Java中的浮点精度和相等性

Question

众所周知，即使是十进制格式的小数点后有固定数字的浮点数也无法准确表示。 因此，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

我无法从以上结果中回答两个问题，目前正在寻求帮助：

1. 为什么的双重代表0.1 ， 0.2和0.3的外观精确，而0.1 + 0.2没有。
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。 一种可靠的获取确切的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true？” 几乎是因为您很幸运：将0.1舍入到最接近的浮点表示形式，将0.2舍入到最接近的浮点表示形式，然后将它们相加，就可以得到最接近的可表示浮点数到0.3。 通常情况并非如此，这些价值观恰好起作用。