Java中的浮点精度和相等性

Question

众所周知，浮点数，即使是小数点后固定数字的十进制格式，也不能准确表示。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

以上结果中有两个问题我无法回答，我正在寻求帮助：

1. 为什么0.1、0.2和0.3的双重表示看起来很精确，而0.1、0.2却不精确。

Answer 1

1. 我怀疑这个系统。出来printf在此正常工作。要获得写入0.1时得到的精确值，可靠的方法是写入新的BigDecimal（0.1）。toString（）