snapToReal.scala

import scala.annotation.tailrec

object SnapToReal {
  def apply(n: Double, limit: Int = 10, thresh: Double = 0.00000000001): (Double, Int, Int) = {
    @tailrec
    def outer(i: Int, ex: Int, div: Int): (Double, Int, Int) = {
      if (i >= limit) {
        (n, 1, 1)
      } else if (div < 1) {
        outer(i + 1, 1, i + 1)
      } else {
        val x = math.pow(n * div, ex)
        val m = x % 1.0
        val d = if (m < 0.5) m else m - 1.0
        if (math.abs(d) < thresh) {
          (x - m, ex, div)
        } else {
          outer(i, ex + 1, div - 1)
        }
      }
    }
    outer(1, 1, 1)
  }
}