std::numeric_limits<T>::epsilon
来自cppreference.com
< cpp | types | numeric limits
| static T epsilon() throw(); |
(C++11 前) | |
| static constexpr T epsilon() noexcept; |
(C++11 起) | |
返回机器 epsilon，即 1.0 与浮点类型 T 的下个可表示值的差。它只有在 std::numeric_limits<T>::is_integer == false 时才有意义。
返回值
T
|
std::numeric_limits<T>::epsilon() |
| /* 未特化 */ | T() |
| bool | false |
| char | 0 |
| signed char | 0 |
| unsigned char | 0 |
| wchar_t | 0 |
| char8_t (C++20 起) | 0 |
| char16_t (C++11 起) | 0 |
| char32_t (C++11 起) | 0 |
| short | 0 |
| unsigned short | 0 |
| int | 0 |
| unsigned int | 0 |
| long | 0 |
| unsigned long | 0 |
| long long (C++11 起) | 0 |
| unsigned long long(C++11 起) | 0 |
| float | FLT_EPSILON |
| double | DBL_EPSILON |
| long double | LDBL_EPSILON |
示例
演示用机器 epsilon 比较浮点值是否相等：
运行此代码
#include <cmath> #include <limits> #include <iomanip> #include <iostream> #include <type_traits> #include <algorithm> template<class T> typename std::enable_if<!std::numeric_limits<T>::is_integer, bool>::type almost_equal(T x, T y, int ulp) { // 机器 epsilon 需要调整到要使用的值的量级， // 并且乘以以 ULP（最后位置单位）为单位的想要的精度 return std::abs(x - y) <= std::numeric_limits<T>::epsilon() * std::abs(x + y) * ulp // unless the result is subnormal || std::abs(x - y) < std::numeric_limits<T>::min(); } int main() { double d1 = 0.2; double d2 = 1 / std::sqrt(5) / std::sqrt(5); std::cout << std::fixed << std::setprecision(20) << "d1=" << d1 << "\nd2=" << d2 << '\n'; if (d1 == d2) std::cout << "d1 == d2\n"; else std::cout << "d1 != d2\n"; if (almost_equal(d1, d2, 2)) std::cout << "d1 几乎等于 d2\n"; else std::cout << "d1 不几乎等于 d2\n"; }
输出：
d1=0.20000000000000001110 d2=0.19999999999999998335 d1 != d2 d1 几乎等于 d2
参阅
| (C++11)(C++11) (C++11)(C++11)(C++11)(C++11) |
趋向给定值的下个可表示浮点值 (函数) |