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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