Re: Zeroes and infinities

[Peter Henderson <petercbh@xxxxxxxxxxx>]

Nick Maclaren wrote:
> Thorsten Siebenborn <7_born@xxxxxx> wrote:
>   
> > The branch cuts which are the whole reason Kahan implemented
> > this abominable negative zero are equally good solvable with
> > infinitesimals.
.
.
.
> Also, branch cuts are not the only reason - there is also interval
> arithmetic.  In my view, branch cuts are an abomination in any
> specification intended to be used by ordinary programmers; I was
> taught them as part of my degree and have never needed to use them
> since - and damn few users of complex numbers have ever HEARD of
> them.  However, they ARE critical in some fields.  It's a thorny
> problem.
>   
To probably misquote Einstein, things should be as simple as possible, 
but no simpler.  Any user who is using a function with a branch cut and 
who ends up computing values near the the branch is going to know about 
them pretty soon, whether they have heard about them or not, in which 
case they better hope they are in the specification.  Fortunately, for 
the basic functions, the branch cuts always occur on the real or 
imaginary axes.  This means +0 and -0 can be used to help the programmer 
deal with them as they see fit.  For other cases, often a related 
function can be obtained using simple shifts, so that this again is the 
case.  So if there is a thorny problem, then at least there is a solution.

Regards,
Peter Henderson