将位转换为 Double 后，如何在不使用 BigDecimal 的情况下存储实际的 float/double 值？

Question

根据几个浮点计算器以及我下面的代码，以下 32 位 00111111010000000100000110001001 的实际浮点值为 (0.750999987125396728515625)。由于它是实际的 Float 值，我认为将它存储在 Double 或 Float 中会保留精度和精确值，只要（1）不执行任何算术（2）使用实际值并且（3）该值是没有被贬低。那么为什么实际值与 (0.7509999871253967) 的转换（示例 1）和文字（示例 2）值不同？

我以这个计算器为例： https://www.h-schmidt.net/FloatConverter/IEEE754.html

import java.math.BigInteger;
import java.math.BigDecimal;

public class MyClass {
    public static void main(String args[]) {
      int myInteger = new BigInteger("00111111010000000100000110001001", 2).intValue();
      Double myDouble = (double) Float.intBitsToFloat(myInteger);
      String myBidDecimal = new BigDecimal(myDouble).toPlainString();

      System.out.println("      bits converted to integer: 00111111010000000100000110001001 = " + myInteger);
      System.out.println("    integer converted to double: " + myDouble);
      System.out.println(" double converted to BigDecimal: " + myBidDecimal);

      Double myDouble2 = 0.750999987125396728515625;
      String myBidDecimal2 = new BigDecimal(myDouble2).toPlainString();

      System.out.println("");
      System.out.println("       Ignore the binary string: ");
      System.out.println("            double from literal: " + myDouble2);
      System.out.println(" double converted to BigDecimal: " + myBidDecimal2);
    }
}

这是输出：

      bits converted to integer: 00111111010000000100000110001001 = 1061175689
    integer converted to double: 0.7509999871253967
 double converted to BigDecimal: 0.750999987125396728515625

       Ignore the binary string: 
            double from literal: 0.7509999871253967
 double converted to BigDecimal: 0.750999987125396728515625

Answer 1

没有实际的精度损失；问题是您对如何将双打转换为 String（例如打印时）的错误期望。

来自the documentation of Double.toString：

How many digits must be printed for the fractional part of m or a? There must be at least one digit to represent the fractional part, and beyond that as many, but only as many, more digits as are needed to uniquely distinguish the argument value from adjacent values of type double. That is, suppose that x is the exact mathematical value represented by the decimal representation produced by this method for a finite nonzero argument d. Then d must be the double value nearest to x; or if two double values are equally close to x, then d must be one of them and the least significant bit of the significand of d must be 0.

因此，当 double 被打印时，它只打印足够的数字来唯一标识 double 值，而不是将精确值描述为实数所需的位数.

如果您想获得 double 的所有可能数字的精确值，new BigDecimal(theDouble).toPlainString() 就是您的方法——而且，正如您所展示的那样，它会得到正确的结果。

将位转换为 Double 后，如何在不使用 BigDecimal 的情况下存储实际的 float/double 值？

After converting bits to Double, how to store actual float/double value without using BigDecimal?

java

floating-point

bigdecimal

ieee-754

single-precision