# [R] seq

Henric Nilsson henric.nilsson at statisticon.se
Fri Sep 3 15:05:43 CEST 2004

```Thanks to all who replied.

I'm not surprised that R uses floating point arithmetics, nor am I
surprised that an object and it's printed version may differ due to e.g.
rounding taking place in the print() function.

I am, however, surprised of the fact that seq() prints it's internal
representation of 0 as 0.0 when `from = 0.5', but as -1.110223e-16 when
`from = 0.7'.

//Henric

At 13:17 2004-09-03 +0100, you wrote:
>On Fri, 3 Sep 2004, Roger Bivand wrote:
>
> > On Fri, 3 Sep 2004, Henric Nilsson wrote:
> >
> > > Hi everyone,
> > >
> > > I've tried the below on R 1.9.1 and the 2004-08-30 builds of R 1.9.1
> > > Patched and R 2.0.0 on Windows 2000, and the results are consistent.
> > >
> > >  > seq(0.5, 0, by = -0.1)
> > > [1] 0.5 0.4 0.3 0.2 0.1 0.0
> > >
> > >  > seq(0.7, 0, by = -0.1)
> > >
> [1]  7.000000e-01  6.000000e-01  5.000000e-01  4.000000e-01  3.000000e-01
> > > 2.000000e-01  1.000000e-01 -1.110223e-16
> > >
> > > Is this really the intended behaviour? I ended up using
> >
> > Well, you are using a floating point representation in a digital computer,
> > so I don't think you should be surprised. Note that the internal
> > representation is also modified by the print() functions, so what you see
> > when an object is printed is not always exactly what is inside the object.
> >
> > >
> > >  > seq(0.7, 0, length = 8)
> > > [1] 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0
> > >
> > > which does what I want.
>
>To expand a little, the code is in seq.default.
>
>seq(0.7, 0, by = -0.1) is done by from + (0:n) * by for n=8
>seq(0.7, 0, length = 8) is done by
>   c(from, from + (1:(length.out - 2)) * by, to))
>
>so the last value is handled differently.  Since 0.1 cannot be represented
>exactly on a binary computer,
>
> > print(7*0.1, digits=16)
>[1] 0.7000000000000001
>
>and you are seeing the result of 0.7 - 7*0.1.
>
>--
>Brian D. Ripley,                  ripley at stats.ox.ac.uk
>Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
>University of Oxford,             Tel:  +44 1865 272861 (self)
>1 South Parks Road,                     +44 1865 272866 (PA)
>Oxford OX1 3TG, UK                Fax:  +44 1865 272595
>
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