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#ifndef __CGLA_ARITHVEC_H__

#define __CGLA_ARITHVEC_H__

#include <iostream>

#include "CGLA.h"

namespace CGLA {

	/** The ArithVec class template represents a generic arithmetic

			vector.  The three parameters to the template are

			T - the scalar type (i.e. float, int, double etc.)

			V - the name of the vector type. This template is always (and

			only) used as ancestor of concrete types, and the name of the

			class _inheriting_ _from_ this class is used as the V argument.

			N - The final argument is the dimension N. For instance, N=3 for a

			3D vector.

			This class template contains all functions that are assumed to be

			the same for any arithmetic vector - regardless of dimension or

			the type of scalars used for coordinates.

			The template contains no virtual functions which is important

			since they add overhead.

	*/

	template <class T, class V, int N> 

	class ArithVec

	{

#define for_all_i(expr) for(int i=0;i<N;i++) {expr;}

	protected:

		/// The actual contents of the vector.

		T data[N];

	protected:

		//----------------------------------------------------------------------

		// Constructors

		//----------------------------------------------------------------------

		/// Construct 0 vector

		ArithVec() 

		{

			for_all_i(data[i]=0);

		}

		/// Construct a vector where all coordinates are identical

		explicit ArithVec(T _a)

		{

			for_all_i(data[i] = _a);

		}

		/// Construct a 2D vector 

		ArithVec(T _a, T _b)

		{

			assert(N==2);

			data[0] = _a;

			data[1] = _b;

		}

		/// Construct a 3D vector

		ArithVec(T _a, T _b, T _c)

		{

			assert(N==3);

			data[0] = _a;

			data[1] = _b;

			data[2] = _c;

		}

		/// Construct a 4D vector

		ArithVec(T _a, T _b, T _c, T _d)

		{

			assert(N==4);

			data[0] = _a;

			data[1] = _b;

			data[2] = _c;

			data[3] = _d;

		}

	public:

		/// For convenience we define a more meaningful name for the scalar type

		typedef T ScalarType;

		/// A more meaningful name for vector type

		typedef V VectorType;

		/// Return dimension of vector

		static int get_dim() {return N;}

		/// Set all coordinates of a 2D vector.

		void set(T _a, T _b)

		{

			assert(N==2);

			data[0] = _a;

			data[1] = _b;

		}

		/// Set all coordinates of a 3D vector.

		void set(T _a, T _b, T _c)

		{

			assert(N==3);

			data[0] = _a;

			data[1] = _b;

			data[2] = _c;

		}

		/// Set all coordinates of a 4D vector.

		void set(T _a, T _b, T _c, T _d)

		{

			assert(N==4);

			data[0] = _a;

			data[1] = _b;

			data[2] = _c;

			data[3] = _d;

		}

		/// Const index operator

		const T& operator [] ( int i ) const

		{

			assert(i<N);

			return data[i];

		}

		/// Non-const index operator

		T& operator [] ( int i ) 

		{

			assert(i<N);

			return data[i];

		}

		/** Get a pointer to first element in data array.

				This function may be useful when interfacing with some other API 

				such as OpenGL (TM) */

		T* get() {return &data[0];}

		/** Get a const pointer to first element in data array.

				This function may be useful when interfacing with some other API 

				such as OpenGL (TM). */

		const T* get() const {return &data[0];}

		//----------------------------------------------------------------------

		// Comparison operators

		//----------------------------------------------------------------------

		/// Equality operator

		bool operator==(const V& v) const 

		{

			for_all_i(if (data[i] != v[i]) return false)

				return true;

		}

		/// Equality wrt scalar. True if all coords are equal to scalar

		bool operator==(T k) const 

		{ 

			for_all_i(if (data[i] != k) return false)

				return true;

		}

		/// Inequality operator

		bool operator!=(const V& v) const 

		{

			return !(*this==v);

		}

		/// Inequality wrt scalar. True if any coord not equal to scalar

		bool operator!=(T k) const 

		{ 

			return !(*this==k);

		}

		//----------------------------------------------------------------------

		// Comparison functions ... of geometric significance 

		//----------------------------------------------------------------------

		/** Compare all coordinates against other vector. ( < )

				Similar to testing whether we are on one side of three planes. */

		bool  all_l  (const V& v) const

		{

			for_all_i(if (data[i] >= v[i]) return false)

				return true;

		}

		/** Compare all coordinates against other vector. ( <= )

				Similar to testing whether we are on one side of three planes. */

		bool  all_le (const V& v) const

		{

			for_all_i(if (data[i] > v[i]) return false)

				return true;

		}

		/** Compare all coordinates against other vector. ( > )

				Similar to testing whether we are on one side of three planes. */

		bool  all_g  (const V& v) const

		{

			for_all_i(if (data[i] <= v[i]) return false)

				return true;

		}

		/** Compare all coordinates against other vector. ( >= )

				Similar to testing whether we are on one side of three planes. */

		bool  all_ge (const V& v) const

		{

			for_all_i(if (data[i] < v[i]) return false);

			return true;

		}

		//----------------------------------------------------------------------

		// Assignment operators

		//----------------------------------------------------------------------

		/// Assigment multiplication with scalar.

		const V& operator *=(T k) 

			{ 

				for_all_i(data[i] *= k); 

				return static_cast<const V&>(*this);

			}

		/// Assignment division with scalar.

		const V& operator /=(T k)

			{ 

				for_all_i(data[i] /= k); 

				return static_cast<const V&>(*this);

			}

		/// Assignment addition with scalar. Adds scalar to each coordinate.

		const V& operator +=(T k) 

			{

				for_all_i(data[i] += k); 

				return  static_cast<const V&>(*this);

			}

		/// Assignment subtraction with scalar. Subtracts scalar from each coord.

		const V& operator -=(T k) 

			{ 

				for_all_i(data[i] -= k); 

				return  static_cast<const V&>(*this);

			}

		/** Assignment multiplication with vector. 

				Multiply each coord independently. */

		const V& operator *=(const V& v) 

			{ 

				for_all_i(data[i] *= v[i]); 

				return  static_cast<const V&>(*this);

			}

		/// Assigment division with vector. Each coord divided independently.

		const V& operator /=(const V& v)

			{

				for_all_i(data[i] /= v[i]); 

				return  static_cast<const V&>(*this);

			}

		/// Assignmment addition with vector.

		const V& operator +=(const V& v) 

			{

				for_all_i(data[i] += v[i]); 

				return  static_cast<const V&>(*this);

			}

		/// Assignment subtraction with vector.

			const V& operator -=(const V& v) 

				{ 

					for_all_i(data[i] -= v[i]); 

					return  static_cast<const V&>(*this);

				}

		//----------------------------------------------------------------------

		// Unary operators on vectors

		//----------------------------------------------------------------------

		/// Negate vector.

		const V operator - () const

		{

			V v_new;

			for_all_i(v_new[i] = - data[i]);

			return v_new;

		}

		//----------------------------------------------------------------------

		// Binary operators on vectors

		//----------------------------------------------------------------------

		/** Multiply vector with vector. Each coord multiplied independently

				Do not confuse this operation with dot product. */

		const V operator * (const V& v1) const

		{

			V v_new;

			for_all_i(v_new[i] = data[i] * v1[i]);

			return v_new;

		}

		/// Add two vectors

		const V operator + (const V& v1) const

		{

			V v_new;

			for_all_i(v_new[i] = data[i] + v1[i]);

			return v_new;

		}

		/// Subtract two vectors. 

		const V operator - (const V& v1) const

		{

			V v_new;

			for_all_i(v_new[i] = data[i] - v1[i]);

			return v_new;

		}

		/// Divide two vectors. Each coord separately

		const V operator / (const V& v1) const

		{

			V v_new;

			for_all_i(v_new[i] = data[i] / v1[i]);

			return v_new;

		}

		//----------------------------------------------------------------------

		// Binary operators on vector and scalar

		//----------------------------------------------------------------------

		/// Multiply scalar onto vector.

		const V operator * (T k) const

		{

			V v_new;

			for_all_i(v_new[i] = data[i] * k);

			return v_new;

		}

		/// Divide vector by scalar.

		const V operator / (T k) const

		{

			V v_new;

			for_all_i(v_new[i] = data[i] / k);

			return v_new;      

		}

		/// Return the smallest coordinate of the vector

		const T min_coord() const 

		{

			T t = data[0];

			for_all_i(t = s_min(t, data[i]));

			return t;

		}

		/// Return the largest coordinate of the vector

		const T max_coord() const

		{

			T t = data[0];

			for_all_i(t = s_max(t, data[i]));

			return t;

		}

#undef for_all_i  

	};

	template <class T, class V, int N> 

	inline std::ostream& operator<<(std::ostream&os, const ArithVec<T,V,N>& v)

	{

		os << "[ ";

		for(int i=0;i<N;i++) os << v[i] << " ";

		os << "]";

		return os;

	}

	/// Get from operator for ArithVec descendants. 

	template <class T,class V, int N>

	inline std::istream& operator>>(std::istream&is, ArithVec<T,V,N>& v)

	{

		for(int i=0;i<N;i++) is>>v[i];

		return is;

	}

	/** Dot product for two vectors. The `*' operator is 

			reserved for coordinatewise	multiplication of vectors. */

	template <class T,class V, int N>

	inline T dot(const ArithVec<T,V,N>& v0, const ArithVec<T,V,N>& v1)

	{

		T x = 0;

		for(int i=0;i<N;i++) x += v0[i]*v1[i];

		return x;

	}

	/** Compute the sqr length by taking dot product of vector with itself. */

	template <class T,class V, int N>

	inline T sqr_length(const ArithVec<T,V,N>& v)

	{

		return dot(v,v);

	}

	/** Multiply double onto vector. This operator handles the case 

			where the vector is on the righ side of the `*'.

			\note It seems to be optimal to put the binary operators inside the

			ArithVec class template, but the operator functions whose 

			left operand is _not_ a vector cannot be inside, hence they

			are here.

			We need three operators for scalar * vector although they are

			identical, because, if we use a separate template argument for

			the left operand, it will match any type. If we use just T as 

			type for the left operand hoping that other built-in types will

			be automatically converted, we will be disappointed. It seems that 

			a float * ArithVec<float,Vec3f,3> function is not found if the

			left operand is really a double.

	*/

	template<class T, class V, int N>

	inline const V operator * (double k, const ArithVec<T,V,N>& v) 

	{

		return v * k;

	}

	/** Multiply float onto vector. See the note in the documentation

			regarding multiplication of a double onto a vector. */

	template<class T, class V, int N>

	inline const V operator * (float k, const ArithVec<T,V,N>& v) 

	{

		return v * k;

	}

	/** Multiply int onto vector. See the note in the documentation

			regarding multiplication of a double onto a vector. */

	template<class T, class V, int N>

	inline const V operator * (int k, const ArithVec<T,V,N>& v) 

	{

		return v * k;

	}

	/** Returns the vector containing for each coordinate the smallest

			value from two vectors. */

	template <class T,class V, int N>

	inline V v_min(const ArithVec<T,V,N>& v0, const ArithVec<T,V,N>& v1)

	{

		V v;

		for(int i=0;i<N;i++)

		v[i] = s_min(v0[i],v1[i]);

		return v;

	}

	/** Returns the vector containing for each coordinate the largest 

			value from two vectors. */

	template <class T,class V, int N>

	inline V v_max(const ArithVec<T,V,N>& v0, const ArithVec<T,V,N>& v1)

	{

		V v;

		for(int i=0;i<N;i++) 

		v[i] = s_max(v0[i],v1[i]);

		return v;

	}

}

#endif