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为什么Math.round(0.49999999999999994)会返回1?

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在以下程序中,您可以看到每个稍微小于 .5 的值都向下舍入,但 0.5 除外 .

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 .

5 回答

  • 554

    我在JDK 1.6 32位上也一样,但是在Java 7 64位上,我得到0为0.49999999999999994,舍入为0,最后一行不打印 . 这似乎是一个VM问题,但是,使用浮点,您应该期望在各种环境(CPU,32位或64位模式)上的结果有所不同 .

    并且,当使用 round 或反转矩阵等时,这些位可以产生巨大的差异 .

    x64输出:

    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 0
    
  • 229

    JDK 6中的源代码:

    public static long round(double a) {
        return (long)Math.floor(a + 0.5d);
    }
    

    JDK 7中的源代码:

    public static long round(double a) {
        if (a != 0x1.fffffffffffffp-2) {
            // a is not the greatest double value less than 0.5
            return (long)Math.floor(a + 0.5d);
        } else {
            return 0;
        }
    }
    

    当值为0.49999999999999994d时,在JDK 6中,它将调用 floor 并因此返回1,但在JDK 7中, if 条件正在检查该数字是否是小于0.5的最大双精度值 . 在这种情况下,数字不是小于0.5的最大双精度值,因此 else 块返回0 .

    您可以尝试0.49999999999999999d,它将返回1,但不返回0,因为这是小于0.5的最大双精度值 .

  • 81

    这似乎是已知的错误(Java bug 6430675: Math.round has surprising behavior for 0x1.fffffffffffffp-2),已在Java 7中修复 .

  • 26

    以下的答案是Oracle bug report 6430675 at的摘录 . 请访问该报告以获取完整说明 .

    The methods {Math, StrictMath.round are operationally defined as

    (long)Math.floor(a + 0.5d)
    

    用于双重参数 . 虽然这个定义通常按预期工作,但它给出了令人惊讶的结果,而不是0,对于0x1.fffffffffffffp-2(0.49999999999999994) .

    值0.49999999999999994是小于0.5的最大浮点值 . 作为十六进制浮点字面值,其值为0x1.fffffffffffffp-2,等于(2 - 2 ^ 52)* 2 ^ -2 . ==(0.5 - 2 ^ 54) . 因此,总和的确切值

    (0.5 - 2^54) + 0.5
    

    是1 - 2 ^ 54 . 这是两个相邻浮点数(1 - 2 ^ 53)和1之间的中间点 . 在Java 754算术轮到Java使用的最接近舍入模式时,当浮点结果不精确时,两者的距离越近必须返回包含确切结果的可表示浮点值;如果两个值都相等,则返回其最后一位为零的值 . 在这种情况下,add的正确返回值为1,而不是小于1的最大值 .

    虽然该方法按照定义运行,但此输入的行为非常令人惊讶;规范可以修改为更像“Round to the long long,rounding tied up”,这将允许更改此输入的行为 .

  • 11

    Summary

    在Java 6中(可能更早), round(x) 被实现为 floor(x+0.5) .1这是一个规范错误,正是这一个病态案例.2 Java 7不再强制执行这个破坏的实现.3

    The problem

    0.5 0.49999999999999994正是双精度中的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,因此当它们被添加时,它的尾数被移位,并且ULP变大 .

    The solution

    从Java 7开始,OpenJDK(例如)实现了它: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(感谢@SimonNickerson查找此内容)

    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

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