比较两个双精度浮点数或两个浮点数最有效的方法是什么?

简单地这样做是不正确的:

bool CompareDoubles1 (double A, double B)
{
   return A == B;
}

比如:

bool CompareDoubles2 (double A, double B) 
{
   diff = A - B;
   return (diff < EPSILON) && (-diff < EPSILON);
}

似乎是浪费加工。

有人知道更聪明的浮点比较器吗?


当前回答

你不能用一个固定的。根据double的值,EPSILON会发生变化。

更好的双比较应该是:

bool same(double a, double b)
{
  return std::nextafter(a, std::numeric_limits<double>::lowest()) <= b
    && std::nextafter(a, std::numeric_limits<double>::max()) >= b;
}

其他回答

我对任何涉及浮点减法的答案都非常谨慎(例如,fabs(a-b) < epsilon)。首先,浮点数在更大的量级上变得更稀疏,在足够大的量级上,当间隔大于时,您可能只需要做a == b。其次,减去两个非常接近的浮点数(因为您正在寻找接近相等的浮点数)正是您得到灾难性抵消的方式。

虽然不能移植,但我认为grom的答案在避免这些问题方面做得最好。

这个怎么样?

template<typename T>
bool FloatingPointEqual( T a, T b ) { return !(a < b) && !(b < a); }

我见过各种方法,但从来没有见过这个,所以我也很好奇听到任何评论!

在这个版本中,你可以检查,这些数字之间的差异并不比某些分数(比如,0.0001%)更大:

bool floatApproximatelyEquals(const float a, const float b) {
    if (b == 0.) return a == 0.; // preventing division by zero
    return abs(1. - a / b) < 1e-6;
}

请注意Sneftel关于浮动可能的分数限制的评论。

还要注意的是,它不同于使用绝对的epsilon的方法——这里你不需要担心“数量级”——数字可能是,比如说1e100,或者1e-100,它们总是会被一致地比较,而且你不必为每一种情况更新epsilon。

在数值软件中,确实有这样的情况,你需要检查两个浮点数是否完全相等。我就一个类似的问题发表了这篇文章

https://stackoverflow.com/a/10973098/1447411

所以你不能说“CompareDoubles1”是错误的。

General-purpose comparison of floating-point numbers is generally meaningless. How to compare really depends on a problem at hand. In many problems, numbers are sufficiently discretized to allow comparing them within a given tolerance. Unfortunately, there are just as many problems, where such trick doesn't really work. For one example, consider working with a Heaviside (step) function of a number in question (digital stock options come to mind) when your observations are very close to the barrier. Performing tolerance-based comparison wouldn't do much good, as it would effectively shift the issue from the original barrier to two new ones. Again, there is no general-purpose solution for such problems and the particular solution might require going as far as changing the numerical method in order to achieve stability.