Proposal: Add "fma" to the RealFloat class

Wed May 6 12:38:52 UTC 2015

Hi Carter,

Uh excuse me, you are BLAS master [1] ;-)

And, thank you for teaching me about #numerical-haskell.
I'll learn it. I like effective performance and abstraction.

[1] http://hackage.haskell.org/package/linear-algebra-cblas

Thank you,
Takenobu

2015-05-05 22:52 GMT+09:00 Carter Schonwald <carter.schonwald at gmail.com>:

> Hey Takenobu,
> Yes both are super useful! I've certainly used the Intel architecture
> manual a few times and I wrote/maintain (in my biased opinion ) one of the
> nicer blas ffi bindings on hackage.
>
> It's worth mentioning that for haskellers who are interested in either
> mathematical computation or performance engineering, on freenode the
> #numerical-haskell channel is pretty good. Though again I'm a bit biased
> about the nice community there
>
>
> On Tuesday, May 5, 2015, Takenobu Tani <takenobu.hs at gmail.com> wrote:
>
>> Hi,
>>
>> Is this useful?
>>
>> BLAS (Basic Linear Algebra Subprograms)
>> http://www.netlib.org/blas/
>> http://en.wikipedia.org/wiki/Basic_Linear_Algebra_Subprograms
>>
>> Regards,
>> Takenobu
>>
>>
>>
>> 2015-05-05 22:06 GMT+09:00 Takenobu Tani <takenobu.hs at gmail.com>:
>>
>>> Hi,
>>>
>>> Related informatioln.
>>>
>>> Intel FMA's information(hardware dependent) is here:
>>>
>>>   Chapter 11
>>>
>>>   Intel 64 and IA-32 Architectures Optimization Reference Manual
>>>
>>> http://www.intel.com/content/dam/www/public/us/en/documents/manuals/64-ia-32-architectures-optimization-manual.pdf
>>>
>>>
>>> Of course, it is information that depends on the particular processor.
>>> And abstraction level is too low.
>>>
>>> PS
>>> I like Haskell's abstruct naming convention more than "fma":-)
>>>
>>> Regards,
>>> Takenobu
>>>
>>>
>>>
>>> 2015-05-05 11:54 GMT+09:00 Carter Schonwald <carter.schonwald at gmail.com>
>>> :
>>>
>>>> pardon the wall of text everyone, but I really want some FMA tooling :)
>>>>
>>>> I am going to spend some time later this week and next adding FMA
>>>> primops to GHC and playing around with different ways to add it to Num
>>>> (which seems pretty straightforward, though I think we'd all agree it
>>>> shouldn't be exported by Prelude). And then depending on how Yitzchak's
>>>> reproposal  of that exactly goes (or some iteration thereof) we can get
>>>> something useful/usable into 7.12
>>>>
>>>> i have codes (ie *dotproducts*!!!!!) where a faster direct FMA for *exact
>>>> numbers*, and a higher precision FMA for *approximate numbers *(*ie
>>>> floating point*),  and where I cant sanely use FMA if it lives
>>>> anywhere but Num unless I rub typeable everywhere and do runtime type
>>>> checks for applicable floating point types, which kinda destroys
>>>> parametrically in engineering nice things.
>>>>
>>>> @levent: ghc doesn't do any optimization for floating point arithmetic
>>>> (aside from 1-2 very simple things that are possibly questionable), and
>>>> until ghc has support for precisly emulating high precision floating point
>>>> computation in a portable way, probably wont have any interesting floating
>>>> point computation.  Mandating that fma a b c === a*b+c for inexact number
>>>> datatypes doesn't quite make sense to me. Relatedly, its a GOOD thing ghc
>>>> is conservative about optimizing floating point, because it makes doing
>>>> correct stability analyses tractable!  I look forward to the day that GHC
>>>> gets a bit more sophisticated about optimizing floating point computation,
>>>> but that day is still a ways off.
>>>>
>>>> relatedly: FMA for float and double are not generally going to be
>>>> faster than the individual primitive operations, merely more accurate when
>>>> used carefully.
>>>>
>>>> point being*, i'm +1 on adding some manner of FMA operations to Num*
>>>> (only sane place to put it where i can actually use it for a general use
>>>> library) and i dont really care if we name it fusedMultiplyAdd,
>>>> multiplyAndAdd accursedFusionOfSemiRingOperations, or fma. i'd favor
>>>> "fusedMultiplyAdd" if we want a descriptive name that will be familiar to
>>>> experts yet easy to google for the curious.
>>>>
>>>> to repeat: i'm going to do some leg work so that the double and float
>>>> prims are portably exposed by ghc-prims (i've spoken with several ghc devs
>>>> about that, and they agree to its value, and thats a decision outside of
>>>> scope of the libraries purview), and I do hope we can to a consensus about
>>>> putting it in Num so that expert library authors can upgrade the guarantees
>>>> that they can provide end users without imposing any breaking changes to
>>>> end users.
>>>>
>>>> A number of folks have brought up "but Num is broken" as a counter
>>>> argument to adding FMA support to Num. I emphatically agree  num is borken
>>>> :), BUT! I do also believe that fixing up Num prelude has the burden of
>>>> providing a whole cloth design for an alternative design that we can get
>>>> broad consensus/adoption with.  That will happen by dint of actually
>>>> experimentation and usage.
>>>>
>>>> Point being, adding FMA doesn't further entrench current Num any more
>>>> than it already is, it just provides expert library authors with a
>>>> transparent way of improving the experience of their users with a free
>>>> upgrade in answer accuracy if used carefully. Additionally, when Num's
>>>> "semiring ish equational laws" are  framed with respect to approximate
>>>> forwards/backwards stability, there is a perfectly reasonable law for FMA.
>>>> I am happy to spend some time trying to write that up more precisely IFF
>>>> that will tilt those in opposition to being in favor.
>>>>
>>>> I dont need FMA to be exposed by *prelude/base*, merely by *GHC.Num*
>>>> as a method therein for Num. If that constitutes a different and *more
>>>> palatable proposal*  than what people have articulated so far (by
>>>> discouraging casual use by dint of hiding) then I am happy to kick off a
>>>> new thread with that concrete design choice.
>>>>
>>>> If theres a counter argument thats a bit more substantive than "Num is
>>>> for exact arithmetic" or "Num is wrong" that will sway me to the other
>>>> side, i'm all ears, but i'm skeptical of that.
>>>>
>>>> I emphatically support those who are displeased with Num to prototype
>>>> some alternative designs in userland, I do think it'd be great to figure
>>>> out a new Num prelude we can migrate Haskell / GHC to over the next 2-5
>>>> years, but again any such proposal really needs to be realized whole cloth
>>>> before it makes its way to being a libraries list proposal.
>>>>
>>>>
>>>> again, pardon the wall of text, i just really want to have nice things
>>>> :)
>>>> -Carter
>>>>
>>>>
>>>> On Mon, May 4, 2015 at 2:22 PM, Levent Erkok <erkokl at gmail.com> wrote:
>>>>
>>>>> I think `mulAdd a b c` should be implemented as `a*b+c` even for
>>>>> Double/Float. It should only be an "optmization" (as in modular
>>>>> arithmetic), not a semantic changing operation. Thus justifying the
>>>>> optimization.
>>>>>
>>>>> "fma" should be the "more-precise" version available for Float/Double.
>>>>> I don't think it makes sense to have "fma" for other types. That's why I'm
>>>>> advocating "mulAdd" to be part of "Num" for optimization purposes; and
>>>>> "fma" reserved for true IEEE754 types and semantics.
>>>>>
>>>>> I understand that Edward doesn't like this as this requires a
>>>>> different class; but really, that's the price to pay if we claim Haskell
>>>>> has proper support for IEEE754 semantics. (Which I think it should.) The
>>>>> operation is just different. It also should account for the rounding-modes
>>>>> properly.
>>>>>
>>>>> I think we can pull this off just fine; and Haskell can really lead
>>>>> the pack here. The situation with floats is even worse in other languages.
>>>>> This is our chance to make a proper implementation, and we have the right
>>>>> tools to do so.
>>>>>
>>>>> -Levent.
>>>>>
>>>>> On Mon, May 4, 2015 at 10:58 AM, Artyom <yom at artyom.me> wrote:
>>>>>
>>>>>>  On 05/04/2015 08:49 PM, Levent Erkok wrote:
>>>>>>
>>>>>> Artyom: That's precisely the point. The true IEEE754 variants where
>>>>>> precision does matter should be part of a different class. What Edward and
>>>>>> Yitz want is an "optimized" multiply-add where the semantics is the same
>>>>>> but one that goes faster.
>>>>>>
>>>>>> No, it looks to me that Edward wants to have a more precise operation
>>>>>> in Num:
>>>>>>
>>>>>> I'd have to make a second copy of the function to even try to see the
>>>>>> precision win.
>>>>>>
>>>>>> Unless I'm wrong, you can't have the following things simultaneously:
>>>>>>
>>>>>>    1. the compiler is free to substitute *a+b*c* with *mulAdd a b c*
>>>>>>    2. *mulAdd a b c* is implemented as *fma* for Doubles (and is
>>>>>>    more precise)
>>>>>>    3. Num operations for Double (addition and multiplication) always
>>>>>>    conform to IEEE754
>>>>>>
>>>>>>  The true IEEE754 variants where precision does matter should be
>>>>>> part of a different class.
>>>>>>
>>>>>> So, does it mean that you're fine with not having point #3 because
>>>>>> people who need it would be able to use a separate class for IEEE754 floats?
>>>>>>
>>>>>>
>>>>>
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>>>>>
>>>>>
>>>>
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>>>
>>
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