是Math.Abs​​（x） double.Epsilon相当于Math.Abs​​（x）== 0d？ [英] Is Math.Abs(x) < double.Epsilon equivalent to Math.Abs(x) == 0d?

问题描述

经过一点点阅读，引发了我的兴趣：

After a bit of light reading, this article piqued my interest:

我以为是的，两个语句是等价的，给出MSDN的声明：

I'd have thought that yes, the two statements are equivalent, given MSDN's statement:

表示大于零的最小正Double值。

Represents the smallest positive Double value that is greater than zero. This field is constant.

很高兴看到人们的想法。

Curious to see what people think.

编辑：找到一台带VS的电脑，并运行这个测试。结果是，正如预期的那样，它们是等价的。

Found a computer with VS on and ran this Test. Turns out that yes, as expected, they're equivalent.

    [Test]
    public void EpsilonTest()
    {
        Compare(0d);
        Compare(double.Epsilon);
        Compare(double.Epsilon * 0.5);
        Compare(double.NaN);
        Compare(double.PositiveInfinity);
        Compare(double.NegativeInfinity);
        Compare(double.MaxValue);
        Compare(double.MinValue);
    }

    public void Compare(double x)
    {
        Assert.AreEqual(Math.Abs(x) == 0d, Math.Abs(x) < double.Epsilon);
    }

推荐答案

IL代码似乎投了一些

IL code seems to cast some light on this.

Epsilon只是一个双数字，分数部分是1，符号0，指数0.
零是一个双数，分数部分为0，符号0，指数0。

Epsilon is simply a double number with the fraction part being 1, sign 0, exponent 0. Zero is a double number with the fraction part being 0, sign 0, exponent 0.

根据 http://en.wikipedia.org/wiki/IEEE_754-1985 ，具有相同符号和指数的浮点数按顺序进行比较，这意味着（x <1）与（x == 0）。

According to http://en.wikipedia.org/wiki/IEEE_754-1985, floating point numbers with the same sign and exponent are compared ordinally, which means that (x < 1) is the same as (x == 0).

现在，可以得到一个零，不是fraction = 0，exponent = 0（我们不在乎符号，有一个Math.Abs​​到位）？

Now, is it possible to get a zero that isn't fraction = 0, exponent = 0 (we don't care about sign, there's a Math.Abs in place)?

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