Proposal: Add "fma" to the RealFloat class

Carter Schonwald carter.schonwald at
Tue May 5 11:40:37 UTC 2015

Hey Levent,
I actually looked into how to do rounding mode setting a while ago, and the
conclusion I came to is that those can simply be ffi calls at the top level
that do a sort of with mode bracketing.  Or at least I'm not sure if
setting the mode in an inner loop is a good idea.

That said, you are making a valid point, and I will investigate to what
extent compiler support is useful for the latter. If bracketed mode setting
and unsetting has a small enough performance overhead, adding support in
ghc primops would be worth while.  Note that those primops would have to be
modeled as doing something thats like io or st, so that when mode switches
happen can be predictable.  Otherwise CSE and related optimizations could
result in evaluating the same code in the wrong mode.  I'll think through
how that can be avoided, as I do have some ideas.

I suspect mode switching code will wind up using new type wrapped floats
and doubles that have a phantom index for the mode, and something like
"runWithModeFoo:: Num a => Mode m->(forall s . Moded s a )  -> a"    to
make sure mode choices happen predictably.  That said, there might be a
better approach that we'll come to after some experimenting
On May 5, 2015 12:54 AM, "Levent Erkok" <erkokl at> wrote:

> Carter: Wall of text is just fine!
> I'm personally happy to see the results of your experiment. In particular,
> the better "code-generation" facilities you add around floats/doubles that
> map to the underlying hardware's native instructions, the better. When we
> do have proper IEEE floats, we shall surely need all that functionality.
> While you're working on this, if you can also watch out for how rounding
> modes can be integrated into the operations, that would be useful as well.
> I can see at least two designs:
>    * One where the rounding mode goes with the operation: `fpAdd
> RoundNearestTiesToEven 2.5 6.4`. This is the "cleanest" and the functional
> solution, but could get quite verbose; and might be costly if the
> implementation changes the rounding-mode at every issue.
>    * The other is where the operations simply assume the
> RoundNearestTiesToEven, but we have lifted IO versions that can be modified
> with a "with" like construct:  `withRoundingMode RoundTowardsPositive $
> fpAddRM 2.5 6.4`. Note that `fpAddRM` (*not* `fpAdd` as before) will have
> to return some sort of a monadic value (probably in the IO monad) since
> it'll need to access the rounding mode currently active.
> Neither choice jumps out at me as the best one; and a hybrid might also be
> possible. I'd love to hear any insight you gain regarding rounding-modes
> during your experiment.
> -Levent.
> On Mon, May 4, 2015 at 7:54 PM, Carter Schonwald <
> carter.schonwald at> wrote:
>> 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> 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> 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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