Create sqrt_double

Calculates the sqrt of every number in O(logn) with fixed precision.

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);
+}