From fa73fcb98392a8adb209175616b7cf6de300a0dd Mon Sep 17 00:00:00 2001
From: Krishna Vedala <krishna.vedala@ieee.org>
Date: Sat, 7 Mar 2020 10:57:52 -0500
Subject: [PATCH] +a much faster fibonacci computation algorithm

---
 misc/Fibonacci_fast.c | 76 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 76 insertions(+)
 create mode 100644 misc/Fibonacci_fast.c

diff --git a/misc/Fibonacci_fast.c b/misc/Fibonacci_fast.c
new file mode 100644
index 00000000..becb8c88
--- /dev/null
+++ b/misc/Fibonacci_fast.c
@@ -0,0 +1,76 @@
+/**
+    @file Fibonacci_fast.c
+    @author: Krishna Vedala
+    @date 2 October, 2019
+    @brief Compute \f$m^{mth}\f$ Fibonacci number using the formulae:
+    \f{eqnarray*}{
+        F_{2n-1} &=& F_n^2 + F_{n-1}^2 \\ 
+        F_{2n}   &=& F_n\left(2F_{n-1} + F_n\right)
+   \f}
+*/
+
+#include<stdio.h> 
+#include<stdlib.h>
+#include<locale.h>
+
+/**
+    Returns the \f$n^{th}\f$ and \f$n+1^{th}\f$ Fibonacci number.
+    The return variables are C & D respectively.
+ */
+void fib(unsigned long n, unsigned long *C, unsigned long *D) 
+{ 
+    //Out of Range checking 
+    if(n < 0){
+        printf("\nNo Such term !\n");
+        exit(0);
+    }
+    
+    unsigned long a, b, c, d;
+    
+    if (n == 0)
+    {
+        C[0] = 0;
+        if(D)
+            D[0] = 1;
+        return;
+    }
+
+    fib(n >> 1, &c, &d); /**< Compute F(n/2) */
+
+    a = c * ((d << 1) - c);
+    b = c * c + d * d;
+    if (n % 2 == 0)   /**< If n is even */
+    {
+        C[0] = a;
+        if(D)
+            D[0] = b;
+        return;
+    }
+    
+    /**< If n is odd */
+    C[0] = b;
+    if(D)
+        D[0] = a + b;
+    return;
+} 
+  
+int main(int argc, char *argv[])
+{
+	unsigned long number, result;
+    
+    setlocale(LC_NUMERIC, "");  // format the printf output
+
+	//Asks for the number/position of term in Fibonnacci sequence
+    if (argc == 2)
+        number = atoi(argv[1]);
+    else {
+        printf("Enter the value of n(n starts from 0 ): ");
+        scanf("%lu", &number);
+    }
+    
+    fib(number, &result, NULL);
+    
+	printf("The nth term is : %'lu \n", result);
+	
+	return 0;
+}
\ No newline at end of file