Initial data commit

Task/Modular-arithmetic/Scala/modular-arithmetic.scala

@@ -0,0 +1,49 @@
+object ModularArithmetic extends App {
+  private val x = new ModInt(10, 13)
+  private val y = f(x)
+
+  private def f[T](x: Ring[T]) = (x ^ 100) + x + x.one
+
+  private trait Ring[T] {
+    def +(rhs: Ring[T]): Ring[T]
+
+    def *(rhs: Ring[T]): Ring[T]
+
+    def one: Ring[T]
+
+    def ^(p: Int): Ring[T] = {
+      require(p >= 0, "p must be zero or greater")
+      var pp = p
+      var pwr = this.one
+      while ( {
+        pp -= 1;
+        pp
+      } >= 0) pwr = pwr * this
+      pwr
+    }
+  }
+
+  private class ModInt(var value: Int, var modulo: Int) extends Ring[ModInt] {
+    def +(other: Ring[ModInt]): Ring[ModInt] = {
+      require(other.isInstanceOf[ModInt], "Cannot add an unknown ring.")
+      val rhs = other.asInstanceOf[ModInt]
+      require(modulo == rhs.modulo, "Cannot add rings with different modulus")
+      new ModInt((value + rhs.value) % modulo, modulo)
+    }
+
+    def *(other: Ring[ModInt]): Ring[ModInt] = {
+      require(other.isInstanceOf[ModInt], "Cannot multiple an unknown ring.")
+      val rhs = other.asInstanceOf[ModInt]
+      require(modulo == rhs.modulo,
+        "Cannot multiply rings with different modulus")
+      new ModInt((value * rhs.value) % modulo, modulo)
+    }
+
+    override def one = new ModInt(1, modulo)
+
+    override def toString: String = f"ModInt($value%d, $modulo%d)"
+  }
+
+  println("x ^ 100 + x + 1 for x = ModInt(10, 13) is " + y)
+
+}