Floats, the true ieee next generation Re: Add Ord Laws to next Haskell Report

Fri Feb 8 20:05:24 UTC 2019

I think the algebraic property we usually want for nice integer ish things
is intergral domain. Which is a stronger property than ring. Pardon the
confusion

On Fri, Feb 8, 2019 at 3:03 PM Carter Schonwald <carter.schonwald at gmail.com>
wrote:

> No.  A ring can’t have 2x=0 for x not zero.  Thus int can’t  be
>
> And by ring I mean an algebraic structure where you have a multiplicative
> group that doesn’t generate zero from products of nonzero elements ...
>
> Phrased differently: Int doesn’t have a multiplicative group structure on
> the nonzero elements. That makes it a pretty nasty ring. Negate on minBound
> should be an overflow exception so you can have actual sane semantics.
> This is an old dead horse with lots of blood written about it.
>
> https://ghc.haskell.org/trac/ghc/ticket/8695 has some related discussions
>
>
> On Fri, Feb 8, 2019 at 2:53 PM Jens Blanck <jens.blanck at gmail.com> wrote:
>
>> > minBound + minBound :: Int
>> 0
>> > negate minBound == (minBound :: Int)
>> True
>> > 42 + negate 17 :: Word
>> 25
>>
>> Int and Word are currently rings. What proportion actually uses them as
>> such would be interesting to know but I guess it is very small. I wouldn't
>> dare to reason about Int and Word as rings as there is no guarantee on
>> which ring they are. Int64 and Word64 and so on; yes, those can be reasoned
>> about.
>>
>> I'd be very happy to see a separate type for signalling integral types.
>> Personally, I'd make them the default choice.
>>
>> On Fri, 8 Feb 2019 at 19:27, Carter Schonwald <carter.schonwald at gmail.com>
>> wrote:
>>
>>> I’m not sure if they currently have full ring structure , but  I do
>>> agree that trapping and non trapping int and word are useful.
>>>
>>> Simple example where all the finite signed ints work wrong today :
>>>
>>> There’s no proper additive inverse for minBound :: int
>>>
>>> Likewise , what’s our current definition of negate on finite word types?
>>>
>>> On Fri, Feb 8, 2019 at 2:12 PM David Feuer <david.feuer at gmail.com>
>>> wrote:
>>>
>>>> No, no, no. Int and Word are *rings*, which let's us apply a ton of
>>>> mathematical reasoning to their arithmetic. Trapping overflow would throw
>>>> all that completely out the window. If you want to trap overflow, please
>>>> use different types!
>>>>
>>>> On Fri, Feb 8, 2019, 2:07 PM Lennart Augustsson <lennart at augustsson.net
>>>> wrote:
>>>>
>>>>> I would *hate* to lose quiet NaNs.  They can be very useful.  But I’d
>>>>> be fine having them as a separate type.
>>>>>
>>>>> And while we’re at it, why not make Int overflow and underflow cause a
>>>>> trap as well?  With a different type if you want to wrap.
>>>>>
>>>>>
>>>>> On Fri, Feb 8, 2019 at 08:34 Carter Schonwald <
>>>>> carter.schonwald at gmail.com> wrote:
>>>>>
>>>>>> Thanks for eloquently summarizing , better than I would , what I
>>>>>> thought I had laid out.
>>>>>>
>>>>>> Ieee floating point has fantastic hardware support .  May as well be
>>>>>> the first real language to actually use it correctly. :)
>>>>>>
>>>>>> On Fri, Feb 8, 2019 at 5:21 AM Merijn Verstraaten <
>>>>>> merijn at inconsistent.nl> wrote:
>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> > On 8 Feb 2019, at 10:57, Sven Panne <svenpanne at gmail.com> wrote:
>>>>>>> >
>>>>>>> > Am Do., 7. Feb. 2019 um 23:31 Uhr schrieb Merijn Verstraaten <
>>>>>>> merijn at inconsistent.nl>:
>>>>>>> > Our goal is to make "compare NaN n" impossible to happen. [...]
>>>>>>> >
>>>>>>> > Well, what is supposed to happen then when you *do* see a NaN,
>>>>>>> e.g. one produced from a foreign call? You *will* see NaNs in Haskell if
>>>>>>> you interact with other languages, most of them take a far less religious
>>>>>>> approach to floating points calculations.
>>>>>>>
>>>>>>> This is not true. As Carter pointed out we can setup the CPU to trap
>>>>>>> NaNs *even in foreign calls*. So, in theory we CAN rule this out safely.
>>>>>>> Doing this we can simply convert the trap into an exception at the FFI
>>>>>>> boundary.
>>>>>>>
>>>>>>> Now, there are cases were this is problematic, so as said before we
>>>>>>> will probably need to allow people to optionally switch on 'value NaNs',
>>>>>>> because the foreign code isn't exception safe or for other reasons, but
>>>>>>> this is manageable. Via, for example having an annotation on foreign
>>>>>>> imports whether you want to trap or not.
>>>>>>>
>>>>>>> In the scenario where someone switches to value NaNs, we are *still*
>>>>>>> not worse off than we are now. The things you suggest already happen *now*,
>>>>>>> so the only thing we're advocating is making it possible to have more sane
>>>>>>> behaviour in the future.
>>>>>>>
>>>>>>> Any IEEE-754 compliant implementation of Double that doesn't use
>>>>>>> trapping NaN can, by definition, never ever be a sane implementation of
>>>>>>> Ord. As IEEE-754 *requires* "NaN /= NaN", so equality symmetry doesn't
>>>>>>> apply to NaNs and there is *no* safe way to sort/order data containing NaNs.
>>>>>>>
>>>>>>> I've run into several nasty issues of trying to sort lists
>>>>>>> containing NaNs (not just Haskell, also Python and C) and it's *not* just
>>>>>>> the NaNs that are affected, entire subsequences end up getting sorted wrong
>>>>>>> based on the comparison with NaN and you end up with completely garbled and
>>>>>>> unsorted data.
>>>>>>>
>>>>>>> In other words, there are only two ways to get sane behaviour from
>>>>>>> Double with regards to ordering:
>>>>>>>
>>>>>>> 1. Trapping NaN represenation
>>>>>>> 2. Deviate from IEEE-754 semantics
>>>>>>>
>>>>>>> To me, option 2 is out of the question, it's the one consistent
>>>>>>> thing across language we have when it comes to floating point. I understand
>>>>>>> that *always* using trap representation isn't feasible, but allowing people
>>>>>>> to optionally switch to value NaNs leaves us no worse off than we are
>>>>>>> *right now*, and per above, there is literally no way to improve the
>>>>>>> situation wrt value NaNs without sacrificing IEEE-754 compliance.
>>>>>>>
>>>>>>> Cheers,
>>>>>>> Merijn
>>>>>>> _______________________________________________
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>>>>>>>
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