quaternion::cross(q, qua<T, Q>(cos(AngleRad * T(0.5)), Tmp.x * fSin, Tmp.y * fSin, Tmp.z * fSin));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER vec<3, T, Q> eulerAngles(qua<T, Q> const& x)
	{
		return vec<3, T, Q>(pitch(x), yaw(x), roll(x));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER T roll(qua<T, Q> const& q)
	{
		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, qualifier Q>
	GLM_FUNC_QUALIFIER T pitch(qua<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));
		T const y = static_cast<T>(2) * (q.y * q.z + q.w * q.x);
		T const x = q.w * q.w - q.x * q.x - q.y * q.y + q.z * q.z;

		if(all(equal(vec<2, T, Q>(x, y), vec<2, T, Q>(0), epsilon<T>()))) //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, qualifier Q>
	GLM_FUNC_QUALIFIER T yaw(qua<T, Q> const& q)
	{
		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, qualifier Q>
	GLM_FUNC_QUALIFIER mat<3, 3, T, Q> mat3_cast(qua<T, Q> const& q)
	{
		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);
		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] = T(1) - T(2) * (qyy +  qzz);
		Result[0][1] = T(2) * (qxy + qwz);
		Result[0][2] = T(2) * (qxz - qwy);

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

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

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER mat<4, 4, T, Q> mat4_cast(qua<T, Q> const& q)
	{
		return mat<4, 4, T, Q>(mat3_cast(q));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER qua<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];
		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 + static_cast<T>(1)) * static_cast<T>(0.5);
		T mult = static_cast<T>(0.25) / biggestVal;

		switch(biggestIndex)
		{
		case 0:
			return qua<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:
			return qua<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:
			return qua<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:
			return qua<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);
			return qua<T, Q>(1, 0, 0, 0);
		}
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> quat_cast(mat<4, 4, T, Q> const& m4)
	{
		return quat_cast(mat<3, 3, T, Q>(m4));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER T angle(qua<T, Q> const& x)
	{
		return acos(x.w) * static_cast<T>(2);
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER vec<3, T, Q> axis(qua<T, Q> const& x)
	{
		T tmp1 = static_cast<T>(1) - x.w * x.w;
		if(tmp1 <= static_cast<T>(0))
			return vec<3, T, Q>(0, 0, 1);
		T tmp2 = static_cast<T>(1) / sqrt(tmp1);
		return vec<3, T, Q>(x.x * tmp2, x.y * tmp2, x.z * tmp2);
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER qua<T, Q> angleAxis(T const& angle, vec<3, T, Q> const& v)
	{
		qua<T, Q> Result;

		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, qualifier Q>
	GLM_FUNC_QUALIFIER vec<4, bool, Q> isnan(qua<T, Q> const& q)
	{
		GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isnan' only accept floating-point inputs");

		return vec<4, bool, Q>(isnan(q.x), isnan(q.y), isnan(q.z), isnan(q.w));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER vec<4, bool, Q> isinf(qua<T, Q> const& q)
	{
		GLM_STATIC_ASSERT(std::numeric_limits<T>::is_iec559, "'isinf' only accept floating-point inputs");

		return vec<4, bool, Q>(isinf(q.x), isinf(q.y), isinf(q.z), isinf(q.w));
	}

	template<typename T, qualifier Q>
	GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThan(qua<T, Q> const& x, qua<T, Q> const& y)
	{
		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, qualifier Q>
	GLM_FUNC_QUALIFIER vec<4, bool, Q> lessThanEqual(qua<T, Q> const& x, qua<T, Q> const& y)
	{
		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, qualifier Q>
	GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThan(qua<T, Q> const& x, qua<T, Q> const& y)
	{
		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, qualifier Q>
	GLM_FUNC_QUALIFIER vec<4, bool, Q> greaterThanEqual(qua<T, Q> const& x, qua<T, Q> const& y)
	{
		vec<4, bool, Q> Result;
		for(length_t i = 0; i < x.length(); ++i)
			Result[i] = x[i] >= y[i];
		return Result;
	}
}//namespace glm

#if GLM_CONFIG_SIMD == GLM_ENABLE
#	include "quaternion_simd.inl"
#endif