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

[Edward Kmett]

On Sun, Apr 20, 2014 at 10:49 PM, John Lato <jwlato at gmail.com> wrote:

> On Sun, Apr 20, 2014 at 6:37 PM, Edward Kmett <ekmett at gmail.com> wrote:
>>
>> On Apr 20, 2014, at 8:49 PM, John Lato <jwlato at gmail.com> wrote:
>>
>> 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.
>

I use log1p as a better log (1 + x).

It lets me pick up a few decimal places worth of accuracy
opportunistically.

>  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!
>

I have code that works with Floating today for everything. It just works
poorly.

I have other code that works with a custom class that works for a very
limited sets of types that works accurately.

I can have both of these things even in the absence of this proposal.

If expm1 goes into the class but randomly crashes then I am _worse_ off
than I am today, because before I at least had the class to tell me if it
would work.


> 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.
>

As it was a rhetorical question, I figured it didn't seek an actual reply.
=P

=)

>   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.
>

 The main cases that are left over are libraries like linear or
vector-space that provide floating instances for vector space types, and
the Complex case which I explicitly covered in the original proposal.

Given that, your numbers leave ~2% of the libraries that would have no
worse performance than they have today and which can be talked to
individually, vs. a situation where I have to live in fear of calling a
combinator for fear that I'll bottom out in my code with no way to detect
it until runtime.


> 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
>

If we're hiding this from the end user, in an extension most users never
have to see that is exported by Numeric, I'm pretty strongly against having
the defaults fail.

If we choose to instead to suck it up and expose them in the class from
Prelude, and just add the members directly, sans default, and make every
one deal with them, then we're at least being fully honest and you can have
your perfect precision and we can know that everyone has considered the
case or been bugged about it by GHC.


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

I'm +1 for the OP.
I'm +0.5 for no defaults, with a full export from the Prelude.
I'm -1 on error defaults, as it leaves me worse off than I am today.

-Edward
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