将浮点数与零比较

问题描述

C ++常见问题解答建议这种平等测试：

  #include< cmath> / * for std :: abs（double）* / 
 
 inline bool isEqual（double x，double y）
 {
 const double epsilon = / *一些小数字1e-5 * /; 
 return std :: abs（x-y） //见Knuth第4.2.2节第217-218页
} 
  

1. 这是正确的，这意味着只有等于零的数字是 +0 和 -0 ？


2. 应该在测试零时使用此函数，或者像 | x | < εilon？
   

更新 $ b

正如丹尼尔·达拉纳斯所指出的，函数应该更好地被调用 isNearlyEqual （这是我关心的情况）。

有人指出了，我想更明显地分享。

解决方案

您的观察是正确的。

如果 x == 0.0 ，则 abs（x）* epsilon 为零，您正在测试 abs（y）。

y == 0.0 那么你正在测试 abs（x）< = abs（x）* epsilon epsilon> = 1 （不是）或 x == 0.0 。

因此 is_equal（val，0.0）或 is_equal（0.0，val）将是无意义的，你可以只说 val == 0.0 。如果您只想接受确切 +0.0 和 -0.0 。

在这种情况下，常见问题建议的作用有限。 没有一刀切的浮点比较。您必须考虑变量的语义，可接受的值范围以及计算引入的误差幅度。即使常见问题提到一个警告，说这个功能通常不是一个问题当x和y的大小明显大于epsilon，但你的里程可能会变化。

The C++ FAQ lite "[29.17] Why doesn't my floating-point comparison work?" recommends this equality test:

#include <cmath>  /* for std::abs(double) */

inline bool isEqual(double x, double y)
{
  const double epsilon = /* some small number such as 1e-5 */;
  return std::abs(x - y) <= epsilon * std::abs(x);
  // see Knuth section 4.2.2 pages 217-218
}

1. Is it correct, that this implies that the only numbers which are equal to zero are +0 and -0?
2. Should one use this function also when testing for zero or rather a test like |x| < epsilon?

Update

As pointed out by Daniel Daranas the function should probably better be called isNearlyEqual(which is the case I care about).

Someone pointed out this link, which I want to share more prominently.

解决方案

You are correct with your observation.

If x == 0.0, then abs(x) * epsilon is zero and you're testing whether abs(y) <= 0.0.

If y == 0.0 then you're testing abs(x) <= abs(x) * epsilon which means either epsilon >= 1 (it isn't) or x == 0.0.

So either is_equal(val, 0.0) or is_equal(0.0, val) would be pointless, and you could just say val == 0.0. If you want to only accept exactly +0.0 and -0.0.

The FAQ's recommendation in this case is of limited utility. There is no "one size fits all" floating-point comparison. You have to think about the semantics of your variables, the acceptable range of values, and the magnitude of error introduced by your computations. Even the FAQ mentions a caveat, saying this function is not usually a problem "when the magnitudes of x and y are significantly larger than epsilon, but your mileage may vary".

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