Re: Bit-exact floating-point computations

Christian Bau <christian.bau@cbau.freeserve.co.uk> wrote:
>
>I am trying desperately here to make you understand what I wrote:
>There is nothing wrong with giving a specification of the sin ()
>function that will always give the same result for the same
>argument. No problem at all demanding that sin (1.0e300) should give
>the same result on any processor. The stupid thing is demanding that
>sin (1.0e300) should return the almost, but not completely guaranteed
>correctly rounded result, because that result is absolutely
>meaningless.


Agreed. The accuracy definition that I favour is that, if we have
an operation (a,b,...) = f(d,e,...), then consider the minimum over
all possible mathematical (i.e. real, not floating-point) values of
A,B,...,D,E,... such that (A,B,...) = F(D,E,...) with no error of
max(err(a,A),err(b,B),...,err(d,D),err(e,E),...).


err(x,y) is defined to be a suitable relative/absolute error, but
assume it to be relative if all values are bounded away from zero.


>PS. When I said there is nothing wrong with a specification that
>demands reproducible results, there have been arguments against
>it. The best argument is that if you run your code on two
>implementations that are both of good quality but not identical, and
>you get different results, then this is often just a sign that there
>is something wrong with your code.


Now, how could you possibly guess what my view on that one is? :-)




Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email: nmm1@cam.ac.uk
Tel.: +44 1223 334761 Fax: +44 1223 334679

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