/**
 * \defgroup Math Math library
 * @{
 */

class Math
{
	private void Math() {}
	private void ~Math() {}
	
	static const float EULER = 2.7182818284590452353;
	static const float PI = 3.14159265358979;
	static const float PI2 = 6.28318530717958;
	static const float PI_HALF = 1.570796326794;

	static const float RAD2DEG = 57.2957795130823208768;
	static const float DEG2RAD = 0.01745329251994329577;

	//! returns the number of bits set in a bitmask i
	proto static int GetNumberOfSetBits(int i);
	
	//! returns the the index of n-th bit set in a bit mask counting from the right, for instance, in a mask ..0110 1000 , the 0th set bit(right-most bit set to 1) is at 3th position(starting at 0), 1st bit is at 5th position, 2nd bit is at 6th position etc..
	proto static int GetNthBitSet(int value, int n);
	
	/**
	\brief Returns a random \p int number between and min [inclusive] and max [exclusive].
		\param min \p int Range starts [inclusive]
		\param max \p int Range ends [exclusive]
		\return \p int - Random number in range
		@code
			Print( Math.RandomInt(0, 1) );	// only 0
			Print( Math.RandomInt(0, 2) );	// 0 or 1

			>> 0
			>> 1
		@endcode
	*/
	proto static int RandomInt(int min, int max);
	
	/**
	\brief Returns a random \p int number between and min [inclusive] and max [inclusive].
		\param min \p int Range starts [inclusive]
		\param max \p int Range ends [inclusive]
		\return \p int - Random number in range
		@code
			Print( Math.RandomIntInclusive(0, 1) );	// 0 or 1
			Print( Math.RandomIntInclusive(0, 2) );	// 0, 1, 2

			>> 1
			>> 2
		@endcode
	*/
	
	static int RandomIntInclusive(int min, int max)
	{
		return Math.RandomInt(min, max+1);
	}
	
	/**
	\brief Returns a random \p bool .
		\return \p bool - Random bool either 0 or 1
		@code
			Print( Math.RandomBool() );
			Print( Math.RandomBool() );
			Print( Math.RandomBool() );
	
			>> true
			>> true
			>> false
		@endcode
	*/
	
	static bool RandomBool()
	{
		return RandomIntInclusive(0,1);
	}
	
	/**
	\brief Returns a random \p float number between and min[inclusive] and max[exclusive].
		\param min \p float Range starts [inclusive]
		\param max \p float Range ends [exclusive]
		\return \p float - Random number in range
		@code
			Print( Math.RandomFloat(0,1) );
			Print( Math.RandomFloat(0,2) );

			>> 0.597561
			>> 1.936456
		@endcode
	*/
	proto static float RandomFloat(float min, float max);

	/**
	\brief Returns a random \p float number between and min [inclusive] and max [inclusive].
		\param min \p float Range starts [inclusive]
		\param max \p float Range ends [inclusive]
		\return \p float - Random number in range
		@code
			Print( Math.RandomFloatInclusive(0, 1) );	// 0.0 .. 1.0
			Print( Math.RandomFloatInclusive(1, 2) );	// 1.0 .. 2.0

			>> 0.3
			>> 2.0
		@endcode
	*/
	static float RandomFloatInclusive(float min, float max)
	{
		int max_range = Math.Pow(2, 30); //max range
		int random_int = Math.RandomInt(0, max_range);
		float rand_float = (float)random_int / (float)max_range;
		float range = max - min;

		return min + (rand_float * range); //rand float
	}

	/**
	\brief Returns a random \p float number between and min [inclusive] and max [inclusive].
		\return \p float - Random number in range 0.0 .. 1.0
		@code
			Print( Math.RandomFloat01() );	// 0.0 .. 1.0

			>> 0.3
			>> 1.0
		@endcode
	*/
	static float RandomFloat01()
	{
		return RandomFloatInclusive(0, 1);
	}
	
	/**
	\brief Sets the seed for the random number generator.
		\param seed \p int New seed for the random number generator, -1 will use time
		\return \p int - Returns new seed
		@code
			Print( Math.Randomize(5) );

			>> 5
		@endcode
	*/
	proto static int Randomize(int seed);
	
	/**
	\brief Normalizes the angle (0...360)
		\param ang \p float Angle for normalizing
		\return \p float - Normalized angle
		@code
			Print( Math.NormalizeAngle(390) );
			Print( Math.NormalizeAngle(-90) );

			>> 30
			>> 270
		@endcode
	*/
	proto static float NormalizeAngle(float ang);

	/**
	\brief Return relative difference between angles
		\param angle1 \p float 
		\param angle2 \p float
		\return \p float Difference between angles (angle1 - angle2)
		@code
			Print( Math.DiffAngle(-45, 45) );
			Print( Math.DiffAngle(90, 80) );

			>> -90
			>> 10
		@endcode
	*/
	proto static float DiffAngle(float angle1, float angle2);
	
	/**
	\brief Return power of v ^ power
		\param v \p float Value
		\param power \p float Power
		\return \p float - The result of raising v to the given power
		@code
			Print( Math.Pow(2, 4) ); // (2*2*2*2)=16

			>> 16
		@endcode
	*/
	proto static float Pow(float v, float power);

	/**
	\brief Returns the floating-point remainder of x/y rounded towards zero
		\param x \p float Value of the quotient numerator
		\param y \p float Value of the quotient denominator
		\return \p float - The remainder of dividing the arguments
		@code
			Print( Math.ModFloat(5.3, 2) );
			Print( Math.ModFloat(18.5, 4.2) );

			>> 1.3
			>> 1.7
		@endcode
	*/
	proto static float ModFloat(float x, float y);

	/**
	\brief Returns the floating-point remainder of x/y rounded to nearest
		\param x \p float Value of the quotient numerator
		\param y \p float Value of the quotient denominator
		\return \p float - The remainder of dividing the arguments
		@code
			Print( Math.RemainderFloat(5.3, 2) );
			Print( Math.RemainderFloat(18.5, 4.2) );

			>> -0.7
			>> 1.7
		@endcode
	*/
	proto static float RemainderFloat(float x, float y);
	
	/**
	\brief Returns absolute value
		\param f \p float Value
		\return \p float - Absolute value
		@code
			Print( Math.AbsFloat(-12.5) );

			>> 12.5
		@endcode
	*/
	proto static float AbsFloat(float f);

	/**
	\brief Returns absolute value
		\param i \p int Value
		\return \p int - Absolute value
		@code
			Print( Math.AbsInt(-12) );

			>> 12
		@endcode
	*/
	proto static int AbsInt(int i);

	/**
	\brief Returns sign of given value
		\param f \p float Value
		\return \p float - Sign of given value
		@code
			Print( Math.SignFloat(-12.0) );
			Print( Math.SignFloat(0.0) );
			Print( Math.SignFloat(12.0) );

			>> -1.0
			>> 0
			>> 1.0
		@endcode
	*/
	proto static float SignFloat(float f);

	/**
	\brief Returns sign of given value
		\param i \p int Value
		\return \p int - Sign of given value
		@code
			Print( Math.SignFloat(-12) );
			Print( Math.SignFloat(0) );
			Print( Math.SignFloat(12) );

			>> -1
			>> 0
			>> 1
		@endcode
	*/
	proto static int SignInt(int i);
	
	/**
	\brief Returns squared value
		\param f \p float Value
		\return \p float - Squared value
		@code
			Print( Math.SqrFloat(12.5) );

			>> 156.25
		@endcode
	*/
	proto static float SqrFloat(float f);

	/**
	\brief Returns squared value
		\param i \p int Value
		\return \p int - Squared value
		@code
			Print( Math.SqrInt(12) );

			>> 144
		@endcode
	*/
	proto static int SqrInt(int i);
	
	/**
	\brief Returns square root
		\param val \p float Value
		\return \p float - Square of value
		@code
			Print( Math.Sqrt(25));

			>> 5
		@endcode
	*/
	proto static float Sqrt(float val);
	
	/**
	\brief Returns the binary (base-2) logarithm of x.
		\param x \p float Value whose logarithm is calculated.
		\return \p float The binary logarithm of x: log2x.
				\n If x is negative, it causes a domain error:
				\n If x is zero, it may cause a pole error (depending on the library implementation).
		@code
			Print( Math.Log2(1.0) ); 
	
			>> 0.0
		@endcode
	*/
	proto static float Log2(float x);

	/**
	\brief Returns sinus of angle in radians
		\param angle \p float Angle in radians
		\return \p float - Sinus of angle
		@code
			Print( Math.Sin(0.785398) ); // (45)

			>> 0.707107
		@endcode
	*/
	proto static float Sin(float angle);

	/**
	\brief Returns cosinus of angle in radians
		\param angle \p float Angle in radians
		\return \p float - Cosinus of angle
		@code
			Print( Math.Cos(0.785398) ); // (45)

			>> 0.707107
		@endcode
	*/
	proto static float Cos(float angle);

	/**
	\brief Returns tangent of angle in radians
		\param angle \p float Angle in radians
		\return \p float - Tangens of angle
		@code
			Print( Math.Tan(0.785398) ); // (45)

			>> 1
		@endcode
	*/
	proto static float Tan(float angle);

	/**
	\brief Returns angle in radians from sinus
		\param s \p float Sinus
		\return \p float - Angle in radians
		@code
			Print( Math.Asin(0.707107) ); // (sinus 45)

			>> 0.785398
		@endcode
	*/
	proto static float Asin(float s);

	/**
	\brief Returns angle in radians from cosinus
		\param c \p float Cosinus
		\return \p float - Angle in radians
		@code
			Print( Math.Acos(0.707107) ); // (cosinus 45)

			>> 0.785398
		@endcode
	*/
	proto static float Acos(float c);
	
	/**
	\brief Returns angle in radians from tangent
		\param x \p float Tangent
		\return \p float - Angle in radians
	*/
	proto static float Atan(float x);

	/**
	\brief Returns angle in radians from tangent
		\param y \p float Tangent
		\param x \p float Tangent
		\return \p float - Angle in radians
		@code
			Print ( Math.Atan2(1, 1) );

			>> 0.785398
		@endcode
	*/
	proto static float Atan2(float y, float x);

	/**
	\brief Returns mathematical round of value
		\param f \p float Value
		\return \p float - closest whole number to 'f'
		@code
			Print( Math.Round(5.3) );
			Print( Math.Round(5.8) );

			>> 5
			>> 6
		@endcode
	*/
	proto static float Round(float f);
		
	/**
	\brief Returns floor of value
		\param f \p float Value
		\return \p float - Floor of value
		@code
			Print( Math.Floor(5.3) );
			Print( Math.Floor(5.8) );

			>> 5
			>> 5
		@endcode
	*/
	proto static float Floor(float f);

	/**
	\brief Returns ceil of value
		\param f \p float Value
		\return \p float - Ceil of value
		@code
			Print( Math.Ceil(5.3) );
			Print( Math.Ceil(5.8) );

			>> 6
			>> 6
		@endcode
	*/
	proto static float Ceil(float f);
	
	/**
	\brief Returns wrap number to specified interval [min, max[
		\param f \p float Value
		\param min \p float Minimum
		\param max \p float Maximum
		\return \p float - number in specified interval [min, max[
		@code
			Print( Math.WrapFloat(9.0, 1.0, 9.0) );

			>> 1.0
		@endcode
	*/
	proto static float WrapFloat(float f, float min, float max);
	
	/**
	\brief Returns wrap number to specified interval, inclusive [min, max]
		\param f \p float Value
		\param min \p float Minimum
		\param max \p float Maximum
		\return \p float - number in specified interval [min, max]
		@code
			Print( Math.WrapFloatInclusive(9.0, 1.0, 9.0) );

			>> 9.0
		@endcode
	*/
	proto static float WrapFloatInclusive(float f, float min, float max);
	
	/**
	\brief Returns wrap number to specified interval [0, max[
		\param f \p float Value
		\param max \p float Maximum
		\return \p float - number in specified interval [0, max[
		@code
			Print( Math.WrapFloat0X(9.0, 9.0) );

			>> 0.0
		@endcode
	*/
	proto static float WrapFloat0X(float f, float max);
	
	/**
	\brief Returns wrap number to specified interval, inclusive [0, max]
		\param f \p float Value
		\param max \p float Maximum
		\return \p float - number in specified interval [0, max]
		@code
			Print( Math.WrapFloat0XInclusive(9.0, 9.0) );

			>> 9.0
		@endcode
	*/
	proto static float WrapFloat0XInclusive(float f, float max);
	
	/**
	\brief Returns wrap number to specified interval [min, max[
		\param i \p int Value
		\param min \p float Minimum
		\param max \p int Maximum
		\return \p int - number in specified interval [min, max[
		@code
			Print( Math.WrapInt(9, 1, 9) );

			>> 1
		@endcode
	*/
	proto static int WrapInt(int i, int min, int max);
	
	/**
	\brief Returns wrap number to specified interval [0, max[
		\param i \p int Value
		\param max \p int Maximum
		\return \p int - number in specified interval [0, max[
		@code
			Print( Math.WrapInt0X(9, 9) );

			>> 0
		@endcode
	*/
	proto static int WrapInt0X(int i, int max);

	/**
	\brief Clamps 'value' to 'min' if it is lower than 'min', or to 'max' if it is higher than 'max'
		\param value \p float Value
		\param min \p float Minimum value
		\param max \p float Maximum value
		\return \p float - Clamped value
		@code
			Print( Math.Clamp(-0.1, 0, 1) );
			Print( Math.Clamp(2, 0, 1) );
			Print( Math.Clamp(0.5, 0, 1) );
	
			>> 0
			>> 1
			>> 0.5
		@endcode
	*/
	proto static float Clamp(float value, float min, float max);
		
	/**
	\brief Returns smaller of two given values
		\param x \p float Value
		\param y \p float Value
		\return \p float  - min value
		@code
			Print( Math.Min(5.3, 2.8) );

			>> 2.8
		@endcode
	*/
	proto static float Min(float x, float y);
	
	/**
	\brief Returns bigger of two given values
		\param x \p float Value
		\param y \p float Value
		\return \p float  - max value
		@code
			Print( Math.Max(5.3, 2.8) );

			>> 5.3
		@endcode
	*/
	proto static float Max(float x, float y);	
	
	/**
	\brief Returns if value is between min and max (inclusive)
		\param v \p float Value
		\param min \p float Minimum value
		\param max \p float Maximum value
		\return \p bool  - if value is within range [min,max]
		@code
			Print( Math.IsInRange(6.9, 3.6, 9.3) );

			>> true
		@endcode
	*/
	proto static bool IsInRange(float v, float min, float max);
	
	/**
	\brief Returns if value is between min and max (inclusive)
		\param v \p int Value
		\param min \p int Minimum value
		\param max \p int Maximum value
		\return \p bool  - if value is within range [min,max]
		@code
			Print( Math.IsInRangeInt(6, 3, 9) );

			>> true
		@endcode
	*/
	proto static bool IsInRangeInt(int v, int min, int max);
	
	/**
	\brief Linearly interpolates between 'a' and 'b' given 'time'.
		\param a \p float Start
		\param b \p float End
		\param time \p float Time [value needs to be between 0..1 for correct results, no auto clamp applied]
		\return \p float - The interpolated result between the two float values. 
		@code
			Print( Math.Lerp(3, 7, 0.5) );
	
			>> 5
		@endcode
	*/ 
	proto static float Lerp(float a, float b, float time);

	/**
	\brief Calculates the linear value that produces the interpolant value within the range [a, b], it's an inverse of Lerp.
		\param a \p float Start
		\param b \p float End
		\param value \p float value
		\return \p float - the time given the position between 'a' and 'b' given 'value', there is no clamp on 'value', to stay between [0..1] use 'value' between 'a' and 'b'
		@code
			Print( Math.InverseLerp(3, 7, 5) );
	
			>> 0.5
		@endcode
	*/
	proto static float InverseLerp(float a, float b, float value);
	
	/**
	\brief Returns area of a right triangle
		\param s \p float Length of adjacent leg
		\param a \p float Angle of corner bordering adjacent which is not the right corner (in radians)
		\return \p float - Area
	*/
	proto static float AreaOfRightTriangle(float s, float a);
	
	/**
	\brief Returns hypotenus of a right triangle
		\param s \p float Length of adjacent leg
		\param a \p float Angle of corner bordering adjacent which is not the right corner (in radians)
		\return \p float - hypotenus
	*/
	proto static float HypotenuseOfRightTriangle(float s, float a);
	
	/**
	\brief Returns if point is inside circle
		\param c \p vector Center of circle ([0] and [2] will be used, as a circle is 2D)
		\param r \p float Radius of circle
		\param p \p vector Point ([0] and [2] will be used, as a circle is 2D)
		\return \p bool - True when point is in circle
	*/
	proto static bool IsPointInCircle(vector c, float r, vector p);
	
	/**
	\brief Returns if point is inside rectangle
		\param mi \p vector Minimums of rectangle ([0] and [2] will be used, as a rectangle is 2D)
		\param ma \p vector Maximums of rectangle ([0] and [2] will be used, as a rectangle is 2D)
		\param p \p vector Point ([0] and [2] will be used, as a rectangle is 2D)
		\return \p bool - True when point is in rectangle
	*/
	proto static bool IsPointInRectangle(vector mi, vector ma, vector p);
	
	//--------------------------------------------------------------------------
	//-------------------------------- filters ---------------------------------
	//--------------------------------------------------------------------------

	/**
	\brief Does the CD smoothing function - easy in | easy out / S shaped smoothing 
		\param val \p actual value 
		\param target \p value we are reaching for -> Target
		\param velocity \p float[1] - array of ONE member - some kind of memory and actual accel/decel rate, need to be zeroed when filter is about to be reset
		\param smoothTime \p smoothing parameter, 0.1 .. 0.4 are resonable values, 0.1 is sharp, 0.4 is very smooth
		\param maxVelocity \p maximal value change when multiplied by dt
		\param dt \p delta time 

		\return \p float smoothed/filtered value 

		@code
			val = EnfMath.SmoothCD(val, varTarget, valVelocity, 0.3, 1000, dt);
		@endcode
	*/

	proto static float SmoothCD(float val, float target, inout float velocity[], float smoothTime, float maxVelocity, float dt);
	
	static float SmoothCDPI2PI(float val, float target, inout float velocity[], float smoothTime, float maxVelocity, float dt)
	{
		float diff = target - val;
		if (diff < -Math.PI)
		{
			target += Math.PI2;
		}
		else if (diff > Math.PI)
		{
			target -= Math.PI2;
		}
		
		float retVal = SmoothCD(val, target, velocity, smoothTime, maxVelocity, dt);
		
		while (retVal > Math.PI)
		{
			retVal -= Math.PI2;
		}
		
		while (retVal < -Math.PI)
		{
			retVal += Math.PI2;
		}
		
		return retVal;
	}
	
	//! occurences values above '12' will cause Factorial to overflow int.
	static float Poisson(float mean, int occurences)
	{
		return Pow(mean, occurences) * Pow(EULER,-mean) / Factorial(occurences);
	}
	
	//! values above '12' will cause int overflow
	static int Factorial(int val)
	{
		if (val > 12)
		{
			ErrorEx("Values above '12' cause int overflow! Returning '1'",ErrorExSeverity.INFO);
			return 1;
		}
		
		int res = 1;
		while (val > 1)
		{
			res *= val--;
		}
		return res;
	}
	
	static vector CenterOfRectangle(vector min, vector max)
	{
		float x = (min[0] + max[0]) * 0.5;
		float z = (min[2] + max[2]) * 0.5;
		
		return Vector(x, 0.0, z);
	}
}

//@}