为什么Math.round(0.49999999999999994)返回1

问题:

在以下程序中,您可以看到,对于每个值略小于.5向下舍入,除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);
}

版画

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

我正在使用Java 6更新31。

回答:

 概要
在Java 6(可能早期)中,round(x)被实现为floor(x+0.5) 1这是一个规范错误,正是这一个病理情况。 2 Java 7不再要求这个破坏的实现。 3
 问题
0.5 + 0.49999999999999994正好是双精度1:

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
}

这是因为0.49999999999999994的指数小于0.5,所以当它们被添加时,其尾数被移位,并且ULP变大。
 解决方案
因为Java 7,OpenJDK(例如)实现它: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

 
 
Code问答: http://codewenda.com/topics/python/
Stackoverflow: Why does Math.round(0.49999999999999994) return 1

*转载请注明本文链接以及stackoverflow的英文链接

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