chore: import upstream snapshot with attribution

math/sqrt_double.cpp

@@ -0,0 +1,49 @@
+/**
+ * @file
+ * @brief Calculate the square root of any positive real number in \f$O(\log
+ * N)\f$ time, with precision fixed using [bisection
+ * method](https://en.wikipedia.org/wiki/Bisection_method) of root-finding.
+ *
+ * @see Can be implemented using faster and better algorithms like
+ * newton_raphson_method.cpp and false_position.cpp
+ */
+#include <cassert>
+#include <iostream>
+
+/** Bisection method implemented for the function \f$x^2-a=0\f$
+ * whose roots are \f$\pm\sqrt{a}\f$ and only the positive root is returned.
+ */
+double Sqrt(double a) {
+    if (a > 0 && a < 1) {
+        return 1 / Sqrt(1 / a);
+    }
+    double l = 0, r = a;
+    /* Epsilon is the precision.
+    A great precision is
+    between 1e-7 and 1e-12.
+    double epsilon = 1e-12;
+    */
+    double epsilon = 1e-12;
+    while (l <= r) {
+        double mid = (l + r) / 2;
+        if (mid * mid > a) {
+            r = mid;
+        } else {
+            if (a - mid * mid < epsilon) {
+                return mid;
+            }
+            l = mid;
+        }
+    }
+    return -1;
+}
+
+/** main function */
+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);
+}