功能风格的Scala Double epsilon计算

Question

A suggested approach to calculate machine epsilon using Java is as follows,

private static float calculateMachineEpsilonFloat() {
    float machEps = 1.0f;
    do
       machEps /= 2.0f;
    while ((float) (1.0 + (machEps / 2.0)) != 1.0);

    return machEps;
}

How to compute epsilon for scala.Double using Scala in an idiomatic / functional style from this suggested code?

Answer 1

Is that OK?

scala> val s: Stream[Float] = 1.0f #:: s.map(f => f / 2.0f)
s: Stream[Float] = Stream(1.0, ?)

scala> val eps = s.takeWhile(e => e + 1.0f != 1.0f).last
eps: Float = 1.1920929E-7

To get another epsilon (2^{-24}), one can use dropWhile (and, consequently, head ) instead.

Answer 2

You can rewrite the do-while loop with recursion:

import scala.annotation.tailrec

def calculateMachineEpsilonFloat = {
  @tailrec
  def calc(machEps: Float): Float = {
    if ((1.0 + (machEps / 2.0)).toFloat != 1.0)
       calc(machEps / 2f)
    else
      machEps
  }
  calc(1f)
}