# Re: [R] Is this correct?

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Tue 11 Oct 2005 - 20:44:48 EST

Joe wrote:
> Dear userR,
>
> With the following results, are they correct or acceptable?

Yes. See the FAQ:

7.31 Why doesn't R think these numbers are equal?

The only numbers that can be represented exactly in R's numeric type are integers and fractions whose denominator is a power of 2. Other numbers have to be rounded to (typically) 53 binary digits accuracy. As a result, two floating point numbers will not reliably be equal unless they have been computed by the same algorithm, and not always even then. For example

```      R> a <- sqrt(2)
R> a * a == 2
 FALSE
R> a * a - 2
 4.440892e-16

```

The function all.equal() compares two objects using a numeric tolerance of .Machine\$double.eps ^ 0.5. If you want much greater accuracy than this you will need to consider error propagation carefully.

For more information, see e.g. David Goldberg (1991), “What Every Computer Scientist Should Know About Floating-Point Arithmetic”, ACM Computing Surveys, 23/1, 5–48, also available via http://docs.sun.com/source/806-3568/ncg_goldberg.html.

>
>

```>>x <- c(1.4, 1.2, 2.8)
>>sum(x)
```

>
>  5.4
>
```>>sum(x) == 5.4
```

>
>  FALSE
>
```>>(1.4 + 1.2 + 2.8) - 5.4
```

>
>  -8.881784e-16
>
```>>(1.4 + 1.2) - 2.6
```

>
>  -4.440892e-16
>
```>>2.6 - 1.5 - 1.1
```

>
>  0
>
>
```>>version

>
>          _
> platform i386-pc-mingw32

> arch     i386
> os       mingw32
```
> system i386, mingw32
> status
> major 2
> minor 2.0
> year 2005
> month 10
> day 06
> svn rev 35749
> language R
>
> What can I do to correct them if they are not correct?
> Thanks!
> --
> C. Joseph Lu
> Department of Statistics
> National Cheng-Kung University
> Tainan, Taiwan, ROC
>
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