README.md

Credit card validation

Credit card number validation using Luhn's algorithm in C. Implemented all other basic built-in required functions except printf(), fgets(), and strtol() by myself for improving skill and logic. Currently supports validation of Visa, American Express and majority of MasterCard credit cards. The program correctly validates majority of Visa, American Express and MasterCard test credit cards provided for testing on PayPal Developer site.

Main logic and Luhn's algorithm is in credit.c file. All other implemented functions are in digit.c file and their declarations are in digit.h header file.

Credit cards

American Express uses 15-digit numbers, MasterCard uses 16-digit numbers, and Visa uses 13- and 16-digit numbers. Credit card numbers actually have some structure to them. All American Express numbers start with 34 or 37; most MasterCard numbers start with 51, 52, 53, 54, or 55 (they also have some other potential starting numbers which I haven't considered in this program); and all Visa numbers start with 4. But credit card numbers also have a “checksum” built into them, a mathematical relationship between at least one number and others. That checksum enables computers (or humans who like math) to detect typos (e.g., transpositions), if not fraudulent numbers, without having to query a database, which can be slow. Of course, a dishonest mathematician could certainly craft a fake number that nonetheless respects the mathematical constraint, so a database lookup is still necessary for more rigorous checks.

Luhn's Algorithm

Most cards use an algorithm invented by Hans Peter Luhn of IBM. According to Luhn’s algorithm, you can determine if a credit card number is (syntactically) valid as follows:

1. Multiply every other digit by 2, starting with the number’s second-to-last digit, and then add those products’ digits together.
2. Add the sum to the sum of the digits that weren’t multiplied by 2.
3. If the total’s last digit is 0 (or, put more formally, if the total modulo 10 is congruent to 0), the number is valid mathematically!

Let's try with a credit card number: 5427660064241339

1. Let's highlight every other digit, starting with the number’s second-to-last digit:

   5 4 2 7 6 6 0 0 6 4 2 4 1 3 3 9

2. Multiply the highlighted digits by two:

   5×2 + 2×2 + 6×2 + 0×2 + 6×2 + 2×2 + 1×2 + 3×2

   That gives us:

   10 + 4 + 12 + 0 + 12 + 4 + 2 + 6

   Now add the individual digits of the product if they are greater than 9:

   (1 + 0) + 4 + (1 + 2) + 0 + (1 + 2) + 4 + 2 + 6 = 23

3. Now add all the digits that weren't multiplied by two:

   4 + 7 + 6 + 0 + 0 + 4 + 4 + 3 + 9 = 37

4. Now add these both sums together:

   37 + 23 = 60

5. The last digit of this sum (60) is 0, so this card is mathematically legit!
6. This credit card number is 16-digit long and it starts with 54 so it is a MasterCard!

Implemented functions

double pow(double n, double p);

This function takes a number and power as input and outputs a double which is the number raised to the power.

For e.g. (long)pow(2, 3) will return 8.

---

long get_long(char *text);

This function takes a string as an argument, prompts user for a number, gets user input and returns a long int. If the user doesn't provide a number then it will keep prompting the user until it gets a number.

Example code:

#include "digit.h"
#include <stdio.h>

int main(void)
{
    long n = get_long("Type a number: ");
    printf("%ld", n);
}

Output:

$ make credit
$ ./credit
Type a number: skdfjlsjaj
Type a number: fs45fd5s454f
Type a number:
Type a number: 675-89855-8558
Type a number: 123456789
123456789
$ 

---

int digit_count(long n);

This function takes a long int as an input and returns the length of the number as an int.

For e.g. digit_count(123456789) will return 9.

---

int prefix(long n, int start);

This function takes two arguments, a number (long n) and the number of digits you want from the start (int start).

For e.g. prefix(681451041, 3) will return 681.
If start argument is less than 1 or greater than the length of the given number, then prefix will return 0.

---

int digit_extractor(long n, int digit);

This function takes two arguments, a number (long n) and the place of digit starting from right (starts from 1). It returns the digit as an int from the position you specified.

For e.g. digit_extractor(7114586319, 1) will return 9. digit_extractor(7114586319, 4) will return 6.
If digit argument is less than 1 or greater than the length of the given number, then it will return 0.