[Rd] Numerical instability in new R Windows development version
Duncan Murdoch
murdoch.duncan at gmail.com
Fri Jan 27 19:37:45 CET 2012
On 27/01/2012 1:26 PM, Duncan Murdoch wrote:
> On 27/01/2012 12:32 PM, Prof Brian Ripley wrote:
> > On 27/01/2012 13:26, Duncan Murdoch wrote:
> > > On 12-01-27 7:23 AM, Hans W Borchers wrote:
> > >> I have a question concerning the new Windows toolchain for R>= 2.14.2.
> > >> When trying out my package 'pracma' on the win-builder development
> > >> version
> > >> it will stop with the following error message:
> > >>
> > >> > f3<- function(x, y) sqrt((1 - (x^2 + y^2)) * (x^2 + y^2<= 1))
> > >> > dblquad(f3, -1, 1, -1, 1) # 2.094395124 , i.e. 2/3*pi , err = 2e-8
> > >> Warning in sqrt((1 - (x^2 + y^2)) * (x^2 + y^2<= 1)) : NaNs produced
> > >> Warning in sqrt((1 - (x^2 + y^2)) * (x^2 + y^2<= 1)) : NaNs produced
> > >> Error in integrate(function(y) f(x, y), ya, yb, subdivisions = subdivs, :
> > >> non-finite function value
> > >> Calls: dblquad ...
> > >> <Anonymous> -> f -> do.call -> mapply -> <Anonymous> -> integrate
> > >> Execution halted
> > >> ** running examples for arch 'x64' ... ERROR
> > >> Running examples in 'pracma-Ex.R' failed
> > >>
> > >> This probably means that the following expression got negative for some
> > >> values x, y:
> > >>
> > >> (1 - (x^2 + y^2)) * (x^2 + y^2<= 1)
> > >
> > > I think you're right, it's a bug, hopefully easy to fix. Here's a
> > > simpler version:
> > >
> > > x<- 0*(-1)
> > > sqrt(x)
> > >
> > > x is a "negative zero", and the sqrt() function incorrectly produces a
> > > NaN in the new toolchain.
> >
> > Well, for some definition of 'incorrectly'. It is clearly what the
> > author of that piece of code intended.
> >
> > It would be helpful if people would cite definitive references. Someone
> > is going to have to report this on the bugtracker, and at present I
> > don't have enough evidence to do so: the C99/C11 standards do not seem
> > to mandate a particular value (they do say what happens for values less
> > than zero, but C compilers are allowed to have or not have signed
> > zeroes). (Various Unix-alikes say what they do, usually -0, but that's
> > not evidence that other answers are 'incorrect'.)
>
> Section 6.3 of IEEE 754-2008 says
>
> Except that squareRoot(−0) shall be −0, every numeric squareRoot result
> shall have a positive sign.
I believe the corresponding ISO standard is ISO/IEC/IEEE 60559:2011, but I don't have a copy, and I don't think my library does.
Duncan Murdoch
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