[R] Why does sin(pi) not return 0?

[David Winsemius]

On Sep 26, 2013, at 8:06 AM, Pierrick Bruneau wrote:

> Just to add a small note,
> sin(pi) is below machine precision :
>
>> .Machine$double.eps
> [1] 2.220446e-16
>
> (see ?.Machine for exact definition)
>
> -> if myval is bounded to be positive, one safe way of testing  
> equality to
> 0 would then be "myval < .Machine$double.eps"

That is a more stringent condition than is applied by `all.equal`  
which instead uses .Machine$double.eps^0.5.

-- 
David.
>
>
>
> On Thu, Sep 26, 2013 at 2:48 PM, Suzen, Mehmet <msuzen at gmail.com>  
> wrote:
>
>> On 26 September 2013 11:30, Rainer M Krug <Rainer at krugs.de> wrote:
>>>>>> Why doesn't return me 0?
>>
>> It isn't R question at all. You might want to read about representing
>> real numbers in a computer using floating point
>> http://en.wikipedia.org/wiki/Floating_point
>>
>> If you want more precision for some reason, you may want to use Rmpfr
>> package from CRAN, for example
>>> require(Rmpfr)
>>> pii <- mpfr(pi, 1200)
>>> sin(pii)
>> 1 'mpfr' number of precision  1200   bits
>> [1]
>> 1.22464679914735317722606593227499799708305390129979194948825771626086960997325810377509325527569013655456428540074414189136673810003656057935764118217436637676835016019778833613838580470703060741630570066750947925902443295873487819032259435513861185501796412843027607796970259523768923503206248925733373776859085615900203929142965774524665617260404787862664073939e-16
>>
>>
>>> | > Is that a Fortune? And, if so, should R be using computers?
>>
>> Don't blame R for real numbers.
>>
>> ______________________________________________
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>> PLEASE do read the posting guide
>> http://www.R-project.org/posting-guide.html
>> and provide commented, minimal, self-contained, reproducible code.
>>
>
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>
> ______________________________________________
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> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
Alameda, CA, USA