Update big-fac.c

jancarauma · web-flow · commit ff76334a402d · 2024-11-30T11:05:25.000-04:00
diff --git a/big-fac.c b/big-fac.c
@@ -1,97 +1,83 @@
 /*************************************************************************
  * big-fac.c
- *
- * Project:	Big-Numbers Factorial Simple Calculator
- * Author:	Janderson Gomes
- * Blog:	artientista.blogspot.com
- * E-mail:	dparicarana@gmail.com
+ * 
+ * Project: Big-Positive-Numbers Factorial Calculator
+ * Author: @jndgomes
  * 
  * Description:
- * A simple program to calculate the factorial of very large numbers,
- * capable of handling results with tens of thousands of digits.
- *
+ * This program calculates the factorial of very large numbers, capable of
+ * handling results with tens of thousands of digits. The number of digits
+ * is estimated using Stirling's approximation.
+ * 
  * Disclaimer:
- * THIS SOFTWARE IS PROVIDED BY AUTHORS "AS IS" AND ANY EXPRESS OR
- * IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
- * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
- * DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT,
- * INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
- * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
- * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
- * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
- * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING 
- * IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
- * POSSIBILITY OF SUCH DAMAGE. 
+ * THIS SOFTWARE IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND.
+ * 
  ************************************************************************/
 
 #include <stdio.h>
+#include <math.h>
 
-// Maximum number of digits the result can hold (e.g., up to 10,000!)
-#define MAX_DIGITS_NUMBER 40000 /* Adjust based on README instructions */
-
-/* Note: This algorithm is not optimized for calculating the factorial 
- * of arbitrary numbers. The variable MAX_DIGITS_NUMBER must be adjusted 
- * to ensure enough memory is allocated for the result.
- */
-
-int main()
-{
-    // Array to store the digits of the result
-    char result[MAX_DIGITS_NUMBER]; 
+int main() {
+    // Variable to store the estimated maximum number of digits
+    int MAX_DIGITS_NUMBER;
 
     // Auxiliary variables
     int i, j, number, dcounter, carry, tmp;
 
     // User input
-    printf("Factorial Simple Calculator\n\n");
-    printf("Enter a number (e.g., 10000): ");
+    printf("Large Number Factorial Calculator\n\n");
+    printf("Enter a number (e.g., 1993): ");
     scanf("%d", &number);
 
-    // Initialize the result array with the first digit (1)
+    // Estimate the number of digits in the factorial using Stirling's formula
+    MAX_DIGITS_NUMBER = (int)(
+        (log(2 * M_PI) / 2 + log(number) / 2 + number * (log(number) - 1)) / log(10)
+    ) + 1;
+
+    // Allocate an array to hold the digits of the result
+    char result[MAX_DIGITS_NUMBER];
+
+    // Initialize the result with the value 1 (the factorial of 0 or 1)
     result[0] = 1;
 
-    // Initialize the digit counter (starting with 1 digit)
+    // Initialize the digit counter and carry-over variable
     dcounter = 1;
-
-    // Initialize the carry to zero
     carry = 0;
 
-    // Empty line for clarity
+    // Print an empty line for formatting
     puts("");
 
-    // Loop through numbers from 1 to the input number
-    for (i = 1; i <= number; i++)
-    {
-        // Multiply each digit in the result array by the current number
-        for (j = 0; j < dcounter; j++)
-        {
-            tmp = result[j] * i + carry; // Multiply and add carry
-            result[j] = tmp % 10;        // Store the single digit
-            carry = tmp / 10;            // Update the carry
+    // Main factorial computation loop
+    for (i = 1; i <= number; i++) {
+        for (j = 0; j < dcounter; j++) {
+            // Multiply the current digit by i and add the carry
+            tmp = result[j] * i + carry;
+            // Update the current digit
+            result[j] = tmp % 10;
+            // Update the carry for the next digit
+            carry = tmp / 10;
         }
 
-        // Handle any leftover carry
-        while (carry > 0)
-        {
+        // Add remaining carry digits to the result array
+        while (carry > 0) {
             result[dcounter] = carry % 10;
             carry /= 10;
             dcounter++;
         }
 
-        // Display progress to the user
+        // Display progress (number of digits calculated so far)
         printf("\r%d digits calculated...", dcounter);
     }
 
-    // Empty line for output formatting
+    // Print an empty line for formatting
     puts("");
 
     // Display the factorial result
     printf("\nFactorial of %d is:\n\n", number);
-    for (i = dcounter - 1; i >= 0; i--)
-    {
+    for (i = dcounter - 1; i >= 0; i--) {
         printf("%d", result[i]);
     }
 
-    // Return successful exit code
+    // Exit the program successfully
     return 0;
 }
