firational.cs

对gif

// ==========================================================
// FreeImage 3 .NET wrapper
// Original FreeImage 3 functions and .NET compatible derived functions
//
// Design and implementation by
// - Jean-Philippe Goerke ([e-mail])
// - Carsten Klein ([e-mail])
//
// Contributors:
// - David Boland ([e-mail])
//
// Main reference : MSDN Knowlede Base
//
// This file is part of FreeImage 3
//
// COVERED CODE IS PROVIDED UNDER THIS LICENSE ON AN "AS IS" BASIS, WITHOUT WARRANTY
// OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, WITHOUT LIMITATION, WARRANTIES
// THAT THE COVERED CODE IS FREE OF DEFECTS, MERCHANTABLE, FIT FOR A PARTICULAR PURPOSE
// OR NON-INFRINGING. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE COVERED
// CODE IS WITH YOU. SHOULD ANY COVERED CODE PROVE DEFECTIVE IN ANY RESPECT, YOU (NOT
// THE INITIAL DEVELOPER OR ANY OTHER CONTRIBUTOR) ASSUME THE COST OF ANY NECESSARY
// SERVICING, REPAIR OR CORRECTION. THIS DISCLAIMER OF WARRANTY CONSTITUTES AN ESSENTIAL
// PART OF THIS LICENSE. NO USE OF ANY COVERED CODE IS AUTHORIZED HEREUNDER EXCEPT UNDER
// THIS DISCLAIMER.
//
// Use at your own risk!
// ==========================================================

// ==========================================================
// CVS
// $Revision: 1.3 $
// $Date: 2008/06/16 15:17:37 $
// $Id: FIRational.cs,v 1.3 2008/06/16 15:17:37 cklein05 Exp $
// ==========================================================

using System;
using System.Collections.Generic;
using System.Runtime.InteropServices;

namespace FreeImageAPI
{
	/// <summary>
	/// The <b>FIRational</b> structure represents a fraction via two <see cref="Int32"/>
	/// instances which are interpreted as numerator and denominator.
	/// </summary>
	/// <remarks>
	/// The structure tries to approximate the value of <see cref="FreeImageAPI.FIRational(decimal)"/>
	/// when creating a new instance by using a better algorithm than FreeImage does.
	/// <para/>
	/// The structure implements the following operators:
	/// +, -, ++, --, ==, != , >, >==, &lt;, &lt;== and ~ (which switches nominator and denomiator).
	/// <para/>
	/// The structure can be converted into all .NET standard types either implicit or
	/// explicit.
	/// </remarks>
	[Serializable, StructLayout(LayoutKind.Sequential), ComVisible(true)]
	public struct FIRational : IConvertible, IComparable, IFormattable, IComparable<FIRational>, IEquatable<FIRational>
	{
		private int numerator;
		private int denominator;

		/// <summary>
		/// Represents the largest possible value of <see cref="FIRational"/>. This field is constant.
		/// </summary>
		public static readonly FIRational MaxValue = new FIRational(Int32.MaxValue, 1);

		/// <summary>
		/// Represents the smallest possible value of <see cref="FIRational"/>. This field is constant.
		/// </summary>
		public static readonly FIRational MinValue = new FIRational(Int32.MinValue, 1);

		/// <summary>
		/// Represents the smallest positive <see cref="FIRational"/> value greater than zero. This field is constant.
		/// </summary>
		public static readonly FIRational Epsilon = new FIRational(1, Int32.MaxValue);

		/// <summary>
		/// Initializes a new instance based on the specified parameters.
		/// </summary>
		/// <param name="n">The numerator.</param>
		/// <param name="d">The denominator.</param>
		public FIRational(int n, int d)
		{
			numerator = n;
			denominator = d;
			Normalize();
		}

		/// <summary>
		/// Initializes a new instance based on the specified parameters.
		/// </summary>
		/// <param name="tag">The tag to read the data from.</param>
		public unsafe FIRational(FITAG tag)
		{
			switch (FreeImage.GetTagType(tag))
			{
				case FREE_IMAGE_MDTYPE.FIDT_SRATIONAL:
					int* value = (int*)FreeImage.GetTagValue(tag);
					numerator = (int)value[0];
					denominator = (int)value[1];
					Normalize();
					return;
				default:
					throw new ArgumentException("tag");
			}
		}

		/// <summary>
		/// Initializes a new instance based on the specified parameters.
		/// </summary>
		/// <param name="value">The value to convert into a fraction.</param>
		/// <exception cref="OverflowException">
		/// <paramref name="value"/> cannot be converted into a fraction
		/// represented by two integer values.</exception>
		public FIRational(decimal value)
		{
			try
			{
				int sign = value < 0 ? -1 : 1;
				value = Math.Abs(value);
				try
				{
					int[] contFract = CreateContinuedFraction(value);
					CreateFraction(contFract, out numerator, out denominator);
					Normalize();
				}
				catch
				{
					numerator = 0;
					denominator = 1;
				}
				if (Math.Abs(((decimal)numerator / (decimal)denominator) - value) > 0.0001m)
				{
					int maxDen = (Int32.MaxValue / (int)value) - 2;
					maxDen = maxDen < 10000 ? maxDen : 10000;
					ApproximateFraction(value, maxDen, out numerator, out denominator);
					Normalize();
					if (Math.Abs(((decimal)numerator / (decimal)denominator) - value) > 0.0001m)
					{
						throw new OverflowException();
					}
				}
				numerator *= sign;
				Normalize();
			}
			catch (Exception ex)
			{
				throw new OverflowException("Unable to calculate fraction.", ex);
			}
		}

		/// <summary>
		/// Initializes a new instance based on the specified parameters.
		/// </summary>
		/// <param name="r">The structure to clone from.</param>
		public FIRational(FIRational r)
		{
			numerator = r.numerator;
			denominator = r.denominator;
			Normalize();
		}

		/// <summary>
		/// The numerator of the fraction.
		/// </summary>
		public int Numerator
		{
			get { return numerator; }
		}

		/// <summary>
		/// The denominator of the fraction.
		/// </summary>
		public int Denominator
		{
			get { return denominator; }
		}

		/// <summary>
		/// Returns the truncated value of the fraction.
		/// </summary>
		/// <returns></returns>
		public int Truncate()
		{
			return denominator > 0 ? (int)(numerator / denominator) : 0;
		}

		/// <summary>
		/// Returns whether the fraction is representing an integer value.
		/// </summary>
		public bool IsInteger
		{
			get
			{
				return (denominator == 1 ||
					(denominator != 0 && (numerator % denominator == 0)) ||
					(denominator == 0 && numerator == 0));
			}
		}

		/// <summary>
		/// Calculated the greatest common divisor of 'a' and 'b'.
		/// </summary>
		private static long Gcd(long a, long b)
		{
			a = Math.Abs(a);
			b = Math.Abs(b);
			long r;
			while (b > 0)
			{
				r = a % b;
				a = b;
				b = r;
			}
			return a;
		}

		/// <summary>
		/// Calculated the smallest common multiple of 'a' and 'b'.
		/// </summary>
		private static long Scm(int n, int m)
		{
			return Math.Abs((long)n * (long)m) / Gcd(n, m);
		}

		/// <summary>
		/// Normalizes the fraction.
		/// </summary>
		private void Normalize()
		{
			if (denominator == 0)
			{
				numerator = 0;
				denominator = 1;
				return;
			}

			if (numerator != 1 && denominator != 1)
			{
				int common = (int)Gcd(numerator, denominator);
				if (common != 1 && common != 0)
				{
					numerator /= common;
					denominator /= common;
				}
			}

			if (denominator < 0)
			{
				numerator *= -1;
				denominator *= -1;
			}
		}

		/// <summary>
		/// Normalizes a fraction.
		/// </summary>
		private static void Normalize(ref long numerator, ref long denominator)
		{
			if (denominator == 0)
			{
				numerator = 0;
				denominator = 1;
			}
			else if (numerator != 1 && denominator != 1)
			{
				long common = Gcd(numerator, denominator);
				if (common != 1)
				{
					numerator /= common;
					denominator /= common;
				}
			}
			if (denominator < 0)
			{
				numerator *= -1;
				denominator *= -1;
			}
		}

		/// <summary>
		/// Returns the digits after the point.
		/// </summary>
		private static int GetDigits(decimal value)
		{
			int result = 0;
			value -= decimal.Truncate(value);
			while (value != 0)
			{
				value *= 10;
				value -= decimal.Truncate(value);
				result++;
			}
			return result;
		}

		/// <summary>
		/// Creates a continued fraction of a decimal value.
		/// </summary>
		private static int[] CreateContinuedFraction(decimal value)
		{
			int precision = GetDigits(value);
			decimal epsilon = 0.0000001m;
			List<int> list = new List<int>();
			value = Math.Abs(value);

			byte b = 0;

			list.Add((int)value);
			value -= ((int)value);

			while (value != 0m)
			{
				if (++b == byte.MaxValue || value < epsilon)
				{
					break;
				}
				value = 1m / value;
				if (Math.Abs((Math.Round(value, precision - 1) - value)) < epsilon)
				{
					value = Math.Round(value, precision - 1);
				}
				list.Add((int)value);
				value -= ((int)value);
			}
			return list.ToArray();
		}

		/// <summary>
		/// Creates a fraction from a continued fraction.
		/// </summary>
		private static void CreateFraction(int[] continuedFraction, out int numerator, out int denominator)
		{
			numerator = 1;
			denominator = 0;
			int temp;

			for (int i = continuedFraction.Length - 1; i > -1; i--)
			{
				temp = numerator;