I realize that it is a rounding error that adds the decimals.
It actually behaves similarily with "percision as shown"
But mystery 2 still stays, why does the function kill itself from line 50+ ?
The spreadsheets are enclosed in the postings on nabble, link below image.
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 (Nilhe AB) 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 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:
- 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:
- which should work more or less indefinitely, though not for the
(exceptional) first row.
I trust this helps.
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