much faster Fibbonacci algorithm

misc/factorial_fast.c

@@ -0,0 +1,67 @@
+#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;
+}