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Fraction class in C#

, 14 Feb 2005 CPOL
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An article representing floating point numbers as fractions.

Introduction

This article demonstrates how to remove the problem of limited precision when numbers such as 1/10, 1/7, 1/3, etc. are represented in a floating point variable type in C#. Yes, you guessed it right, this problem can be solved by storing such numbers in a fraction format. As a fraction object stores its numerator and denominator as integer variables, there is no loss of accuracy. For this purpose, I have written a simple C# class representing fractions. It can be used in various applications, e.g., equation solving, matrix transformations, etc.

Features of class

The class contains a variety of overloaded constructors and operators for certain situations. It also throws certain exceptions, e.g., when denominator is tried to assign a 0 value, when the result of an arithmetic exceeds the limit (range), etc. One more feature is the automatic normalization (simplification) of fractions. The class uses data type 'long integer' for storing numerator and denominator, hence its range is upper bounded by the range of Int64 in .NET framework.

Using the code

The class includes a variety of constructors, e.g., one that takes an integer like 123, one that takes a double like 156.25, one that takes a string that has all the above qualities (e.g., string can be "32/77" or "213" or "321.44"), one that takes values of numerator and denominator like 231 and 101, and, of course, a parameter-less constructor for a "zero" fraction stored as 0/1.

Fraction frac=new Fraction(); // we'll get 0/1
frac=new Fraction(1,5);       // we'll get 1/5
frac=new Fraction(25);        // we'll get 25/1
frac=new Fraction(9.25);      // we'll get 37/4
frac=new Fraction("6.25");    // we'll get 25/4

frac=new Fraction( System.Console.ReadLine() );
     // we can enter anything like "213" or 
     // "23/3" or "4.27"

Console.WriteLine( frac );
// displays the current value of frac1 object;

Operators overloaded (overloaded for fractions, integers and doubles) for Fraction object include:

  • Unary: - (Negation)
  • Binary +, -, *, /
  • Relational operators such as ==, !=, <, >, <=, >=.
Fraction frac=new Fraction("1/2"); // initialize a fraction with 1/2
Console.WriteLine( frac+2.5 );     // will display 3

Overloaded conversion further enhances the capabilities of the class. See how simple it is to work with fractions:

Fraction frac="1/2" // implicit cast from string to 
frac="22.5"         // implicit cast from string to fraction
frac=10.25          // implicit cast from double to fraction
frac=15             // implicit cast from integer/long to fraction

Finally, as an exercise, guess the output of the following code:

Fraction f=0.5;                 // initialize frac=1/2
Console.WriteLine( f-0.25 );    // Yes, you are right. "1/4" is displayed
Console.WriteLine( f+"1/4" );
   // not sure??? It will display "3/4" because "1/4" has 
   // been converted to fraction and then added to our frac object

Implementation details

The class uses simple mathematics to do all the work. Let us see some of these simple techniques:

  • To convert a double to a fraction, we keep multiplying the given double number with 10 until it is converted to an integer number.
  • To convert a given string to a fraction, we treat all the value before "/" as numerator and after "/" as denominator.
  • To normalize a fraction, we divide its numerator and denominator by their GCD (found by famous Euler's formula).
  • To add two fractions, we use simple school formula to get numerator and denominator of the resultant fraction and then normalize it:
    Numerator = frac1.Numerator*frac2.Denominator 
                + frac2.Numerator*frac1.Denominator;
    Denominator = frac1.Denominator*frac2.Denominator;
  • To overload arithmetic operators for integers and doubles, we first convert them to fractions and then perform the operation.

Applications

There are a lot of applications of Fraction class. An example is a matrix class, see my article on Matrix class in C#.

History

Version 2.0

  • Changed Numerator and Denominator from Int32 (integer) to Int64 (long) for increased range.
  • Renamed ConvertToString() to ToString().
  • Added the capability of detecting/raising overflow exceptions.
  • Fixed the bug that very small numbers, e.g. 0.00000001, could not be converted to fraction.
  • Fixed other minor bugs.

Version 2.1

  • Overloaded conversions from/to fractions.

Version 2.2 (changes by Marc Brooks and Jeffrey Sax).

  • Less overflows by finding the GCD for Add [Jeffery Sax] and Multiply [Marc C. Brooks]
  • Understands and handles NaN, PositiveInfinity, NegativeInfinity just like double [Marc C. Brooks]
  • Fixed several uses of int where long was correct [Marc C. Brooks]
  • Made value-type (struct) [Jeffery Sax]
  • Added ToInt32(), ToInt64() which throw for invalid (NaN, PositiveInfinity, NegativeInfinity) [Marc C. Brooks]
  • Removed redundant Value property [Jeffery Sax]
  • Added explicit conversion to Int32 and Int64 [Marc C. Brooks]
  • Better handling of exceptions [Marc C. Brooks]
  • Reorganized code, added XML doc and regions [Marc C. Brooks]
  • Proper implementations of Equals [Marc C. Brooks, Jeffery Sax]
  • Uses Math.Log(xx,2) and Math.Pow(xx,2) to get the best accuracy possible when converting doubles [Marc C. Brooks, Jeffery Sax]

Version 2.3 (changes by Marc Brooks and Jeffrey Sax)

  • Fixed double-to-fraction logic to use continued fraction rules to get best possible precision [bug fix for Syed Mehroz Alam, idea from Jeffery Sax]
  • Added static readonly values for NaN, PositiveInfinity, NegativeInfinity [idea from Jeffery Sax]
  • Moved comparisons into an implementation of IComparer [idea from Jeffery Sax]
  • No longer throws for NaN(s) involved in Add, Subtract, Multiply, Divide operations [idea from Jeffery Sax]
  • Added static readonly values for Zero, MinValue, MaxValue, Epsilon to better mirror double [Marc C. Brooks]
  • Added IsInfinity to better mirror double [Marc C. Brooks]
  • Added modulus and % operators [Marc C. Brooks]

License

This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)

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About the Author

Syed Mehroz Alam
Software Developer
Pakistan Pakistan

Syed Mehroz Alam, living in Karachi, Pakistan, is a developer focusing Microsoft technologies. He has completed his bachelors as a Computer Systems Engineer in 2006 and is currently pursuing a Masters degree in Computer Science. He loves to learn, discover and master all aspects of .NET and SQL Server. Mehroz has developed rich internet enterprise applications using Silverlight in addition to the traditional ASP.NET and Windows Forms applications. He has worked with all three components of SQL Business Intelligence Studio: SSIS, SSRS and SSAS for developing BI Solutions and Data warehouse. He loves to write complex TSQL queries and evaluate his skills by participating in various TSQL Challenges. His blog can be viewed at http://smehrozalam.wordpress.com.


Comments and Discussions

 
QuestionGlobalization issue PinmemberAnders Eriksson17-Feb-14 2:58 
SuggestionHandling Radios & Percents PinmemberDuane McKinney19-Jun-13 6:46 
SuggestionRe: Square roots [modified] Pinmembermla15425-Jul-12 5:13 
GeneralUnit tests for this class using NUnit PinmemberSyed Mehroz Alam16-Feb-10 2:07 
GeneralThanks a million! Pinmemberanhldbk27-Oct-09 19:59 
GeneralAlso check out the Fraction class from Apache PinmemberSire40427-Mar-09 3:03 
Generalgcd in binary PinmemberTheKing28-Mar-07 10:35 
Apart from being an excellent class I'd like to note that the GCD method is done in base 10 arithmatic. It would benefit greatly if done in binary using binary shifts doing the division. I've located a C++ algorithm on wikipedia to do exactly that http://en.wikipedia.org/wiki/Binary_GCD_algorithm[^]

GeneralSimple change PinmemberDaenris24-Sep-06 13:26 
GeneralRe: Simple change PinmemberDaenris24-Sep-06 13:33 
GeneralRe: Simple change Pinmemberdodiggitydag12-Oct-06 15:10 
GeneralRe: Simple change PinmemberNick Alexeev12-Oct-14 9:40 
GeneralA very good class PinmemberMina Momtaz13-May-06 22:33 
GeneralBug in CompareTo(Fraction right) method. PinmemberMarc Brooks9-Nov-05 7:25 
GeneralSome improvements for this class. PinsussMarc C. Brooks20-Dec-04 13:22 
GeneralRe: Some improvements for this class. PinmemberSyed Mehroz Alam20-Dec-04 20:06 
GeneralRe: Some improvements for this class. PinmemberJeffrey Sax20-Dec-04 21:28 
GeneralRe: Some improvements for this class. PinsussMarc Brooks11-Jan-05 10:26 
GeneralRe: Some improvements for this class. PinmemberHardy Wang7-Mar-09 7:01 
GeneralA few suggestions PinmemberJeffrey Sax16-Dec-04 16:19 
GeneralRe: A few suggestions PinmemberSyed Mehroz Alam20-Dec-04 19:54 
GeneralRe: A few suggestions PinmemberJeffrey Sax20-Dec-04 21:45 

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