Damm algorithm

Damm algorithm is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

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.

C

<lang c>#include <stdbool.h>

1. include <stddef.h>
2. 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

Works with: Rakudo version 2017.05

<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

}

1. 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.

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