Proposal: Add log1p and expm1 to GHC.Float.Floating

[John Lato]

On Sun, Apr 20, 2014 at 6:37 PM, Edward Kmett <ekmett at gmail.com> wrote:

>
>
> Sent from my iPad
>
> On Apr 20, 2014, at 8:49 PM, John Lato <jwlato at gmail.com> wrote:
>
> On Sun, Apr 20, 2014 at 5:20 PM, Edward Kmett <ekmett at gmail.com> wrote:
>
>> The proposal is worded the way it is to get a strict monotonic
>> improvement over the status quo.
>>
>> With them in the class it becomes possible to get the instances fixed.
>> With them outside of the class in some needless extra hair-splitting class
>> added on later like we have to use today, then someone who would otherwise
>> just use them is needlessly hoist on the dilemma of using a more
>> restrictive class and just accepting the fact that they can't work with
>> third party numeric types for the most part at all, or reverting to the
>> poor version of the numerics to widen their audience.
>>
>> This leads to the equivalent of needless divisions between 'traverse' vs.
>> 'mapM' forever.
>>
>
> I don't think a separate class is ideal, I just think it's better than
> your original proposal.
>
>
>
> I think reasonable people can disagree and come down on either side of
> this issue.
>

Sure.

>
>
> With defaults you are never worse off than you are today, but defaults you
>> *always* have to worry about whether you should use them.
>>
>
> This isn't correct.  Today, I don't have exp1m.  I have no expectation
> that any type will use an appropriate fused algorithm, nor that I won't
> lose precision.  If exp1m is defined with defaults as proposed, and I use
> exp1m for a type that doesn't define it, I may lose precision, leading to
> compounding errors in my code, *even though I used the right function*.
>
>
> I'm coming at this from the perspective that I should never be worse off
> having called expm1 than I would be in the world before it existed. Your
> way I just crash making me much worse off. I'm asking for extra bits of
> precision if the type I'm using can offer them. Nothing more.
>

And I'm saying that if you ask for extra bits of precision, and the type
could offer them but doesn't, a crash is better than not giving extra
precision.  FP algorithms can be highly sensitive to precision, and it's a
good bet that if somebody is asking for specialized behavior there's a
reason why.  I think it's better to fail loudly and point a finger than to
fail silently.

If I'm using log1p because my algorithm requires that precision, replacing
log1p with log (1+x) is not a safe transformation.  But that's what your
default instance does.


>
>
>> Let's look at it another way.
>>
>> By putting in defaults the costs of the proposal are borne by the people
>> who want to use the new feature.
>>
>
> Yes.  When users use the new feature with types that don't implement it
> and get an incorrect answer, there will certainly be high costs involved.
>
> Let's look at it another way.
>
> Do you want to track down bugs due to exp1m not implementing the
> appropriate fused algorithm?
>
> Or alternatively, do you want to implement a default function that's not
> even guaranteed to work as documented?  With a silent failure mode?  So
> library authors don't have to fix up their libraries?  That seems very
> wrong to me.
>
>
>> Moreover, if we should decide to adopt wren's half-suggestion of
>> continuing to expand support for other numerical primitives that have broad
>> support we could do so without  great deal of fanfare, and the handful of
>> people who actually do numeric computation can talk to the handful of
>> people who write numeric instances that high up the foodchain to get the
>> important ones fixed in packages like vector-space, linear, diagrams, etc.
>>
>
>> Without defaults everyone who ever wrote a Floating instance by hand
>> would need to know about log1p or wren's log1mexp and they would be
>> forced into using CPP in their code to work around a feature they don't
>> care about and if they couldn't be bothered then the user who wanted a bit
>> of extra precision now just starts crashing. The risk averse would
>> simply take the path with worse precision or get shoved back into the
>> world of code duplication and 'mapM' vs 'traverse'.
>>
>
> Are you arguing for a separate class?  Because that's what it sounds like.
>  Besides, if you aren't familiar with precision issues you have no business
> writing a Floating instance by hand that does anything more than lift over
> more fundamental types.
>
> I think it's better that exp1m crash than that it not give extra
> precision, since the extra precision is the whole point of the function.
>  When I call a function, I want to get the function I mean.
>
> I'm not actually arguing for a separate class.  I think these belong in
> Floating as well.  I'm just arguing against a default that doesn't work as
> specified.
>
>
> If expm1 crashes I'm back to duplicating code and this proposal does
> nothing to improve my life over doing exactly what I can do now, but do not
> wish to continue doing, which is maintain a separate code path entirely
> with no effective way to transparently switch when greater precision is
> available.
>

You wouldn't duplicate code.  You would go to the author of the type that
doesn't implement that function and ask them to implement it.  Isn't that
exactly what you said you wanted?  To get the function you mean and know
who to talk to in order to get it implemented?  Your proposal doesn't even
provide the function you mean!

Also, I note you neglected to answer my rhetorical question :)
Introducing bugs whereby functions don't behave according to standards is
really, really poor design.  I don't see how saving some library authors
some work is worth that cost to users.


>
>
>> I know for me personally it would force me to double the amount of
>> numeric code I write, just to maximize my audience. I really don't want to
>> go there. I just want to be able to call the function I mean, and to be
>> able to talk to the right people to make it do the right thing.
>>
>
> exp1m = error "Go bug some library author to implement exp1m"
>
> would accomplish that even more efficiently, since it will directly point
> users to the right people.
>
>
> And in exchange, ever library author even the vast majority of whom will
> never have a user who cares about this feature needs to care or get a
> warning or we silently cover up a real error that should be a warning
> behind their back, and no user can trust that it is safe to call the
> function.
>

I think just providing implementations for Float/Double will cover >90% of
use cases and convince users that it's safe to call the function.  GND will
probably cover another 5-8% of uses.  I think it's a quite small tail we're
discussing here.  And I'll even admit that, since for *some* types log1p x
= log (1+x) will work correctly, it's an even smaller group of users I'm
concerned about.  But I still think it's an unreasonable price to pay.


>
> I don't want to duplicate all my code and I don't want to randomly crash,
> I want to eke out a few bits of mantissa if they are available and not be
> worse off than I am today for that privilege.
>

If you wrote code that crashed under an error default, that same code would
be worse off than it is today because users would expect that it does the
right thing and it fails silently.

The point of these functions isn't just to provide convenient algebraic
shortcuts.  It's to provide extra precision for numerically-sensitive
computations.  If users don't know about it, they'll just use exp/log and
be ok.  But users who require that extra precision should either get it or
be informed that it's not available.  Ideally by a compile-time error, but
I don't know a reasonable way to implement that, so a run-time error is the
next best thing.

I simply do not understand why you think it's appropriate to provide a
function that explicitly doesn't do what it's supposed to.  But we're
unlikely to sway each other here without further input, so I guess

+0.1 to the OP
+0.5 for error defaults
+1 for no defaults

John L.




>
> -Edward
>
>
>  -Edward
>>
>>
>> On Sun, Apr 20, 2014 at 7:32 PM, John Lato <jwlato at gmail.com> wrote:
>>
>>> On Sat, Apr 19, 2014 at 5:49 AM, Edward Kmett <ekmett at gmail.com> wrote:
>>>
>>>> With the defaults the code is never worse than it is forced to be right
>>>> now and users do not need to create CPP blocked code to work around this
>>>> addition.
>>>>
>>>
>>> I usually like defaults, and avoiding CPP is good, however with the
>>> defaults users will expect better code than they get.  We aren't doing
>>> anyone any favors by introducing the possibility of silent floating-point
>>> precision loss from 'exp1m'.  An "error" default would be better.
>>>
>>> Besides, the code would be worse than it's forced to be now.  At least
>>> now users who care about this run headlong into the issue.  If we provide
>>> exp1m and log1p, users who use those functions should get the advertised
>>> behavior, not loss of precision (I realize not all types would lose
>>> precision, but some will).
>>>
>>>
>>>>
>>>> Without the defaults this becomes a much bigger request, as I'd be
>>>> asking _every_ author of Floating to add CPP to their packages for a
>>>> feature they never heard of and probably will never use, and in that
>>>> situation we'd have to export it from Prelude.
>>>>
>>>
>>> It's perfectly fine to leave some methods blank; IMHO the resulting
>>> run-time error is better than an incorrect default.  Plus, it's useful for
>>> library authors to know that the class has changed; if a default is
>>> provided everything will build properly and there is no compile-time
>>> indication that library authors should adjust their code.
>>>
>>> Originally I was +1 for everything except the defaults, but I'm
>>> reconsidering.  If this is something that most Floating instance authors
>>> don't know about and probably won't ever use, do these functions really
>>> belong in that class?  Why not make a separate class for fused algorithms?
>>>
>>> John L.
>>>
>>>
>>>
>>>>
>>>> -Edward
>>>>
>>>>
>>>> On Sat, Apr 19, 2014 at 5:42 AM, Scott Turner <2haskell at pkturner.org>wrote:
>>>>
>>>>>  On 2014-04-17 15:08, Edward Kmett wrote:
>>>>>
>>>>>  On Thu, Apr 17, 2014 at 2:48 PM, Henning Thielemann <
>>>>> schlepptop at henning-thielemann.de> wrote:
>>>>>
>>>>>> I think one should add default implementations. They don't have an
>>>>>> numerical advantage but they save programmers from code breakage.
>>>>>
>>>>>
>>>>>  I included the default definitions in code snippet in the proposal,
>>>>> so user code that remains unaware of them would be unaffected, while
>>>>> packages like compensated, or a wrapper around libqd could implement them
>>>>> as needed.
>>>>>
>>>>>  expm1 :: Floating a => a -> a
>>>>> expm1 x = exp x - 1
>>>>>
>>>>>  log1p :: Floating a => a -> a
>>>>> log1p x = log (1 + x)
>>>>>
>>>>> On the contrary, code that explicitly uses these functions is likely
>>>>> to need the precision. Defaults would cause subtle breakage.
>>>>>
>>>>> -- Scott
>>>>>
>>>>
>>>>
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>>>>
>>>
>>
>
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