Re: [eigen] Matrix2i mean

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

I agree with Peter here. Trying to workaround overflow behavior for 
sum/prod/mean would be way to complicated to implement generically.

We _could_ provide something like `stable_mean()` which with some 
sophisticated algorithm works around overflows. If larger types are 
available, this could just cast to that type before summing.

But you can do that manually already:

    int32_t mean = m.cast<int32_t>().mean();
    // convert back to int16_t, if you like ...




The reason that this line worked as you expected:

    double mean = (INT16_MAX / 2.0 + INT16_MAX + 2 + 2) / 4.0;

is that due to the `2.0` in `INT16_MAX / 2.0` the expression gets 
converted to `double` and stays to be `double` even after adding more 
integers or `uint16_t`. And `double` is perfectly capable of adding your 
values without overflowing.

If you insert `INT16_MAX / 2.0` into your matrix, it gets converted to a 
`int16_t` (already truncating away the `.5` part) and additions for 
`mean()` happen in the `int16_t` domain, which overflows (which is 
technically undefined behavior).


Christoph

On 05/11/2019 10.07, Peter wrote:
> Dear Petr,
>
>
> Am 05.11.19 um 00:35 schrieb Petr Kubánek:
> > Hi,
> >
> > calculating mean on int matrix fails to produce expected results - see
> > below. I noticed
> [...]
> > Obviously all similar reduxes (sum, prod) fails as well. Is there a way
> > how to change type used as the internal storage and result for sum.
> > mean calculations?
>
> In my opinion Eigen behaves perfectly well.
> The problem you face is related to the fact, that the compiler can 
> calculate known
> expression with higher precision, see the example below, where I also 
> introduced
> the argc/argv only to avoid further compiler optimizations.
>
> Output on my machine:
>
> -4095 12288 -4095
> 12288.5 12288 -4095
>
> Best regards,
> Peter
>
>
> #include <Eigen/Eigen>
> #include <iostream>
>
> int main( const int argc, const char *argv[] )
> {
>    int16_t  Two = (argc>1) ? atoi(argv[1]) : 2;
>    int16_t  Max = (argc>99) ? atoi(argv[99]) : INT16_MAX;
>
>    Eigen::Matrix<int16_t, 2, 2> m;
>    m <<
>      INT16_MAX / 2, INT16_MAX,
>      2, 2;
>
>    int16_t mean = ( Max/2 + Max + Two + Two ) / int16_t(4);
>    int16_t mean2 = Max/2;
>    mean2 += Max;
>    mean2 += Two;
>    mean2 += Two;
>    mean2 /= int16_t(4);
>    std::cout << m.mean() << " " << mean << " " << mean2 << std::endl;
>
>    Eigen::Matrix<double, 2, 2> md = m.cast<double>();
>    std::cout << md.mean() << " " << mean << " " << mean2 << std::endl;
> }

--
 Dr.-Ing. Christoph Hertzberg

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