count(from:to:by:).swift

/// Performs an exponential search to find the number of steps from `start` to `end`
/// without using division.
func count<T: Numeric & Comparable>(from start: T, to end: T, by step: T) -> Int {
  var count = 1
  var current = start
  var stepMultipliers = [1]
  while current < end {
    count += stepMultipliers.last!
    current += step * T(exactly: stepMultipliers.last!)!
    stepMultipliers.append(stepMultipliers.last! * 2)
  }

  _ = stepMultipliers.removeLast()

  while current >= end {
    let subtract = stepMultipliers.removeLast()
    let test = current - step * T(exactly: subtract)!
    if test >= end {
      current = test
      count -= subtract
      continue
    }
    if end - test <= step {
      count -= subtract
      break
    }
  }
  return count
}

let start = 0
let end = 10_000
let step = 3
print("count:", Array(stride(from: start, to: end, by: step)).count)
print("calculated:", count(from: start, to: end, by: step))