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@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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