你必须为浮点数比较做这个处理，因为浮点数不能像整数类型那样完美地比较。下面是各种比较运算符的函数。

浮点数等于(==)

我也更喜欢减法技术，而不是依赖于fabs()或abs()，但我必须在从64位PC到ATMega328微控制器(Arduino)的各种架构上快速配置它，才能真正看到它是否会产生很大的性能差异。

所以，让我们忘记这些绝对值的东西，只做一些减法和比较!

从微软的例子修改如下:

/// @brief      See if two floating point numbers are approximately equal.
/// @param[in]  a        number 1
/// @param[in]  b        number 2
/// @param[in]  epsilon  A small value such that if the difference between the two numbers is
///                      smaller than this they can safely be considered to be equal.
/// @return     true if the two numbers are approximately equal, and false otherwise
bool is_float_eq(float a, float b, float epsilon) {
    return ((a - b) < epsilon) && ((b - a) < epsilon);
}
bool is_double_eq(double a, double b, double epsilon) {
    return ((a - b) < epsilon) && ((b - a) < epsilon);
}

使用示例:

constexpr float EPSILON = 0.0001; // 1e-4
is_float_eq(1.0001, 0.99998, EPSILON);

我不完全确定，但在我看来，对基于epsilon的方法的一些批评，正如这个高度好评的答案下面的评论所描述的那样，可以通过使用变量epsilon来解决，根据比较的浮点值缩放，像这样:

float a = 1.0001;
float b = 0.99998;
float epsilon = std::max(std::fabs(a), std::fabs(b)) * 1e-4;

is_float_eq(a, b, epsilon);

通过这种方式，epsilon值随浮点值伸缩，因此它的值不会小到不重要。

为了完整起见，让我们添加剩下的:

大于(>)小于(<):

/// @brief      See if floating point number `a` is > `b`
/// @param[in]  a        number 1
/// @param[in]  b        number 2
/// @param[in]  epsilon  a small value such that if `a` is > `b` by this amount, `a` is considered
///             to be definitively > `b`
/// @return     true if `a` is definitively > `b`, and false otherwise
bool is_float_gt(float a, float b, float epsilon) {
    return a > b + epsilon;
}
bool is_double_gt(double a, double b, double epsilon) {
    return a > b + epsilon;
}

/// @brief      See if floating point number `a` is < `b`
/// @param[in]  a        number 1
/// @param[in]  b        number 2
/// @param[in]  epsilon  a small value such that if `a` is < `b` by this amount, `a` is considered
///             to be definitively < `b`
/// @return     true if `a` is definitively < `b`, and false otherwise
bool is_float_lt(float a, float b, float epsilon) {
    return a < b - epsilon;
}
bool is_double_lt(double a, double b, double epsilon) {
    return a < b - epsilon;
}

大于或等于(>=)，小于或等于(<=)

/// @brief      Returns true if `a` is definitively >= `b`, and false otherwise
bool is_float_ge(float a, float b, float epsilon) {
    return a > b - epsilon;
}
bool is_double_ge(double a, double b, double epsilon) {
    return a > b - epsilon;
}

/// @brief      Returns true if `a` is definitively <= `b`, and false otherwise
bool is_float_le(float a, float b, float epsilon) {
    return a < b + epsilon;
}
bool is_double_le(double a, double b, double epsilon) {
    return a < b + epsilon;
}

额外的改进:

A good default value for epsilon in C++ is std::numeric_limits<T>::epsilon(), which evaluates to either 0 or FLT_EPSILON, DBL_EPSILON, or LDBL_EPSILON. See here: https://en.cppreference.com/w/cpp/types/numeric_limits/epsilon. You can also see the float.h header for FLT_EPSILON, DBL_EPSILON, and LDBL_EPSILON. See https://en.cppreference.com/w/cpp/header/cfloat and https://www.cplusplus.com/reference/cfloat/ You could template the functions instead, to handle all floating point types: float, double, and long double, with type checks for these types via a static_assert() inside the template. Scaling the epsilon value is a good idea to ensure it works for really large and really small a and b values. This article recommends and explains it: http://realtimecollisiondetection.net/blog/?p=89. So, you should scale epsilon by a scaling value equal to max(1.0, abs(a), abs(b)), as that article explains. Otherwise, as a and/or b increase in magnitude, the epsilon would eventually become so small relative to those values that it becomes lost in the floating point error. So, we scale it to become larger in magnitude like they are. However, using 1.0 as the smallest allowed scaling factor for epsilon also ensures that for really small-magnitude a and b values, epsilon itself doesn't get scaled so small that it also becomes lost in the floating point error. So, we limit the minimum scaling factor to 1.0. If you want to "encapsulate" the above functions into a class, don't. Instead, wrap them up in a namespace if you like in order to namespace them. Ex: if you put all of the stand-alone functions into a namespace called float_comparison, then you could access the is_eq() function like this, for instance: float_comparison::is_eq(1.0, 1.5);. It might also be nice to add comparisons against zero, not just comparisons between two values. So, here is a better type of solution with the above improvements in place: namespace float_comparison { /// Scale the epsilon value to become large for large-magnitude a or b, /// but no smaller than 1.0, per the explanation above, to ensure that /// epsilon doesn't ever fall out in floating point error as a and/or b /// increase in magnitude. template<typename T> static constexpr T scale_epsilon(T a, T b, T epsilon = std::numeric_limits<T>::epsilon()) noexcept { static_assert(std::is_floating_point_v<T>, "Floating point comparisons " "require type float, double, or long double."); T scaling_factor; // Special case for when a or b is infinity if (std::isinf(a) || std::isinf(b)) { scaling_factor = 0; } else { scaling_factor = std::max({(T)1.0, std::abs(a), std::abs(b)}); } T epsilon_scaled = scaling_factor * std::abs(epsilon); return epsilon_scaled; } // Compare two values /// Equal: returns true if a is approximately == b, and false otherwise template<typename T> static constexpr bool is_eq(T a, T b, T epsilon = std::numeric_limits<T>::epsilon()) noexcept { static_assert(std::is_floating_point_v<T>, "Floating point comparisons " "require type float, double, or long double."); // test `a == b` first to see if both a and b are either infinity // or -infinity return a == b || std::abs(a - b) <= scale_epsilon(a, b, epsilon); } /* etc. etc.: is_eq() is_ne() is_lt() is_le() is_gt() is_ge() */ // Compare against zero /// Equal: returns true if a is approximately == 0, and false otherwise template<typename T> static constexpr bool is_eq_zero(T a, T epsilon = std::numeric_limits<T>::epsilon()) noexcept { static_assert(std::is_floating_point_v<T>, "Floating point comparisons " "require type float, double, or long double."); return is_eq(a, (T)0.0, epsilon); } /* etc. etc.: is_eq_zero() is_ne_zero() is_lt_zero() is_le_zero() is_gt_zero() is_ge_zero() */ } // namespace float_comparison

参见:

The macro forms of some of the functions above in my repo here: utilities.h. UPDATE 29 NOV 2020: it's a work-in-progress, and I'm going to make it a separate answer when ready, but I've produced a better, scaled-epsilon version of all of the functions in C in this file here: utilities.c. Take a look. ADDITIONAL READING I need to do now have done: Floating-point tolerances revisited, by Christer Ericson. VERY USEFUL ARTICLE! It talks about scaling epsilon in order to ensure it never falls out in floating point error, even for really large-magnitude a and/or b values!

在c++中获取的可移植方法是

#include <limits>
std::numeric_limits<double>::epsilon()

然后比较函数变成

#include <cmath>
#include <limits>

bool AreSame(double a, double b) {
    return std::fabs(a - b) < std::numeric_limits<double>::epsilon();
}

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。

Qt实现了两个函数，也许你可以从中学到一些东西:

static inline bool qFuzzyCompare(double p1, double p2)
{
    return (qAbs(p1 - p2) <= 0.000000000001 * qMin(qAbs(p1), qAbs(p2)));
}

static inline bool qFuzzyCompare(float p1, float p2)
{
    return (qAbs(p1 - p2) <= 0.00001f * qMin(qAbs(p1), qAbs(p2)));
}

您可能需要以下函数，因为

请注意，比较p1或p2为0.0的值是无效的， 也不会比较其中一个值为NaN或无穷大的值。 如果其中一个值总是0.0，则使用qFuzzyIsNull代替。如果一个人 其中的值很可能是0.0，一种解决方案是将两者都加上1.0 值。

static inline bool qFuzzyIsNull(double d)
{
    return qAbs(d) <= 0.000000000001;
}

static inline bool qFuzzyIsNull(float f)
{
    return qAbs(f) <= 0.00001f;
}

使用任何其他建议都要非常小心。这完全取决于上下文。

我花了很长时间在一个系统中追踪错误，该系统假设|a-b|<epsilon，则a==b。潜在的问题是:

The implicit presumption in an algorithm that if a==b and b==c then a==c. Using the same epsilon for lines measured in inches and lines measured in mils (.001 inch). That is a==b but 1000a!=1000b. (This is why AlmostEqual2sComplement asks for the epsilon or max ULPS). The use of the same epsilon for both the cosine of angles and the length of lines! Using such a compare function to sort items in a collection. (In this case using the builtin C++ operator == for doubles produced correct results.)

就像我说的，这完全取决于上下文和a和b的预期大小。

顺便说一下，std::numeric_limits<double>::epsilon()是“机器epsilon”。它是1.0和下一个用double表示的值之间的差值。我猜它可以用在比较函数中，但只有当期望值小于1时。(这是对@cdv的回答的回应…)

同样，如果你的int算术是双精度的(这里我们在某些情况下使用双精度来保存int值)，你的算术是正确的。例如，4.0/2.0将等同于1.0+1.0。只要你不做导致分数(4.0/3.0)的事情，或者不超出int的大小。

不幸的是，即使您的“浪费”代码也是不正确的。EPSILON是可以添加到1.0并更改其值的最小值。值1.0非常重要——更大的数字在添加到EPSILON时不会改变。现在，您可以将这个值缩放到您正在比较的数字，以判断它们是否不同。比较两个双精度对象的正确表达式是:

if (fabs(a - b) <= DBL_EPSILON * fmax(fabs(a), fabs(b)))
{
    // ...
}

这是最小值。一般来说，你会想要在计算中考虑噪声，并忽略一些最不重要的位，所以更现实的比较应该是这样的:

if (fabs(a - b) <= 16 * DBL_EPSILON * fmax(fabs(a), fabs(b)))
{
    // ...
}

如果比较性能对您非常重要，并且您知道值的范围，那么您应该使用定点数字。