Re: [sage-devel] Dealing with libc math differences

[Erik Bray]

On Fri, Aug 12, 2016 at 9:42 AM, Jeroen Demeyer  wrote:
> On 2016-08-11 12:24, Erik Bray wrote:
>>
>> In this case the difference is just one ulp.
>
>
> To be more precise: the difference is actually about 0.59 ulp on Cygwin:
>
> sage: R = RealField(256)
> sage: log3_exact = R(3).log()
> sage: log3_cygwin = RDF(1.0986122886681096)
> sage: (R(log3_cygwin) - log3_exact)/log3_cygwin.ulp()
> -0.5914650915268009

Oh nice, I did't know you could do that.
In the above I meant the difference between the result I had on Linux
and on Cygwin which of course have the same floating point precision,
not the difference from the (closer to) exact value.  Using the same
calculation as above the difference of the Linux result from exact is
~0.41 ulp.

All the more reason to just add a small tolerance on this particular
test.  Thanks again!

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Re: [sage-devel] Dealing with libc math differences

[Jeroen Demeyer]

On 2016-08-11 12:24, Erik Bray wrote:

In this case the difference is just one ulp.


To be more precise: the difference is actually about 0.59 ulp on Cygwin:

sage: R = RealField(256)
sage: log3_exact = R(3).log()
sage: log3_cygwin = RDF(1.0986122886681096)
sage: (R(log3_cygwin) - log3_exact)/log3_cygwin.ulp()
-0.5914650915268009

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Re: [sage-devel] Dealing with libc math differences

[Erik Bray]

On Wed, Aug 10, 2016 at 2:45 PM, Thierry Dumont
 wrote:
> Le 10/08/2016 à 13:38, Erik Bray a écrit :
>> Hi all,
>>
>> Sorry if this has been discussed ad-infinitum before--I looked around
>> a bit but didn't find a definitive answer.
>>
>> I have one (well at least one) test that's failing on Cygwin due to
>> tiny difference in the last digit of the result of log(3).
>>
>> This leads to to several questions:
>>
>> 1) Is it worth investigating the reason for the difference?
>> 2) Is it worth trying to provide a workaround for the difference?
>> 3) Or should the test just be updated to ignore the last couple digits
>> of the result, and if so how (ellipses?)
>>
>> Thanks,
>> Erik
>>
> Hello,
>
> What do you mean by log(3) ?
>
> Is it log(3.) or log(RDF(3)) ?

Really what I meant was `float(log(3))` which I guess in Sage ends up
being same as `log(RDF(3))`

> With log(RDF(3)), this is classical; changing the library version, or
> the compiler version often changes the way some expressions and
> functions are computed. As floating point arithmetic is not associative,
> this is classical. With log(3.) (RealField()), I don't know.
> When we wrote the book "Calcul Mathématique avec Sage", we had this
> problem: after some release (some months) some  doctests of the chapter
> on numerical algebra and floating point numbers failed. The only work
> around we found was to truncate the last digit in the output, to try to
> test what should remain constant.

I have:

sage: R = RealField(100)
sage: log(R(3))
1.0986122886681096913952452369

Okay.  With Cygwin's libm:

sage: float(log(3))
1.0986122886681096

While on Linux I get:

sage: float(log(3))
1.0986122886681098

It looks like the latter result is properly rounded up (with an error
of 1ulp) while my result on Cygwin is just truncated.

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Re: [sage-devel] Dealing with libc math differences

[Erik Bray]

On Wed, Aug 10, 2016 at 3:08 PM, Jeroen Demeyer  wrote:
> On 2016-08-10 13:38, Erik Bray wrote:
>>
>> 1) Is it worth investigating the reason for the difference?
>
>
> No, but it is worth determining how bad the error is. In all cases, I would
> say that an error of less than 1 ulp is totally acceptable. If the error is
> 1 ulp or more for a basic function (like log) on a reasonable
> non-pathological input (like 3.0), I would consider that an upstream bug.
> Still, it would not necessarily be a problem for Sage if the error is a few
> ulp.

In this case the difference is just one ulp.

>> 3) Or should the test just be updated to ignore the last couple digits
>> of the result, and if so how (ellipses?)
>
>
> The best way is to use # (rel|abs) tol in the doctest.

Great, I found that shortly after posting.  I think in this case it
should probably be fine?

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Re: [sage-devel] Dealing with libc math differences

[Jeroen Demeyer]

On 2016-08-10 13:38, Erik Bray wrote:

1) Is it worth investigating the reason for the difference?


No, but it is worth determining how bad the error is. In all cases, I 
would say that an error of less than 1 ulp is totally acceptable. If the 
error is 1 ulp or more for a basic function (like log) on a reasonable 
non-pathological input (like 3.0), I would consider that an upstream 
bug. Still, it would not necessarily be a problem for Sage if the error 
is a few ulp.



3) Or should the test just be updated to ignore the last couple digits
of the result, and if so how (ellipses?)


The best way is to use # (rel|abs) tol in the doctest.

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Re: [sage-devel] Dealing with libc math differences

[Thierry Dumont]

Le 10/08/2016 à 13:38, Erik Bray a écrit :
> Hi all,
> 
> Sorry if this has been discussed ad-infinitum before--I looked around
> a bit but didn't find a definitive answer.
> 
> I have one (well at least one) test that's failing on Cygwin due to
> tiny difference in the last digit of the result of log(3).
> 
> This leads to to several questions:
> 
> 1) Is it worth investigating the reason for the difference?
> 2) Is it worth trying to provide a workaround for the difference?
> 3) Or should the test just be updated to ignore the last couple digits
> of the result, and if so how (ellipses?)
> 
> Thanks,
> Erik
> 
Hello,

What do you mean by log(3) ?

Is it log(3.) or log(RDF(3)) ?


With log(RDF(3)), this is classical; changing the library version, or
the compiler version often changes the way some expressions and
functions are computed. As floating point arithmetic is not associative,
this is classical. With log(3.) (RealField()), I don't know.
When we wrote the book "Calcul Mathématique avec Sage", we had this
problem: after some release (some months) some  doctests of the chapter
on numerical algebra and floating point numbers failed. The only work
around we found was to truncate the last digit in the output, to try to
test what should remain constant.

Note that:

sage: log(RDF(3))
1.0986122886681098
sage: log(3.)
1.09861228866811

But:
sage: log(RDF(3)).n(prec=53)
1.09861228866811
sage: log(3.).n(prec=53)
1.09861228866811

sage: log(RDF(3))==log(3.)
True

as we also know that:
sage: RDF.prec()==RealField().prec()
True


So in this case it is only a problem of rounding output.


Good luck.

Yours
t.



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<>

[sage-devel] Dealing with libc math differences

[Erik Bray]

Hi all,

Sorry if this has been discussed ad-infinitum before--I looked around
a bit but didn't find a definitive answer.

I have one (well at least one) test that's failing on Cygwin due to
tiny difference in the last digit of the result of log(3).

This leads to to several questions:

1) Is it worth investigating the reason for the difference?
2) Is it worth trying to provide a workaround for the difference?
3) Or should the test just be updated to ignore the last couple digits
of the result, and if so how (ellipses?)

Thanks,
Erik

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