Question

知道浮点数，即使十进制格式小数点后的固定位数，也无法准确表示。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

我无法从上述结果中回答两个问题，我正在寻求帮助：

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则不然。
为什么0.1f + 0.2f == 0.3f会返回true？

Answer 1

我怀疑System.out.printf在这里工作正常。获得写入0.1时获得的确切double值的可靠方法是写new BigDecimal(0.1).toString()。
“为什么0.1f + 0.2f == 0.3f返回true？”几乎是因为你很幸运：将0.1舍入到最接近的浮点表示，将0.2舍入到最接近的浮点表示并添加它们使得最接近的可表示浮点数达到0.3。一般情况下这不正确，这些价值恰好可行。

Java中的浮点精度和相等性

1 个答案: