RE: [R] strange result of acos

From: Ted Harding <Ted.Harding_at_nessie.mcc.ac.uk>
Date: Tue 29 Mar 2005 - 22:27:11 EST


On 29-Mar-05 Ted Harding wrote:
> The explanation is:
>
> sin(10.74*pi/180)**2
> +(cos(10.74*pi/180)*cos(10.74*pi/180)
> *cos(0*pi/180))
> -1
>
> [1] 2.220446e-16
>
> I.e. the expression, as internally evaluated, is very
> slightly greater than 1. When you multiply ss by
> 0.999999999, you bring it back down a bit.
>
> Theoretically, of course, it is sin(t)^2 + cos(t)^2,
> which should be exactly 1, but you can't count on it
> in digital computation. As you suspected, it is indeed
> a question of precision.

Just to make more explicit what's happening here:

t<-0.01*(0:200)*pi

sin(t)^2 + cos(t)^2 -1
##[output omitted]

unique(sin(t)^2 + cos(t)^2 -1)
##[1] 0.000000e+00 -1.110223e-16 2.220446e-16

2^(-53)
##[1] 1.110223e-16

so the error is either +2^(-52) or -2^(-53)

Best wishes,
Ted.



E-Mail: (Ted Harding) <Ted.Harding@nessie.mcc.ac.uk> Fax-to-email: +44 (0)870 094 0861
Date: 29-Mar-05                                       Time: 12:27:11
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