# [GRASS-dev] [GRASS GIS] #1976: r.mapcalc: Allow rounding of floating numbers

GRASS GIS trac at osgeo.org
Tue May 21 08:00:31 PDT 2013

```#1976: r.mapcalc: Allow rounding of floating numbers
-------------------------+--------------------------------------------------
Reporter:  pvanbosgeo   |       Owner:  grass-dev@…
Type:  enhancement  |      Status:  new
Priority:  normal       |   Milestone:  7.0.0
Component:  Raster       |     Version:  unspecified
Keywords:  r.mapcalc    |    Platform:  Unspecified
Cpu:  Unspecified  |
-------------------------+--------------------------------------------------

Comment(by mmetz):

Replying to [comment:4 glynn]:
> Replying to [comment:2 mmetz]:
>
> > The output type of round() is now the same like the input type.
>
> This changes long-standing behaviour in a way which could break scripts.

OK. Restoring the original behaviour for round(x) is easy. But it would be
nice to have a round(x, y) function that preserves the data type of x in
order to have a possibility to avoid integer overflow.

>
> > Rounding to a given number of decimal places is supported with
round(x, y)
>
> From the mailing list discussion ...
>
> Rounding to a given number of decimals is unnecessarily limiting. The
algorithm for generalised rounding is essentially:
>
{{{
roundTo(x, k) = round(x / k) * k.
}}}
> Rounding to N decimal places is just a case of using k=1/10^N^. If you
> allow k to be specified directly, then you can round to arbitrary
> steps (e.g. k=5 would round to the nearest multiple of 5, etc).

I was just looking at the function round() in R which rounds to decimal
places. Generalised rounding makes more sense.

>
> However: there's a slight problem with doing it that way: 0.1 isn't
> exactly representable in binary, so e.g. x/0.1 isn't equal to x*10; it
> would be more accurate to use:
{{{
roundTo(x, k) = round(x * k) / k
}}}
> where k is the reciprocal of the step, so k=10^N^ to round to N decimal
> places (or k=2 to round to 1/2).

>
> Unless someone has a better idea, I plan to change the round() function
so that the second argument is the step value, and add an roundi() (round-
inverse) function where the second argument is the reciprocal of the step
value (to avoid the rounding error when using a step of 10^-N^).

Sounds good to me.

--
Ticket URL: <http://trac.osgeo.org/grass/ticket/1976#comment:5>
GRASS GIS <http://grass.osgeo.org>

```