From a23baf9db11959f4d9f117fb7c7be52b33cd9416 Mon Sep 17 00:00:00 2001
From: DarkWarrior703 <56077342+DarkWarrior703@users.noreply.github.com>
Date: Fri, 24 Apr 2020 20:54:32 +0300
Subject: [PATCH] Create sqrt_double

Calculates the sqrt of every number in O(logn) with fixed precision.
---
 math/sqrt_double | 32 ++++++++++++++++++++++++++++++++
 1 file changed, 32 insertions(+)
 create mode 100644 math/sqrt_double

diff --git a/math/sqrt_double b/math/sqrt_double
new file mode 100644
index 000000000..ee0c723ef
--- /dev/null
+++ b/math/sqrt_double
@@ -0,0 +1,32 @@
+#include <iostream>
+#include <cassert>
+
+/* Calculate the square root of any number in O(logn) time, with precision fixed */
+
+double Sqrt(double x){
+    double l = 0, r = x;
+    //Epsilon is the precision. A great precision is between 1e-7 and 1e-12.
+    double epsilon = 1e-12;
+    while(l <= r){
+        double mid = (l + r) / 2;
+        if(mid * mid > x){
+            r = mid;
+        } else {
+            if(x - mid * mid < epsilon){
+                return mid;
+            }
+            l = mid;
+        }
+    }
+    return -1;
+}
+
+int main()
+{
+  double n{};
+  std::cin >> n;
+  assert(n >= 0);
+  //Change this line for a better precision
+  std::cout.precision(12);
+  std::cout << std::fixed << Sqrt(n);
+}