! Copyright (c) 2012 Anonymous
! See http://factorcode.org/license.txt for BSD license.
USING: kernel math sequences ;
IN: rosetta-code.luhn-test

! http://rosettacode.org/wiki/Luhn_test_of_credit_card_numbers

! The Luhn test is used by some credit card companies to
! distinguish valid credit card numbers from what could be a
! random selection of digits.

! Those companies using credit card numbers that can be
! validated by the Luhn test have numbers that pass the following
! test:

! 1. Reverse the order of the digits in the number.

! 2. Take the first, third, ... and every other odd digit in the
!    reversed digits and sum them to form the partial sum s1

! 3. Taking the second, fourth ... and every other even digit in
!    the reversed digits:
!    a. Multiply each digit by two and sum the digits if the
!       answer is greater than nine to form partial sums for the
!       even digits
!    b. Sum the partial sums of the even digits to form s2

! 4. If s1 + s2 ends in zero then the original number is in the
!    form of a valid credit card number as verified by the Luhn test.

! For example, if the trial number is 49927398716:

! Reverse the digits:
!   61789372994
! Sum the odd digits:
!   6 + 7 + 9 + 7 + 9 + 4 = 42 = s1
! The even digits:
!     1,  8,  3,  2,  9
!   Two times each even digit:
!     2, 16,  6,  4, 18
!   Sum the digits of each multiplication:
!     2,  7,  6,  4,  9
!   Sum the last:
!     2 + 7 + 6 + 4 + 9 = 28 = s2

! s1 + s2 = 70 which ends in zero which means that 49927398716
! passes the Luhn test

! The task is to write a function/method/procedure/subroutine
! that will validate a number with the Luhn test, and use it to
! validate the following numbers:
!   49927398716
!   49927398717
!   1234567812345678
!   1234567812345670

: reversed-digits ( n -- list )
    { } swap
    [ dup 0 > ]
        [ 10 /mod  swapd suffix  swap ]
    while drop ;

: luhn-digit  ( n -- n )
    reversed-digits dup length <iota> [
        2dup swap nth
        swap odd? [ 2 *  10 /mod + ] when
    ] map sum 10 mod
    nip ;

: luhn? ( n -- ? )
    luhn-digit 0 = ;