/// <summary>
/// <para>Creates a <c>Fraction</c> instance with the 2 parts
/// of a fraction Y/Z.</para>
/// <para>Any negative signs are resolved to be on the numerator.</para>
/// </summary>
/// <param name="numerator">the numerator, for example the three in 'three sevenths'
/// </param>
/// <param name="denominator">the denominator, for example the seven in 'three sevenths'
/// </param>
/// <returns>a new fraction instance, with the numerator and denominator reduced</returns>
/// <exception cref="MathArithmeticException"> if the denominator is <c>zero</c>
/// </exception>
public static Fraction getReducedFraction(int numerator, int denominator)
{
if (denominator == 0)
{
throw new MathArithmeticException(new LocalizedFormats("ZERO_DENOMINATOR_IN_FRACTION"),
numerator, denominator);
}
if (numerator == 0)
{
return(ZERO); // normalize zero.
}
// allow 2^k/-2^31 as a valid fraction (where k>0)
if (denominator == Int32.MinValue && (numerator & 1) == 0)
{
numerator /= 2; denominator /= 2;
}
if (denominator < 0)
{
if (numerator == Int32.MinValue ||
denominator == Int32.MinValue)
{
throw new MathArithmeticException(new LocalizedFormats("OVERFLOW_IN_FRACTION"),
numerator, denominator);
}
numerator = -numerator;
denominator = -denominator;
}
// simplify fraction.
int gcd = ArithmeticUtils.gcd(numerator, denominator);
numerator /= gcd;
denominator /= gcd;
return(new Fraction(numerator, denominator));
}
/// <summary>
/// Implement add and subtract using algorithm described in Knuth 4.5.1.
/// </summary>
/// <param name="fraction">the fraction to subtract, must not be <c>null</c></param>
/// <param name="isAdd">true to add, false to subtract</param>
/// <returns>a <c>Fraction</c> instance with the resulting values</returns>
/// <exception cref="NullArgumentException"> if the fraction is <c>null</c></exception>
/// <exception cref="MathArithmeticException"> if the resulting numerator or denominator
/// cannot be represented in an <c>int</c>.</exception>
private Fraction addSub(Fraction fraction, Boolean isAdd)
{
if (fraction == null)
{
throw new NullArgumentException(new LocalizedFormats("FRACTION"));
}
// zero is identity for addition.
if (numerator == 0)
{
return(isAdd ? fraction : fraction.negate());
}
if (fraction.numerator == 0)
{
return(this);
}
// if denominators are randomly distributed, d1 will be 1 about 61%
// of the time.
int d1 = ArithmeticUtils.gcd(denominator, fraction.denominator);
if (d1 == 1)
{
// result is ( (u*v' +/- u'v) / u'v')
int uvp = ArithmeticUtils.mulAndCheck(numerator, fraction.denominator);
int upv = ArithmeticUtils.mulAndCheck(fraction.numerator, denominator);
return(new Fraction
(isAdd ? ArithmeticUtils.addAndCheck(uvp, upv) :
ArithmeticUtils.subAndCheck(uvp, upv),
ArithmeticUtils.mulAndCheck(denominator, fraction.denominator)));
}
// the quantity 't' requires 65 bits of precision; see knuth 4.5.1
// exercise 7. we're going to use a BigInteger.
// t = u(v'/d1) +/- v(u'/d1)
BigInteger uvpb = new BigInteger(numerator) * new BigInteger(fraction.denominator / d1);
BigInteger upvb = new BigInteger(fraction.numerator) * new BigInteger(denominator / d1);
BigInteger t = isAdd ? (uvpb + upvb) : (uvpb - upvb);
// but d2 doesn't need extra precision because
// d2 = gcd(t,d1) = gcd(t mod d1, d1)
int tmodd1 = Convert.ToInt32(t % (new BigInteger(d1)));
int d2 = (tmodd1 == 0) ? d1 : ArithmeticUtils.gcd(tmodd1, d1);
// result is (t/d2) / (u'/d1)(v'/d2)
BigInteger w = t / (new BigInteger(d2));
if ((w.ToByteArray().Length / 8) > 31)
{
throw new MathArithmeticException(new LocalizedFormats("NUMERATOR_OVERFLOW_AFTER_MULTIPLY"), w);
}
return(new Fraction(Convert.ToInt32(w), ArithmeticUtils.mulAndCheck(denominator / d1, fraction.denominator / d2)));
}
/// <summary>
/// <para>Multiplies the value of this fraction by another, returning the
/// result in reduced form.</para>
/// </summary>
/// <param name="fraction">the fraction to multiply by, must not be <c>null</c></param>
/// <returns>a <c>Fraction</c> instance with the resulting values</returns>
/// <exception cref="NullArgumentException"> if the fraction is <c>null</c></exception>
/// <exception cref="MathArithmeticException"> if the resulting numerator or denominator
/// exceeds <c>Int32.MaxValue</c></exception>
public Fraction multiply(Fraction fraction)
{
if (fraction == null)
{
throw new NullArgumentException(new LocalizedFormats("FRACTION"));
}
if (numerator == 0 || fraction.numerator == 0)
{
return(ZERO);
}
// knuth 4.5.1
// make sure we don't overflow unless the result *must* overflow.
int d1 = ArithmeticUtils.gcd(numerator, fraction.denominator);
int d2 = ArithmeticUtils.gcd(fraction.numerator, denominator);
return(getReducedFraction
(ArithmeticUtils.mulAndCheck(numerator / d1, fraction.numerator / d2),
ArithmeticUtils.mulAndCheck(denominator / d2, fraction.denominator / d1)));
}
/// <summary>
/// Create a fraction given the numerator and denominator. The fraction is
/// reduced to lowest terms.
/// </summary>
/// <param name="num">the numerator.</param>
/// <param name="den">the denominator.</param>
/// <exception cref="MathArithmeticException"> if the denominator is <c>zero</c>
/// </exception>
public Fraction(int num, int den)
{
if (den == 0)
{
throw new MathArithmeticException(new LocalizedFormats("ZERO_DENOMINATOR_IN_FRACTION"),
num, den);
}
if (den < 0)
{
if (num == Int32.MinValue ||
den == Int32.MaxValue)
{
throw new MathArithmeticException(new LocalizedFormats("OVERFLOW_IN_FRACTION"),
num, den);
}
num = -num;
den = -den;
}
// reduce numerator and denominator by greatest common denominator.
int d = ArithmeticUtils.gcd(num, den);
if (d > 1)
{
num /= d;
den /= d;
}
// move sign to numerator.
if (den < 0)
{
num = -num;
den = -den;
}
this.numerator = num;
this.denominator = den;
}