spire.algebra.Signed.scala Maven / Gradle / Ivy

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package spire.algebra

import scala.{ specialized => spec }

/**
 * A trait for things that have some notion of sign and the ability to ensure
 * something has a positive sign.
 */
trait Signed[@spec(Double, Float, Int, Long) A] extends Any {
  /** Returns Zero if `a` is 0, Positive if `a` is positive, and Negative is `a` is negative. */
  def sign(a: A): Sign = Sign(signum(a))

  /** Returns 0 if `a` is 0, > 0 if `a` is positive, and < 0 is `a` is negative. */
  def signum(a: A): Int

  /** An idempotent function that ensures an object has a non-negative sign. */
  def abs(a: A): A

  def isSignZero(a: A): Boolean = signum(a) == 0
  def isSignPositive(a: A): Boolean = signum(a) > 0
  def isSignNegative(a: A): Boolean = signum(a) < 0

  def isSignNonZero(a: A): Boolean = signum(a) != 0
  def isSignNonPositive(a: A): Boolean = signum(a) <= 0
  def isSignNonNegative(a: A): Boolean = signum(a) >= 0
}

object Signed {
  implicit def orderedRingIsSigned[A: Order: Ring]: Signed[A] = new OrderedRingIsSigned[A]

  def apply[A](implicit s: Signed[A]): Signed[A] = s
}

private[algebra] class OrderedRingIsSigned[A](implicit o: Order[A], r: Ring[A]) extends Signed[A] {
  def signum(a: A): Int = o.compare(a, r.zero)
  def abs(a: A): A = if (signum(a) < 0) r.negate(a) else a
}