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 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 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 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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