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?
在https://en.cppreference.com/w/cpp/types/numeric_limits/epsilon上找到了另一个有趣的实现
#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)
{
// the machine epsilon has to be scaled to the magnitude of the values used
// and multiplied by the desired precision in ULPs (units in the last place)
return std::fabs(x-y) <= std::numeric_limits<T>::epsilon() * std::fabs(x+y) * ulp
// unless the result is subnormal
|| std::fabs(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 almost equals d2\n";
else
std::cout << "d1 does not almost equal d2\n";
}
我的方法也许不正确,但很有用
将两个浮点数都转换为字符串,然后进行字符串比较
bool IsFlaotEqual(float a, float b, int decimal)
{
TCHAR form[50] = _T("");
_stprintf(form, _T("%%.%df"), decimal);
TCHAR a1[30] = _T(""), a2[30] = _T("");
_stprintf(a1, form, a);
_stprintf(a2, form, b);
if( _tcscmp(a1, a2) == 0 )
return true;
return false;
}
也可以做到操作人员超载
我为java编写这篇文章,但是您可能会发现它很有用。它使用长变量而不是双变量,但会处理nan、亚法线等。
public static boolean equal(double a, double b) {
final long fm = 0xFFFFFFFFFFFFFL; // fraction mask
final long sm = 0x8000000000000000L; // sign mask
final long cm = 0x8000000000000L; // most significant decimal bit mask
long c = Double.doubleToLongBits(a), d = Double.doubleToLongBits(b);
int ea = (int) (c >> 52 & 2047), eb = (int) (d >> 52 & 2047);
if (ea == 2047 && (c & fm) != 0 || eb == 2047 && (d & fm) != 0) return false; // NaN
if (c == d) return true; // identical - fast check
if (ea == 0 && eb == 0) return true; // ±0 or subnormals
if ((c & sm) != (d & sm)) return false; // different signs
if (abs(ea - eb) > 1) return false; // b > 2*a or a > 2*b
d <<= 12; c <<= 12;
if (ea < eb) c = c >> 1 | sm;
else if (ea > eb) d = d >> 1 | sm;
c -= d;
return c < 65536 && c > -65536; // don't use abs(), because:
// There is a posibility c=0x8000000000000000 which cannot be converted to positive
}
public static boolean zero(double a) { return (Double.doubleToLongBits(a) >> 52 & 2047) < 3; }
请记住,在一些浮点运算之后,number可能与我们期望的非常不同。没有代码可以解决这个问题。