[Rd] Numerical instability in new R Windows development version

[Stephen Weston]

On Fri, Jan 27, 2012 at 1:40 PM, Duncan Murdoch
<murdoch.duncan at gmail.com> 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'.)
>
>
> This page:
>
> http://pubs.opengroup.org/onlinepubs/9699919799/functions/sqrt.html
>
> also says that the correct answer is -0.  I don't know if that has any
> authority at all...
>
> Duncan Murdoch

Section 5.4.1 "Arithmetic operations" of "IEEE Standard for Floating-
Point Arithmetic", IEEE Std 754-2008 says:

  "The operation squareRoot(x) computes √ x. It has a positive sign for
all operands ≥ 0, except that squareRoot(−0) shall be −0."

- Steve