GrayCounter found in rocket-chip repo, and verify their index generation logic (why double the gray code space and then calc them down?)

GrayCodeIndex.scala

import chisel3._
import chisel3.util._
import chisel3.iotesters._

object GrayCounter {
  def apply(bits: Int, inc: Bool = Bool(true), clear: Bool = Bool(false)): UInt = {
    // Incremented
    val next = Wire(UInt(width = bits))
    val curr = Reg(next = next)
    next := Mux(clear, UInt(0), curr + inc.asUInt)
    next ^ (next >> UInt(1))
  }
}   
  
class Index(val depth: Int) extends Module {
  val bits = log2Ceil(depth)

  val io = IO(new Bundle {
    val gray = Output(UInt((bits + 1).W))
    val index = Output(UInt(bits.W))
  })
  
  io.gray := GrayCounter(bits + 1)

  io.index := io.gray(bits - 1, 0) ^ (io.gray(bits, bits) << (bits - 1))
} 

class TestIndex(idx: Index) extends PeekPokeTester(idx) {
  def binary(u: UInt): String = peek(u).toInt.toBinaryString
    
  for (x <- 0 until idx.depth * 2) {
    step(1)
    println(s"gray: ${binary(idx.io.gray)}, index: ${binary(idx.io.index)}")
  }
}

object Index extends App {
  chisel3.iotesters.Driver(() => new Index(4)) { idx => new TestIndex(idx) }
}