Re: floating point display problem
Screamin Lord Byron wrote:
On 07/13/2010 03:11 AM, Arne Vajh??j wrote:
On 12-07-2010 12:36, Screamin Lord Byron wrote:
On 07/12/2010 05:15 PM, markspace wrote:
J.H.Kim wrote:
Hi, everyone
My java compiler and interpreter cannot display floating point
variable.
public class PrintTest {
public static void main(String[] args) {
double a = 3.141592;
System.out.println(a);
}
}
The routine above does not display 3.141592.
<http://docs.sun.com/source/806-3568/ncg_goldberg.html>
Floating point numbers aren't exact. You can't get exactly 3.141592 out
of any floating point system. Consider using BigDecimal if you need
"exact" numbers.
Well, in this example there is no calculation, and significand fits
within 52 bits of IEEE 754 double type so it should be printed out as
expected: 3.141592. Please someone correct me if I'm wrong.
Even though 7 decimals digits is less than 52 bits, then it is
far from guaranteed that a 7 decimals number can be represented
exact within 52 bit.
I am aware there is a problem of representing fractions in any numeral
system (for example, decimal 0.1 can't be exactly represented in binary,
just as 1/3 can't be exactly represented in decimal), and here we're not
saying nothing like double d = 2. - 0.1;
Am I wrong if I say that the literal 3.141592 is represented in memory
like this: the sign is 0, the significand is 3141592 and the exponent is
-6. There are no mathematical operations with this number, so it's sole
representation is in fact exact, is it not? The println should print it
like it's represented, just like it prints 0.8999999999999999 as a
result of 2. - 0.1.
You are wrong. 3.141592 in Java is a double literal, and double is a
binary floating point type. See
http://java.sun.com/docs/books/jls/third_edition/html/lexical.html#3.10.2
"The details of proper input conversion from a Unicode string
representation of a floating-point number to the internal IEEE 754
binary floating-point representation are described for the methods
valueOf of class Float and class Double of the package java.lang."
The actual rule for double is described in
http://download.oracle.com/docs/cd/E17409_01/javase/6/docs/api/java/lang/Double.html#valueOf(java.lang.String)
"Otherwise, s is regarded as representing an exact decimal value in the
usual "computerized scientific notation" or as an exact hexadecimal
value; this exact numerical value is then conceptually converted to an
"infinitely precise" binary value that is then rounded to type double by
the usual round-to-nearest rule of IEEE 754 floating-point arithmetic,
which includes preserving the sign of a zero value."
The compiler's input conversion for 3.141592 is necessarily inexact for
the reason you mentioned in the first paragraph.
Patricia