java - Why does Math.round(0.49999999999999994) return 1?
itemprop="text">
In the following program you can see
that each value slightly less than .5
is rounded down, except
for
0.5
.
for
(int i = 10; i >= 0; i--) {
long l = Double.doubleToLongBits(i +
0.5);
double x;
do {
x =
Double.longBitsToDouble(l);
System.out.println(x + " rounded is " +
Math.round(x));
l--;
} while (Math.round(x) >
i);
}
prints
10.5
rounded is 11
10.499999999999998 rounded is 10
9.5 rounded is
10
9.499999999999998 rounded is 9
8.5 rounded is
9
8.499999999999998 rounded is 8
7.5 rounded is
8
7.499999999999999 rounded is 7
6.5 rounded is
7
6.499999999999999 rounded is 6
5.5 rounded is
6
5.499999999999999 rounded is 5
4.5 rounded is
5
4.499999999999999 rounded is 4
3.5 rounded is
4
3.4999999999999996 rounded is 3
2.5 rounded is
3
2.4999999999999996 rounded is 2
1.5 rounded is
2
1.4999999999999998 rounded is 1
0.5 rounded is
1
0.49999999999999994 rounded is 1
0.4999999999999999 rounded is
0
I am using Java 6
update 31.
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Summary
In
Java 6 (and presumably earlier), round(x)
is implemented as
floor(x+0.5)
.1 This is a specification
bug, for precisely this one pathological case.2 Java 7 no longer
mandates this broken
implementation.3
The
problem
0.5+0.49999999999999994
is exactly 1 in double
precision:
static void
print(double d) {
System.out.printf("%016x\n",
Double.doubleToLongBits(d));
}
public static
void main(String args[]) {
double a = 0.5;
double b =
0.49999999999999994;
print(a); // 3fe0000000000000
print(b); // 3fdfffffffffffff
print(a+b); // 3ff0000000000000
print(1.0); //
3ff0000000000000
}
This
is because 0.49999999999999994 has a smaller exponent than 0.5, so when they're added,
its mantissa is shifted, and the ULP gets
bigger.
The
solution
Since Java 7, OpenJDK
(for example) implements it
thus:4
public
static long round(double a) {
if (a != 0x1.fffffffffffffp-2) //
greatest double value less than 0.5
return (long)floor(a + 0.5d);
else
return
0;
}
/>
1. href="http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html#round%28double%29"
rel="noreferrer">http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html#round%28double%29
2.
rel="noreferrer">http://bugs.java.com/bugdatabase/view_bug.do?bug_id=6430675
(credits to @SimonNickerson for finding
this)
3.
href="http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#round%28double%29"
rel="noreferrer">http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#round%28double%29
4.
href="http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/7u40-b43/java/lang/Math.java#Math.round%28double%29"
rel="noreferrer">http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/7u40-b43/java/lang/Math.java#Math.round%28double%29
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