document fibonacci fast & link to fibonacci numbers

math/fibonacci.cpp

@@ -6,7 +6,7 @@
  * integer as input.
  * \f[\text{fib}(n) = \text{fib}(n-1) + \text{fib}(n-2)\f]
  *
- * @see fibonacci_large.cpp
+ * @see fibonacci_large.cpp, fibonacci_fast.cpp
  */
 #include <cassert>
 #include <iostream>

others/fibonacci_fast.cpp

@@ -1,25 +1,39 @@
-// An efficient way to calculate nth fibonacci number faster and simpler than
+/**
-// O(nlogn) method of matrix exponentiation This works by using both recursion
+ * @file
-// and dynamic programming. as 93rd fibonacci exceeds 19 digits, which cannot be
+ * @brief Faster computation of Fibonacci series
-// stored in a single long long variable, we can only use it till 92nd fibonacci
+ *
-// we can use it for 10000th fibonacci etc, if we implement bigintegers.
+ * An efficient way to calculate nth fibonacci number faster and simpler than
-// This algorithm works with the fact that nth fibonacci can easily found if we
+ * \f$O(n\log n)\f$ method of matrix exponentiation This works by using both
-// have already found n/2th or (n+1)/2th fibonacci It is a property of fibonacci
+ * recursion and dynamic programming. as 93rd fibonacci exceeds 19 digits, which
-// similar to matrix exponentiation.
+ * cannot be stored in a single long long variable, we can only use it till 92nd
+ * fibonacci we can use it for 10000th fibonacci etc, if we implement
+ * bigintegers. This algorithm works with the fact that nth fibonacci can easily
+ * found if we have already found n/2th or (n+1)/2th fibonacci It is a property
+ * of fibonacci similar to matrix exponentiation.
+ *
+ * @see fibonacci_large.cpp, fibonacci.cpp
+ */
 
 #include <cinttypes>
 #include <cstdio>
 #include <iostream>
 
+/** maximum number that can be computed - The result after 93 cannot be stored
+ * in a `uint64_t` data type. */
 const uint64_t MAX = 93;
 
+/** Array of computed fibonacci numbers */
 uint64_t f[MAX] = {0};
 
+/** Algorithm */
 uint64_t fib(uint64_t n) {
-    if (n == 0) return 0;
+    if (n == 0)
-    if (n == 1 || n == 2) return (f[n] = 1);
+        return 0;
+    if (n == 1 || n == 2)
+        return (f[n] = 1);
 
-    if (f[n]) return f[n];
+    if (f[n])
+        return f[n];
 
     uint64_t k = (n % 2 != 0) ? (n + 1) / 2 : n / 2;
 
@@ -28,10 +42,11 @@ uint64_t fib(uint64_t n) {
     return f[n];
 }
 
+/** Main function */
 int main() {
     // Main Function
     for (uint64_t i = 1; i < 93; i++) {
-        std::cout << i << " th fibonacci number is " << fib(i) << "\n";
+        std::cout << i << " th fibonacci number is " << fib(i) << std::endl;
     }
     return 0;
 }

others/fibonacci_large.cpp

@@ -7,7 +7,7 @@
  * Took 0.608246 seconds to compute 50,000^th Fibonacci
  * number that contains 10450 digits!
  *
- * @see fibonacci.cpp
+ * @see fibonacci.cpp, fibonacci_fast.cpp
  */
 
 #include <cinttypes>