// 複素数(お題:http://ja.doukaku.org/247/)
// http://ja.doukaku.org/comment/----/
// snaさん作を改変( : http://ja.doukaku.org/comment/8851/)
// 参考 : http://en.literateprograms.org/Complex_numbers_(Scala)

trait Arithmetic[T<:AnyVal]{
  def unary_+ : T
  def unary_- : T
  def + (that:T):T
  def - (that:T):T
  def * (that:T):T
  def / (that:T):T
  def abs : T
  //
  def lt0 : Boolean  // >   0
  def gt0 : Boolean  // <   0
  def eq0 : Boolean  // ==  0
  //
  def eqp1 : Boolean // ==  1
  def eqm1 : Boolean // == -1
  //
}

case class Complex[ T<%Arithmetic[T] ](real:T, imag:T) {
  // +(a + bi) = (a + bi)
  def unary_+ = this
  
  // -(a + bi) = (-a - bi)
  def unary_- = Complex[T](-real, -imag)
  
  // (a + bi) + (c + di) = (a + c) + (b + d)i
  def + (that: Complex[T]) = Complex(this.real + that.real, this.imag + that.imag)
  
  // (a + bi) - (c + di) = (a - c) + (b - d)i
  def - (that: Complex[T]) = Complex(this.real - that.real, this.imag - that.imag)
  
  // (a + bi) * (c + di) = (ac - bd) + (bc + ad)i
  def * (that: Complex[T]) = {
    val Complex(a, b) = this
    val Complex(c, d) = that
    Complex(a*c - b*d, b*c + a*d)
  }
  
  // (a + bi) / (c + di) = (ac + bd) / (c^2 + d^2) + (bc - ad) / (c^2 + d^2)
  def / (that: Complex[T]) = {
    val Complex(a, b) = this
    val Complex(c, d) = that
    val deno = c*c + d*d
    Complex((a*c + b*d) / deno, (b*c - a*d) / deno)
  }
  
  // Conjugate
  def conjugate() : Complex[T] = Complex(real,-imag)
  
  override def toString = this match {
    case Complex(re, im) if im.eq0            => re.toString
    case Complex(re, im) if re.eq0 && im.eqp1 => "i"
    case Complex(re, im) if re.eq0 && im.eqm1 => "-i"
    case Complex(re, im) if re.eq0            => im.toString + "i"
    case Complex(re, im) if           im.eqp1 => re.toString + " + i"
    case Complex(re, im) if           im.eqm1 => re.toString + " - i"
    case Complex(re, im) if           im.gt0  => re.toString + " + " + im.toString + "i"
    case Complex(re, im) if           im.lt0  => re.toString + " - " + im.abs.toString + "i"
  }

}

object test{
  implicit def int2Arithmeic(n:Int) : Arithmetic[Int] = 
                    new Arithmetic[Int]{
                         def unary_+ : Int  = n.unary_+
                         def unary_- : Int  = n.unary_-
                         def + (that:Int):Int = n+that
                         def - (that:Int):Int = n-that
                         def * (that:Int):Int = n*that
                         def / (that:Int):Int = n/that
                         def abs = Math.abs(n)
                         //
                         def lt0 = n<0
                         def gt0 = n>0
                         def eq0 = n==0
                         //
                         def eqp1 = n==1 
                         def eqm1 = n== -1  }
  
  implicit def double2Arithmeic(n:Double) : Arithmetic[Double] = 
                    new Arithmetic[Double]{
                         def unary_+ : Double  = n.unary_+
                         def unary_- : Double  = n.unary_-
                         def + (that:Double):Double = n+that
                         def - (that:Double):Double = n-that
                         def * (that:Double):Double = n*that
                         def / (that:Double):Double = n/that
                         def abs = Math.abs(n)
                         //
                         def lt0 = n<0
                         def gt0 = n>0
                         def eq0 = n==0
                         //
                         def eqp1 = n==1 
                         def eqm1 = n== -1  }
  
  implicit def int2Complex   (n:Int   ):Complex[Int   ] = Complex(n,0)
  implicit def double2Complex(n:Double):Complex[Double] = Complex(n,0)
  implicit def icomp2dcomp   (z:Complex[Int]):Complex[Double] = Complex(z.real,z.imag)
  
  implicit def dcomp2richer  (z:Complex[Double]) = new Proxy{
       val self=z
       def abs = self match {
         case Complex(re, im) => Math.sqrt(re*re + im*im)
       }
    }
  
  implicit def icomp2richer  (z:Complex[int]) = new Proxy{
       val self=z
       def abs = self match {
         case Complex(re, im) => Math.sqrt(re*re + im*im)
       }
    }
  
  
  def main( args:Array[String] ) : Unit = {
    {
      val i = Complex(0,1)
      println( (3 + i  ) + (4 - i  ) )
      println( (5 - 9*i) - (2 + 6*i) )
      println( (5 + 3*i) * (5 + 8*i) )
      println( (9 - 7*i) / (9 - 3*i) )
      println( (2 + 3*i).abs         )
    }
    
    {
      val i = Complex(0.,1.)
      println( (3. + i  ) + (4. - i  ) )
      println( (5. - 9.*i) - (2. + 6.*i) )
      println( (5. + 3.*i) * (5. + 8.*i) )
      println( (9. - 7.*i) / (9. - 3.*i) )
      println( (2. + 3.*i).abs         )
    }
  }
}