Mod.scala

  case class Mod(q: BigInt) {

    def apply(x: BigInt): BigIntModQ = x

    class BigIntModQ private (val $: BigInt) {
      def pow(exp: BigInt): BigIntModQ = $ modPow (exp, q)
    }

    object BigIntModQ {
      implicit def apply(x: BigInt): BigIntModQ = new BigIntModQ(x mod q)
      def unapply(x: BigIntModQ): BigInt = x.$
    }

    implicit object BigIntModQIsIntegral extends Integral[BigIntModQ] with Ordering[BigIntModQ] {
      def plus(x: BigIntModQ, y: BigIntModQ): BigIntModQ = x.$ + y.$
      def minus(x: BigIntModQ, y: BigIntModQ): BigIntModQ = x.$ - y.$
      def times(x: BigIntModQ, y: BigIntModQ): BigIntModQ = x.$ * y.$
      def quot(x: BigIntModQ, y: BigIntModQ): BigIntModQ = x.$ * (y.$ modInverse q) mod q
      def rem(x: BigIntModQ, y: BigIntModQ): BigIntModQ = 0: BigInt
      def negate(x: BigIntModQ): BigIntModQ = -x.$
      def fromInt(x: Int): BigIntModQ = x: BigInt
      def toInt(x: BigIntModQ): Int = x.$.intValue()
      def toLong(x: BigIntModQ): Long = x.$.longValue()
      def toFloat(x: BigIntModQ): Float = x.$.floatValue()
      def toDouble(x: BigIntModQ): Double = x.$.doubleValue()
      def compare(x: BigIntModQ, y: BigIntModQ): Int = x.$ compare y.$
    }
  }