舍入错误？ [英] Rounding Errors?

问题描述

在我的课程中，我被告知：

In my course, I am told:

连续值大约在内存中表示，因此使用浮点数计算涉及舍入错误。这些是位模式的微小差异;因此，如果 e 和 f e == f 是不安全的c>是花车。

Continuous values are represented approximately in memory, and therefore computing with floats involves rounding errors. These are tiny discrepancies in bit patterns; thus the test e==f is unsafe if e and f are floats.

参考Java。

这是真的吗？我已经使用了与 double 和 float s的比较语句，并且从未遇到过舍入问题。我从未在教科书中读过类似的东西。当然虚拟机会解释这个吗？

Is this true? I've used comparison statements with doubles and floats and have never had rounding issues. Never have I read in a textbook something similar. Surely the virtual machine accounts for this?

推荐答案

这是真的。

浮点值在内存中以有限位数表示的固有限制。

It is an inherent limitation of how floating point values are represented in memory in a finite number of bits.

例如，此程序打印false：

This program, for instance, prints "false":

public class Main {
  public static void main(String[] args) {
    double a = 0.7;
    double b = 0.9;
    double x = a + 0.1;
    double y = b - 0.1;
    System.out.println(x == y);
  }
}

而不是与'=='进行精确比较决定某种程度的精确度，并询问这些数字是否足够接近：

Instead of exact comparison with '==' you usually decide on some level of precision and ask if the numbers are "close enough":

System.out.println(Math.abs(x - y) < 0.0001);

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