Float precision and float equality

[dbd]

On Dec 7, 4:28 am, sturlamolden <sturlamol... at yahoo.no> wrote:
> ...
>
> You don't understand this at all do you?
>
> If you have a sine wave with an amplitude less than the truncation
> error, it will always be approximately equal to zero.
>
> Numerical maths is about approximations, not symbolic equalities.
>
> > 1.0 + eps is the smallest value greater than 1.0, distinguishable from
> > 1.0.
>
> Which is the reason 0.5*eps*sin(x) is never distinguishable from 0.
> ...

A calculated value of 0.5*eps*sin(x) has a truncation error on the
order of eps squared. 0.5*eps and 0.495*eps are readily distinguished
(well, at least for values of eps << 0.01 :).

At least one of us doesn't understand floating point.

Dale B. Dalrymple