Re: [libreoffice-users] Error

At 22:46 12/08/2014 +0200, Skiper Skippers wrote:
> Error
> Check =2^53 it shows 9007199254740990

This is not an error!

You are using a finite computing machine - one in which each number 
in a cell is stored in a memory location of finite length. So there 
is always a limit to how large an integer can be stored and to how 
great a precision a floating-point value can be stored. Your computer 
is probably using "double-precision binary floating-point format", in 
which numbers are stored in eight-byte (sixty-four-bit) words. This 
allows around fifty-three significant binary digits, the rest being 
taken up by the sign and exponent. This level of precision 
corresponds to between fifteen and sixteen significant decimal 
digits, so integers can be stored precisely only up to this length of 
number, above which values can be stored, but only to around fifteen 
significant digits.

2^53 is one followed by fifty-three zeroes, of course - so is just 
too long to be stored accurately. You are very unlikely to need 
numbers of this magnitude as final results, and if you come across 
this problem, you can usually find a simple way to reorganise your 
calculation to avoid the problem.

Note that the (biased) exponent is stored in an eleven-bit field, so 
a separate problem occurs if you try to calculate with numbers above 
about 2^1023.

For a fuller explanation, see 
http://en.wikipedia.org/wiki/Double-precision_floating-point_format .

I trust this helps.

Brian Barker


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