Addendum to the above. In an exercise in the Knuth book Knuth does indeed state that "If the inputs are n-bit binary numbers, 2N+1 bits may be necessary to represent t." where t is a derived quantity that would take some time to explain.
So that means in extreme cases, the needed precision to represent a fraction operation with 32 bits ints is 65 bits, one more than a long has. The present code solves this by using BigInteger briefly in the code, which strikes me as an awfully big performance hit for what must surely be very occasional and very extreme cases. I think the most sensible strategy would be to restrict the precision of Fraction to longs, with user guidance to use BigFraction if there is concern of overflow. Eric On Thu, Nov 8, 2018 at 11:11 AM Gary Gregory <garydgreg...@gmail.com> wrote: > I'm all for the Javadoc made to reflect the reality of the code. It is fine > to have an additional section that points out Knuth and how we may want to > change things as a hint or request to contributors. > > Gary > > On Wed, Nov 7, 2018 at 10:52 AM Eric Barnhill <ericbarnh...@gmail.com> > wrote: > > > I read Kunth's "Art of Computer Programming 4.5.1" that is referenced > many > > times in the doc as the guidance for the commons-math/commons-numbers > > Fraction class. It is an interesting read. Also, for all the times it is > > cited in the doc, it is interesting that Fraction doesn't really use it > as > > implemented. Here is one example. > > > > Knuth is concerned about overflow in multiplication and division, because > > numerator of f1 is multiplied by denominator of f2 and so forth, so he > > suggests a technique called "mediant rounding" that allows for > intermediate > > quantities in fraction multiplication to be rounded. > > > > It is a clever technique and probably works well, however the current > > Fraction class cites this chapter, then implements multiplication with > > BigInteger instead, ignoring this suggestion. > > > > First of all, the doc should be clear that the code is NOT following > 4.5.1, > > while it gives the opposite impression. And that's ok but the use of > > BigInteger creates additional inconsistency: Multiply and divide are > > accomplished using ArithmeticUtils.addAndCheck and > > ArithmeticUtils.mulAndCheck . These convert the relevant ints to longs, > > then perform the operation, then if the resulting long is greater than > the > > range of an int, throw an OverflowException. So some parts of Fraction > > check for overflow using longs and others use BigInteger. > > > > It seems to me that BigInteger is overkill here for the vast majority of > > practical uses of Fraction in a way that could be damaging for > performance. > > And furthermore, we already have a BigFraction class to handle cases that > > require BigInteger. > > > > So, I propose rewriting the doc to say the opposite of what it currently > > says when appropriate, and get usages of BigInteger out of Fraction, use > > them only in BigFraction, and use the long-based ArithmeticUtils methods > to > > check for overflow and underflow in fraction addition and subtraction. > > > > Eric > > >
