/**
* 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));
}
