Re: [libreoffice-users] Error or what?

At 22:56 03/02/2014 +0100, Erik Erlandsson wrote:
> On 2014-02-03 22:20, Brian Barker wrote:
> > At 06:21 03/02/2014 +0100, Erik Erlandsson wrote:
> > > I'm seeing this "odd" behavior in a series. Around line 30 
> > > additional decimals are showing up  What am I doing wrong?
> >
> > At 20:29 03/02/2014 +0100, Erik Erlandsson wrote:
> > > I hope this works: http://shared.59551.x6.nabble.com/Error-or-td2.html
> >
> > I'm having to guess, as you've posted a screenshot but not the 
> > spreadsheet itself.  But your column appears to be calculated by an 
> > iterative formula, with each row calculated from the previous 
> > one.  As you do this, rounding errors will be introduced, and these 
> > will increase in size as you double the value at each step. Since 
> > you take only the fractional part of the result, the number in each 
> > row does not generally grow in size, so the rounding errors 
> > eventually become significant compared with the values you have.
> >
> > The calculation is probably being carried out internally to around 
> > fifteen significant figures.  When I try this calculation, rounding 
> > errors appear at row 8, but only in the fifteenth significant figure.
> > This will be happening in your calculation too, but becomes visible 
> > only in row 26, where the difference begins to show in the nine 
> > significant figures you chose to display.  Note that the rounding 
> > will occur in the binary numbers being used in the calculation by 
> > your computer hardware, not in the decimal values being 
> > displayed.  Your results all terminate after the first fractional 
> > place in decimal, but they will not do so in binary, where even 0.1 
> > is the recurring fraction 0.0[0011] with those last four digits repeating.
> >
> > You will see different results - perhaps even those you seek - if 
> > you tick Tools | Options... | LibreOffice Calc | Calculate | 
> > Precision as shown.  This causes the displayed value you see to be 
> > used in each calculation instead of the true value hidden in the cell.
> >
> > Of course, you could apply some mathematics and find a simpler way 
> > of calculating these values - which, after the first, simply repeat 
> > the sequence 0.2, 0.4, 0.8, and 0.6.  One example is:
> > =MOD(2^(ROW()-1);10)/10
> > - but this will go awry at row 52, since 2^51 is so large (around 
> > fifteen digits) that its units digit is no longer reliable.
> >
> > So here's a better version:
> > =MOD(2^(MOD(ROW()-2;4)+1);10)/10
> > - which should work more or less indefinitely, though not for the 
> > (exceptional) first row.

At 22:38 03/02/2014 +0100, Erik Erlandsson wrote:
> It behaves more or less the same in Excel 2003 in Win7.

It will.  You have called your spreadsheet document "Calcbug" - but 
this is not a bug, but the inevitable consequence of using a finite 
computing machine.

> The formula is from a book on chaos, it describes a way to simulate 
> a controlled chaotic sequence: ...

It's perhaps unfortunate, then, that you misrepresented your original 
query, suggesting that it was odd behaviour and asking what you were 
doing wrong.

> I expected something unpredictable, but not this!

It's all predictable if you understand what is happening under the 
bonnet ("hood").

> I realize that it is a rounding error that adds the decimals.  It 
> actually behaves similarly with "precision as shown"

No, with "Precision as shown" the calculation proceeds differently 
and straightforwardly, since the rounding errors are dropped at each 
stage.  But you may have to save and reopen the document file in 
order to see the difference.

> But mystery 2 still stays, why does the function kill itself from line 50+ ?

There's no mystery.  The rounding errors become visible at your 
chosen display precision at row 28, but by about row 52 they have 
started to interfere with the single significant digit you are 
attempting to calculate with - so even that becomes unstable.  Once 
the errors happen to cause a result to be zero, that special case 
will be preserved without further error.

> The spreadsheets are enclosed in the postings on nabble, link below image.

Sorry if I missed that earlier.  Fortunately I guessed accurately 
what you were doing.

Brian Barker


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