math.random 在 Java 中的分布是怎样的？

Question

我想在 Java 程序中使用 math.random()。

这种获得双打的方式分布情况如何？

Answer 1

public static double random()

Returns a double value with a positive sign, greater than or equal to 0.0 and less than 1.0. Returned values are chosen pseudorandomly with (approximately) uniform distribution from that range.

文档继续提到它在幕后使用 java.util.Random，大概是 nextDouble()（尽管没有明确说明）。

关于nextDouble中不均匀性的说明如下：

The method nextDouble is implemented by class Random as if by:
 public double nextDouble() {
   return (((long)next(26) << 27) + next(27))
     / (double)(1L << 53);
 }
The hedge "approximately" is used in the foregoing description only because the next method is only approximately an unbiased source of independently chosen bits. If it were a perfect source of randomly chosen bits, then the algorithm shown would choose double values from the stated range with perfect uniformity.

看来 non-uniformity 只是由于 next 的潜在不均匀性，而不是 nextDouble 算法本身的重大偏差：

[In early versions of Java, the result was incorrectly calculated as:
  return (((long)next(27) << 27) + next(27))
     / (double)(1L << 54);
This might seem to be equivalent, if not better, but in fact it introduced a large nonuniformity because of the bias in the rounding of floating-point numbers: it was three times as likely that the low-order bit of the significand would be 0 than that it would be 1! This nonuniformity probably doesn't matter much in practice, but we strive for perfection.]

注意，这里是从区间[0,1]统一绘制的，分成2^-53等步长，也就是不是等同于从0到1之间的所有double值的集合中统一抽取。这是一个细微的区别：所有double值的集合如图所示，0 和 1 本身在数轴上的间隔不均匀：

^{图片转自docs.oracle.com}

math.random 在 Java 中的分布是怎样的？

What is the distribution of math.random in Java?

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