/**
* Multiplies the value of this fraction by another, returning the result in reduced form.
*
* @param fraction the fraction to multiply by, must not be <code>null</code>
* @return a <code>Fraction</code> instance with the resulting values
* @throws IllegalArgumentException if the fraction is <code>null</code>
* @throws ArithmeticException if the resulting numerator or denominator exceeds <code>
* Integer.MAX_VALUE</code>
*/
public Fraction multiply(Fraction fraction) {
if (fraction == null) {
throw MathRuntimeException.createIllegalArgumentException("null 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 = MathUtils.gcd(numerator, fraction.denominator);
int d2 = MathUtils.gcd(fraction.numerator, denominator);
return getReducedFraction(
MathUtils.mulAndCheck(numerator / d1, fraction.numerator / d2),
MathUtils.mulAndCheck(denominator / d2, fraction.denominator / d1));
}
/**
* Creates a <code>Fraction</code> instance with the 2 parts of a fraction Y/Z.
*
* <p>Any negative signs are resolved to be on the numerator.
*
* @param numerator the numerator, for example the three in 'three sevenths'
* @param denominator the denominator, for example the seven in 'three sevenths'
* @return a new fraction instance, with the numerator and denominator reduced
* @throws ArithmeticException if the denominator is <code>zero</code>
*/
public static Fraction getReducedFraction(int numerator, int denominator) {
if (denominator == 0) {
throw MathRuntimeException.createArithmeticException(
"zero denominator in fraction {0}/{1}", numerator, denominator);
}
if (numerator == 0) {
return ZERO; // normalize zero.
}
// allow 2^k/-2^31 as a valid fraction (where k>0)
if (denominator == Integer.MIN_VALUE && (numerator & 1) == 0) {
numerator /= 2;
denominator /= 2;
}
if (denominator < 0) {
if (numerator == Integer.MIN_VALUE || denominator == Integer.MIN_VALUE) {
throw MathRuntimeException.createArithmeticException(
"overflow in fraction {0}/{1}, cannot negate", numerator, denominator);
}
numerator = -numerator;
denominator = -denominator;
}
// simplify fraction.
int gcd = MathUtils.gcd(numerator, denominator);
numerator /= gcd;
denominator /= gcd;
return new Fraction(numerator, denominator);
}
/**
* Create a fraction given the numerator and denominator. The fraction is reduced to lowest terms.
*
* @param num the numerator.
* @param den the denominator.
* @throws ArithmeticException if the denominator is <code>zero</code>
*/
public Fraction(int num, int den) {
if (den == 0) {
throw MathRuntimeException.createArithmeticException(
"zero denominator in fraction {0}/{1}", num, den);
}
if (den < 0) {
if (num == Integer.MIN_VALUE || den == Integer.MIN_VALUE) {
throw MathRuntimeException.createArithmeticException(
"overflow in fraction {0}/{1}, cannot negate", num, den);
}
num = -num;
den = -den;
}
// reduce numerator and denominator by greatest common denominator.
final int d = MathUtils.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;
}
/**
* Creates a <code>Fraction</code> instance with the 2 parts of a fraction Y/Z.
*
* <p>Any negative signs are resolved to be on the numerator.
*
* @param numerator the numerator, for example the three in 'three sevenths'
* @param denominator the denominator, for example the seven in 'three sevenths'
* @return a new fraction instance, with the numerator and denominator reduced
* @throws ArithmeticException if the denominator is <code>zero</code>
*/
public static Fraction getReducedFraction(int numerator, int denominator) {
if (denominator == 0) {
throw MathRuntimeException.createArithmeticException(
ZERO_DENOMINATOR_MESSAGE, numerator, denominator);
}
if (numerator == 0) {
return ZERO; // normalize zero.
}
// allow 2^k/-2^31 as a valid fraction (where k>0)
if (denominator == Integer.MIN_VALUE && (numerator & 1) == 0) {
numerator /= 2;
denominator /= 2;
}
if (denominator < 0) {
if (numerator == Integer.MIN_VALUE || denominator == Integer.MIN_VALUE) {
throw MathRuntimeException.createArithmeticException(
OVERFLOW_MESSAGE, numerator, denominator);
}
numerator = -numerator;
denominator = -denominator;
}
// simplify fraction.
int gcd = MathUtils.gcd(numerator, denominator);
numerator /= gcd;
denominator /= gcd;
return new Fraction(numerator, denominator);
}
/**
* Create a fraction given the numerator and denominator. The fraction is reduced to lowest terms.
*
* @param num the numerator.
* @param den the denominator.
* @throws ArithmeticException if the denominator is <code>zero</code>
*/
public Fraction(int num, int den) {
if (den == 0) {
throw MathRuntimeException.createArithmeticException(ZERO_DENOMINATOR_MESSAGE, num, den);
}
if (den < 0) {
if (num == Integer.MIN_VALUE || den == Integer.MIN_VALUE) {
throw MathRuntimeException.createArithmeticException(OVERFLOW_MESSAGE, num, den);
}
num = -num;
den = -den;
}
// reduce numerator and denominator by greatest common denominator.
final int d = MathUtils.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;
}
/**
* Implement add and subtract using algorithm described in Knuth 4.5.1.
*
* @param fraction the fraction to subtract, must not be <code>null</code>
* @param isAdd true to add, false to subtract
* @return a <code>Fraction</code> instance with the resulting values
* @throws IllegalArgumentException if the fraction is <code>null</code>
* @throws ArithmeticException if the resulting numerator or denominator cannot be represented in
* an <code>int</code>.
*/
private Fraction addSub(Fraction fraction, boolean isAdd) {
if (fraction == null) {
throw MathRuntimeException.createIllegalArgumentException("null 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 = MathUtils.gcd(denominator, fraction.denominator);
if (d1 == 1) {
// result is ( (u*v' +/- u'v) / u'v')
int uvp = MathUtils.mulAndCheck(numerator, fraction.denominator);
int upv = MathUtils.mulAndCheck(fraction.numerator, denominator);
return new Fraction(
isAdd ? MathUtils.addAndCheck(uvp, upv) : MathUtils.subAndCheck(uvp, upv),
MathUtils.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 uvp =
BigInteger.valueOf(numerator).multiply(BigInteger.valueOf(fraction.denominator / d1));
BigInteger upv =
BigInteger.valueOf(fraction.numerator).multiply(BigInteger.valueOf(denominator / d1));
BigInteger t = isAdd ? uvp.add(upv) : uvp.subtract(upv);
// but d2 doesn't need extra precision because
// d2 = gcd(t,d1) = gcd(t mod d1, d1)
int tmodd1 = t.mod(BigInteger.valueOf(d1)).intValue();
int d2 = (tmodd1 == 0) ? d1 : MathUtils.gcd(tmodd1, d1);
// result is (t/d2) / (u'/d1)(v'/d2)
BigInteger w = t.divide(BigInteger.valueOf(d2));
if (w.bitLength() > 31) {
throw MathRuntimeException.createArithmeticException(
"overflow, numerator too large after multiply: {0}", w);
}
return new Fraction(
w.intValue(), MathUtils.mulAndCheck(denominator / d1, fraction.denominator / d2));
}
