Re: [numbers] Fraction() and Knuth 4.5.1 -- overflow, BigInteger, long, and rounding

[Gilles <gi...@harfang.homelinux.org>]

On Fri, 30 Nov 2018 15:56:54 -0800, Eric Barnhill wrote:
> Here is what I propose for the Fraction doc text regarding this 
> issue:
>
>      * Implement add and subtract. This algorithm is similar to that
>      * described in Knuth 4.5.1. while making some concessions to
>      * performance. Note Knuth 4.5.1 Exercise 7, which observes that
>      * adding two fractions with 32-bit numerators and denominators
>      * requires 65 bits in extreme cases. Here calculations are 
> performed
>      * with 64-bit longs and the BigFraction class is recommended for
> numbers
>      * that may grow large enough to be in danger of overflow.

Does this mean that computations can "unpredictably" overflow
(or throw an exception)?
Is it acceptable, or should we enclose the problematic code in
a "try" block and redo the computation with "BigInteger" when
necessary?

What is the performance hit of using "BigFraction" rather than
"Fraction"?
Are there use-cases that would need the ultimate performance from
"Fraction" while not worry about overflow?

Regards,
Gilles

>
>
> On Fri, Nov 9, 2018 at 4:33 PM Eric Barnhill <er...@gmail.com> 
> wrote:
>
>> 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 
>> <ga...@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 
>>> <er...@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
>>> >
>>>
>>


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Re: [numbers] Fraction() and Knuth 4.5.1 -- overflow, BigInteger, long, and rounding

[Gilles <gi...@harfang.homelinux.org>]

Hi Eric.

On Mon, 3 Dec 2018 10:01:39 -0800, Eric Barnhill wrote:
>>
>>
>> Does this mean that computations can "unpredictably" overflow
>> (or throw an exception)?
>>
>
> The ArithmeticUtils() methods mulAndCheck and addAndCheck throw 
> exceptions
> if there is overflow during primitive operations. That is the "check" 
> part
> of the method name.
>
>
>> Is it acceptable, or should we enclose the problematic code in
>> a "try" block and redo the computation with "BigInteger" when
>> necessary?
>>
>> What is the performance hit of using "BigFraction" rather than
>> "Fraction"?
>>
>
> I once used BigDecimal for a project, it is great code but the 
> performance
> is nothing close to using primitives.
>
>
>> Are there use-cases that would need the ultimate performance from
>> "Fraction" while not worry about overflow?
>>
>
> You would need a greatest common factor between the two fractions 
> that was
> larger than 64 bits.
>
> Again, BigFraction is there for anyone worried about such a case and 
> there
> is no significant performance hit to switching over to BigFraction 
> compared
> to a Fraction class that was using BigInteger under the hood. But I
> suspect  there would be a substantial performance gain if longs were 
> being
> used under the hood for the Fraction class for the more common use 
> case of
> smaller fractions. If it would be best practice, a bit of 
> microbenchmarking
> could be done to check.
>
> A FractionOverflowException could be specifically tailored to this 
> use case
> and the error message can suggest using BigFraction. Or as you 
> suggest, the
> catch block could silently or with warning return a BigFraction. If 
> we have
> class inheritance straight, and both Fraction and BigFraction have 
> the
> exact same interface, this could be an elegant solution.

Maybe I misunderstood, but I thought that only intermediate results
would require "BigInteger"; if the result needs to be converted to
"BigFraction", than I'd favour raising an exception (with the advice
which you mention).
If later on someone comes up with a use-case for the alternate 
solution,
we can revisit.

Regards,
Gilles

>
> Eric


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Re: [numbers] Fraction() and Knuth 4.5.1 -- overflow, BigInteger, long, and rounding

[Eric Barnhill <er...@gmail.com>]

>
>
> Does this mean that computations can "unpredictably" overflow
> (or throw an exception)?
>

The ArithmeticUtils() methods mulAndCheck and addAndCheck throw exceptions
if there is overflow during primitive operations. That is the "check" part
of the method name.


> Is it acceptable, or should we enclose the problematic code in
> a "try" block and redo the computation with "BigInteger" when
> necessary?
>
> What is the performance hit of using "BigFraction" rather than
> "Fraction"?
>

I once used BigDecimal for a project, it is great code but the performance
is nothing close to using primitives.


> Are there use-cases that would need the ultimate performance from
> "Fraction" while not worry about overflow?
>

You would need a greatest common factor between the two fractions that was
larger than 64 bits.

Again, BigFraction is there for anyone worried about such a case and there
is no significant performance hit to switching over to BigFraction compared
to a Fraction class that was using BigInteger under the hood. But I
suspect  there would be a substantial performance gain if longs were being
used under the hood for the Fraction class for the more common use case of
smaller fractions. If it would be best practice, a bit of microbenchmarking
could be done to check.

A FractionOverflowException could be specifically tailored to this use case
and the error message can suggest using BigFraction. Or as you suggest, the
catch block could silently or with warning return a BigFraction. If we have
class inheritance straight, and both Fraction and BigFraction have the
exact same interface, this could be an elegant solution.

Eric