Equation.scala

/*     / \____  _    _  ____   ______  / \ ____  __    _______
 *    /  /    \/ \  / \/    \ /  /\__\/  //    \/  \  //  /\__\   JΛVΛSLΛNG
 *  _/  /  /\  \  \/  /  /\  \\__\\  \  //  /\  \ /\\/ \ /__\ \   Copyright 2014-2016 Javaslang, http://javaslang.io
 * /___/\_/  \_/\____/\_/  \_/\__\/__/\__\_/  \_//  \__/\_____/   Licensed under the Apache License, Version 2.0
 *//*     / \____  _    _  ____   ______  / \ ____  __    _______
 *    /  /    \/ \  / \/    \ /  /\__\/  //    \/  \  //  /\__\   JΛVΛSLΛNG
 *  _/  /  /\  \  \/  /  /\  \\__\\  \  //  /\  \ /\\/ \ /__\ \   Copyright 2014-2016 Javaslang, http://javaslang.io
 * /___/\_/  \_/\____/\_/  \_/\__\/__/\__\_/  \_//  \__/\_____/   Licensed under the Apache License, Version 2.0
 */
package tutorial.webapp

import java.lang.Math._

import scala.Double.{MinValue => MinDouble}
import scala.Iterator._

class Equation {
  /* bx + a = 0 */
  def solve(b: Double, a: Double) = b match {
    case 0 ⇒ a match {
      case 0 ⇒ iterate(MinDouble)(nextUp)
      case _ ⇒ Seq() // inconsistent
    }
    case _ ⇒ Seq(-a / b)
  }

  /* cx^2 + bx + a = 0 */
  def solve(c: Double, b: Double, a: Double) = c match {
    case 0 ⇒ solve(b, a)
    case _ ⇒ b match {
      case 0 ⇒ Seq(-c / a)
      case _ ⇒
        a match {
          case 0 ⇒ Seq(0, -c / a)
          case _ ⇒
            val `-b` = -b
            val `2a` = 2 * a
            val `2c` = 2 * c
            val `b²` = b * b
            `b²` - `2a` * `2c` match {
              case d if d > 0  ⇒
                val part = `-b` - copySign(sqrt(d), b) // b ≠ 0
                Seq(part / `2a`, `2c` / part)
              case d if d == 0 ⇒ Seq(`-b` / `2a`)
              case _           ⇒ Seq() // complex roots
            }
        }
    }
  }
}