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For pretty fractions (like ²²⁄₇ and -14¹⁷⁄₃₂ etc.)...
public override string ToString() => ToString(false, false);
public string ToString(bool allowMixedNumeral, bool characterize = false) {
if(Denominator == 1) {
return Numerator.ToString();
} else if(allowMixedNumeral) {
var integer = (Numerator / Denominator);
if(integer == 0) {
if(characterize) {
return _Characterize(Numerator, Denominator);
} else {
return $"{Numerator}/{Denominator}";
}
} else {
var numerator = (Numerator % Denominator);
if(numerator < 0) numerator = -numerator;
if(characterize) {
return $"{integer}{_Characterize(numerator, Denominator)}";
} else {
return $"{integer} {numerator}/{Denominator}";
}
}
} else {
if(characterize) {
return _Characterize(Numerator, Denominator);
} else {
return $"{Numerator}/{Denominator}";
}
}
}
private static string _Characterize(long numerator, long denominator) => $"{_ToSuperscript(numerator)}⁄{_ToSubscript(denominator)}";
private static string _ToSuperscript(long value) {
var ʀ = new StringBuilder();
var negative = (value < 0);
if(negative) {
value = -value;
ʀ.Append((char)0x207B);
}
var text = value.ToString();
foreach(var ɪ in text) {
switch(ɪ) {
case '1': ʀ.Append((char)0x00B9); break;
case '2':
case '3': ʀ.Append((char)(ɪ + 0x0080)); break;
default: ʀ.Append((char)(ɪ + 0x2040)); break;
}
}
return ʀ.ToString();
}
private static string _ToSubscript(long value) {
var text = value.ToString();
var ʀ = new StringBuilder();
foreach(var ɪ in text) ʀ.Append((char)(ɪ + 0x2050));
return ʀ.ToString();
}
Example:
var prettyFraction = (new Fraction(-5,4)).ToString(true, true)); Result is
-1¹⁄₄
The logic can probably be cleaned up a little, but the results sure are pretty 
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It work fine in operators (+-*/) but do not give correct result for comparison.
e.g new Fraction(24) > new Fraction(17,16) results false
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I think its better to add this feature to class becase maybe someone want to work with numbers more than long or double capacity
I suggest system.numerics.bigInteger
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I tried using this class as part of a matrix class i'm making and it failed when fractions are to have larger digits than long or even ulong. funny thing is the try catch will not fire up when doing arithmetic operations, it just give wrong answer.
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Looks pretty good, I'd guess, but haven't tested much. I see it takes NaN and Infinities and Overflow into account, and that's good. I'm curious as to why you used signed numbers for both the Numerator and Denominator. Doesn't that shorten the possible values? ...though I wonder, if you did leave one of them unsigned, which one would it be? ...how might that affect retrieving and setting each? Or maybe store the sign separately?
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Just tried the class and it works better than any other fraction class I have tried. One, maybe very specific for me, problem is if you read a decimal number (from a file) that is written in an another culture than what the program is run under. E.g. Living in Sweden we have comma as the decimal separator. Using the testFraction.cs with it's test data it will crash...
So I added a regex statement that replaces all different separators for the current one. Just one line, but it makes the class more resilient.
// Anders
public static Fraction ToFraction(string inValue)
{
if (inValue == null || inValue == string.Empty)
throw new ArgumentNullException("inValue");
NumberFormatInfo info = NumberFormatInfo.CurrentInfo;
string trimmedValue = inValue.Trim();
if (trimmedValue == info.NaNSymbol)
return NaN;
else if (trimmedValue == info.PositiveInfinitySymbol)
return PositiveInfinity;
else if (trimmedValue == info.NegativeInfinitySymbol)
return NegativeInfinity;
else
{
int slashPos = inValue.IndexOf('/');
if (slashPos > -1)
{
long numerator = Convert.ToInt64(inValue.Substring(0, slashPos));
long denominator = Convert.ToInt64(inValue.Substring(slashPos + 1));
return new Fraction(numerator, denominator);
}
else
{
inValue = Regex.Replace(inValue, @"[\.\?,;/-]", CultureInfo.CurrentCulture.NumberFormat.CurrencyDecimalSeparator);
int decimalPos = inValue.IndexOf(info.CurrencyDecimalSeparator);
if (decimalPos > -1)
return new Fraction(Convert.ToDouble(inValue));
else
return new Fraction(Convert.ToInt64(inValue));
}
}
}
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This is a trivial change, but one that i needed to make for my app. Would you be interested in the changes?
Additional Input strings accepted now include
1:5
20%
Comment probably isn't the best place for this but to get this functionality, replace the ToFraction function with these changes.
public static Fraction ToFraction(string inValue)
{
if (inValue == null || inValue == string.Empty)
throw new ArgumentNullException("inValue");
NumberFormatInfo info = NumberFormatInfo.CurrentInfo;
string trimmedValue = inValue.Trim();
if (trimmedValue == info.NaNSymbol)
return NaN;
else if (trimmedValue == info.PositiveInfinitySymbol)
return PositiveInfinity;
else if (trimmedValue == info.NegativeInfinitySymbol)
return NegativeInfinity;
else
{
int slashPos = inValue.IndexOf('/');
if (slashPos == -1)
slashPos = inValue.IndexOf(':');
int percentPos = inValue.IndexOf('%');
long numerator = 0;
if (slashPos > -1)
{
numerator = Convert.ToInt64(inValue.Substring(0, slashPos));
long denominator = Convert.ToInt64(inValue.Substring(slashPos + 1));
return new Fraction(numerator, denominator);
}
else if (percentPos > -1 && long.TryParse(inValue.Substring(0, percentPos), out numerator))
{
return new Fraction(numerator, 100);
}
else
{
int decimalPos = inValue.IndexOf(info.CurrencyDecimalSeparator);
if (decimalPos > -1)
return new Fraction(Convert.ToDouble(inValue));
else
return new Fraction(Convert.ToInt64(inValue));
}
}
}
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Your program fails when taking a square root as an argument. For example,
Mehroz.Fraction f1 = new Mehroz.Fraction(Math.Sqrt(2));
will cause an OverflowException. So my suggestion is: allow square roots to be entered. The "ToString" override in the Fraction class could be rewritten to return this (for the above example):
√2
Regards,
Mike
modified 25-Jul-12 13:45pm.
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Got an email from Krzysztof Kniaz[^]. He has written the following NUnit tests to test this. Thanks Knaiz.
using System;
using System.Globalization;
using NUnit.Framework;
using Mehroz;
namespace TestFraction
{
[TestFixture()]
public class TestFraction
{
[Test()]
public void NaN()
{
Fraction frac=new Fraction();
Assert.AreEqual(Fraction.NaN,frac);
Assert.AreEqual(NumberFormatInfo.CurrentInfo.NaNSymbol, frac.ToString());
}
[Test()]
public void OneFifth()
{
Fraction frac = new Fraction(1,5);
Assert.AreEqual("1/5", frac.ToString());
}
[Test()]
public void TwentyFive()
{
Fraction frac=new Fraction(25);
Assert.AreEqual("25", frac.ToString());
}
[Test()]
public void Zero()
{
Fraction frac = new Fraction(0, 0);
Assert.AreEqual("NaN", frac.ToString());
}
[Test()]
public void OneFourthFromDecimal()
{
Fraction frac = new Fraction(0.25);
Assert.AreEqual("1/4", frac.ToString());
}
[Test()]
public void ThirtySevenFourthsFromDecimal()
{
Fraction frac = new Fraction(9.25);
Assert.AreEqual("37/4", frac.ToString());
}
[Test()]
public void LongMaxValDivbyZero()
{
Fraction frac = new Fraction(1, long.MaxValue);
string compareTo = string.Format("1/{0}", long.MaxValue);
Assert.AreEqual(compareTo, frac.ToString());
}
[Test()]
public void LongMaxVal()
{
Fraction frac = new Fraction(long.MaxValue, 1);
string compareTo = string.Format("{0}", long.MaxValue);
Assert.AreEqual(compareTo,frac.ToString());
}
[Test()]
public void TwoPlusOneIssue()
{
Fraction frac = new Fraction(long.MinValue + 1, 1);
string compareTo = string.Format("{0}", long.MinValue + 1);
Assert.AreEqual(compareTo, frac.ToString());
}
[Test()]
public void LongMaxbyLongMax()
{
Fraction frac = new Fraction(long.MaxValue, long.MaxValue);
Assert.AreEqual("1",frac.ToString());
}
[Test()]
public void LongMinPlusOne()
{
Fraction frac = new Fraction(1, long.MinValue + 1);
string compareTo = string.Format("-1/{0}", Math.Abs(long.MinValue + 1));
Assert.AreEqual(compareTo,frac.ToString());
}
[Test()]
public void LongMinByLongMin()
{
Fraction frac = new Fraction(long.MinValue + 1, long.MinValue + 1);
Assert.AreEqual("1",frac.ToString());
}
[Test()]
public void LongMaxByLongMinMinusOne()
{
Fraction frac=new Fraction(long.MaxValue, long.MinValue + 1);
Assert.AreEqual("-1", frac.ToString());
}
[Test()]
public void LongMinPlusOneByLongMax()
{
Fraction frac = new Fraction(long.MinValue + 1, long.MaxValue);
Assert.AreEqual("-1", frac.ToString());
}
[Test()]
public void OneFourthieth()
{
Fraction frac = new Fraction(0.025);
Assert.AreEqual("1/40",frac.ToString());
}
[Test()]
public void HalfFromFractionalTwo()
{
Fraction frac = new Fraction(1 / 2.0);
Assert.AreEqual("1/2",frac.ToString() );
}
[Test()]
public void ThirdFromFractionalThree()
{
Fraction frac = new Fraction(1 / 3.0);
Assert.AreEqual("1/3", frac.ToString());
}
[Test()]
public void QuarterFromFractionalFour()
{
Fraction frac = new Fraction(1 / 4.0);
Assert.AreEqual("1/4",frac.ToString());
}
[Test()]
public void FifthFromFractionalFive()
{
Fraction frac = new Fraction(1 / 5.0);
Assert.AreEqual("1/5", frac.ToString());
}
[Test()]
public void SixthFromFractionalSix()
{
Fraction frac = new Fraction(1 / 6.0);
Assert.AreEqual("1/6",frac.ToString());
}
[Test()]
public void SeventhFromFractionalSeven()
{
Fraction frac = new Fraction(1 / 7.0);
Assert.AreEqual("1/7",frac.ToString());
}
[Test()]
public void EigthFromFractionalEigt()
{
Fraction frac = new Fraction(1 / 8.0);
Assert.AreEqual("1/8", frac.ToString());
}
[Test()]
public void NinethFromFractionalNine()
{
Fraction frac = new Fraction(1 / 9.0);
Assert.AreEqual("1/9",frac.ToString());
}
[Test()]
public void TenthFromFractionalTen()
{
Fraction frac = new Fraction(1 / 10.0);
Assert.AreEqual("1/10",frac.ToString());
}
[Test()]
public void FourthyNinethFromFractional49()
{
Fraction frac = new Fraction(1 / 49.0);
Assert.AreEqual("1/49",frac.ToString());
}
[Test()]
public void SixFromIntSix()
{
Fraction frac = new Fraction(6);
Assert.AreEqual("6", frac.ToString() );
}
[Test()]
public void FourFromIntFour()
{
Fraction frac = new Fraction(4);
Assert.AreEqual("4",frac.ToString());
}
[Test()]
public void Modulo2()
{
Fraction frac = new Fraction(6);
Fraction divisor = new Fraction(4);
frac %= divisor;
Assert.AreEqual("2",frac.ToString() );
}
[Test()]
public void FractionalDivision1()
{
Fraction frac = new Fraction(9,4);
Fraction divisor = new Fraction(2);
frac %= divisor;
Assert.AreEqual("1/4",frac.ToString());
}
[Test()]
public void FractionalDivision2()
{
Fraction frac = new Fraction(5, 12);
Fraction divisor = new Fraction(1,4);
frac %= divisor;
Assert.AreEqual("1/6",frac.ToString());
}
[Test()]
public void FromDecimal1()
{
Fraction frac = new Fraction(1.0);
Assert.AreEqual("1",frac.ToString() );
}
[Test()]
public void FromDecimal2()
{
Fraction frac = new Fraction(2.0);
Assert.AreEqual("2",frac.ToString());
}
[Test()]
public void FromDecimalMinus2()
{
Fraction frac = new Fraction(-2.0);
Assert.AreEqual("-2",frac.ToString());
}
[Test()]
public void FromDecimalMinus1()
{
Fraction frac = new Fraction(-1.0);
Assert.AreEqual("-1",frac.ToString() );
}
[Test()]
public void HalfFromDecimal()
{
Fraction frac = new Fraction(0.5);
Assert.AreEqual("1/2",frac.ToString() );
}
[Test()]
public void OneAndHalfFromDecimal()
{
Fraction frac = new Fraction(1.5);
Assert.AreEqual("3/2",frac.ToString());
}
[Test()]
public void LoopCheck()
{
for (int numerator = -100; numerator < 100; numerator++)
{
for (int denominator = -100; denominator < 100; denominator++)
{
Fraction frac1 = new Fraction(numerator, denominator);
double dbl = (double)numerator / (double)denominator;
Fraction frac2 = new Fraction(dbl);
Assert.AreEqual(frac2,frac1);
}
}
}
[Test()]
public void SixandQuarter()
{
Fraction frac = new Fraction("6.25");
Assert.AreEqual("25/4", frac.ToString());
}
[Test()]
public void AssignZero()
{
Fraction frac = new Fraction("0.5");
frac = 0;
Assert.AreEqual("0", frac.ToString() );
}
[Test()]
public void AssignOne()
{
Fraction frac = new Fraction("0.5");
frac = 1;
Assert.AreEqual("1", frac.ToString() );
}
[Test()]
public void PositiveInfinity()
{
Fraction frac = new Fraction("2");
frac /= new Fraction(0);
Assert.AreEqual(Fraction.PositiveInfinity, frac);
}
[Test()]
public void NegativeInfinity()
{
Fraction frac = new Fraction("-1");
frac /= new Fraction(0);
Assert.AreEqual(Fraction.NegativeInfinity, frac);
}
[Test()]
public void Addition()
{
Fraction frac = new Fraction("1/2");
frac += new Fraction(2.5);
Assert.AreEqual("3", frac.ToString());
}
[Test()]
public void Deduction()
{
Fraction frac = new Fraction(0.5);
frac -= new Fraction("1/4");
Assert.AreEqual("1/4", frac.ToString());
}
[Test()]
public void Equation1()
{
Fraction frac = new Fraction("1/2");
Assert.IsFalse(frac.Equals(0.5));
}
[Test()]
public void Equation2()
{
Fraction frac = new Fraction("1/2");
Fraction frac1 = new Fraction(0.5);
bool stmtm = frac==frac1;
Assert.IsTrue(stmtm);
}
[Test()]
public void Multiplication()
{
Fraction frac = new Fraction("1/3");
frac *= 3;
Assert.AreEqual("1", frac.ToString());
}
[Test()]
public void Division()
{
Fraction frac = new Fraction("1/3");
frac /= 15;
Assert.AreEqual("1/45", frac.ToString());
}
[Test()]
public void ImplicitCast1()
{
Fraction frac = new Fraction();
frac = "1/2";
Assert.AreEqual("1/2", frac.ToString());
}
[Test()]
public void ImplicitCast2()
{
Fraction frac = new Fraction();
frac = "22.5";
Assert.AreEqual("45/2", frac.ToString());
}
[Test()]
public void ImplicitCast3()
{
Fraction frac = new Fraction();
frac = 10.25;
Assert.AreEqual("41/4", frac.ToString());
}
[Test()]
public void ImplicitCast4()
{
Fraction frac = new Fraction();
frac = 15;
Assert.AreEqual("15", frac.ToString());
}
[Test()]
public void DoubleNan()
{
Fraction frac = new Fraction();
frac = double.NaN;
Assert.AreEqual(NumberFormatInfo.CurrentInfo.NaNSymbol,frac.ToString());
}
[Test()]
public void DoublePositiveInfinity()
{
Fraction frac = new Fraction();
frac = double.PositiveInfinity;
Assert.AreEqual(NumberFormatInfo.CurrentInfo.PositiveInfinitySymbol,frac.ToString());
}
[Test()]
public void DoubleNegativeInfinity()
{
Fraction frac = new Fraction();
frac = double.NegativeInfinity;
Assert.AreEqual(NumberFormatInfo.CurrentInfo.NegativeInfinitySymbol, frac.ToString());
}
}
}
Regards,Syed Mehroz Alam
My Blog | My Articles
Computers are incredibly fast, accurate, and stupid; humans are incredibly slow, inaccurate and brilliant; together they are powerful beyond imagination. - Albert Einstein
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anhld
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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[^]
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Hey, I needed a fraction class that would display things like "1 1/2" and such, instead of showing it as 3/2.
A quick change to the ToSting() function provides this. Certainly not the best solution, but it was quick and it does what I needed. Great class all around though.
public override string ToString()
{
if (this.m_Denominator == 1)
{
return this.m_Numerator.ToString();
}
else if (this.m_Denominator == 0)
{
return IndeterminateTypeName(this.m_Numerator);
}
else
{
if (this.m_Numerator > this.m_Denominator)
{
long div = this.m_Numerator / this.m_Denominator;
float rem = (float)this.m_Numerator / (float)this.m_Denominator - (float)div;
return div.ToString() + " " + new Fraction(rem).ToString();
}
else
{
return this.m_Numerator.ToString() + "/" + this.m_Denominator.ToString();
}
}
}
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Okay... that's what I get for posting before thinking. The last version introduced potential rounding problems... but using the following instead solves that.
<code>if (this.m_Numerator > this.m_Denominator)
{
long div = this.m_Numerator / this.m_Denominator;
Fraction rem = new Fraction(this.m_Numerator - (div*this.m_Denominator),this.m_Denominator);
return div.ToString() + " " + rem.ToString();
}</code>
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Why not just encapsulate that method in a different method name?
ToMixedNumber()
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I've put the mixed fraction formatting in the IFormattable.ToString(…).
string IFormattable.ToString(string format, IFormatProvider formatProvider) {
this.Reduce();
switch (format)
{
case "mixed":
long wholeInteger = this.Numerator / this.Denominator;
long properNumerator = Math.Abs(this.Numerator % this.Denominator);
StringBuilder result = new StringBuilder(32);
if (wholeInteger != 0) {
result.Append(String.Format("{0} ", wholeInteger));
}
result.Append(String.Format("{0}/{1}", properNumerator, this.Denominator));
return result.ToString();
default:
return String.Format("{0}/{1}", m_numerator, m_denominator);
};
}
Just my $0.02
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this is a very good class. and i used it in my graduation project but do u have the c++ version or do u know any other jordan gaussian class but in c++
Mina Momtaz
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An old coworker reported an error to me when doing a comparison of 14/5 and 20/1 would yeild the wrong result. For some stupid reason, I was doing a CrossReducePair (which is only safe when doing multiplication; comparisons are subtraction). Replace that method with this corrected version.
public int CompareTo(Fraction right)
{
if (this.m_Denominator == 0)
{
return IndeterminantCompare(NormalizeIndeterminate(this.m_Numerator), right);
}
if (right.m_Denominator == 0)
{
return - IndeterminantCompare(NormalizeIndeterminate(right.m_Numerator), this);
}
right.m_Numerator = -right.m_Numerator;
Fraction difference = Add(this, right);
if (difference.m_Numerator < 0)
return -1;
else if (difference.m_Numerator > 0)
return 1;
else
return 0;
}Sorry...
-- modified at 13:28 Wednesday 9th November, 2005
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 Thanks for this class! I needed something like this just the other day. I incorporated my needs and the changes suggested by Jeffery Sax.
It avoids most 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]
Reorganize code, add 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]
Due to limitations of the CodeProject message system, the XML docs have been stripped. If you want a copy of the revised class, just e-mail me
Here's the revised Fraction.cs class.
using System;
using System.Globalization;
namespace Mehroz
{
public struct Fraction
{
#region Constructors
public Fraction(long wholeNumber)
{
m_Numerator = wholeNumber;
m_Denominator = 1;
}
public Fraction(double floatingPointNumber)
{
this = ToFraction(floatingPointNumber);
}
public Fraction(string inValue)
{
this = ToFraction(inValue);
}
public Fraction(long numerator, long denominator)
{
m_Numerator = numerator;
m_Denominator = denominator;
ReduceFraction(ref this);
}
private Fraction(Indeterminates type)
{
m_Denominator = 0;
m_Numerator = (long)type;
}
#endregion
#region Properties
public long Numerator
{
get
{
return m_Numerator;
}
set
{
m_Numerator = value;
}
}
public long Denominator
{
get
{
return m_Denominator;
}
set
{
m_Denominator = value;
}
}
#endregion
#region Explicit conversions
#region To primitives
public Int32 ToInt32()
{
if (this.Denominator == 0)
{
throw new FractionException(string.Format("Cannot convert {0} to Int32", IndeterminateTypeName(this.Numerator)), new System.NotFiniteNumberException());
}
long bestGuess = this.Numerator / this.Denominator;
if (bestGuess > Int32.MaxValue || bestGuess < Int32.MinValue)
{
throw new FractionException("Cannot convert to Int32", new System.OverflowException());
}
return (Int32)bestGuess;
}
public Int64 ToInt64()
{
if (this.Denominator == 0)
{
throw new FractionException(string.Format("Cannot convert {0} to Int64", IndeterminateTypeName(this.Numerator)), new System.NotFiniteNumberException());
}
return this.Numerator / this.Denominator;
}
public double ToDouble()
{
if (this.Denominator == 1)
return this.Numerator;
else if (this.Denominator == 0)
{
switch (NormalizeIndeterminate(this.Numerator))
{
case Indeterminates.NegativeInfinity:
return double.NegativeInfinity;
case Indeterminates.PositiveInfinity:
return double.PositiveInfinity;
case Indeterminates.NaN:
default:
return double.NaN;
}
}
else
{
return (double)this.Numerator / (double)this.Denominator;
}
}
public override string ToString()
{
if (this.Denominator == 1)
{
return this.Numerator.ToString();
}
else if (this.Denominator == 0)
{
return IndeterminateTypeName(this.Numerator);
}
else
{
return this.Numerator.ToString() + "/" + this.Denominator.ToString();
}
}
#endregion
#region From primitives
public static Fraction ToFraction(long inValue)
{
return new Fraction(inValue);
}
public static Fraction ToFraction(double inValue)
{
if (double.IsNegativeInfinity(inValue))
{
return new Fraction(Indeterminates.NegativeInfinity);
}
else if (double.IsPositiveInfinity(inValue))
{
return new Fraction(Indeterminates.PositiveInfinity);
}
else if (double.IsNaN(inValue))
{
return new Fraction(Indeterminates.NaN);
}
else if (inValue % 1 == 0)
{
return new Fraction((Int64) inValue);
}
else
{
try
{
checked
{
int sign = Math.Sign(inValue);
double numerator = Math.Abs(inValue);
long inScale = (long)Math.Log(numerator, 2);
double denominator = Math.Pow(2, Math.Abs(inScale));
return new Fraction((long)Math.Round(numerator * denominator * sign), (long)Math.Floor(denominator));
}
}
catch (Exception e)
{
throw new FractionException("Assigned from double", e);
}
}
}
public static Fraction ToFraction(string inValue)
{
if (inValue == null)
throw new ArgumentNullException("inValue");
NumberFormatInfo info = NumberFormatInfo.CurrentInfo;
string trimmedValue = inValue.Trim();
if (trimmedValue == info.NaNSymbol)
return new Fraction(Indeterminates.NaN);
else if (trimmedValue == info.PositiveInfinitySymbol)
return new Fraction(Indeterminates.PositiveInfinity);
else if (trimmedValue == info.NegativeInfinitySymbol)
return new Fraction(Indeterminates.NegativeInfinity);
else
{
int slashPos = inValue.IndexOf('/');
if (slashPos > -1)
{
long numerator = Convert.ToInt64(inValue.Substring(0, slashPos));
long denominator = Convert.ToInt64(inValue.Substring(slashPos + 1));
return new Fraction(numerator, denominator);
}
else
{
int decimalPos = inValue.IndexOf(info.CurrencyDecimalSeparator);
if (decimalPos > -1)
return new Fraction(Convert.ToDouble(inValue));
else
return new Fraction(Convert.ToInt64(inValue));
}
}
}
#endregion
#endregion
#region Indeterminate classifications
public bool IsNaN()
{
if (this.Denominator == 0
&& NormalizeIndeterminate(this.Numerator) == Indeterminates.NaN)
return true;
else
return false;
}
public bool IsPositiveInfinity()
{
if (this.Denominator == 0
&& NormalizeIndeterminate(this.Numerator) == Indeterminates.PositiveInfinity)
return true;
else
return false;
}
public bool IsNegativeInfinity()
{
if (this.Denominator == 0
&& NormalizeIndeterminate(this.Numerator) == Indeterminates.NegativeInfinity)
return true;
else
return false;
}
#endregion
#region Inversion
public Fraction Inverse()
{
Fraction frac = new Fraction();
frac.Numerator = this.Denominator;
frac.Denominator = this.Numerator;
return frac;
}
public static Fraction Inverted(long value)
{
Fraction frac = new Fraction(value);
return frac.Inverse();
}
public static Fraction Inverted(double value)
{
Fraction frac = new Fraction(value);
return frac.Inverse();
}
#endregion
#region Operators
#region Unary Negation operator
public static Fraction operator -(Fraction left)
{
return Negate(left);
}
#endregion
#region Addition operators
public static Fraction operator +(Fraction left, Fraction right)
{
return Add(left, right);
}
public static Fraction operator +(long left, Fraction right)
{
return Add(new Fraction(left), right);
}
public static Fraction operator +(Fraction left, long right)
{
return Add(left, new Fraction(right));
}
public static Fraction operator +(double left, Fraction right)
{
return Add(ToFraction(left), right);
}
public static Fraction operator +(Fraction left, double right)
{
return Add(left, ToFraction(right));
}
#endregion
#region Subtraction operators
public static Fraction operator -(Fraction left, Fraction right)
{
return Add(left, - right);
}
public static Fraction operator -(long left, Fraction right)
{
return Add(new Fraction(left), - right);
}
public static Fraction operator -(Fraction left, long right)
{
return Add(left, new Fraction(- right));
}
public static Fraction operator -(double left, Fraction right)
{
return Add(ToFraction(left), - right);
}
public static Fraction operator -(Fraction left, double right)
{
return Add(left, ToFraction(- right));
}
#endregion
#region Multiplication operators
public static Fraction operator *(Fraction left, Fraction right)
{
return Multiply(left, right);
}
public static Fraction operator *(long left, Fraction right)
{
return Multiply(new Fraction(left), right);
}
public static Fraction operator *(Fraction left, long right)
{
return Multiply(left, new Fraction(right));
}
public static Fraction operator *(double left, Fraction right)
{
return Multiply(ToFraction(left), right);
}
public static Fraction operator *(Fraction left, double right)
{
return Multiply(left, ToFraction(right));
}
#endregion
#region Division operators
public static Fraction operator /(Fraction left, Fraction right)
{
return Multiply(left, right.Inverse());
}
public static Fraction operator /(long left, Fraction right)
{
return Multiply(new Fraction(left), right.Inverse());
}
public static Fraction operator /(Fraction left, long right)
{
return Multiply(left, Inverted(right));
}
public static Fraction operator /(double left, Fraction right)
{
return Multiply(ToFraction(left), right.Inverse());
}
public static Fraction operator /(Fraction left, double right)
{
return Multiply(left, Inverted(right));
}
#endregion
#region Equal operators
public static bool operator ==(Fraction left, Fraction right)
{
return left.Equals(right);
}
public static bool operator ==(Fraction left, long right)
{
return left.Equals(new Fraction(right));
}
public static bool operator ==(Fraction left, double right)
{
return left.Equals(new Fraction(right));
}
#endregion
#region Not-equal operators
public static bool operator !=(Fraction left, Fraction right)
{
return ! left.Equals(right);
}
public static bool operator !=(Fraction left, long right)
{
return ! left.Equals(new Fraction(right));
}
public static bool operator !=(Fraction left, double right)
{
return ! left.Equals(new Fraction(right));
}
#endregion
#region Inequality operators
public static bool operator <(Fraction left, Fraction right)
{
if (left.Denominator == 0)
{
return IndeterminantLess(NormalizeIndeterminate(left.Numerator), right);
}
if (right.Denominator == 0)
{
return (NormalizeIndeterminate(right.Numerator) == Indeterminates.PositiveInfinity);
}
CrossReducePair(ref left, ref right);
try
{
checked
{
long leftScale = left.Numerator * right.Denominator;
long rightScale = left.Denominator * right.Numerator;
return leftScale < rightScale;
}
}
catch (Exception e)
{
throw new FractionException("Compare < error", e);
}
}
public static bool operator >(Fraction left, Fraction right)
{
if (right.Denominator == 0)
{
return IndeterminantLess(NormalizeIndeterminate(right.Numerator), left);
}
if (left.Denominator == 0)
{
return (NormalizeIndeterminate(left.Numerator) == Indeterminates.PositiveInfinity);
}
CrossReducePair(ref left, ref right);
try
{
checked
{
long leftScale = left.Numerator * right.Denominator;
long rightScale = left.Denominator * right.Numerator;
return leftScale > rightScale;
}
}
catch (Exception e)
{
throw new FractionException("Compare > error", e);
}
}
public static bool operator <=(Fraction left, Fraction right)
{
return ! (right > left);
}
public static bool operator >=(Fraction left, Fraction right)
{
return ! (right < left);
}
#endregion
#region Implict conversion from primitive operators
public static implicit operator Fraction(long value)
{
return new Fraction(value);
}
public static implicit operator Fraction(double value)
{
return new Fraction(value);
}
public static implicit operator Fraction(string value)
{
return new Fraction(value);
}
#endregion
#region Explicit converstion to primitive operators
public static explicit operator int(Fraction frac)
{
return frac.ToInt32();
}
public static explicit operator long(Fraction frac)
{
return frac.ToInt64();
}
public static explicit operator double(Fraction frac)
{
return frac.ToDouble();
}
public static implicit operator string(Fraction frac)
{
return frac.ToString();
}
#endregion
#endregion
#region Equals and GetHashCode overrides
public override bool Equals(object obj)
{
if (obj == null)
return false;
try
{
Fraction frac;
if (obj is Fraction)
frac = (Fraction)obj;
else if (obj is long)
frac = new Fraction((long)obj);
else if (obj is int)
frac = new Fraction((int)obj);
else if (obj is double)
frac = new Fraction((double)obj);
else if (obj is float)
frac = new Fraction((float)obj);
else if (obj is string)
frac = new Fraction((string)obj);
else
return false;
ReduceFraction(ref this);
ReduceFraction(ref frac);
return (this.Numerator == frac.Numerator && this.Denominator == frac.Denominator);
}
catch
{
return false;
}
}
public override int GetHashCode()
{
ReduceFraction(ref this);
return Convert.ToInt32((Numerator ^ Denominator) & 0xFFFFFFFF);
}
#endregion
#region Reduction
public static void ReduceFraction(ref Fraction frac)
{
if (frac.Denominator == 0)
{
frac.Numerator = (long)NormalizeIndeterminate(frac.Numerator);
return;
}
if (frac.Numerator == 0)
{
frac.Denominator = 1;
return;
}
long iGCD = GCD(frac.Numerator, frac.Denominator);
frac.Numerator /= iGCD;
frac.Denominator /= iGCD;
if ( frac.Denominator < 0 )
{
frac.Numerator = - frac.Numerator;
frac.Denominator = - frac.Denominator;
}
}
public static void CrossReducePair(ref Fraction frac1, ref Fraction frac2)
{
if (frac1.Denominator == 0 || frac2.Denominator == 0)
return;
long gcdTop = GCD(frac1.Numerator, frac2.Denominator);
frac1.Numerator = frac1.Numerator / gcdTop;
frac2.Denominator = frac2.Denominator / gcdTop;
long gcdBottom = GCD(frac1.Denominator, frac2.Numerator);
frac2.Numerator = frac2.Numerator / gcdBottom;
frac1.Denominator = frac1.Denominator / gcdBottom;
}
#endregion
#region Implementation
#region Inequality helper
private static bool IndeterminantLess(Indeterminates frac1Type, Fraction frac2)
{
switch (frac1Type)
{
case Indeterminates.NaN:
return ! (frac2.IsNaN() || frac2.IsNegativeInfinity());
case Indeterminates.NegativeInfinity:
return ! frac2.IsNegativeInfinity();
case Indeterminates.PositiveInfinity:
return false;
default:
return false;
}
}
#endregion
#region Math helpers
private static Fraction Negate(Fraction frac)
{
return new Fraction( - frac.Numerator, frac.Denominator);
}
private static Fraction Add(Fraction left, Fraction right)
{
long gcd = GCD(left.Denominator, right.Denominator);
long leftDenominator = left.Denominator / gcd;
long rightDenominator = right.Denominator / gcd;
try
{
checked
{
if (left.IsNaN() || right.IsNaN())
throw new ArithmeticException("Not-a-Number");
long numerator = left.Numerator * rightDenominator + right.Numerator * leftDenominator;
long denominator = leftDenominator * rightDenominator * gcd;
return new Fraction(numerator, denominator);
}
}
catch (Exception e)
{
throw new FractionException("Add error", e);
}
}
private static Fraction Multiply(Fraction left, Fraction right)
{
CrossReducePair(ref left, ref right);
try
{
checked
{
if (left.IsNaN() || right.IsNaN())
throw new ArithmeticException("Not-a-Number");
long numerator = left.Numerator * right.Numerator;
long denominator = left.Denominator * right.Denominator;
return new Fraction(numerator, denominator);
}
}
catch (Exception e)
{
throw new FractionException("Multiply error", e);
}
}
private static long GCD(long left, long right)
{
if (left < 0)
left = - left;
if (right < 0)
right = - right;
if (left < 2 || right < 2)
return 1;
do
{
if (left < right)
{
long temp = left;
left = right;
right = temp;
}
left %= right;
} while (left != 0);
return right;
}
#endregion
#region Indeterminate helpers
private static string IndeterminateTypeName(long numerator)
{
System.Globalization.NumberFormatInfo info = NumberFormatInfo.CurrentInfo;
switch (NormalizeIndeterminate(numerator))
{
case Indeterminates.PositiveInfinity:
return info.PositiveInfinitySymbol;
case Indeterminates.NegativeInfinity:
return info.NegativeInfinitySymbol;
default:
case Indeterminates.NaN:
return info.NaNSymbol;
}
}
private static Indeterminates NormalizeIndeterminate(long numerator)
{
switch (Math.Sign(numerator))
{
case 1:
return Indeterminates.PositiveInfinity;
case -1:
return Indeterminates.NegativeInfinity;
default:
case 0:
return Indeterminates.NaN;
}
}
#endregion
private long m_Numerator;
private long m_Denominator;
private enum Indeterminates
{
NaN = 0
, PositiveInfinity = 1
, NegativeInfinity = -1
}
#endregion
}
public class FractionException : Exception
{
public FractionException(string Message, Exception InnerException) : base(Message, InnerException)
{
}
}
}
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Thank you very much for your nice work. You saved me from rewriting all the code again (taking into account all the suggestions by Jeffrey). I wrote such a simple and in-efficient(in many cases) class because all I wanted to do, was to write a matrix class using fractions so that I can verify my answers to questions of linear algebra.
Congratulations on your nice work.
Thanks,
Syed Mehroz Alam
Email: smehrozalam@yahoo.com
Homepage: Programming Home
URL: http://www.geocities.com/smehrozalam/
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Interesting implementation of 'indeterminates.' Maybe 'special values' would have been a better name. Infinities are quite determined. There are a few things you should be aware of, however:- Operations on
NaNs do not throw exceptions. Instead, so the IEEE-754 standard for binary floating-point arithmetic[^] states, the return value should be once again NaN.
On that same note, you need to handle the special case that NaN != NaN is true. In fact, this is the only logical operation with a NaN operand that doesn't return false. - To be consistent with the rest of the Base Class Libraries, you may want to make these special values available as static readonly fields of the type. You may also want to add the related static methods defined in
Double, like IsPositiveInfinity, etc. - Your implementation of
Equals still doesn't comply with standard practices, although this is not stated as clearly as it should. Equals is used for object equality, and so should return false if the object being compared is not of type Fraction. Instead, the code in your Equals method belongs in a static, type safe Compare method that behaves like the Compare method of the IComparer interface. All logical operators should call this same method, or a st.
See the Shared Source CLI[^] for details. - The conversion from
Double can be made simpler by decoding the 64 bit floating-point number. The binary layout is fixed by the CLI standard as that of IEEE-754 double-precision numbers, so it is safe to do this. The way to do this would be to use BitConverter.DoubleToInt64Bits to obtain a usable binary representation, and then move some bits around. This method is guaranteed to work, and is much faster than using Math.Log and Math.Pow.
You've added a lot of value to this class. Well done!
Jeffrey
Everything should be as simple as possible, but not simpler.
-- Albert Einstein
Numerical components for C# and VB.NET
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Jeffrey Sax wrote:
Operations on NaNs do not throw exceptions. Instead, so the IEEE-754 standard for binary floating-point arithmetic[^] states, the return value should be once again NaN.
Done. Changed Add and Multiply methods (used for all operations) to return NaN for operations involving left or right of NaN.
On that same note, you need to handle the special case that NaN != NaN is true. In fact, this is the only logical operation with a NaN operand that doesn't return false.
Done. Added a helper for comparing equality of two Fractions, made == and != call down to it. Double returns true from Equals if both values are NaN, so I do too.
Your implementation of Equals still doesn't comply with standard practices, although this is not stated as clearly as it should. Equals is used for object equality, and so should return false if the object being compared is not of type Fraction.
Done. The override now returns false for non-Fraction right-side, otherwise calls the new helper. Since Fraction is a value type, I wonder what object equality means in this case, so I just compare for same values after reduction.
Instead, the code in your Equals method belongs in a static, type safe Compare method that behaves like the Compare method of the IComparer interface. All logical operators should call this same method
Done. Added ICompare.CompareTo method. Since this is a value-type I made it handle the automatic conversions as appropriate. All the operator comparisons now use the type-safe CompareTo method (and internal helpers)
To be consistent with the rest of the Base Class Libraries, you may want to make these special values available as static readonly fields of the type
Done. Added Fraction.NaN, Fraction.PositiveInfinity and Fraction.NegativeInfinity. Also added MinValue, MaxValue and Epsilon. Also added Zero to deal with the issue of no-default constructor for structs (because it's a NaN otherwise).
You may also want to add the related static methods defined in Double, like IsPositiveInfinity, etc.
Those were already there. :grin: I did add IsInfinity
I also fixed the issues this code had with imprecise doubles (repeating decimals). I'm now using the repeating fraction logic I found here which does as good a job as possible and is relatively quick.
Here's the revised code:
using System;
using System.Runtime.InteropServices;
using System.Globalization;
namespace Mehroz
{
[Serializable, StructLayout(LayoutKind.Sequential)]
public struct Fraction : IComparable, IFormattable
{
#region Constructors
public Fraction(long wholeNumber)
{
if (wholeNumber == long.MinValue)
wholeNumber++;
m_Numerator = wholeNumber;
m_Denominator = 1;
}
public Fraction(double floatingPointNumber)
{
this = ToFraction(floatingPointNumber);
}
public Fraction(string inValue)
{
this = ToFraction(inValue);
}
public Fraction(long numerator, long denominator)
{
if (numerator == long.MinValue)
numerator++;
if (denominator == long.MinValue)
denominator++;
m_Numerator = numerator;
m_Denominator = denominator;
ReduceFraction(ref this);
}
private Fraction(Indeterminates type)
{
m_Numerator = (long)type;
m_Denominator = 0;
}
#endregion
#region Properties
public long Numerator
{
get
{
return m_Numerator;
}
set
{
m_Numerator = value;
}
}
public long Denominator
{
get
{
return m_Denominator;
}
set
{
m_Denominator = value;
}
}
#endregion
#region Expose constants
public static readonly Fraction NaN = new Fraction(Indeterminates.NaN);
public static readonly Fraction PositiveInfinity = new Fraction(Indeterminates.PositiveInfinity);
public static readonly Fraction NegativeInfinity = new Fraction(Indeterminates.NegativeInfinity);
public static readonly Fraction Zero = new Fraction(0,1);
public static readonly Fraction Epsilon = new Fraction(1, Int64.MaxValue);
private static readonly double EpsilonDouble = 1.0 / Int64.MaxValue;
public static readonly Fraction MaxValue = new Fraction(Int64.MaxValue, 1);
public static readonly Fraction MinValue = new Fraction(Int64.MinValue, 1);
#endregion
#region Explicit conversions
#region To primitives
public Int32 ToInt32()
{
if (this.m_Denominator == 0)
{
throw new FractionException(string.Format("Cannot convert {0} to Int32", IndeterminateTypeName(this.m_Numerator)), new System.NotFiniteNumberException());
}
long bestGuess = this.m_Numerator / this.m_Denominator;
if (bestGuess > Int32.MaxValue || bestGuess < Int32.MinValue)
{
throw new FractionException("Cannot convert to Int32", new System.OverflowException());
}
return (Int32)bestGuess;
}
public Int64 ToInt64()
{
if (this.m_Denominator == 0)
{
throw new FractionException(string.Format("Cannot convert {0} to Int64", IndeterminateTypeName(this.m_Numerator)), new System.NotFiniteNumberException());
}
return this.m_Numerator / this.m_Denominator;
}
public double ToDouble()
{
if (this.m_Denominator == 1)
return this.m_Numerator;
else if (this.m_Denominator == 0)
{
switch (NormalizeIndeterminate(this.m_Numerator))
{
case Indeterminates.NegativeInfinity:
return double.NegativeInfinity;
case Indeterminates.PositiveInfinity:
return double.PositiveInfinity;
case Indeterminates.NaN:
default:
return double.NaN;
}
}
else
{
return (double)this.m_Numerator / (double)this.m_Denominator;
}
}
public override string ToString()
{
if (this.m_Denominator == 1)
{
return this.m_Numerator.ToString();
}
else if (this.m_Denominator == 0)
{
return IndeterminateTypeName(this.m_Numerator);
}
else
{
return this.m_Numerator.ToString() + "/" + this.m_Denominator.ToString();
}
}
#endregion
#region From primitives
public static Fraction ToFraction(long inValue)
{
return new Fraction(inValue);
}
public static Fraction ToFraction(double inValue)
{
if (double.IsNaN(inValue))
return NaN;
else if (double.IsNegativeInfinity(inValue))
return NegativeInfinity;
else if (double.IsPositiveInfinity(inValue))
return PositiveInfinity;
else if (inValue == 0.0d)
return Zero;
if (inValue > Int64.MaxValue)
throw new OverflowException(string.Format("Double {0} too large", inValue));
if (inValue < -Int64.MaxValue)
throw new OverflowException(string.Format("Double {0} too small", inValue));
if (-EpsilonDouble < inValue && inValue < EpsilonDouble)
throw new ArithmeticException(string.Format("Double {0} cannot be represented", inValue));
int sign = Math.Sign(inValue);
inValue = Math.Abs(inValue);
return ConvertPositiveDouble(sign, inValue);
}
public static Fraction ToFraction(string inValue)
{
if (inValue == null || inValue == string.Empty)
throw new ArgumentNullException("inValue");
NumberFormatInfo info = NumberFormatInfo.CurrentInfo;
string trimmedValue = inValue.Trim();
if (trimmedValue == info.NaNSymbol)
return NaN;
else if (trimmedValue == info.PositiveInfinitySymbol)
return PositiveInfinity;
else if (trimmedValue == info.NegativeInfinitySymbol)
return NegativeInfinity;
else
{
int slashPos = inValue.IndexOf('/');
if (slashPos > -1)
{
long numerator = Convert.ToInt64(inValue.Substring(0, slashPos));
long denominator = Convert.ToInt64(inValue.Substring(slashPos + 1));
return new Fraction(numerator, denominator);
}
else
{
int decimalPos = inValue.IndexOf(info.CurrencyDecimalSeparator);
if (decimalPos > -1)
return new Fraction(Convert.ToDouble(inValue));
else
return new Fraction(Convert.ToInt64(inValue));
}
}
}
#endregion
#endregion
#region Indeterminate classifications
public bool IsNaN()
{
if (this.m_Denominator == 0
&& NormalizeIndeterminate(this.m_Numerator) == Indeterminates.NaN)
return true;
else
return false;
}
public bool IsInfinity()
{
if (this.m_Denominator == 0
&& NormalizeIndeterminate(this.m_Numerator) != Indeterminates.NaN)
return true;
else
return false;
}
public bool IsPositiveInfinity()
{
if (this.m_Denominator == 0
&& NormalizeIndeterminate(this.m_Numerator) == Indeterminates.PositiveInfinity)
return true;
else
return false;
}
public bool IsNegativeInfinity()
{
if (this.m_Denominator == 0
&& NormalizeIndeterminate(this.m_Numerator) == Indeterminates.NegativeInfinity)
return true;
else
return false;
}
#endregion
#region Inversion
public Fraction Inverse()
{
Fraction frac = new Fraction();
frac.m_Numerator = this.m_Denominator;
frac.m_Denominator = this.m_Numerator;
return frac;
}
public static Fraction Inverted(long value)
{
Fraction frac = new Fraction(value);
return frac.Inverse();
}
public static Fraction Inverted(double value)
{
Fraction frac = new Fraction(value);
return frac.Inverse();
}
#endregion
#region Operators
#region Unary Negation operator
public static Fraction operator -(Fraction left)
{
return Negate(left);
}
#endregion
#region Addition operators
public static Fraction operator +(Fraction left, Fraction right)
{
return Add(left, right);
}
public static Fraction operator +(long left, Fraction right)
{
return Add(new Fraction(left), right);
}
public static Fraction operator +(Fraction left, long right)
{
return Add(left, new Fraction(right));
}
public static Fraction operator +(double left, Fraction right)
{
return Add(ToFraction(left), right);
}
public static Fraction operator +(Fraction left, double right)
{
return Add(left, ToFraction(right));
}
#endregion
#region Subtraction operators
public static Fraction operator -(Fraction left, Fraction right)
{
return Add(left, - right);
}
public static Fraction operator -(long left, Fraction right)
{
return Add(new Fraction(left), - right);
}
public static Fraction operator -(Fraction left, long right)
{
return Add(left, new Fraction(- right));
}
public static Fraction operator -(double left, Fraction right)
{
return Add(ToFraction(left), - right);
}
public static Fraction operator -(Fraction left, double right)
{
return Add(left, ToFraction(- right));
}
#endregion
#region Multiplication operators
public static Fraction operator *(Fraction left, Fraction right)
{
return Multiply(left, right);
}
public static Fraction operator *(long left, Fraction right)
{
return Multiply(new Fraction(left), right);
}
public static Fraction operator *(Fraction left, long right)
{
return Multiply(left, new Fraction(right));
}
public static Fraction operator *(double left, Fraction right)
{
return Multiply(ToFraction(left), right);
}
public static Fraction operator *(Fraction left, double right)
{
return Multiply(left, ToFraction(right));
}
#endregion
#region Division operators
public static Fraction operator /(Fraction left, Fraction right)
{
return Multiply(left, right.Inverse());
}
public static Fraction operator /(long left, Fraction right)
{
return Multiply(new Fraction(left), right.Inverse());
}
public static Fraction operator /(Fraction left, long right)
{
return Multiply(left, Inverted(right));
}
public static Fraction operator /(double left, Fraction right)
{
return Multiply(ToFraction(left), right.Inverse());
}
public static Fraction operator /(Fraction left, double right)
{
return Multiply(left, Inverted(right));
}
#endregion
#region Modulus operators
public static Fraction operator %(Fraction left, Fraction right)
{
return Modulus(left, right);
}
public static Fraction operator %(long left, Fraction right)
{
return Modulus(new Fraction(left), right);
}
public static Fraction operator %(Fraction left, long right)
{
return Modulus(left, right);
}
public static Fraction operator %(double left, Fraction right)
{
return Modulus(ToFraction(left), right);
}
public static Fraction operator %(Fraction left, double right)
{
return Modulus(left, right);
}
#endregion
#region Equal operators
public static bool operator ==(Fraction left, Fraction right)
{
return left.CompareEquality(right, false);
}
public static bool operator ==(Fraction left, long right)
{
return left.CompareEquality(new Fraction(right), false);
}
public static bool operator ==(Fraction left, double right)
{
return left.CompareEquality(new Fraction(right), false);
}
#endregion
#region Not-equal operators
public static bool operator !=(Fraction left, Fraction right)
{
return left.CompareEquality(right, true);
}
public static bool operator !=(Fraction left, long right)
{
return left.CompareEquality(new Fraction(right), true);
}
public static bool operator !=(Fraction left, double right)
{
return left.CompareEquality(new Fraction(right), true);
}
#endregion
#region Inequality operators
public static bool operator <(Fraction left, Fraction right)
{
return left.CompareTo(right) < 0;
}
public static bool operator >(Fraction left, Fraction right)
{
return left.CompareTo(right) > 0;
}
public static bool operator <=(Fraction left, Fraction right)
{
return left.CompareTo(right) <= 0;
}
public static bool operator >=(Fraction left, Fraction right)
{
return left.CompareTo(right) >= 0;
}
#endregion
#region Implict conversion from primitive operators
public static implicit operator Fraction(long value)
{
return new Fraction(value);
}
public static implicit operator Fraction(double value)
{
return new Fraction(value);
}
public static implicit operator Fraction(string value)
{
return new Fraction(value);
}
#endregion
#region Explicit converstion to primitive operators
public static explicit operator int(Fraction frac)
{
return frac.ToInt32();
}
public static explicit operator long(Fraction frac)
{
return frac.ToInt64();
}
public static explicit operator double(Fraction frac)
{
return frac.ToDouble();
}
public static implicit operator string(Fraction frac)
{
return frac.ToString();
}
#endregion
#endregion
#region Equals and GetHashCode overrides
public override bool Equals(object obj)
{
if (obj == null || ! (obj is Fraction))
return false;
try
{
Fraction right = (Fraction)obj;
return this.CompareEquality(right, false);
}
catch
{
return false;
}
}
public override int GetHashCode()
{
ReduceFraction(ref this);
int numeratorHash = this.m_Numerator.GetHashCode();
int denominatorHash = this.m_Denominator.GetHashCode();
return (numeratorHash ^ denominatorHash);
}
#endregion
#region IComparable member and type-specific version
public int CompareTo(object obj)
{
if (obj == null)
return 1;
Fraction right;
if (obj is Fraction)
right = (Fraction)obj;
else if (obj is long)
right = (long)obj;
else if (obj is double)
right = (double)obj;
else if (obj is string)
right = (string)obj;
else
throw new ArgumentException("Must be convertible to Fraction", "obj");
return this.CompareTo(right);
}
public int CompareTo(Fraction right)
{
if (this.m_Denominator == 0)
{
return IndeterminantCompare(NormalizeIndeterminate(this.m_Numerator), right);
}
if (right.m_Denominator == 0)
{
return - IndeterminantCompare(NormalizeIndeterminate(right.m_Numerator), this);
}
CrossReducePair(ref this, ref right);
try
{
checked
{
long leftScale = this.m_Numerator * right.m_Denominator;
long rightScale = this.m_Denominator * right.m_Numerator;
if (leftScale < rightScale)
return -1;
else if (leftScale > rightScale)
return 1;
else
return 0;
}
}
catch (Exception e)
{
throw new FractionException(string.Format("CompareTo({0}, {1}) error", this, right), e);
}
}
#endregion
#region IFormattable Members
string System.IFormattable.ToString(string format, IFormatProvider formatProvider)
{
return this.m_Numerator.ToString(format, formatProvider) + "/" + this.m_Denominator.ToString(format, formatProvider);
}
#endregion
#region Reduction
public static void ReduceFraction(ref Fraction frac)
{
if (frac.m_Denominator == 0)
{
frac.m_Numerator = (long)NormalizeIndeterminate(frac.m_Numerator);
return;
}
if (frac.m_Numerator == 0)
{
frac.m_Denominator = 1;
return;
}
long iGCD = GCD(frac.m_Numerator, frac.m_Denominator);
frac.m_Numerator /= iGCD;
frac.m_Denominator /= iGCD;
if ( frac.m_Denominator < 0 )
{
frac.m_Numerator = - frac.m_Numerator;
frac.m_Denominator = - frac.m_Denominator;
}
}
public static void CrossReducePair(ref Fraction frac1, ref Fraction frac2)
{
if (frac1.m_Denominator == 0 || frac2.m_Denominator == 0)
return;
long gcdTop = GCD(frac1.m_Numerator, frac2.m_Denominator);
frac1.m_Numerator = frac1.m_Numerator / gcdTop;
frac2.m_Denominator = frac2.m_Denominator / gcdTop;
long gcdBottom = GCD(frac1.m_Denominator, frac2.m_Numerator);
frac2.m_Numerator = frac2.m_Numerator / gcdBottom;
frac1.m_Denominator = frac1.m_Denominator / gcdBottom;
}
#endregion
#region Implementation
#region Convert a double to a fraction
private static Fraction ConvertPositiveDouble(int sign, double inValue)
{
long fractionNumerator = (long)inValue;
double fractionDenominator = 1;
double previousDenominator = 0;
double remainingDigits = inValue;
int maxIterations = 594;
while (remainingDigits != Math.Floor(remainingDigits)
&& Math.Abs(inValue - (fractionNumerator / fractionDenominator)) > double.Epsilon)
{
remainingDigits = 1.0 / (remainingDigits - Math.Floor(remainingDigits));
double scratch = fractionDenominator;
fractionDenominator =(Math.Floor(remainingDigits) * fractionDenominator) + previousDenominator;
fractionNumerator = (long)(inValue * fractionDenominator + 0.5);
previousDenominator = scratch;
if (maxIterations-- < 0)
break;
}
return new Fraction(fractionNumerator * sign, (long)fractionDenominator);
}
#endregion
#region Equality helper
private bool CompareEquality(Fraction right, bool notEqualCheck)
{
ReduceFraction(ref this);
ReduceFraction(ref right);
if (this.m_Numerator == right.m_Numerator && this.m_Denominator == right.m_Denominator)
{
if (notEqualCheck && this.IsNaN())
return true;
else
return ! notEqualCheck;
}
else
{
return notEqualCheck;
}
}
#endregion
#region Comparison helper
private static int IndeterminantCompare(Indeterminates leftType, Fraction right)
{
switch (leftType)
{
case Indeterminates.NaN:
if (right.IsNaN())
return 0;
else if (right.IsNegativeInfinity())
return 1;
else
return -1;
case Indeterminates.NegativeInfinity:
if (right.IsNegativeInfinity())
return 0;
else
return -1;
case Indeterminates.PositiveInfinity:
if (right.IsPositiveInfinity())
return 0;
else
return 1;
default:
return 0;
}
}
#endregion
#region Math helpers
private static Fraction Negate(Fraction frac)
{
return new Fraction( - frac.m_Numerator, frac.m_Denominator);
}
private static Fraction Add(Fraction left, Fraction right)
{
if (left.IsNaN() || right.IsNaN())
return NaN;
long gcd = GCD(left.m_Denominator, right.m_Denominator);
long leftDenominator = left.m_Denominator / gcd;
long rightDenominator = right.m_Denominator / gcd;
try
{
checked
{
long numerator = left.m_Numerator * rightDenominator + right.m_Numerator * leftDenominator;
long denominator = leftDenominator * rightDenominator * gcd;
return new Fraction(numerator, denominator);
}
}
catch (Exception e)
{
throw new FractionException("Add error", e);
}
}
private static Fraction Multiply(Fraction left, Fraction right)
{
if (left.IsNaN() || right.IsNaN())
return NaN;
CrossReducePair(ref left, ref right);
try
{
checked
{
long numerator = left.m_Numerator * right.m_Numerator;
long denominator = left.m_Denominator * right.m_Denominator;
return new Fraction(numerator, denominator);
}
}
catch (Exception e)
{
throw new FractionException("Multiply error", e);
}
}
private static Fraction Modulus(Fraction left, Fraction right)
{
if (left.IsNaN() || right.IsNaN())
return NaN;
try
{
checked
{
Int64 quotient = (Int64)(left / right);
Fraction whole = new Fraction(quotient * right.m_Numerator, right.m_Denominator);
return left - whole;
}
}
catch (Exception e)
{
throw new FractionException("Modulus error", e);
}
}
private static long GCD(long left, long right)
{
if (left < 0)
left = - left;
if (right < 0)
right = - right;
if (left < 2 || right < 2)
return 1;
do
{
if (left < right)
{
long temp = left;
left = right;
right = temp;
}
left %= right;
} while (left != 0);
return right;
}
#endregion
#region Indeterminate helpers
private static string IndeterminateTypeName(long numerator)
{
System.Globalization.NumberFormatInfo info = NumberFormatInfo.CurrentInfo;
switch (NormalizeIndeterminate(numerator))
{
case Indeterminates.PositiveInfinity:
return info.PositiveInfinitySymbol;
case Indeterminates.NegativeInfinity:
return info.NegativeInfinitySymbol;
default:
case Indeterminates.NaN:
return info.NaNSymbol;
}
}
private static Indeterminates NormalizeIndeterminate(long numerator)
{
switch (Math.Sign(numerator))
{
case 1:
return Indeterminates.PositiveInfinity;
case -1:
return Indeterminates.NegativeInfinity;
default:
case 0:
return Indeterminates.NaN;
}
}
private enum Indeterminates
{
NaN = 0
, PositiveInfinity = 1
, NegativeInfinity = -1
}
#endregion
#region Member variables
private long m_Numerator;
private long m_Denominator;
#endregion
#endregion
}
public class FractionException : Exception
{
public FractionException(string Message, Exception InnerException) : base(Message, InnerException)
{
}
}
}
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Very cool code.
Just one comment, is it possible to add some fuzzy logic to convert something like 0.166666666667 into 1/6?
Thanks!
Hardy
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I added my own DenominateTo() method. That does what you're talking about. I prefer methods that provide a new result, so note that in the following code, Reduce() returns a new Fraction, as does my method. Also, I used "this" for clarification but it's unnecessary...
public Fraction DenominateTo(long denominator) {
var ʀ = new Fraction (
(long)Math.Round(this.ToDouble() * denominator),
denominator
);
return ʀ.Reduce();
}
So if you want to get the nearest sixth....
var oneSixthFraction = FromDouble(0.1666667).DenominateTo(6);
I also overloaded the static FromDouble() method (I renamed it) to accept a double value as well as a denominator to simplify things...
public static Fraction FromDouble(double value, long denominator) {
return FromDouble(value).DenominateTo(denominator);
}
... which can be used like...
var oneSixthFraction = Fraction.FromDouble(0.1666667, 6);
And you can make the Reduce() optional or remove it.
=)
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Overall, this is a nice implementation of basic fraction functionality. There is still room for improvement, however:- Conversion from Double should use base 2 rather than base 10. The 'ToString()' causes loss of precision in several ways, most notably due to the fact that it uses only 15 digits of precision.
Every double value within the range of Fraction is exactly representable by a Fraction, and so you should make this conversion exact. A round-trip cast expression like (double)(Fraction)x should return the original value x, or throw an OverflowException if x is out of range.
Ideally, you would also offer to find the fraction closest to the number, using Euclid's GCD algorithm backwards. You could put an upper limit on the size of the denominator, so that, for example, 0.333333334 gets converted to 1/3 rather than 166666667/500000000. - Your addition method can cause overflow when that is not necessary. You should divide out any common factors of the denominators. This common factor will only be divided out in the normalization. You could do something like:
long gcd = GCD(frac1.Denominator, frac2.Denominator);
long denominator1 = frac1.Denominator / gcd;
long denominator2 = frac2.Denominator / gcd;
long iNumerator=frac1.Numerator*denominator2 + frac2.Numerator*denominator1;
long iDenominator=denominator1*denominator2*gcd;
return ( new Fraction(iNumerator, iDenominator) ); Similar improvements are possible for the other operators. - You may want to consider making this a value type (
struct). The reasoning? We definitely have an object with value semantics here - it is just an alternate representation of a number. Moreover, it is small enough (16 bytes) so the by-value passing of value types shouldn't hinder performance.
It would also eliminate the need for methods like Duplicate and properties like Value, since you can use direct assignments. - Your implementation of
Equals does not comply with the guidelines[^]. For example, your code throws an exception if the argument isn't of type Fraction. Equals should never throw an exception.
There may well be more. Improving code is like ironing out all the wrinkles: you get some of the bigger ones first, and then take care of the progressively smaller ones.
Nice work!
Jeffrey
Everything should be as simple as possible, but not simpler.
-- Albert Einstein
Numerical components for C# and VB.NET
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