Java中的浮点精度和相等性

Question

众所周知，浮点数，即使是十进制格式中小数点后固定位数的浮点数，也不能精确表示。所以我有以下程序要测试：

public class Main {
  public static void main(String[] args) {
    System.out.printf("0.1 in single precision is %.50f\n", 0.1f);
    System.out.printf("0.2 in single precision is %.50f\n", 0.2f);
    System.out.printf("0.3 in single precision is %.50f\n", 0.3f);
    System.out.printf("0.1 + 0.2 in single precision is %.50f\n", 0.1f + 0.2f);
    System.out.printf("0.1 + 0.2 == 0.3 is %b in single precision\n", 0.1123f * 0.4f + 0.2f * 0.5f == 0.2f * 0.7f + 0.0123f * 0.4f);

    System.out.println();

    System.out.printf("0.1 in double precision is %.50f\n", 0.1);
    System.out.printf("0.2 in double precision is %.50f\n", 0.2);
    System.out.printf("0.3 in double precision is %.50f\n", 0.3);
    System.out.printf("0.1 + 0.2 in double precision is %.50f\n", 0.1 + 0.2);
    System.out.printf("0.1 + 0.2 == 0.3 is %b in double precision\n", 0.1 + 0.2 == 0.3);
  }
}

输出如下：

0.1 in single precision is 0.10000000149011612000000000000000000000000000000000
0.2 in single precision is 0.20000000298023224000000000000000000000000000000000
0.3 in single precision is 0.30000001192092896000000000000000000000000000000000
0.1 + 0.2 in single precision is 0.30000001192092896000000000000000000000000000000000
0.1 + 0.2 == 0.3 is true in single precision

0.1 in double precision is 0.10000000000000000000000000000000000000000000000000
0.2 in double precision is 0.20000000000000000000000000000000000000000000000000
0.3 in double precision is 0.30000000000000000000000000000000000000000000000000
0.1 + 0.2 in double precision is 0.30000000000000004000000000000000000000000000000000
0.1 + 0.2 == 0.3 is false in double precision

我无法从上述结果中回答两个问题，我正在寻求帮助：

1. 为什么0.1、0.2 和0.3 的双重表示看起来准确，而0.1 + 0.2 不准确。
2. 为什么0.1f + 0.2f == 0.3f 返回true？

Answer 1

1. 我怀疑System.out.printf 在这里正常工作。在编写 0.1 时获得准确的 double 值的可靠方法是编写 new BigDecimal(0.1).toString()。
2. “为什么 0.1f + 0.2f == 0.3f 返回真？”很大程度上是因为您很幸运：将 0.1 舍入为最接近的浮点表示，将 0.2 舍入为最接近的浮点表示，然后将它们相加即可使您最接近的可表示浮点为 0.3。一般来说，这不是真的，这些值只是碰巧起作用。