[Cuis-dev] Negative sqrt

[Juan Vuletich]

Hi Gerald,

On 12/30/2020 9:32 AM, Gerald Klix via Cuis-dev wrote:
> Hi Juan,
>
> please see below.
...
>> Note that if you haven't selected "Install Complex" or "Don't ask 
>> again", `-4.0 sqrt` will still ask the question, the same as if the 
>> receiver was an integer.
>>
>> The difference is if you chose not to install Complex. And, yes, it 
>> is the intended behavior.
>>
>> If Complex is installed, -4 sqrt and -4.0 sqrt answer Complex. But if 
>> not, -4 sqrt is an error, but -4.0 sqrt isNaN. This is because of the 
>> Floating Point standard.
>>
>> Floats play by their own rules, stated in the IEEE 754 standard. They 
>> include special values Float infinity (so 1.0 / 0.0 = Float infinity) 
>> and Float nan (so -4.0 sqrt isNaN). The other Number classes don't 
>> handle these concepts, and just give errors.
> OK, point taken: I agree.
>>
>> Strict compliance of IEEE 754 is important. Most well known numeric 
>> algorithms are guaranteed to give the expected results if the 
>> standard is followed, and might break otherwise.
> Well, strict IEEE 754 compliance will also require  the programming 
> language to raise/signal/throw
> exceptions for certain types of NaNs, if
> the program/programmer requests those.

Yes. For Signaling NaNs. Section 6.2 of the standard says that the only 
way to generate a Signaling NaN is as a constant set by the programmer. 
This behavior can easily be implemented in Smalltalk with a SignalingNaN 
class, perhaps inheriting from Object, so no numeric operation will work 
on them, and an exception will be raised. The usual Smalltalk practice 
is to just use nil.

Supporting that behavior for signaling NaNs would require modifying the 
VM: Just did a quick experiment, and all NaNs are treated as silent NaN 
by the VM.

>
> IEEE-754 2019 Clause 8.3 specifies so
> called "immediate exception handling",
> which, IHMO, should be implemented by signaling
> Smalltalk exceptions. But this interpretation
> is based on my limited understanding of the standard's concepts and 
> may be wrong.
> I am by no means an expert in this domain,
> I only want to express my impression,
> that full IEEE-754 is probably not easy to achieve. Let's be careful 
> here!
>
>
> Best Regards,
>
> Gerald

Having worked with numerical algorithms using floating point, mainly in 
image and signal processing, but also in numerical linear algebra and 
discrete simulations, I never saw Signaling NaNs have any relevance. I 
don't think they are used much in practice. And they can be implemented 
in Smalltalk.

Still, you may bring the issue to VM-Dev. If floating point primitives 
are made to fail when encountering a Signaling NaN, I'll be happy to 
raise an appropriate Smalltalk exception.

Thanks,

-- 
Juan Vuletich
www.cuis-smalltalk.org
https://github.com/Cuis-Smalltalk/Cuis-Smalltalk-Dev
https://github.com/jvuletich
https://www.linkedin.com/in/juan-vuletich-75611b3
@JuanVuletich