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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