From cecf806d488937c5917488fbdb0428f3419987c3 Mon Sep 17 00:00:00 2001
From: AKS1996 <sushsilsharma.ss451@gmail.com>
Date: Sat, 21 Oct 2017 14:18:15 +0000
Subject: [PATCH] Guass Legendre Algorithm for approximation of pi

---
 Others/GuassLengendre.java | 44 ++++++++++++++++++++++++++++++++++++++
 1 file changed, 44 insertions(+)
 create mode 100644 Others/GuassLengendre.java

diff --git a/Others/GuassLengendre.java b/Others/GuassLengendre.java
new file mode 100644
index 00000000..289516ae
--- /dev/null
+++ b/Others/GuassLengendre.java
@@ -0,0 +1,44 @@
+import java.lang.Math;
+/*
+ * author: @AKS1996
+ * Guass Legendre Algorithm
+ * ref https://en.wikipedia.org/wiki/Gauss–Legendre_algorithm
+ *
+ */
+
+public class GuassLegendre {
+
+	public static void main(String[] args) {
+		for(int i=1;i<=3;++i)
+			System.out.println(pi(i));
+
+	}
+
+	static double pi(int l){
+		/*
+		 * l: No of loops to run
+		 */
+
+		double a = 1,b=Math.pow(2,-0.5),t=0.25,p=1;
+		for(int i=0;i<l;++i){
+			double temp[] = update(a,b,t,p);
+			a = temp[0];
+			b = temp[1];
+			t = temp[2];
+			p = temp[3];
+		}
+
+		return Math.pow(a+b, 2)/(4*t);
+	}
+
+	static double[] update(double a, double b, double t, double p){
+		double values[] = new double[4];
+		values[0] = (a+b)/2;
+		values[1] = Math.sqrt(a*b);
+		values[2] = t - p*Math.pow(a - values[0],2);
+		values[3] = 2*p;
+
+		return values;
+	}
+
+}