Proposal: Add "fma" to the RealFloat class

[Roman Cheplyaka]

I think there *should* be a default definition in terms of (+) and (*).

A person who defines their own instance for their own purpose should be
free to ignore this function if it's not needed for their specific
application.

On 29/04/15 10:21, Levent Erkok 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
> 
> 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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