Data.Ratio

import io.hascalator._
import Prelude._
import data.Ratio

Rational numbers, with numerator and denominator of some Integral type.

scala> val oneThird = Ratio[Int](1, 3)
oneThird: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 1/3

scala> val twoThirds = Ratio[Int](2, 3)
twoThirds: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 2/3

Trying to create a new Ratio with denominator equals to 0 will result in an error:

scala> Ratio[Int](4, 0)
java.lang.IllegalArgumentException: requirement failed
  at scala.Predef$.require(Predef.scala:212)
  at io.hascalator.Prelude$.require(Prelude.scala:193)
  at io.hascalator.data.Ratio$.apply(Ratio.scala:143)
  ... 250 elided

Since denominator may be equal to one, every integer is a Ratio number:

scala> Ratio[Int](42, 1)
res1: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 42

scala> Ratio[Int](42)
res2: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 42

Both numerator and denominator values are reduced when a new Ratio number is created:

scala> val threeFourths = Ratio[Int](9, 16)
threeFourths: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 9/16

numerator extract the numerator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

scala> oneThird.numerator
res3: io.hascalator.Prelude.Int = 1

scala> twoThirds.numerator
res4: io.hascalator.Prelude.Int = 2

denominator extract the denominator of the ratio in reduced form: the numerator and denominator have no common factor and the denominator is positive.

scala> oneThird.denominator
res5: io.hascalator.Prelude.Int = 3

scala> twoThirds.denominator
res6: io.hascalator.Prelude.Int = 3

Operations

Addition

scala> oneThird + twoThirds
res7: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 1

Subtraction

scala> oneThird - twoThirds
res8: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = -1/3

Multiplication

scala> oneThird * twoThirds
res9: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 2/9

Division

scala> oneThird / twoThirds
res10: io.hascalator.data.Ratio[io.hascalator.Prelude.Int] = 1/2

Typeclasses

Ratio was made an instance of Eq, Ord, Enum and Show typeclasses

scala> Show[Ratio[Int]].show(twoThirds)
res11: io.hascalator.Prelude.String = 2/3

scala> Eq[Ratio[Int]].eq(twoThirds, twoThirds)
res12: io.hascalator.Prelude.Boolean = true

scala> Eq[Ratio[Int]].eq(oneThird, twoThirds)
res13: io.hascalator.Prelude.Boolean = false

scala> Ord[Ratio[Int]].compare(twoThirds, twoThirds)
res14: io.hascalator.typeclasses.Ordering = EQ

scala> Ord[Ratio[Int]].compare(twoThirds, oneThird)
res15: io.hascalator.typeclasses.Ordering = GT

scala> Ord[Ratio[Int]].compare(oneThird, twoThirds)
res16: io.hascalator.typeclasses.Ordering = LT