feat: Add inverse inverse root functions (TheAlgorithms#1570)

* Add inverse inverse root function Add inverse inverse root function Signed-off-by: Bensuperpc <[email protected]> * Update comment Update comment Signed-off-by: Bensuperpc <[email protected]> * Update math/inv_sqrt.cpp Change to IO operations Co-authored-by: David Leal <[email protected]> * Update math/inv_sqrt.cpp Update comment Co-authored-by: David Leal <[email protected]> * Update math/inv_sqrt.cpp Update comment Co-authored-by: David Leal <[email protected]> * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Fix fist warning Fix fist warning Signed-off-by: Bensuperpc <[email protected]> * Fix warning N2 Fix warning N2 Signed-off-by: Bensuperpc <[email protected]> * Fix warning N3 Fix warning N3 Signed-off-by: Bensuperpc <[email protected]> * Fix warning N4 Fix warning N4 Signed-off-by: Bensuperpc <[email protected]> * updating DIRECTORY.md * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * clang-format and clang-tidy fixes for 1acc777 * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Add tests and improve comment Add tests and improve comment Signed-off-by: Bensuperpc <[email protected]> * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Add default template type (double) Add default template type (double) Signed-off-by: Bensuperpc <[email protected]> * Update comment Update comment Signed-off-by: Bensuperpc <[email protected]> * Update math/inv_sqrt.cpp Co-authored-by: David Leal <[email protected]> * Add comments Add comments Signed-off-by: Bensuperpc <[email protected]> * updating DIRECTORY.md Co-authored-by: David Leal <[email protected]> Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
Rijul24 · Sep 1, 2021 · f7d656c · f7d656c
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diff --git a/DIRECTORY.md b/DIRECTORY.md
@@ -174,6 +174,7 @@
  * [Gcd Of N Numbers](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_of_n_numbers.cpp)
  * [Gcd Recursive Euclidean](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/gcd_recursive_euclidean.cpp)
  * [Integral Approximation](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/integral_approximation.cpp)
+ * [Inv Sqrt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/inv_sqrt.cpp)
  * [Large Factorial](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_factorial.cpp)
  * [Large Number](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/large_number.h)
  * [Largest Power](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/math/largest_power.cpp)
@@ -330,5 +331,5 @@
  * [Brute Force String Searching](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/brute_force_string_searching.cpp)
  * [Horspool](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/horspool.cpp)
  * [Knuth Morris Pratt](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/knuth_morris_pratt.cpp)
- * [Manacher's Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/manacher_algorithm.cpp)
- * [Rabin Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/rabin_karp.cpp)
+ * [Manacher Algorithm](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/manacher_algorithm.cpp)
+ * [Rabin Karp](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/strings/rabin_karp.cpp)
diff --git a/math/inv_sqrt.cpp b/math/inv_sqrt.cpp
@@ -0,0 +1,103 @@
+/**
+ * @file
+ * @brief Implementation of [the inverse square root
+ * Root](https://medium.com/hard-mode/the-legendary-fast-inverse-square-root-e51fee3b49d9).
+ * @details
+ * Two implementation to calculate inverse inverse root,
+ * from Quake III Arena (C++ version) and with a standard library (`cmath`).
+ * This algorithm is used to calculate shadows in Quake III Arena.
+ */
+
+#include <cassert> /// for assert
+#include <cmath> /// for `std::sqrt`
+#include <iostream> /// for IO operations
+#include <limits> /// for numeric_limits
+
+/**
+ * @brief This is the function that calculates the fast inverse square root.
+ * The following code is the fast inverse square root implementation from
+ * Quake III Arena (Adapted for C++). More information can be found at
+ * [Wikipedia](https://en.wikipedia.org/wiki/Fast_inverse_square_root)
+ * @tparam T floating type
+ * @tparam iterations inverse square root, the greater the number of
+ * iterations, the more exact the result will be (1 or 2).
+ * @param x value to calculate
+ * @return the inverse square root
+ */
+template <typename T = double, char iterations = 2>
+inline T Fast_InvSqrt(T x) {
+ using Tint = typename std::conditional<sizeof(T) == 8, std::int64_t,
+ std::int32_t>::type;
+ T y = x;
+ T x2 = y * 0.5;
+
+ Tint i =
+ *reinterpret_cast<Tint *>(&y); // Store floating-point bits in integer
+
+ i = (sizeof(T) == 8 ? 0x5fe6eb50c7b537a9 : 0x5f3759df) -
+ (i >> 1); // Initial guess for Newton's method
+
+ y = *reinterpret_cast<T *>(&i); // Convert new bits into float
+
+ y = y * (1.5 - (x2 * y * y)); // 1st iteration Newton's method
+ if (iterations == 2) {
+ y = y * (1.5 - (x2 * y * y)); // 2nd iteration, the more exact result
+ }
+ return y;
+}
+
+/**
+ * @brief This is the function that calculates the fast inverse square root.
+ * The following code is the fast inverse square root with standard lib (cmath)
+ * More information can be found at
+ * [LinkedIn](https://www.linkedin.com/pulse/fast-inverse-square-root-still-armin-kassemi-langroodi)
+ * @tparam T floating type
+ * @param number value to calculate
+ * @return the inverse square root
+ */
+template <typename T = double>
+T Standard_InvSqrt(T number) {
+ T squareRoot = sqrt(number);
+ return 1.0f / squareRoot;
+}
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void test() {
+ const float epsilon = 1e-3f;
+
+ /* Tests with multiple values */
+ assert(std::fabs(Standard_InvSqrt<float>(100.0f) - 0.0998449f) < epsilon);
+ assert(std::fabs(Standard_InvSqrt<double>(36.0f) - 0.166667f) < epsilon);
+ assert(std::fabs(Standard_InvSqrt(12.0f) - 0.288423f) < epsilon);
+ assert(std::fabs(Standard_InvSqrt<double>(5.0f) - 0.447141f) < epsilon);
+
+ assert(std::fabs(Fast_InvSqrt<float, 1>(100.0f) - 0.0998449f) < epsilon);
+ assert(std::fabs(Fast_InvSqrt<double, 1>(36.0f) - 0.166667f) < epsilon);
+ assert(std::fabs(Fast_InvSqrt(12.0f) - 0.288423) < epsilon);
+ assert(std::fabs(Fast_InvSqrt<double>(5.0f) - 0.447141) < epsilon);
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+ test(); // run self-test implementations
+ std::cout << "The Fast inverse square root of 36 is: "
+ << Fast_InvSqrt<float, 1>(36.0f) << std::endl;
+ std::cout << "The Fast inverse square root of 36 is: "
+ << Fast_InvSqrt<double, 2>(36.0f) << " (2 iterations)"
+ << std::endl;
+ std::cout << "The Fast inverse square root of 100 is: "
+ << Fast_InvSqrt(100.0f)
+ << " (With default template type and iterations: double, 2)"
+ << std::endl;
+ std::cout << "The Standard inverse square root of 36 is: "
+ << Standard_InvSqrt<float>(36.0f) << std::endl;
+ std::cout << "The Standard inverse square root of 100 is: "
+ << Standard_InvSqrt(100.0f)
+ << " (With default template type: double)" << std::endl;
+}