SCALA-3484: Introduction to Spire (#685)

* chore(wip): introduce spire

* chore(spire): init lib

* chore(spire): add number types, macros & monoids samples

* lint: format code

* chore: high level type classes

* lint: fmt tests

* chore: curate groups examples

- SemiGroups
- Monoids
- Groups

* chore: add rings examples

- Rings
- EuclideanRings

* refactor: move to scala-libraries-5

see https://jira.baeldung.com/browse/SCALA-384?focusedCommentId=258512&page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel#comment-258512

Author: exaucae

build.sbt

@@ -228,6 +228,7 @@ val fs2Version = "3.7.0"
 val AkkaVersion = "2.8.0"
 val AkkaHttpVersion = "10.5.0"
 val reactiveMongo = "1.0.10"
+val spireVersion = "0.18.0"
 
 lazy val scala_libraries = (project in file("scala-libraries"))
   .settings(
@@ -390,7 +391,8 @@ lazy val scala_libraries_5 = (project in file("scala-libraries-5"))
     libraryDependencies ++= scalaTestDeps,
     libraryDependencies ++= Seq(
       sparkSqlDep,
-      sparkCoreDep
+      sparkCoreDep,
+      "org.typelevel" %% "spire" % spireVersion
     )
   )
 

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/Fractional.scala

@@ -0,0 +1,11 @@
+package com.baeldung.scala.spire
+
+import spire.implicits._
+import spire.math.Fractional
+
+object Fractional {
+  def avg[T](values: List[T])(implicit fractional: Fractional[T]): T = {
+    val sum = values.foldLeft(fractional.zero)(fractional.plus)
+    fractional.div(sum, fractional.fromInt(values.length))
+  }
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/Integral.scala

@@ -0,0 +1,16 @@
+package com.baeldung.scala.spire
+
+import spire.implicits._
+import spire.math._
+
+object Integral {
+  def factorial[@specialized(Int) T](
+    n: T
+  )(implicit integral: Integral[T]): T = {
+    if (integral.lt(n, integral.one)) integral.one
+    else integral.times(n, factorial(integral.minus(n, integral.one)))
+  }
+
+  def gcd[T](a: T, b: T)(implicit ev: Integral[T]): T = ev.gcd(a, b)
+
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/Numeric.scala

@@ -0,0 +1,9 @@
+package com.baeldung.scala.spire
+
+import spire.implicits._
+import spire.math._
+object Numeric {
+  def sum[T](values: List[T])(implicit numeric: Numeric[T]): T = {
+    values.foldLeft(numeric.zero)(numeric.plus)
+  }
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/groups/Semigroups.scala

@@ -0,0 +1,10 @@
+package com.baeldung.scala.spire.groups
+
+import spire.algebra._
+import spire.implicits._
+
+object Semigroups extends App {
+  val a: Int = 5
+  val b: Int = 7
+  val result: Int = Semigroup[Int].combine(a, b)
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/groups/TranscationGroup.scala

@@ -0,0 +1,14 @@
+package com.baeldung.scala.spire.groups
+
+import spire.algebra._
+import spire.implicits._
+
+case class Transaction(amount: Int)
+
+object TransactionGroup extends Group[Transaction] {
+  def combine(x: Transaction, y: Transaction): Transaction = Transaction(
+    x.amount + y.amount
+  )
+  def empty: Transaction = Transaction(0)
+  def inverse(a: Transaction): Transaction = Transaction(-a.amount)
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/macros/CFor.scala

@@ -0,0 +1,10 @@
+package com.baeldung.scala.spire.macros
+
+import spire.implicits.cfor
+
+object CFor extends App {
+
+  cfor(9)(_ >= 0, _ - 1) { i =>
+    println(i)
+  }
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/macros/LiteralNumberSyntax.scala

@@ -0,0 +1,12 @@
+package com.baeldung.scala.spire.macros
+
+import spire.implicits._
+
+object LiteralNumberSyntax extends App {
+
+  val poly1 = poly"3x^2 - 5x + 1"
+  val poly2 = poly"5/4x^6 - 7x - 2"
+  val poly3 = poly1.-(poly2)
+  println(poly3)
+
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/monoids/AdditiveMonoid.scala

@@ -0,0 +1,9 @@
+package com.baeldung.scala.spire.monoids
+
+import spire.algebra._
+import spire.implicits._
+
+object AdditiveMonoid extends App {
+  def sum[T](values: List[T])(implicit ev: AdditiveMonoid[T]): T =
+    values.foldLeft(ev.zero)(ev.plus)
+}

scala-libraries-5/src/main/scala-2/com/baeldung/scala/spire/numbers/Complexes.scala

@@ -0,0 +1,28 @@
+package com.baeldung.scala.spire.numbers
+
+import spire.implicits._
+import spire.math._
+
+object Complexes extends App {
+
+  private def quadraticRoots(
+    x: Complex[Double],
+    y: Complex[Double],
+    z: Complex[Double]
+  ): (Complex[Double], Complex[Double]) = {
+    val discriminant = y * y - Complex(4.0) * x.*(z)
+    val sqrtDiscriminant = discriminant.sqrt
+    val r1 = (-y + sqrtDiscriminant) / (Complex(2.0) * x)
+    val r2 = (-y - sqrtDiscriminant) / (Complex(2.0) * x)
+    (r1, r2)
+  }
+
+  val x = Complex(2.0, 0.0)
+  val y = Complex(-3.0, 4.0)
+  private val z = Complex(5.0, -6.0)
+
+  private val (r1, r2) = quadraticRoots(x, y, z)
+  println(s"Root 1: $r1")
+  println(s"Root 2: $r2")
+
+}