dynamically large factorial computation

misc/factorial_fast.c

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

misc/factorial_large_number.c

@@ -0,0 +1,113 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <time.h>
+#include "function_timer.h"
+
+/**
+ * dynamically large number 
+ **/
+typedef struct _large_num
+{
+    char *digits;            /**< array to store individual digits */
+    unsigned int num_digits; /**< number of digits in the number */
+} large_num;
+
+/**
+ * create a new large number
+ **/
+large_num *new_number(void)
+{
+    large_num *new_num = (large_num *)malloc(sizeof(large_num));
+    new_num->num_digits = 1;
+    new_num->digits = (char *)malloc(1 * sizeof(char));
+    new_num->digits[0] = 1;
+    return new_num;
+}
+
+/**
+ * delete all memory allocated for large number
+ **/
+void delete_number(large_num *num)
+{
+    free(num->digits);
+    free(num);
+}
+
+/**
+ * add a digit to the large number
+ **/
+void add_digit(large_num *num, unsigned int value)
+{
+    if (value > 9)
+    {
+        fprintf(stderr, "digit > 9!!\n");
+        delete_number(num);
+        exit(EXIT_FAILURE);
+    }
+
+    num->num_digits++;
+    num->digits = (char *)realloc(num->digits, num->num_digits * sizeof(char));
+    num->digits[num->num_digits - 1] = value;
+}
+
+/**
+ * multiply large number with another integer and 
+ * store the result in the same large number
+ **/
+void multiply(large_num *num, unsigned long n)
+{
+    int i;
+    unsigned long carry = 0, temp;
+    for (i = 0; i < num->num_digits; i++)
+    {
+        temp = num->digits[i] * n;
+        temp += carry;
+        if (temp < 10)
+            carry = 0;
+        else
+        {
+            carry = temp / 10;
+            temp = temp % 10;
+        }
+        num->digits[i] = temp;
+    }
+
+    while (carry != 0)
+    {
+        add_digit(num, carry % 10);
+        carry /= 10;
+    }
+}
+
+int main(int argc, char *argv[])
+{
+    int number, i;
+
+    //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("%d", &number);
+    }
+
+    large_num *result = new_number();
+
+    function_timer *timer = new_timer();
+    clock_t start_time = clock();
+    start_timer(timer);
+    for (i = 2; i <= number; i++)
+        /* Multiply every number from 2 thru N */
+        multiply(result, i);
+    double time_taken = end_timer_delete(timer) * (double)1e3;
+    // time_taken = (clock() - start_time) / (double) CLOCKS_PER_SEC;
+
+    printf("%d! = ", number);
+    for (i = result->num_digits; i > 0; i--)
+        putchar(result->digits[i - 1] + '0');
+    printf("\nTime taken: %.4g ms\n", time_taken);
+
+    delete_number(result);
+    return 0;
+}