[Python-ideas] Fused multiply-add (FMA)

[Stephan Houben]

Hi Steve,

Very good!
Here is a version which also handles the nan's, infinities,
negative zeros properly.

===============
import math
from fractions import Fraction

def fma2(x, y, z):
    if math.isfinite(x) and math.isfinite(y) and math.isfinite(z):
        result = float(Fraction(x)*Fraction(y) + Fraction(z))
        if not result and not z:
            result = math.copysign(result, x*y+z)
    else:
        result = x * y + z
        assert not math.isfinite(result)
    return result
===========================

Stephan


2017-01-16 12:04 GMT+01:00 Steven D'Aprano <steve at pearwood.info>:

> On Mon, Jan 16, 2017 at 11:01:23AM +0100, Stephan Houben wrote:
>
> [...]
> > So the following would not be a valid FMA fallback
> >
> > double bad_fma(double x, double y, double z) {
> >   return x*y + z;
> > }
> [...]
> > Upshot: if we want to provide a software fallback in the Python code, we
> > need to do something slow and complicated like musl does.
>
> I don't know about complicated. I think this is pretty simple:
>
> from fractions import Fraction
>
> def fma(x, y, z):
>     # Return x*y + z with only a single rounding.
>     return float(Fraction(x)*Fraction(y) + Fraction(z))
>
>
> When speed is not the number one priority and accuracy is important,
> its hard to beat the fractions module.
>
>
> --
> Steve
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