# Java – Why does Math.round(0.49999999999999994) return 1

doublefloating pointjavarounding

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.

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. http://docs.oracle.com/javase/6/docs/api/java/lang/Math.html#round%28double%29

2. http://bugs.java.com/bugdatabase/view_bug.do?bug_id=6430675 (credits to @SimonNickerson for finding this)

3. http://docs.oracle.com/javase/7/docs/api/java/lang/Math.html#round%28double%29

4. http://grepcode.com/file/repository.grepcode.com/java/root/jdk/openjdk/7u40-b43/java/lang/Math.java#Math.round%28double%29