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?
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。
/// testing whether two doubles are almost equal. We consider two doubles
/// equal if the difference is within the range [0, epsilon).
///
/// epsilon: a positive number (supposed to be small)
///
/// if either x or y is 0, then we are comparing the absolute difference to
/// epsilon.
/// if both x and y are non-zero, then we are comparing the relative difference
/// to epsilon.
bool almost_equal(double x, double y, double epsilon)
{
double diff = x - y;
if (x != 0 && y != 0){
diff = diff/y;
}
if (diff < epsilon && -1.0*diff < epsilon){
return true;
}
return false;
}
我在我的小项目中使用了这个函数,它是有效的,但注意以下几点:
双精度误差可以为你制造惊喜。假设epsilon = 1.0e-6,那么根据上面的代码,1.0和1.000001不应该被认为是相等的,但在我的机器上,函数认为它们是相等的,这是因为1.000001不能精确地转换为二进制格式,它可能是1.0000009xxx。我用1.0和1.0000011测试了它,这次我得到了预期的结果。