June 2018 Update

Task/Arithmetic-geometric-mean-Calculate-Pi/Scala/arithmetic-geometric-mean-calculate-pi.scala

@@ -0,0 +1,36 @@
+import java.math.MathContext
+
+import scala.annotation.tailrec
+import scala.compat.Platform.currentTime
+import scala.math.BigDecimal
+
+object Calculate_Pi extends App {
+  val precision = new MathContext(32768 /*65536*/)
+  val (bigZero, bigOne, bigTwo, bigFour) =
+    (BigDecimal(0, precision), BigDecimal(1, precision), BigDecimal(2, precision), BigDecimal(4, precision))
+
+  def bigSqrt(bd: BigDecimal) = {
+    @tailrec
+    def iter(x0: BigDecimal, x1: BigDecimal): BigDecimal =
+      if (x0 == x1) x1 else iter(x1, (bd / x1 + x1) / bigTwo)
+
+    iter(bigZero, BigDecimal(Math.sqrt(bd.toDouble), precision))
+  }
+
+  @tailrec
+  private def loop(a: BigDecimal, g: BigDecimal, sum: BigDecimal, pow: BigDecimal): BigDecimal = {
+    if (a == g) (bigFour * (a * a)) / (bigOne - sum)
+    else {
+      val (_a, _g, _pow) = ((a + g) / bigTwo, bigSqrt(a * g), pow * bigTwo)
+      loop(_a, _g, sum + ((_a * _a - (_g * _g)) * _pow), _pow)
+    }
+  }
+
+  println(precision)
+  val pi = loop(bigOne, bigOne / bigSqrt(bigTwo), bigZero, bigTwo)
+  println(s"This are ${pi.toString.length - 1} digits of π:")
+  val lines = pi.toString().sliding(103, 103).mkString("\n")
+  println(lines)
+
+  println(s"Successfully completed without errors. [total ${currentTime - executionStart} ms]")
+}