[racket-dev] Floating-Point Compliance Testing

Excellent test! I can think of two things that could cause the difference:

  1. `flexpt' works around `pow' bugs on 64-bit Linux but not 32-bit
     (Racket can fix this one)

  2. 64-bit compile uses SSE instructions, and the SSE unit is better
     than the FPU

There are probably more possibilities.

Neil ⊥

On 02/08/2013 11:53 AM, Tobias Hammer wrote:
> Tested it too and got an interesting result. On a 32bit linux its:
>
> +nan.0
> +nan.0
> +nan.0
> +nan.0
> +nan.0
> +nan.0
> +nan.0
> +nan.0
>
> so, completely wrong. But on a 64bit Linux its correct if i use the 64bit
> racket version. When i try the 32bit build i get the wrong results again.
> I think you can blame it on 32 implementation of racket/libc/compiler or
> whatever. Not on the actual cpu in use because the hardware was always the
> same (2 identical computers, identical OS + version, only 32bit in one, 64
> in the other).
>
> Tobias
>
>
>
> On Fri, 08 Feb 2013 19:07:53 +0100, Neil Toronto <neil.toronto at gmail.com>
> wrote:
>
>> Back on list.
>>
>> A lot of things point to general sloppiness in either the FPU or C
>> libraries, but I'd like more information just in case. Can you reply
>> with the values of the following expressions on the Athlon?
>>
>>    (flexpt -1001.0 -1.3407807929942596e+154)
>>    (flexpt -1001.0 1.3407807929942596e+154)
>>    (flexpt -0.1 -1.3407807929942596e+154)
>>    (flexpt -0.1 1.3407807929942596e+154)
>>    (flexpt -744.4400719213812 -1.3407807929942596e+154)
>>    (flexpt -744.4400719213812 1.3407807929942596e+154)
>>    (flexpt -1.0 -1.3407807929942596e+154)
>>    (flexpt -1.0 1.3407807929942596e+154)
>>
>> You should get these values:
>>
>>    0.0 +inf.0 +inf.0 0.0 0.0 +inf.0 1.0 1.0
>>
>> I think these are cases Racket handles specially instead of handing
>> off to C's `pow' on platforms where we know `pow' handles them
>> wrongly. We might need to ask Matthew to expand that set of platforms.
>>
>> Small rounding errors like this:
>>
>>    ((fl*/error -6.87181640380727e-156 2.3341566035927725e-153)
>>     0.7079979032237692)
>>
>> which are only 1 bit off, are probably the cause of these errors:
>>
>>    ((fl2log 1.5124390004859715e-308 0.0) 4294967296.220986)
>>    ((fl2log1p 3.799205740343036e+246 1.4492752004468653e+230)
>>     549755813887.9473))
>>
>> `fl2log' and `fl2log1p' are 103-ish-bit logarithm implementations used
>> in certain tricky subdomains of a few special functions. They assume
>> arithmetic is always correct and are very sensitive to rounding
>> errors. You're getting about 65-bit output precision for certain
>> inputs. We can almost certainly blame the FPU because IEEE 754
>> requires arithmetic to be implemented and correctly rounded.
>>
>> IEEE 754 only *recommends* typical irrational functions. When they're
>> not implemented in hardware, C libraries compute them in software. So
>> I don't know whether these and others are the FPU's or C library's fault:
>>
>>    ((flsin 2.5489254492488616e+52) 22637349860729424.0)
>>    ((flcos 3.91520018229574e+49) 6369061509154398.0)
>>    ((fltan 1.6614020610450763e+21) 9158003261155244.0)
>>    ((flexp 16.938769136983012) 7.0)
>>    ((flexp 282.52374429474406) 102.0)
>>    ((flexp -10.0) 4.0)
>>    ((flexp -708.3964185322641) 124.0)
>>
>> These errors come from not doing argument reductions carefully enough.
>> The trigonometric functions probably don't compute x % 2*pi using a
>> high-precision 2*pi when x is large. They seem to be correct enough
>> when x is small, though.
>>
>> The exponential function wasn't tested well at the boundaries of its
>> domain:
>>
>>    ((flexp 709.782712893384) +inf.0)
>>
>> 709.782712893384 is (fllog +max.0), and (flexp (fllog +max.0)) should
>> be near +max.0, not (as I suspect) +inf.0.
>>
>> I don't know whether Racket should do anything about these errors. I
>> don't think it would be too hard to do something like Java's
>> StrictMath, but it would take time.
>>
>> In the meantime, don't use the Athlon for serious numerical computation.
>>
>> Neil ⊥
>>
>> On 02/08/2013 12:13 AM, Laurent wrote:
>>> Hi Neil,
>>>
>>> Interaction in a terminal is attached, using Racket 5.3.2.3.
>>>
>>> Some details about my machine:
>>> Linux 3.2.0-37-generic-pae #58-Ubuntu SMP Thu Jan 24 15:51:02 UTC 2013
>>> i686 athlon i386 GNU/Linux
>>>
>>> In particular, I use a 32bits Ubuntu 12.04.2 on a 686 processor, if
>>> that's of any interest.
>>>
>>> Cheers,
>>> Laurent
>>>
>>>
>>>
>>>
>>> On Fri, Feb 8, 2013 at 1:15 AM, Neil Toronto <neil.toronto at gmail.com
>>> <mailto:neil.toronto at gmail.com>> wrote:
>>>
>>>     On 02/07/2013 12:09 PM, Laurent wrote:
>>>
>>>         On Thu, Feb 7, 2013 at 5:50 PM, Neil Toronto
>>>         <neil.toronto at gmail.com <mailto:neil.toronto at gmail.com>
>>>         <mailto:neil.toronto at gmail.com
>>>         <mailto:neil.toronto at gmail.com>__>> wrote:
>>>
>>>              Today is not that day, but thanks for asking about this
>>>         anyway. :)
>>>
>>>
>>>         On one machine with Ubuntu 12.10, I get no error, but on another
>>>         machine
>>>         with Ubuntu 12.04, I get more than 14000 errors, many of them
>>> being
>>>         +inf.0 and other numbers with big exponents (is my machine
>>>         really that
>>>         bad?).
>>>         Is this exactly the kind of reply you want to avoid for now or
>>>         are you
>>>         interested in a report?
>>>
>>>
>>>     Alrighty, you've piqued my interest. Better send it off-list,
>>> though. :)
>>>
>>>     Neil ⊥
>>
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>
>