Scala Nimbers

Nimber.scala

import scala.language.implicitConversions

class Nimber(val value: BigInt) extends AnyVal {
  def size: Int = {
    val bitSize =
      if (value == 1) 0
      else if (value <= 3) 1
      else value.bitLength - 1
    val logBits =
      if (bitSize > 0)
        Math.log(bitSize) / Math.log(2)
      else
        0
    val result = BigInt(0).flipBit(logBits.floor.toInt)
    result.toInt
  }

  override def toString: String =
    value.toString

  def +(other: Nimber): Nimber =
    Nimber(value ^ other.value)

  def *(other: Nimber): Nimber =
    Nimber.multiply(this, other)

  def split: (Nimber, Nimber) =
    split(size)

  def split(at: Int): (Nimber, Nimber) =
    (Nimber(value >> at), Nimber(value & ~(BigInt(-1) << at)))

  def square: Nimber = {
    if (value == 0) return this
    if (value == 1) return this
    val k = size
    val ps = split(k)
    val p1 = ps._1.square
    val p2 = ps._2.square

    Nimber.join(k, p1, p2 + (p1 * Nimber.bit(k - 1)))
  }
}

object Nimber {

  implicit def apply(value: BigInt): Nimber =
    new Nimber(value)

  implicit def apply(value: Int): Nimber =
    Nimber(BigInt(value))

  def bit(position: Int): Nimber =
    Nimber(BigInt(0).flipBit(position))

  def join(at: Int, left: Nimber, right: Nimber): Nimber =
    Nimber((left.value << at) | right.value)

  def multiply(a: Nimber, b: Nimber): Nimber = {
    if (a.value == 0) return Nimber(0)
    if (b.value == 0) return Nimber(0)
    if (a.value == 1) return b
    if (b.value == 1) return a
    if (a.value == b.value) return a.square

    val k = Math.max(a.size, b.size)
    val as = a.split(k)
    val bs = b.split(k)
    val p1 = as._1 * bs._1
    val p2 = as._2 * bs._2

    join(
      k,
      p2 + (as._1 + as._2) * (bs._1 + bs._2),
      p2 + (p1 * bit(k - 1))
    )

  }


}