RE: Decimal rounding of a float data type in Java.

["Clapham, Paul" <pclapham@xxxxxxxxxxxxx>]

The Java "float" data type is based on a specific binary representation
(IEEE 745 I think).  But saying that they are actually decimal is slightly
misleading... you see them represented as decimal, because Java converts
them to human-readable form before displaying them.  You can run into
problems if you don't distinguish between internal and external
representations of objects.  And in the case of "float" variables, thinking
of dividing by 100 as a two digit shift is the external-representation view,
which may not be precisely mirrored in the internal representation because
of possible binary round-off.

If you write a Java program that starts with "float x = 0" and then executes
"x = x + 0.01" in a loop, you'll see round-off happening very quickly.  In
fact in my test, after only 6 iterations x has become 0.059999995.  This
wouldn't happen in a system of decimal numbers.

(And in fact 8.23999999999993753 is a rational number, because it can be
expressed as a fraction, but the mathematical definition of "rational" is an
irrelevance I should not have bothered with in my earlier post.)

-----Original Message-----
From: James Donkin [mailto:James@DuMaurier.co.uk]
Sent: March 3, 2001 01:12
To: JAVA400-L@midrange.com
Subject: Re: Decimal rounding of a float data type in Java.

<snip>

Java data types are decimal not binary. The underlying implementation might
be binary but the float is a decimal number - dividing it by one hundred is
a two digit shift.

> And by the way,
> 323/34 is no more irrational than 422/100.  Both are rational numbers.

true - but is 8.23999999999993753  ?
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