Would it make sense to create a new class for operations like fma that has accuracy guarantees as part of its typeclass laws? Or would managing a bunch of typeclasses like that create too much syntactic, conceptual or performance overhead for actual use?

To me, that seems like it could be better than polluting Num—which, after all, features prominently in the Prelude—but it might make for worse discoverability.

If we do add it to Num, I strongly support having a default implementation. We don't want to make implementing a custom numeric type any more difficult than it has to be, and somebody unfamiliar with fma would just manually implement it without any optimizations anyhow or just leave it out, incomplete instantiation warnings nonwithstanding. Num is already a bit to big for casual use (I rarely care about signum and abs myself), so making it *bigger* is not appealing.

Personally, I'm a bit torn on the naming. Something like mulAdd or fusedMultiplyAdd is great for non-experts, but it feels like fma is something that we only expect experts to care about, so perhaps it's better to name it in line with their expectations.

On Fri, May 1, 2015 at 10:52 AM, David Feuer <david.feuer@gmail.com> wrote:

I'm somewhat opposed to the Num class in general, and very much opposed to calling floating point representations "numbers" in particular. How are they numbers when they don't obey associative or distributive laws, let alone cancellation, commutativity, ....? I know Carter disagrees with me, but I'll stand my ground, resolute! I suppose adding some more nonsense into the trash heap won't do too much more harm, but I'd much rather see some deeper thought about how we want to deal with floating point.

On May 1, 2015 1:35 PM, "adam vogt" <vogt.adam@gmail.com> wrote:
The Num class is defined in GHC.Num, so Prelude could import GHC.Num hiding (fma) to avoid having another round of prelude changes breaking code.



On Fri, May 1, 2015 at 12:44 PM, Twan van Laarhoven <twanvl@gmail.com> wrote:
I agree that Num is the place to put this function, with a default implementation. In my mind it is a special combination of (+) and (*), which both live in Num as well.

I dislike the name fma, as that is a three letter acronym with no meaning to people who don't do numeric programming. And by putting the function in Num the name would end up in the Prelude.

For further bikeshedding: my proposal for a name would mulAdd. But fusedMulAdd or fusedMultiplyAdd would also be fine.


Twan


On 2015-04-30 00:19, Ken T Takusagawa wrote:
On Wed, 29 Apr 2015, Edward Kmett wrote:

Good point. If we wanted to we could push this all the way up to Num given the operations
involved, and I could see that you could benefit from it there for types that have nothing
to do with floating point, e.g. modular arithmetic could get away with using a single 'mod'.

I too advocate this go in Num.  The place I anticipate
seeing fma being used is in some polymorphic linear algebra
library, and it is not uncommon (having recently done this
myself) to do linear algebra on things that aren't
RealFloat, e.g., Rational, Complex, or number-theoretic
fields.

--ken
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