Re: Timestamp precision and rounding

Stephan Szabo <sszabo(at)megazone(dot)bigpanda(dot)com> writes:

> > That is, why doesn't the second operation result in the same timestamp
> > as the first? Is it a floating-point representation issue, or are the
> > mathematical rules of rounding not being followed correctly (as I
> > understand them, anyway)?
>
> My first guess would be that your system probably implements its default
> rounding as nearest even for .5 results, what does 9:00:01.5 give you?

Fwiw, the floating point timestamp representation is seconds-based. So 0.5s
should be exactly representable. (Though 0.500001 wouldn't, but that shouldn't
matter.)

On my machine it seems to always round away from 0, but this comment from
timestamp.c seems relevant. It would imply my build was build with integer
timestamps and yours was built with floating point timestamps:

/*
* Note: this round-to-nearest code is not completely consistent
* about rounding values that are exactly halfway between integral
* values. On most platforms, rint() will implement
* round-to-nearest-even, but the integer code always rounds up
* (away from zero). Is it worth trying to be consistent?
*/

And this is from the glibc Info page:

> IEEE 754 defines four possible rounding modes:
>
> Round to nearest.
> This is the default mode. It should be used unless there is a
> specific need for one of the others. In this mode results are
> rounded to the nearest representable value. If the result is
> midway between two representable values, the even representable is
> chosen. "Even" here means the lowest-order bit is zero. This
> rounding mode prevents statistical bias and guarantees numeric
> stability: round-off errors in a lengthy calculation will remain
> smaller than half of `FLT_EPSILON'.

[And the other rounding directions are useless;
this is the default and the only one that matters.]

--
greg