Fractions 7.2.1

Introduction

This package contains a data type to calculate with rational numbers. It supports basic mathematic operators such as:

• addition
• subtraction
• multiplication
• division
• remainder
• ..

The fraction data type implements operator overloads and implicit type conversion for convenience.

Creation

You can implicitly cast int, uint, long, ulong or BigInteger to Fraction:

Fraction a = 3;  // int
Fraction b = 4L; // long
Fraction c = new BigInteger(3);
// ..

You can explicitly cast decimal and double to Fraction:

var a = (Fraction)3.3m; // decimal
var b = (Fraction)3.3;  // double

You can explicitly cast from Fraction to any supported data type (int, uint, long, ulong, BigInteger, decimal, double). However, be aware that an OverflowException will be thrown, if the target data type's boundary values are exceeded.

Constructors

There a three types of constructors available:

• new Fraction (<value>) for int, uint, long, ulong, BigInteger, decimal and double.
• new Fraction (<numerator>, <denominator>) using BigInteger for numerator and denominator.
• new Fraction (<numerator>, <denominator>, <reduce>) using BigInteger for numerator and denominator + bool to indicate if the resulting fraction shall be normalized (reduced).

Static creation methods

• Fraction.FromDecimal(decimal)
• Fraction.FromDouble(double)
• Fraction.FromDoubleRounded(double)
• Fraction.FromString(string) (using current culture)
• Fraction.FromString(string, IFormatProvider)
• Fraction.FromString(string, NumberStyles, IFormatProvider)
• Fraction.TryParse(string, out Fraction) (using current culture)
• Fraction.TryParse(string, NumberStyles, IFormatProvider, out Fraction)

Creation from double

The double data type stores its values as 64bit floating point numbers that comply with IEC 60559:1989 (IEEE 754) standard for binary floating-point arithmetic. double cannot store some binary fractions. For example, 1/10, which is represented precisely by .1 as a decimal fraction, is represented by .0001100110011... as a binary fraction, with the pattern 0011 repeating to infinity. In this case, the floating-point value provides an imprecise representation of the number that it represents:

var value = Fraction.FromDouble(0.1);
/* Returns 3602879701896397/36028797018963968
 * which is 0.10000000000000000555111512312578 */ 
Console.WriteLine(value);

You can use the Fraction.FromDoubleRounded(double) method to avoid big numbers in numerator and denominator. But please keep in mind that the creation speed is significantly slower than using the pure value from Fraction.FromDouble(double). Example:

var value = Fraction.FromDoubleRounded(0.1);
// Returns 1/10 which is 0.1 
Console.WriteLine(value);

Creation from string

The following string patterns can be parsed:

• [+/-]n where n is an integer. Examples: +5, -6, 1234, 0
• [+/-]n.m where n and m are integers. The decimal point symbol depends on the system's culture settings. Examples: -4.3, 0.45
• [+/-]n/[+/-]m where n and m are integers. Examples: 1/2, -4/5, +4/-3, 32/100 Example:

var value = Fraction.FromString("1,5", new CultureInfo("de-DE"))
// Returns 3/2 which is 1.5
Console.WriteLine(value);

You should consider the TryParse methods when reading numbers as text from user input. Furthermore it is best practice to always supply a culture information (e.g. CultureInfo.InvariantCulture). Otherwise you will sooner or later parse wrong numbers because of different decimal point symbols or included Thousands character.

Conversion

You can convert a Fraction to any supported data type by calling:

• .ToInt32()
• .ToUInt32()
• .ToInt64()
• .ToUInt64()
• .ToBigInteger()
• .ToDecimal()
• .ToDouble()
• .ToString() (using current culture)
• .ToString(string) (using format string and the system's current culture)
• .ToString(string,IFormatProvider)

If the target's data type boundary values are exceeded the system will throw an OverflowException.

Example:

var rationalNumber = new Fraction(1, 3);
var value = rationalNumber.ToDecimal();
// result is 0.33333
Console.WriteLine(Math.Round(value, 5));

String format

Note: The special characters #, and 0 like in #.### are not supported. Convert the Fraction to decimal if you want to display rounded decimal values.

Example:

var value = new Fraction(3, 2);
// returns 1 1/2
Console.WriteLine(value.ToString("m", new CultureInfo("de-DE")));

Mathematic operators

The following mathematic operations are supported:

• .Reduce() returns a normalized fraction (e.g. 2/4 → 1/2)
• .Add(Fraction) returns the sum of (a + b)
• .Subtract(Fraction) returns the difference of (a - b)
• .Multiply(Fraction) returns the product of (a * b)
• .Divide(Fraction) returns the quotient of (a / b)
• .Remainder(Fraction) returns the remainder (or left over) of (a % b)
• .Invert() returns an inverted fraction (same operation as (a * -1))
• .Abs() returns the absolute value |a|
• Fraction.Pow(Fraction, int) returns a base raised to a power (a ^ exponent) (e.g. 1/10^(-1) → 10/1)

As extension method:

• FractionExt.Sqrt(this Fraction, int) returns the square root, specifying the precision after the decimal point.

Example:

 var a = new Fraction(1, 3);
 var b = new Fraction(2, 3);
 var result = a * b;
 // returns 2/9 which is 0,2222...
 Console.WriteLine(result);

Equality operators

Fraction implements the following interfaces:

• IEquatable<Fraction>,
• IComparable,
• IComparable<Fraction>

Please note that .Equals(Fraction) will compare the exact values of numerator and denominator. That said:

var a = new Fraction(1, 2, true);
var b = new Fraction(1, 2, false);
var c = new Fraction(2, 4, false);

// result1 is true
var result1 = a == a;

// result2 is true
var result2 = a == b;

// result3 is false
var result3 = a == c;

You have to use .IsEquivalentTo(Fraction) if want to test non-normalized fractions for value-equality.

Under the hood

The data type stores the numerator and denominator as BigInteger. Per default it will reduce fractions to its normalized form during creation. The result of each mathematical operation will be reduced as well. There is a special constructor to create a non-normalized fraction. Be aware that Equals relies on normalized values when comparing two different instances.

Build from source

Required software frameworks

• .Net Core 6.0 SDK

Required build tools

• Fake (https://fake.build/fake-gettingstarted.html),

Please run:

dotnet tool install fake-cli -g

to install fake as global tool. On Linux you may have to add the following lines into your .profile or .bashrc file:

if [ -d "$HOME/.dotnet/tools" ] ; then
  PATH="$HOME/.dotnet/tools:$PATH"
fi

Fractions uses the great FAKE DSL for build tasks. To build the solution, simply start the build.cmd on Windows or the build.sh shell script on Unix.