Damm algorithm
The Damm algorithm is a checksum algorithm which detects all single digit errors and adjacent transposition errors. The task is to verify the checksum, stored as last digit of an input.
ALGOL 68
<lang algol68>BEGIN
# returns TRUE if the check digit of s is correct according to the Damm algorithm, # # FALSE otherwise # PROC has valid damm check digit = ( STRING s )BOOL: BEGIN # operation table - as per wikipedia example # [,]INT operation table = ( [,]INT( ( 0, 3, 1, 7, 5, 9, 8, 6, 4, 2 ) , ( 7, 0, 9, 2, 1, 5, 4, 8, 6, 3 ) , ( 4, 2, 0, 6, 8, 7, 1, 3, 5, 9 ) , ( 1, 7, 5, 0, 9, 8, 3, 4, 2, 6 ) , ( 6, 1, 2, 3, 0, 4, 5, 9, 7, 8 ) , ( 3, 6, 7, 4, 2, 0, 9, 5, 8, 1 ) , ( 5, 8, 6, 9, 7, 2, 0, 1, 3, 4 ) , ( 8, 9, 4, 5, 3, 6, 2, 0, 1, 7 ) , ( 9, 4, 3, 8, 6, 1, 7, 2, 0, 5 ) , ( 2, 5, 8, 1, 4, 3, 6, 7, 9, 0 ) ) ) [ AT 0, AT 0 ] ; INT interim digit := 0; FOR s pos FROM LWB s TO UPB s DO INT next digit = ABS s[ s pos ] - ABS "0"; IF next digit < 0 OR next digit > 9 THEN # invalid digit # print( ( "Invalid damm digit: ", s[ s pos ], newline ) ); stop ELSE # have a valid digit # interim digit := operation table[ interim digit, next digit ] FI OD; interim digit = 0 END # has valid damm check digit # ; # test the damm algorithm # PROC test damm algorithm = ( STRING s, BOOL expected )VOID: BEGIN BOOL valid = has valid damm check digit( s ); print( ( "check digit of ", s, " is " , IF valid THEN "valid" ELSE "invalid" FI , IF valid = expected THEN "" ELSE " *** NOT AS EXPECTED" FI , newline ) ) END # test damm algorithm # ; # test cases - as per other language samples # test damm algorithm( "5724", TRUE ); test damm algorithm( "5727", FALSE ); test damm algorithm( "112946", TRUE )
END</lang>
- Output:
check digit of 5724 is valid check digit of 5727 is invalid check digit of 112946 is valid
C
<lang c>#include <stdbool.h>
- include <stddef.h>
- include <stdio.h>
bool damm(unsigned char *input, size_t length) {
static const unsigned char table[10][10] = { {0, 3, 1, 7, 5, 9, 8, 6, 4, 2}, {7, 0, 9, 2, 1, 5, 4, 8, 6, 3}, {4, 2, 0, 6, 8, 7, 1, 3, 5, 9}, {1, 7, 5, 0, 9, 8, 3, 4, 2, 6}, {6, 1, 2, 3, 0, 4, 5, 9, 7, 8}, {3, 6, 7, 4, 2, 0, 9, 5, 8, 1}, {5, 8, 6, 9, 7, 2, 0, 1, 3, 4}, {8, 9, 4, 5, 3, 6, 2, 0, 1, 7}, {9, 4, 3, 8, 6, 1, 7, 2, 0, 5}, {2, 5, 8, 1, 4, 3, 6, 7, 9, 0}, }; unsigned char interim = 0; for (size_t i = 0; i < length; i++) { interim = table[interim][input[i]]; } return interim == 0;
}
int main() {
unsigned char input[4] = {5, 7, 2, 4}; puts(damm(input, 4) ? "Checksum correct" : "Checksum incorrect"); return 0;
}</lang>
J
Solution: <lang j>OpTbl=: _99 ". ];._2 noun define 0 3 1 7 5 9 8 6 4 2 7 0 9 2 1 5 4 8 6 3 4 2 0 6 8 7 1 3 5 9 1 7 5 0 9 8 3 4 2 6 6 1 2 3 0 4 5 9 7 8 3 6 7 4 2 0 9 5 8 1 5 8 6 9 7 2 0 1 3 4 8 9 4 5 3 6 2 0 1 7 9 4 3 8 6 1 7 2 0 5 2 5 8 1 4 3 6 7 9 0 )
getdigits=: 10&#.inv
getDamm=: verb define
row=. 0 for_digit. getdigits y do. row=. OpTbl {~ <row,digit end.
)
checkDamm=: 0 = getDamm</lang> Example Usage: <lang j> checkDamm&> 5724 5727 112946 1 0 1</lang>
Perl 6
<lang perl6>sub damm ( *@digits ) {
my @tbl = [0, 3, 1, 7, 5, 9, 8, 6, 4, 2], [7, 0, 9, 2, 1, 5, 4, 8, 6, 3], [4, 2, 0, 6, 8, 7, 1, 3, 5, 9], [1, 7, 5, 0, 9, 8, 3, 4, 2, 6], [6, 1, 2, 3, 0, 4, 5, 9, 7, 8], [3, 6, 7, 4, 2, 0, 9, 5, 8, 1], [5, 8, 6, 9, 7, 2, 0, 1, 3, 4], [8, 9, 4, 5, 3, 6, 2, 0, 1, 7], [9, 4, 3, 8, 6, 1, 7, 2, 0, 5], [2, 5, 8, 1, 4, 3, 6, 7, 9, 0]; my $row = 0; for @digits -> $col { $row = @tbl[$row][$col] } not $row
}
- Testing
for 5724, 5727, 112946 {
say "$_:\tChecksum digit { damm( $_.comb ) ?? !! 'in' }correct."
}</lang>
- Output:
5724: Checksum digit correct. 5727: Checksum digit incorrect. 112946: Checksum digit correct.
Rexx
<lang rexx>Call init Call test 5724 Call test 5727 Call test 112946 Call test 112940 Exit
test: Parse Arg number int_digit=0 Do p=1 To length(number)
d=substr(number,p,1) int_digit=grid.int_digit.d If p<length(number) Then cd=int_digit End
If int_digit=0 Then
Say number 'is ok'
Else
Say number 'is not ok, check-digit should be' cd '(instead of' d')'
Return
init: i=-2 Call setup '* 0 1 2 3 4 5 6 7 8 9' Call setup '0 0 3 1 7 5 9 8 6 4 2' Call setup '1 7 0 9 2 1 5 4 8 6 3' Call setup '2 4 2 0 6 8 7 1 3 5 9' Call setup '3 1 7 5 0 9 8 3 4 2 6' Call setup '4 6 1 2 3 0 4 5 9 7 8' Call setup '5 3 6 7 4 2 0 9 5 8 1' Call setup '6 5 8 6 9 7 2 0 1 3 4' Call setup '7 8 9 4 5 3 6 2 0 1 7' Call setup '8 9 4 3 8 6 1 7 2 0 5' Call setup '9 2 5 8 1 4 3 6 7 9 0' Return setup:
Parse Arg list i=i+1 Do col=-1 To 9 grid.i.col=word(list,col+2) End Return</lang>
- Output:
5724 is ok 5727 is not ok, check-digit should be 4 (instead of 7) 112946 is ok 112940 is not ok, check-digit should be 6 (instead of 0)
zkl
<lang zkl>fcn damm(digits){ // digits is something that supports an iterator of integers
var [const] tbl=Data(0,Int, // 10x10 byte bucket 0, 3, 1, 7, 5, 9, 8, 6, 4, 2, 7, 0, 9, 2, 1, 5, 4, 8, 6, 3, 4, 2, 0, 6, 8, 7, 1, 3, 5, 9, 1, 7, 5, 0, 9, 8, 3, 4, 2, 6, 6, 1, 2, 3, 0, 4, 5, 9, 7, 8, 3, 6, 7, 4, 2, 0, 9, 5, 8, 1, 5, 8, 6, 9, 7, 2, 0, 1, 3, 4, 8, 9, 4, 5, 3, 6, 2, 0, 1, 7, 9, 4, 3, 8, 6, 1, 7, 2, 0, 5, 2, 5, 8, 1, 4, 3, 6, 7, 9, 0); 0 == digits.reduce(fcn(interim,digit){ tbl[interim*10 + digit] },0)
}</lang> <lang zkl>damm(List(5,7,2,4)).println(); // True damm(Data(0,Int,5,7,2,7).howza(0)).println(); // stream bytes, False damm((112946).split()).println(); // True</lang>
- Output:
True False True