Looking for the last point in a continuous function where the predicat "test" is true

Dichotomy.scala

import scala.annotation.tailrec
//Looking for the last point in a continuous function where the predicat "test" is true
@tailrec
def dichotomy(lower : Double, upper: Double)( test: Double => Boolean) : Double = {
  val gap = (upper-lower)/ 2
  val middle = lower + gap
  if(gap <= 1)
    lower
  else if(test(middle)) {
    if(middle == lower) //Float or Double precision error
      lower
    else
      dichotomy(middle,upper)(test)
  } else {
    if(middle == upper) //Float or Double precision error
      lower
    else
      dichotomy(lower,middle)(test)
  }
}