/// <summary>
/// Compares this Fraction to another Fraction
/// </summary>
/// <param name="right">The Fraction to compare against</param>
/// <returns>-1 if this is less than <paramref name="right"></paramref>,
/// 0 if they are equal,
/// 1 if this is greater than <paramref name="right"></paramref></returns>
public int CompareTo(Fraction right)
{
// if left is an indeterminate, punt to the helper...
if (this.m_Denominator == 0)
{
return IndeterminantCompare(NormalizeIndeterminate(this.m_Numerator), right);
}
// if right is an indeterminate, punt to the helper...
if (right.m_Denominator == 0)
{
// note sign-flip...
return - IndeterminantCompare(NormalizeIndeterminate(right.m_Numerator), this);
}
// they're both normal Fractions
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);
}
}
/// <summary>
/// Reduces (simplifies) a Fraction by dividing down to lowest possible denominator (via GCD)
/// </summary>
/// <param name="frac">The Fraction to be reduced [WILL BE MODIFIED IN PLACE]</param>
/// <remarks>Modifies the input arguments in-place! Will normalize the NaN and infinites
/// representation. Will set Denominator to 1 for any zero numerator. Moves sign to the
/// Numerator.</remarks>
/// <example>2/4 will be reduced to 1/2</example>
public static void ReduceFraction(ref Fraction frac)
{
// clean up the NaNs and infinites
if (frac.m_Denominator == 0)
{
frac.m_Numerator = (long)NormalizeIndeterminate(frac.m_Numerator);
return;
}
// all forms of zero are alike.
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 negative sign in denominator
if ( frac.m_Denominator < 0 )
{
//move negative sign to numerator
frac.m_Numerator = - frac.m_Numerator;
frac.m_Denominator = - frac.m_Denominator;
}
}
/// <summary>
/// Inverts a Fraction
/// </summary>
/// <returns>The inverted Fraction (with Denominator over Numerator)</returns>
/// <remarks>Does NOT throw for zero Numerators as later use of the fraction will catch the error.</remarks>
public Fraction Inverse()
{
// don't use the obvious constructor because we do not want it normalized at this time
Fraction frac = new Fraction();
frac.m_Numerator = this.m_Denominator;
frac.m_Denominator = this.m_Numerator;
return frac;
}
/// <summary>
/// Creates an inverted Fraction
/// </summary>
/// <returns>The inverted Fraction (with Denominator over Numerator)</returns>
/// <remarks>Does NOT throw for zero Numerators as later use of the fraction will catch the error.</remarks>
public static Fraction Inverted(double value)
{
Fraction frac = new Fraction(value);
return frac.Inverse();
}
/// <summary>
/// Multiplies two Fractions
/// </summary>
/// <param name="left">A Fraction</param>
/// <param name="right">Another Fraction</param>
/// <returns>Product of the Fractions. Returns NaN if either Fraction is a NaN.</returns>
/// <exception cref="FractionException">Will throw if an overflow occurs. Does a cross-reduce to
/// insure only the unavoidable overflows occur.</exception>
private static Fraction Multiply(Fraction left, Fraction right)
{
if (left.IsNaN() || right.IsNaN())
return NaN;
// this would be unsafe if we were not a ValueType, because we would be changing the
// caller's values. If we change back to a class, must use temporaries
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);
}
}
/// <summary>
/// Returns the modulus (remainder after dividing) two Fractions
/// </summary>
/// <param name="left">A Fraction</param>
/// <param name="right">Another Fraction</param>
/// <returns>Modulus of the Fractions. Returns NaN if either Fraction is a NaN.</returns>
/// <exception cref="FractionException">Will throw if an overflow occurs. Does a cross-reduce to
/// insure only the unavoidable overflows occur.</exception>
private static Fraction Modulus(Fraction left, Fraction right)
{
if (left.IsNaN() || right.IsNaN())
return NaN;
try
{
checked
{
// this will discard any fractional places...
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);
}
}
/// <summary>
/// Adds two Fractions
/// </summary>
/// <param name="left">A Fraction</param>
/// <param name="right">Another Fraction</param>
/// <returns>Sum of the Fractions. Returns NaN if either Fraction is a NaN.</returns>
/// <exception cref="FractionException">Will throw if an overflow occurs when computing the
/// GCD-normalized values.</exception>
private static Fraction Add(Fraction left, Fraction right)
{
if (left.IsNaN() || right.IsNaN())
return NaN;
long gcd = GCD(left.m_Denominator, right.m_Denominator); // cannot return less than 1
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);
}
}
/// <summary>
/// Negates the Fraction
/// </summary>
/// <param name="frac">Value to negate</param>
/// <returns>A new Fraction that is sign-flipped from the input</returns>
private static Fraction Negate(Fraction frac)
{
// for a NaN, it's still a NaN
return new Fraction( - frac.m_Numerator, frac.m_Denominator);
}
/// <summary>
/// Determines how this Fraction, of an indeterminate type, compares to another Fraction
/// </summary>
/// <param name="leftType">What kind of indeterminate</param>
/// <param name="right">The other Fraction to compare against</param>
/// <returns>-1 if this is less than <paramref name="right"></paramref>,
/// 0 if they are equal,
/// 1 if this is greater than <paramref name="right"></paramref></returns>
/// <remarks>NaN is less than anything except NaN and Negative Infinity. Negative Infinity is less
/// than anything except Negative Infinity. Positive Infinity is greater than anything except
/// Positive Infinity.</remarks>
private static int IndeterminantCompare(Indeterminates leftType, Fraction right)
{
switch (leftType)
{
case Indeterminates.NaN:
// A NaN is...
if (right.IsNaN())
return 0; // equal to a NaN
else if (right.IsNegativeInfinity())
return 1; // great than Negative Infinity
else
return -1; // less than anything else
case Indeterminates.NegativeInfinity:
// Negative Infinity is...
if (right.IsNegativeInfinity())
return 0; // equal to Negative Infinity
else
return -1; // less than anything else
case Indeterminates.PositiveInfinity:
if (right.IsPositiveInfinity())
return 0; // equal to Positive Infinity
else
return 1; // greater than anything else
default:
// this CAN'T happen, something VERY wrong is going on...
return 0;
}
}
/// <summary>
/// Compares for equality the current Fraction to the value passed.
/// </summary>
/// <param name="right">A Fraction to compare against</param>
/// <param name="notEqualCheck">If true, we're looking for not-equal</param>
/// <returns>True if the <paramref name="right"></paramref> equals the current
/// fraction, false otherwise. If comparing two NaNs, they are always equal AND
/// not-equal.</returns>
private bool CompareEquality(Fraction right, bool notEqualCheck)
{
// insure we're normalized first
ReduceFraction(ref this);
// now normalize the comperand
ReduceFraction(ref right);
if (this.m_Numerator == right.m_Numerator && this.m_Denominator == right.m_Denominator)
{
// special-case rule, two NaNs are always both equal
if (notEqualCheck && this.IsNaN())
return true;
else
return ! notEqualCheck;
}
else
{
return notEqualCheck;
}
}
/// <summary>
/// Cross-reduces a pair of Fractions so that we have the best GCD-reduced values for multiplication
/// </summary>
/// <param name="frac1">The first Fraction [WILL BE MODIFIED IN PLACE]</param>
/// <param name="frac2">The second Fraction [WILL BE MODIFIED IN PLACE]</param>
/// <remarks>Modifies the input arguments in-place!</remarks>
/// <example>(3/4, 5/9) = (1/4, 5/3)</example>
public static void CrossReducePair(ref Fraction frac1, ref Fraction frac2)
{
// leave the indeterminates alone!
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;
}