[Numpy-discussion] Behavior of rint?

[Charles R Harris]

On Fri, Jan 19, 2018 at 8:27 AM, Matthew Brett <matthew.brett at gmail.com>
wrote:

> Hi,
>
> On Fri, Jan 19, 2018 at 3:24 PM, Charles R Harris
> <charlesr.harris at gmail.com> wrote:
> >
> >
> > On Fri, Jan 19, 2018 at 7:48 AM, Matthew Brett <matthew.brett at gmail.com>
> > wrote:
> >>
> >> Hi Chuck,
> >>
> >> Thanks for the replies, they are very helpful.
> >>
> >> On Fri, Jan 19, 2018 at 1:51 PM, Charles R Harris
> >> <charlesr.harris at gmail.com> wrote:
> >> >
> >> >
> >> > On Fri, Jan 19, 2018 at 6:41 AM, Charles R Harris
> >> > <charlesr.harris at gmail.com> wrote:
> >> >>
> >> >>
> >> >>
> >> >> On Fri, Jan 19, 2018 at 3:30 AM, Matthew Brett
> >> >> <matthew.brett at gmail.com>
> >> >> wrote:
> >> >>>
> >> >>> Hi,
> >> >>>
> >> >>> Sorry for my confusion, but I noticed (as a result of the discussion
> >> >>> here [1]) that np.rint and the fallback C function [2] seem to round
> >> >>> to even.  But - my impression was that C rint, by default, rounds
> down
> >> >>> [3].   Is numpy rint not behaving the same way as the GNU C library
> >> >>> rint?
> >> >>>
> >> >>> In [4]: np.rint(np.arange(0.5, 11))
> >> >>> Out[4]: array([ 0.,  2.,  2.,  4.,  4.,  6.,  6.,  8.,  8., 10.,
> 10.])
> >> >>>
> >> >>> In [5]: np.round(np.arange(0.5, 11))
> >> >>> Out[5]: array([ 0.,  2.,  2.,  4.,  4.,  6.,  6.,  8.,  8., 10.,
> 10.])
> >> >>
> >> >>
> >> >> The GNU C documentation says that rint "round(s) x to an integer
> value
> >> >> according to the current rounding mode." The rounding mode is
> >> >> determined by
> >> >> settings in the FPU control word. Numpy runs with it set to round to
> >> >> even,
> >> >> although, IIRC, there is a bug on windows where the library is not
> >> >> setting
> >> >> those  bits correctly.
> >> >
> >> >
> >> > Round to even is also the Python default rounding mode.
> >>
> >> Do you mean that it is Python setting the FPU control word?  Or do we
> >> set it?  Do you happen to know where that is in the source?  I did a
> >> quick grep just now without anything obvious.
> >
> >
> > I can't find official (PEP) documentation, but googling indicates that in
> > Python 3, `round` rounds to even, and in Python 2 it rounds up. See also
> > https://docs.python.org/3/whatsnew/3.0.html.
>
> But I guess this could be the Python implementation of round, rather
> than rint and the FPU control word?  I'm asking because the question
> arose about npy_rint at the C level ...
>

I'm pretty sure Python sets the FPU control word. Note that Python itself
doesn't have a public interface for setting it, nor does Java. The GNU
library documentation has the following:

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.

Chuck
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