Is super-accuracy matters?

[Albert Chan]

(10-06-2023 08:40 AM)J-F Garnier Wrote:  The main goal of the PI/4 double precision value was not to manage huge exact arguments, since this has no real-life interest and there will always be a limit unless storing 500 digits, but to guarantee 12-digit accuracy trig results for all "realistic" arguments, especially SIN(X) with X close to PI.

I've been thinking about this for a while.

Many years ago, I made strod-fast.c that return correctly rounded decimal → binary result.
To do this required, on rare occasion, upto 751 digits exact math calculations.
(all this hard work to get a 1 bit answer of which float to return!)

If we can accept very rare 1 ULP error, there is no need for all this (see strtod-lite.c)

Someone asked why I wasted time getting perfect (correctly rounded) result.
Float is "supposed" to be fuzzy ... 1 ULP error doesn't matter.

I have no good answer, and asked Rick Regan, blog author of https://www.exploringbinary.com/
This is a great site, if we want to know about binary/decimal.

Comments from https://www.exploringbinary.com/visual-c...ll-broken/

Albert Wrote:Just curious, how to you convince someone who say the last ULP bad conversion does not matter ?

Rick Regan Wrote:I don’t know how to convince someone. I guess it depends on the context of their application. On the other hand, many software products have come to support correct conversion over the years that I’ve been writing about conversion inaccuracy, so that might be an indirect argument in itself.

Answer somehow felt unsatisfactory. We do it because others do it?

Now, I think we should shoot for better accuracy, whether or not it matters in real life.
No need to convince others!

What do you think?