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#region --- License ---

/* Licensed under the MIT/X11 license.

 * Copyright (c) 2006-2008 the OpenTK Team.

 * This notice may not be removed from any source distribution.

 * See license.txt for licensing detailed licensing details.

 *

 * Contributions by Andy Gill, James Talton and Georg Wächter.

 */

#endregion

using System;

using System.Collections.Generic;

using System.Text;

namespace OpenTK

{

    /// <summary>

    /// Contains common mathematical functions and constants.

    /// </summary>

    public static class MathHelper

    {

        #region Fields

        /// <summary>

        /// Defines the value of Pi as a <see cref="System.Single"/>.

        /// </summary>

        public const float Pi = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930382f;

        /// <summary>

        /// Defines the value of Pi divided by two as a <see cref="System.Single"/>.

        /// </summary>

        public const float PiOver2 = Pi / 2;

        /// <summary>

        /// Defines the value of Pi divided by three as a <see cref="System.Single"/>.

        /// </summary>

        public const float PiOver3 = Pi / 3;

        /// <summary>

        /// Definesthe value of  Pi divided by four as a <see cref="System.Single"/>.

        /// </summary>

        public const float PiOver4 = Pi / 4;

        /// <summary>

        /// Defines the value of Pi divided by six as a <see cref="System.Single"/>.

        /// </summary>

        public const float PiOver6 = Pi / 6;

        /// <summary>

        /// Defines the value of Pi multiplied by two as a <see cref="System.Single"/>.

        /// </summary>

        public const float TwoPi = 2 * Pi;

        /// <summary>

        /// Defines the value of Pi multiplied by 3 and divided by two as a <see cref="System.Single"/>.

        /// </summary>

        public const float ThreePiOver2 = 3 * Pi / 2;

        /// <summary>

        /// Defines the value of E as a <see cref="System.Single"/>.

        /// </summary>

        public const float E = 2.71828182845904523536f;

        /// <summary>

        /// Defines the base-10 logarithm of E.

        /// </summary>

        public const float Log10E = 0.434294482f;

        /// <summary>

        /// Defines the base-2 logarithm of E.

        /// </summary>

        public const float Log2E = 1.442695041f;

        #endregion

        #region Public Members

        #region NextPowerOfTwo

        /// <summary>

        /// Returns the next power of two that is larger than the specified number.

        /// </summary>

        /// <param name="n">The specified number.</param>

        /// <returns>The next power of two.</returns>

        public static long NextPowerOfTwo(long n)

        {

            if (n < 0) throw new ArgumentOutOfRangeException("n", "Must be positive.");

            return (long)System.Math.Pow(2, System.Math.Ceiling(System.Math.Log((double)n, 2)));

        }

        /// <summary>

        /// Returns the next power of two that is larger than the specified number.

        /// </summary>

        /// <param name="n">The specified number.</param>

        /// <returns>The next power of two.</returns>

        public static int NextPowerOfTwo(int n)

        {

            if (n < 0) throw new ArgumentOutOfRangeException("n", "Must be positive.");

            return (int)System.Math.Pow(2, System.Math.Ceiling(System.Math.Log((double)n, 2)));

        }

        /// <summary>

        /// Returns the next power of two that is larger than the specified number.

        /// </summary>

        /// <param name="n">The specified number.</param>

        /// <returns>The next power of two.</returns>

        public static float NextPowerOfTwo(float n)

        {

            if (n < 0) throw new ArgumentOutOfRangeException("n", "Must be positive.");

            return (float)System.Math.Pow(2, System.Math.Ceiling(System.Math.Log((double)n, 2)));

        }

        /// <summary>

        /// Returns the next power of two that is larger than the specified number.

        /// </summary>

        /// <param name="n">The specified number.</param>

        /// <returns>The next power of two.</returns>

        public static double NextPowerOfTwo(double n)

        {

            if (n < 0) throw new ArgumentOutOfRangeException("n", "Must be positive.");

            return System.Math.Pow(2, System.Math.Ceiling(System.Math.Log((double)n, 2)));

        }

        #endregion

        #region Factorial

        /// <summary>Calculates the factorial of a given natural number.

        /// </summary>

        /// <param name="n">The number.</param>

        /// <returns>n!</returns>

        public static long Factorial(int n)

        {

            long result = 1;

            for (; n > 1; n--)

                result *= n;

            return result;

        }

        #endregion

        #region BinomialCoefficient

        /// <summary>

        /// Calculates the binomial coefficient <paramref name="n"/> above <paramref name="k"/>.

        /// </summary>

        /// <param name="n">The n.</param>

        /// <param name="k">The k.</param>

        /// <returns>n! / (k! * (n - k)!)</returns>

        public static long BinomialCoefficient(int n, int k)

        {

            return Factorial(n) / (Factorial(k) * Factorial(n - k));

        }

        #endregion

        #region InverseSqrtFast

        /// <summary>

        /// Returns an approximation of the inverse square root of left number.

        /// </summary>

        /// <param name="x">A number.</param>

        /// <returns>An approximation of the inverse square root of the specified number, with an upper error bound of 0.001</returns>

        /// <remarks>

        /// This is an improved implementation of the the method known as Carmack's inverse square root

        /// which is found in the Quake III source code. This implementation comes from

        /// http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see

        /// http://www.beyond3d.com/content/articles/8/

        /// </remarks>

        public static float InverseSqrtFast(float x)

        {

            unsafe

            {

                float xhalf = 0.5f * x;

                int i = *(int*)&x;              // Read bits as integer.

                i = 0x5f375a86 - (i >> 1);      // Make an initial guess for Newton-Raphson approximation

                x = *(float*)&i;                // Convert bits back to float

                x = x * (1.5f - xhalf * x * x); // Perform left single Newton-Raphson step.

                return x;

            }

        }

        /// <summary>

        /// Returns an approximation of the inverse square root of left number.

        /// </summary>

        /// <param name="x">A number.</param>

        /// <returns>An approximation of the inverse square root of the specified number, with an upper error bound of 0.001</returns>

        /// <remarks>

        /// This is an improved implementation of the the method known as Carmack's inverse square root

        /// which is found in the Quake III source code. This implementation comes from

        /// http://www.codemaestro.com/reviews/review00000105.html. For the history of this method, see

        /// http://www.beyond3d.com/content/articles/8/

        /// </remarks>

        public static double InverseSqrtFast(double x)

        {

            return InverseSqrtFast((float)x);

            // TODO: The following code is wrong. Fix it, to improve precision.

#if false

            unsafe

            {

                double xhalf = 0.5f * x;

                int i = *(int*)&x;              // Read bits as integer.

                i = 0x5f375a86 - (i >> 1);      // Make an initial guess for Newton-Raphson approximation

                x = *(float*)&i;                // Convert bits back to float

                x = x * (1.5f - xhalf * x * x); // Perform left single Newton-Raphson step.

                return x;

            }

#endif

        }

        #endregion

        #region DegreesToRadians

        /// <summary>

        /// Convert degrees to radians

        /// </summary>

        /// <param name="degrees">An angle in degrees</param>

        /// <returns>The angle expressed in radians</returns>

        public static float DegreesToRadians(float degrees)

        {

            const float degToRad = (float)System.Math.PI / 180.0f;

            return degrees * degToRad;

        }

        /// <summary>

        /// Convert radians to degrees

        /// </summary>

        /// <param name="radians">An angle in radians</param>

        /// <returns>The angle expressed in degrees</returns>

        public static float RadiansToDegrees(float radians)

        {

            const float radToDeg = 180.0f / (float)System.Math.PI;

            return radians * radToDeg;

        }

        #endregion

        #region Swap

        /// <summary>

        /// Swaps two double values.

        /// </summary>

        /// <param name="a">The first value.</param>

        /// <param name="b">The second value.</param>

        public static void Swap(ref double a, ref double b)

        {

            double temp = a;

            a = b;

            b = temp;

        }

        /// <summary>

        /// Swaps two float values.

        /// </summary>

        /// <param name="a">The first value.</param>

        /// <param name="b">The second value.</param>

        public static void Swap(ref float a, ref float b)

        {

            float temp = a;

            a = b;

            b = temp;

        }

        #endregion

        #endregion

    }

}