On Wed, 29 Apr 2015, 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
Btw. what was the final decision with respect to log1p and expm1? I suggest that the decision for 'fma' will be made consistently with 'log1p' and 'expm1'.
"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.
Ok, the proposal is about increasing precision. One could also hope that a single fma operation is faster than separate addition and multiplication but as far as I know, fma can even be slower since it has more data dependencies.
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
RealFloat excludes Complex.
There should be no default definitions; as an incorrect (two-rounding version) would essentially beat the purpose of having fma in the first place.
I just read again the whole expm1 thread and default implementations with possible loss of precision seem to be the best option. This way, one can mechanically replace all occurrences of (x*y+z) by (fma x y z) and will not make anything worse. Types with a guaranteed high precision should be put in a Fused class.
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.
Although I like descriptive names, the numeric classes already contain mostly abbreviations (abs, exp, sin, tanh, ...) Thus I would prefer the abbreviation for consistency. Btw. in DSP 56002 the same operation is called MAC (multiply-accumulate).