Re: [eigen] Overflow in sum()

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

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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