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, a) match {
    case (0, 0) ⇒ iterate(MinDouble)(nextUp)
    case (0, _) ⇒ Seq() // inconsistent
    case _      ⇒ Seq(-a / b)
  }

  /* cx^2 + bx + a = 0 */
  def solve(c: Double, b: Double, a: Double) = (c, b, a) match {
    case (0, _, _) ⇒ solve(b, a)
    case (_, 0, _) ⇒ Seq(-a / c)
    case (_, _, 0) ⇒ Seq(0, -b / c)
    case _         ⇒
      val `-b` = -b
      val `b²` = b * b
      val `2a` = 2 * a
      val `2c` = 2 * c

      `b²` - `2c` * `2a` match {
        case d if d > 0  ⇒ val part = `-b` - copySign(sqrt(d), b) // b ≠ 0
                           Seq(part / `2c`, `2a` / part)
        case d if d == 0 ⇒ Seq(`-b` / `2c`)
        case _           ⇒ Seq() // complex roots
      }
  }
}