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: Antony Polukhin (antoshkka_at_[hidden])
Date: 2014-06-09 08:33:00

2014-06-09 10:53 GMT+04:00 Olaf Peter <ope-devel_at_[hidden]>:

> 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()

-- 
Best regards,
Antony Polukhin