Re: [eigen] Matrix2i mean

[Christoph Hertzberg <chtz@xxxxxxxxxxxxxxxxxxxxxxxx>]

On 05/11/2019 16.11, Peter wrote:
> [...]
>
> actually, this would also be interesting for the scalar products in 
> general, namely a different
> type for accumulating the sums within a scalar product, e.g. as yet 
> another template parameter for the matrices.

Adding another template parameter to basic types is not an option. This 
would break ABI and API compatibility (even if the parameter has a default).

You could create your own custom type `my_int16` for which `my_int16 * 
my_int16` results in a `my_int32` (this needs to be told to Eigen, 
similar to how real*complex products are handled).

> > [...]
>
> I think it's more subtle than that.
> Even
>
>    int16_t  Two =  2;
>    int16_t  Max =  INT16_MAX;
>    int16_t mean = ( Max/2 + Max + Two + Two ) / int16_t(4);
>
> doesn't produce an overflow.

Yes, because `Max/2` gets implicitly converted to `int`. Actually, even 
adding two `int16_t` get implicitly converted to `int` (search for 
integer promotion rules -- I don't know them entirely either). And 
dividing an `int` by an `int16_t` results in an `int` which is only 
afterwards converted to `int16_t`.

In contrast, Eigen::DenseBase::sum() does something (more or less) 
equivalent to:

    T sum = T(0);
    for(Index i=0; i< size(); ++i)
        sum+=coeff(i);
    return sum;

i.e., after each addition the result gets reduced to the scalar type of 
the matrix, thus it will immediately overflow.

And mean() essentially just takes the return value of `sum()` and 
divides it by the size.


Christoph


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