Re: Is this a numerical problem?

[Lukas Reichlin]

On 19.08.2010, at 18:36, Jordi Gutiérrez Hermoso wrote:

> 2010/8/19 Judd Storrs <address@hidden>:
>> 2010/8/19 Jordi Gutiérrez Hermoso <address@hidden>
>>> 
>>> I believe the inconsistency is how 0.999995 is displayed in each with
>>> "format short". Octave displays 0.99999 and Matlab displays 1.0000,
>>> from what I can read in the bug report.
>> 
>> I don't understand this comparison. Matlab is displaying four digits after
>> the decimal whereas octave is displaying five. If octave displayed four
>> digits it would also display 1.0000.
> 
> It's five digits total. Format short displays five digtis.
> 
>> Why is Matlab more correct? The inaccuracy of the Matlab representation is
>> +0.000005 and the inaccuracy of the Octave representation is -0.000005. Why
>> is one "correct" and the other wrong?
> 
> Because 5 should round up. Precisely for reasons like this.
> 
>> Last time I checked GCC has very excellent binary to decimal conversion
>> routines.
> 
> They're not perfect. It's a very fiddly picky thing to worry about.
> Here's a blog post with links to gcc bug reports:
> 
>     
> http://www.exploringbinary.com/incorrectly-rounded-conversions-in-gcc-and-glibc/
> 
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Your link is very interesting. As far as I understood, an 8-bit mantissa 
approximates a decimal number with x/256, where x is an 8-bit integer. Now it 
might happen that the closest approximation of, let's say, 0.9995 is a binary 
value representing a fraction  which is slightly smaller than 0.9995. Thus it 
gets rounded down when we cut off the last decimal digit, whereas I expected 
the opposite, regarding the decimal representation.

Best Regards,
Lukas