Re: [Boost-users] [numeric conversation] behavior on std::numeric_limits<double>::max() + eps with numeric_cast

Subject: Re: [Boost-users] [numeric conversation] behavior on std::numeric_limits<double>::max() + eps with numeric_cast
From: Olaf Peter (ope-devel_at_[hidden])
Date: 2014-06-09 14:33:59

Am 09.06.2014 14:33, schrieb Antony Polukhin:
>
>
>     Hello,
>
>     at this time I play with numeric_cast and struggle with this:
>
>     first:
>                 double z = std::numeric_limits<double>::max();
>                 z += 2*std::numeric_limits<double>::epsilon(); //
>     doesn't matter if 1*eps
>                 std::cout << z << std::endl;
>                 std::cout << boost::numeric_cast<double>(z) << '\n';
>
>     I would expect that an exception is thrown which isn't, the output is
>     1.79769e+308
>     1.79769e+308
>
>
> Machine epsilon gives an upper bound on the relative error due to 
> rounding in floating point arithmetic.
> In other words absolute error for max value would be:
>
> double non_rel = std::numeric_limits<double>::max() * 
> std::numeric_limits<double>::epsilon();
>
> 2*std::numeric_limits<double>::epsilon() is much less than non_rel and 
> adding it won't cause overflow: number will be rounded to 
> std::numeric_limits<double>::max()
thanks for answer, but

eps = 2.22045e-16
max*eps = 3.99168e+292

on my machine, no_rel is a high value ... Is this right?,  I thought eps 
is the absolute error/uncertainly of representation in real values. But 
probably I have to read about FP ...

Thanks,
Olaf