[R] double.xmin really the smallest non-zero normalized floating-point number?

[Marius Hofert]

On Wed, Sep 11, 2013 at 12:07 AM, William Dunlap <wdunlap at tibco.com> wrote:
> 'normalized' is key.  A normalized double precision floating point
> number has 52 binary digits of precision and .Machine$double.eps/2
> does not.  E.g.,
>
>   > bitsOfPrecision <- function(x)max(which( x != x*(1+2^-(1:60))))

what a nice function :-)

>   > bitsOfPrecision(4)
>   [1] 52
>   > bitsOfPrecision(.Machine$double.xmin)
>   [1] 52
>   > bitsOfPrecision(.Machine$double.xmin/2)
>   [1] 51
>   > bitsOfPrecision(.Machine$double.xmin/4)
>   [1] 50
>
> Google for 'normalized floating point'.

Okay, thanks a lot.

Do you know whether one can find out the smallest positive number on
the current machine?
Or, actually, I was wondering what the smallest number x is, such that
exp(-x) = 0 in machine arithmetic.
On my machine, x=745 leads to exp(-x) being not quite 0, but x=746
leads to exp(-x)==0 being TRUE. But these are integer x's...

Many thanks and cheers,

Marius


>
> Bill Dunlap
> Spotfire, TIBCO Software
> wdunlap tibco.com
>
>
>> -----Original Message-----
>> From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org] On Behalf
>> Of Marius Hofert
>> Sent: Tuesday, September 10, 2013 2:50 PM
>> To: R-help
>> Subject: [R] double.xmin really the smallest non-zero normalized floating-point number?
>>
>> Hi,
>>
>> ?.Machine says that 'double.xmin' is 'the smallest non-zero normalized
>> floating-point number'. On my machine, this is 2.225074e-308. However,
>> 2.225074e-308 / 2 is > 0 and smaller than 2.225074e-308, so
>> double.xmin is not the smallest such number (?) Am I missing anything?
>>
>> Cheers,
>>
>> Marius
>>
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