Add Ord Laws to next Haskell Report

[Merijn Verstraaten]

> 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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