Re: [eigen] Overflow in sum()

[Benoit Jacob <jacob.benoit.1@xxxxxxxxx>]

The idea was also to use it in matrix products, dot product, etc.
But then I have doubts: if really all these operations overflow then
maybe the user really needs to use a bigger scalar type in the first
place. There isn't much of a point in using uint8 if you need to cast
everytime you do something nontrivial... i'd need to see how this is
used in practice.

Benoit

2009/4/2 Gael Guennebaud <gael.guennebaud@xxxxxxxxx>:
> I have to say I'm not sure to fully understand your proposal. Where
> would you use the additional scalar type and ei_saturate ? only in
> sum() ? to tweak the return type of operator+ and so ?
>
>
> On Thu, Apr 2, 2009 at 1:56 PM, Benoit Jacob <jacob.benoit.1@xxxxxxxxx> wrote:
>> I agree, that for Jens' use case, the cast() approach works well; now
>> what do the dense-matrix-of-uint8 guys think? If they need to cast all
>> the time then I guess this isn't convenient. Putting that into the
>> NumTraits had the advantage of being very extensible without making
>> the rest of Eigen significantly more complex. But we'll do it only if
>> people need it...
>>
>> Benoit
>>
>> 2009/4/2 Jens Mueller <jens.k.mueller@xxxxxx>:
>>> Oh yes. You are right. For me cast<>() is best. And even for the others,
>>> I guess. Just cast the values such that there will be no overflows.
>>>
>>> Regards,
>>> Jens
>>>
>>> Gael Guennebaud wrote:
>>>> what about:
>>>>
>>>> mat.cast<uint>().sum()
>>>>
>>>> (this already works without creating any temporary matrix)
>>>>
>>>> gael.
>>>>
>>>> On Thu, Apr 2, 2009 at 11:03 AM, Jens Mueller <jens.k.mueller@xxxxxx> wrote:
>>>> > The first proprosed plugin solution is acceptable for me. Since this
>>>> > plugin feature is neat anyway.
>>>> > If this overflow thing really matters for users, then extending
>>>> > NumTraits is reasonable, since people with custom matrices write their
>>>> > own NumTraits declarations anyway. So at the moment there are three
>>>> > users bothered with this problem. Is this considered enough?
>>>> >
>>>> > Regards,
>>>> > Jens
>>>> >
>>>> > Benoit Jacob wrote:
>>>> >> Thanks for your input; here's a proposal.
>>>> >>
>>>> >> First of all, what I really don't want is to add another template
>>>> >> parameter to Matrix and to add more enums/typedefs in xpr classes. So
>>>> >> I'm trying to put all the stuff related to that issue in the numeric
>>>> >> type itself. This way, only people who use that feature, pay for it.
>>>> >>
>>>> >> So here's the proposal. in NumTraits<T> we just add another typedef
>>>> >> for the accumulation type, and we define a function ei_saturate<T>(T
>>>> >> t) for all possible accumulation types T. For all basic types
>>>> >> (including uint8) we define the accumulation type to be just T and
>>>> >> ei_saturate(t) returns just t, so the default for integer types is the
>>>> >> clipping behavior. But then we can define (or let the user define)
>>>> >> more types, like a type that is a wrapper around uint8 with the
>>>> >> accumulation type set to uint32 and ei_saturate(t) actually saturating
>>>> >> to 255, etc. The user can then use a matrix with that type as scalar
>>>> >> type. If for a different matrix he wants a different accum type, he
>>>> >> just uses a different scalar type with a different type as
>>>> >> NumTraits<T>::AccumType. In fact, it's even OK to let the AccumType be
>>>> >> a template parameter of the wrapper-around-uint8 scalar type.
>>>> >>
>>>> >> Cheers,
>>>> >> Benoit
>>>> >>
>>>> >> 2009/4/1 Christian Mayer <mail@xxxxxxxxxxxxxxxxx>:
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>>>> >> > Benoit Jacob schrieb:
>>>> >> >> ah that's yet another different problem...
>>>> >> >>
>>>> >> >> with sparse matrices, the overflow problem arises only with a few
>>>> >> >> operations like sum().
>>>> >> >>
>>>> >> >> But with what you say, dense matrices of uint8, the overflow can
>>>> >> >> happen with a lot more operations: for example, any matrix product
>>>> >> >> will typically overflow! So I guess that a matrix product of unit8
>>>> >> >> matrices should return a matrix with a bigger scalar type...
>>>> >> >
>>>> >> > I'm working in the area of embedded software development where huge
>>>> >> > amounts of numerical software has to be dealt with in real time. As some
>>>> >> > of that code is quite old it's mostly written in fixed point, i.e. it's
>>>> >> > using normal integer operations (the variables usually have to be
>>>> >> > multiplied by a factor and an offset has to be added to get the "real
>>>> >> > world meaning" of each variable).
>>>> >> >
>>>> >> > In this context lots of programmers are looking for data types and
>>>> >> > possible overflows just to handle that problem, as each multiplication
>>>> >> > and addition could cause a problem.
>>>> >> >
>>>> >> > And there are usually two solutions: saturate or clip (i.e. just use the
>>>> >> > modulo value).
>>>> >> >
>>>> >> > => that's too far for eigen to handle
>>>> >> >
>>>> >> > But it might be a nice solution to offer (as a template parameter) a
>>>> >> > different data type as an result, so that the eigen user can handle this
>>>> >> > requirement each time it could appear in the best way for his algorithm.
>>>> >> > (And if possible we could also offer an saturating and an clipping
>>>> >> > version of the algorithm)
>>>> >> >
>>>> >> > CU,
>>>> >> > Chris
>>>> >> >
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