为什么Math.round(0.49999999999999994)返回1 [英] Why does Math.round(0.49999999999999994) return 1

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问题描述

在以下程序中,您可以看到,对于每个值略小于 .5 的四舍五入,除了 0.5

In the following program you can see that for each value slightly less that .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);
}

打印

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。

I am using Java 6 update 31.

推荐答案

摘要

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

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

问题

0.5+ 0.49999999999999994正好是双精度1:

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
}

这是因为0.49999999999999994的指数小于0.5,所以当

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.

解决方案

由于Java 7,OpenJDK(例如)实现了它: 4

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 (以@SimonNickerson为单位查询)

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/7 u40-b43 / java / lang / Math.java#Math.round%28double%29

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