Re: [R] Precision

From: Duncan Murdoch <murdoch_at_stats.uwo.ca>
Date: Wed 06 Apr 2005 - 22:46:08 EST

Josef Eschgfaeller wrote:

>
> How precise is R numerically? For example I
> wrote the following function for calculating
> the volume of the ball inscribed in the
> unit cube in m dimensions. In order to see what
> happens in 40 dimensions, I created an output
> of 24 digits. But how many are precise?

For most floating point operations R uses "double precision", which gives about 18-19 significant digit precision. Leading zeros don't count.

Duncan Murdoch

>
> Thanks
> Josef Eschgfäller
> Ferrara
> ---------------------------------------
> Vol = function (m)
> {if (m<=1) 1
> else Vol(m-2)*pi/(m+m)}
>
>
> for (m in 1:40)
> {x=sprintf('%2d %.24f',m,Vol(m))
> print(x)}
> ---------------------------------------
> 1 1.000000000000000000000000
> 2 0.785398163397448278999491
> 3 0.523598775598298815658893
> 4 0.308425137534042437259529
> 5 0.164493406684822623953224
> 6 0.080745512188280771370685
> 7 0.036912234143214060766436
> 8 0.015854344243815498421979
> 9 0.006442400200661534299951
> 10 0.002490394570192719803786
> 11 0.000919972597358349329817
> 12 0.000325991886927389960208
> 13 0.000111160736667881195885
> 14 0.000036576204182177245747
> 15 0.000011640725122781503579
> 16 0.000003590860448591509251
> 17 0.000001075600486123191399
> 18 0.000000313361689037812061
> 19 0.000000088923646984269168
> 20 0.000000024611369504941992
> 21 0.000000006651473240385528
> 22 0.000000001757247673443401
> 23 0.000000000454265640598788
> 24 0.000000000115011591279740
> 25 0.000000000028542351985668
> 26 0.000000000006948453273887
> 27 0.000000000001660526728044
> 28 0.000000000000389807317126
> 29 0.000000000000089943078792
> 30 0.000000000000020410263397
> 31 0.000000000000004557492187
> 32 0.000000000000001001886462
> 33 0.000000000000000216936121
> 34 0.000000000000000046287046
> 35 0.000000000000000009736070
> 36 0.000000000000000002019653
> 37 0.000000000000000000413335
> 38 0.000000000000000000083486
> 39 0.000000000000000000016648
> 40 0.000000000000000000003278
>
>------------------------------------------------------------------------
>
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R-help@stat.math.ethz.ch mailing list
https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Wed Apr 06 22:53:57 2005

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