Proposal: Add "fma" to the RealFloat class

[Ivan Lazar Miljenovic]

On 29 April 2015 at 17:21, Levent Erkok <erkokl at gmail.com> wrote:
> This proposal is very much in the spirit of the earlier proposal on adding
> new float/double functions; for instance see here:
> https://mail.haskell.org/pipermail/libraries/2014-April/022667.html
>
> "fma" (a.k.a. fused-multiply-add) is one of those functions; which is the
> workhorse in many HPC applications. The idea is to multiply two floats and
> add a third with just one rounding, and thus preserving more precision.
> There are a multitude of applications for this operation in engineering
> data-analysis, and modern processors come with custom implementations and a
> lot of hardware to support it natively.
>
> I created a ticket along these lines already:
> https://ghc.haskell.org/trac/ghc/ticket/10364
>
> Edward suggested that the matter should further be discussed here.
>
> I think the proposal is rather straightforward, and should be
> noncontroversial. To wit, we shall add a new method to the RealFloat class:
>
>   class (RealFrac a, Floating a) => RealFloat a where
>       ...
>       fma :: a -> a -> a -> a
>
> The intention is that
>
>       fma x y z = x * y + z

Can we please have a better name (even if it's just
"fusedMultipleAdd")?  I have no real opinion on adding this function
or not, but just seeing that function (in other code, doing ":info
RealFloat" in ghci, etc.) tells me nothing about what it is.  Ideally
we wouldn't have to rely upon reading Haddock to understand random
TLAs in code.

>
> except the multiplication and addition are done infinitely-precisely, and
> then rounded only once; as opposed to two roundings as one would get with
> the above implementation. Most modern architectures directly support this
> operation so we can map it easily; and in case the architecture does not
> have it available, we can get it via the C-math libraries, where it appears
> under the names fma (the double version), and fmaf (the float version.)
>
> There should be no default definitions; as an incorrect (two-rounding
> version) would essentially beat the purpose of having fma in the first
> place.
>
> While the name "fma" is well-established in the arithmetic/hardware
> community and in the C-library, we can also go with "fusedMultiplyAdd," if
> that is deemed more clear.
>
> Discussion period: 2 weeks.
>
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-- 
Ivan Lazar Miljenovic
Ivan.Miljenovic at gmail.com
http://IvanMiljenovic.wordpress.com