This is the mail archive of the mailing list for the GCC project.

Index Nav: [Date Index] [Subject Index] [Author Index] [Thread Index]
Message Nav: [Date Prev] [Date Next] [Thread Prev] [Thread Next]
Other format: [Raw text]

Re: weird optimization in sin+cos, x86 backend

On 2012-02-05 20:52:39 +0000, Dave Korn wrote:
> On 05/02/2012 19:01, Vincent Lefevre wrote:
> > On 2012-02-04 13:00:45 +0100, Andreas Schwab wrote:
> >> But it is indistinguishable from 10^22+pi.  So both -0.8522008497671888
> >> and 0.8522008497671888 are correct results, or anything inbetween.
> > 
> > No, 10^22 and 10^22+pi are different numbers. 
>   Only one of which can be represented in floating point.
>   So, the gist of the argument is that FP numbers do not represent ranges;
> they are a precise but sparse representation of the number line.
>   It's still not a lot of use doing trig up at the top end of the FP range
> where 1 ulp > 2pi.  The odds of the value that you wanted to represent
> actually being representable are tiny, and hence so are the odds of getting
> anything like the result you were hoping for.  But, at least identities should
> work.

Yes, but one point I'd like to make is that one may want to specify a
portable result, as for instance, one may want to perform computations
on a heterogeneous network of machines. Even on a single machine,
there may be different algorithms/implementations to evaluate some
function (e.g., compile time vs runtime, and grouped evaluations such
as with a sincos function if both sin and cos are evaluated on the
same argument). And correct rounding is the only good specification
if one wants a portable result.

Vincent Lefèvre <> - Web: <>
100% accessible validated (X)HTML - Blog: <>
Work: CR INRIA - computer arithmetic / AriC project (LIP, ENS-Lyon)

Index Nav: [Date Index] [Subject Index] [Author Index] [Thread Index]
Message Nav: [Date Prev] [Date Next] [Thread Prev] [Thread Next]