Re: POSIX and float rounding

[Guy Harris <gharris () sonic net>]

On Mar 19, 2026, at 9:45 AM, Guy Harris <gharris () sonic net> wrote:
> On Mar 19, 2026, at 9:30 AM, Denis Ovsienko <denis () ovsienko info> wrote:
>
> > On Thu, 19 Mar 2026 09:16:47 -0700
> > Guy Harris <gharris () sonic net> wrote:
> >
> > > Try that on the platforms in question and see what it reports.
> >
> > $ ./roundingmode 
> > Rounding mode: to nearest
> >
> > fenv.h defines exactly the four FE_ rounding modes.
>
> So that's true on *all* of the platforms, including QNX?
>
> That's annoying. It appears that QNX's definition of "to nearest", in the "the two choices are equidistant" case, is 
> different from that of all other platforms (and from what I guess I was taught in school, as I've always thought you 
> were supposed to round 0.5 up to 1).
>
> Perhaps it's time to see what IEEE 754 has to say on the topic.

The Wikipedia says:

        https://en.wikipedia.org/wiki/IEEE_754#Rounding_rules

Tl;dr: there are *five* rounding rules:

    • Round to nearest, ties to even – rounds to the nearest value; if the number falls midway, it is rounded to the 
nearest value with an even least significant digit.
    • Round to nearest, ties away from zero (or ties to away)  – rounds to the nearest value; if the number falls 
midway, it is rounded to the nearest value above (for positive numbers) or below (for negative numbers).
    • Round toward 0 – directed rounding towards zero (also known as truncation).
    • Round toward +∞ – directed rounding towards positive infinity (also known as rounding up or ceiling).
    • Round toward −∞ – directed rounding towards negative infinity (also known as rounding down or floor).

and in the two "to nearest" cases, you get:

                                        +11.5 +12.5 −11.5 −12.5
        to nearest, ties to even        +12.0 +12.0 −12.0 −12.0
        to nearest, ties away from zero +12.0 +13.0 −12.0 −13.0

Your Linux examples appear to be "to nearest, ties to even", as "Format %.0f rounds 0.50 to 0." and "Format %.0f rounds 
1.50 to 2.", and your QNX examples appear to be "to nearest, ties away from zero", as "Format %.0f rounds 0.50 to 1." 
and "Format %.0f rounds 1.50 to 2.".

This Stack Overflow answer:

        https://stackoverflow.com/a/37000031

claims that

        Its implementation defined. Assuming IEEE 754:

        The standard defines 5 rounding modes, which might be used. The two modes of interest are:

            • Round to nearest, ties to even (*this is the default for binary floating-point and the recommended 
default for decimal*)

            • Round to nearest, ties away from zero

so, for whatever reason, QNX isn't implementing what's claimed to be the default.

And the answer appears to be correct; IEEE 754-2019 says, in 4.3.3 "Rounding attribute requirements":

        An implementation of this standard shall provide roundTiesToEven and the three directed rounding attributes. A 
decimal format implementation of this standard shall provide roundTiesToAway as a user-selectable rounding-direction 
attribute. The rounding attribute roundTiesToAway is not required for a binary format implementation.

        The roundTiesToEven rounding-direction attribute shall be the default rounding-direction attribute for results 
in binary formats. The default rounding-direction attribute for results in decimal formats is language-defined, but 
should be roundTiesToEven.

So, in the environment on your QNX box, the IEEE 754-2019 default appears *not* to be implemented, as it's doing 
roundTiesToAway. Unfortunately, I don't have the phone number for the IEEE Police Department. :-)
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