# Verhoeff algorithm

Verhoeff algorithm
You are encouraged to solve this task according to the task description, using any language you may know.
Description

The Verhoeff algorithm is a checksum formula for error detection developed by the Dutch mathematician Jacobus Verhoeff and first published in 1969. It was the first decimal check digit algorithm which detects all single-digit errors, and all transposition errors involving two adjacent digits, which was at the time thought impossible with such a code.

As the workings of the algorithm are clearly described in the linked Wikipedia article they will not be repeated here.

Write routines, methods, procedures etc. in your language to generate a Verhoeff checksum digit for non-negative integers of any length and to validate the result. A combined routine is also acceptable.

The more mathematically minded may prefer to generate the 3 tables required from the description provided rather than to hard-code them.

Write your routines in such a way that they can optionally display digit by digit calculations as in the Wikipedia example.

Use your routines to calculate check digits for the integers: 236, 12345 and 123456789012 and then validate them. Also attempt to validate the same integers if the check digits in all cases were 9 rather than what they actually are.

Display digit by digit calculations for the first two integers but not for the third.

## 11l

Translation of: Python
```V MULTIPLICATION_TABLE = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]]

V INV = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

V PERMUTATION_TABLE = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
[5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
[9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
[2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
[7, 0, 4, 6, 9, 1, 3, 2, 5, 8]]

F verhoeffchecksum(n, validate = 1B, terse = 1B, verbose = 0B)
‘
Calculate the Verhoeff checksum over `n`.
Terse mode or with single argument: return True if valid (last digit is a correct check digit).
If checksum mode, return the expected correct checksum digit.
If validation mode, return True if last digit checks correctly.
’
I verbose
print(("\n"(I validate {‘Validation’} E ‘Check digit’))‘ ’(‘calculations for ’n":\n\n i  ni  p[i,ni] c\n------------------"))
V (c, dig) = (0, Array(String(I validate {n} E 10 * n)))
L(ni) reversed(dig)
V i = L.index
V p = :PERMUTATION_TABLE[i % 8][Int(ni)]
c = :MULTIPLICATION_TABLE[c][p]
I verbose
print(f:‘{i:2}  {ni}      {p}    {c}’)

I verbose & !validate
print("\ninv("c‘) = ’:INV[c])
I !terse
print(I validate {"\nThe validation for '"n‘' is ’(I c == 0 {‘correct’} E ‘incorrect’)‘.’} E "\nThe check digit for '"n‘' is ’:INV[c]‘.’)
R I validate {c == 0} E :INV[c]

L(n, va, t, ve) [(Int64(236), 0B, 0B, 1B),
(Int64(2363), 1B, 0B, 1B),
(Int64(2369), 1B, 0B, 1B),
(Int64(12345), 0B, 0B, 1B),
(Int64(123451), 1B, 0B, 1B),
(Int64(123459), 1B, 0B, 1B),
(Int64(123456789012), 0B, 0B, 0B),
(Int64(1234567890120), 1B, 0B, 0B),
(Int64(1234567890129), 1B, 0B, 0B)]
verhoeffchecksum(n, va, t, ve)```
Output:

The same as in Python.

## C

```#include <assert.h>
#include <stdbool.h>
#include <stdio.h>
#include <string.h>

static const int d[][10] = {
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, {1, 2, 3, 4, 0, 6, 7, 8, 9, 5},
{2, 3, 4, 0, 1, 7, 8, 9, 5, 6}, {3, 4, 0, 1, 2, 8, 9, 5, 6, 7},
{4, 0, 1, 2, 3, 9, 5, 6, 7, 8}, {5, 9, 8, 7, 6, 0, 4, 3, 2, 1},
{6, 5, 9, 8, 7, 1, 0, 4, 3, 2}, {7, 6, 5, 9, 8, 2, 1, 0, 4, 3},
{8, 7, 6, 5, 9, 3, 2, 1, 0, 4}, {9, 8, 7, 6, 5, 4, 3, 2, 1, 0},
};

static const int inv[] = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9};

static const int p[][10] = {
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, {1, 5, 7, 6, 2, 8, 3, 0, 9, 4},
{5, 8, 0, 3, 7, 9, 6, 1, 4, 2}, {8, 9, 1, 6, 0, 4, 3, 5, 2, 7},
{9, 4, 5, 3, 1, 2, 6, 8, 7, 0}, {4, 2, 8, 6, 5, 7, 3, 9, 0, 1},
{2, 7, 9, 3, 8, 0, 6, 4, 1, 5}, {7, 0, 4, 6, 9, 1, 3, 2, 5, 8},
};

int verhoeff(const char* s, bool validate, bool verbose) {
if (verbose) {
const char* t = validate ? "Validation" : "Check digit";
printf("%s calculations for '%s':\n\n", t, s);
puts(u8" i  n\xE1\xB5\xA2  p[i,n\xE1\xB5\xA2]  c");
puts("------------------");
}
int len = strlen(s);
if (validate)
--len;
int c = 0;
for (int i = len; i >= 0; --i) {
int ni = (i == len && !validate) ? 0 : s[i] - '0';
assert(ni >= 0 && ni < 10);
int pi = p[(len - i) % 8][ni];
c = d[c][pi];
if (verbose)
printf("%2d  %d      %d     %d\n", len - i, ni, pi, c);
}
if (verbose && !validate)
printf("\ninv[%d] = %d\n", c, inv[c]);
return validate ? c == 0 : inv[c];
}

int main() {
const char* ss[3] = {"236", "12345", "123456789012"};
for (int i = 0; i < 3; ++i) {
const char* s = ss[i];
bool verbose = i < 2;
int c = verhoeff(s, false, verbose);
printf("\nThe check digit for '%s' is '%d'.\n", s, c);
int len = strlen(s);
char sc[len + 2];
strncpy(sc, s, len + 2);
for (int j = 0; j < 2; ++j) {
sc[len] = (j == 0) ? c + '0' : '9';
int v = verhoeff(sc, true, verbose);
printf("\nThe validation for '%s' is %s.\n", sc,
v ? "correct" : "incorrect");
}
}
return 0;
}
```
Output:
```Check digit calculations for '236':

i  nᵢ  p[i,nᵢ]  c
------------------
0  0      0     0
1  6      3     3
2  3      3     1
3  2      1     2

inv[2] = 3

The check digit for '236' is '3'.
Validation calculations for '2363':

i  nᵢ  p[i,nᵢ]  c
------------------
0  3      3     3
1  6      3     1
2  3      3     4
3  2      1     0

The validation for '2363' is correct.
Validation calculations for '2369':

i  nᵢ  p[i,nᵢ]  c
------------------
0  9      9     9
1  6      3     6
2  3      3     8
3  2      1     7

The validation for '2369' is incorrect.
Check digit calculations for '12345':

i  nᵢ  p[i,nᵢ]  c
------------------
0  0      0     0
1  5      8     8
2  4      7     1
3  3      6     7
4  2      5     2
5  1      2     4

inv[4] = 1

The check digit for '12345' is '1'.
Validation calculations for '123451':

i  nᵢ  p[i,nᵢ]  c
------------------
0  1      1     1
1  5      8     9
2  4      7     2
3  3      6     8
4  2      5     3
5  1      2     0

The validation for '123451' is correct.
Validation calculations for '123459':

i  nᵢ  p[i,nᵢ]  c
------------------
0  9      9     9
1  5      8     1
2  4      7     8
3  3      6     2
4  2      5     7
5  1      2     5

The validation for '123459' is incorrect.

The check digit for '123456789012' is '0'.

The validation for '1234567890120' is correct.

The validation for '1234567890129' is incorrect.
```

## C++

```#include <cstdint>
#include <iostream>
#include <string>
#include <array>
#include <iomanip>

typedef std::pair<std::string, bool> data;

const std::array<const std::array<int32_t, 10>, 10>  multiplication_table = { {
{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 },
{ 1, 2, 3, 4, 0, 6, 7, 8, 9, 5 },
{ 2, 3, 4, 0, 1, 7, 8, 9, 5, 6 },
{ 3, 4, 0, 1, 2, 8, 9, 5, 6, 7 },
{ 4, 0, 1, 2, 3, 9, 5, 6, 7, 8 },
{ 5, 9, 8, 7, 6, 0, 4, 3, 2, 1 },
{ 6, 5, 9, 8, 7, 1, 0, 4, 3, 2 },
{ 7, 6, 5, 9, 8, 2, 1, 0, 4, 3 },
{ 8, 7, 6, 5, 9, 3, 2, 1, 0, 4 },
{ 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 }
} };

const std::array<int32_t, 10> inverse = { 0, 4, 3, 2, 1, 5, 6, 7, 8, 9 };

const std::array<const std::array<int32_t, 10>, 8> permutation_table = { {
{ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 },
{ 1, 5, 7, 6, 2, 8, 3, 0, 9, 4 },
{ 5, 8, 0, 3, 7, 9, 6, 1, 4, 2 },
{ 8, 9, 1, 6, 0, 4, 3, 5, 2, 7 },
{ 9, 4, 5, 3, 1, 2, 6, 8, 7, 0 },
{ 4, 2, 8, 6, 5, 7, 3, 9, 0, 1 },
{ 2, 7, 9, 3, 8, 0, 6, 4, 1, 5 },
{ 7, 0, 4, 6, 9, 1, 3, 2, 5, 8 }
} };

int32_t verhoeff_checksum(std::string number, const bool doValidation, const bool doDisplay) {
if ( doDisplay ) {
std::string calculationType = doValidation ? "Validation" : "Check digit";
std::cout << calculationType << " calculations for " << number << "\n" << std::endl;
std::cout << " i  ni  p[i, ni]  c" << std::endl;
std::cout << "-------------------" << std::endl;
}

if ( ! doValidation ) {
number += "0";
}

int32_t c = 0;
const int32_t le = number.length() - 1;
for ( int32_t i = le; i >= 0; i-- ) {
const int32_t ni = number[i] - '0';
const int32_t pi = permutation_table[(le - i) % 8][ni];
c = multiplication_table[c][pi];

if ( doDisplay ) {
std::cout << std::setw(2) << le - i << std::setw(3) << ni
<< std::setw(8) << pi << std::setw(6) << c << "\n" << std::endl;
}
}

if ( doDisplay && ! doValidation ) {
std::cout << "inverse[" << c << "] = " << inverse[c] << "\n" << std::endl;;
}

return doValidation ? c == 0 : inverse[c];
}

int main( ) {
const std::array<data, 3> tests = {
std::make_pair("123", true), std::make_pair("12345", true), std::make_pair("123456789012", false) };

for ( const data& test : tests ) {
int32_t digit = verhoeff_checksum(test.first, false, test.second);
std::cout << "The check digit for " << test.first << " is " << digit << "\n" << std::endl;

std::string numbers[2] = { test.first + std::to_string(digit), test.first + "9" };
for ( const std::string& number : numbers ) {
digit = verhoeff_checksum(number, true, test.second);
std::string result = ( digit == 1 ) ? "correct" : "incorrect";
std::cout << "The validation for " << number << " is " << result << ".\n" << std::endl;
}
}
}
```
Output:
```The same as the Wren example.
```

## FreeBASIC

Translation of: Wren
```Dim Shared As Integer d(9, 9) = { _
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, _
{1, 2, 3, 4, 0, 6, 7, 8, 9, 5}, _
{2, 3, 4, 0, 1, 7, 8, 9, 5, 6}, _
{3, 4, 0, 1, 2, 8, 9, 5, 6, 7}, _
{4, 0, 1, 2, 3, 9, 5, 6, 7, 8}, _
{5, 9, 8, 7, 6, 0, 4, 3, 2, 1}, _
{6, 5, 9, 8, 7, 1, 0, 4, 3, 2}, _
{7, 6, 5, 9, 8, 2, 1, 0, 4, 3}, _
{8, 7, 6, 5, 9, 3, 2, 1, 0, 4}, _
{9, 8, 7, 6, 5, 4, 3, 2, 1, 0} }

Dim Shared As Integer inv(9) = {0, 4, 3, 2, 1, 5, 6, 7, 8, 9}

Dim Shared As Integer p(7, 9) = { _
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9}, _
{1, 5, 7, 6, 2, 8, 3, 0, 9, 4}, _
{5, 8, 0, 3, 7, 9, 6, 1, 4, 2}, _
{8, 9, 1, 6, 0, 4, 3, 5, 2, 7}, _
{9, 4, 5, 3, 1, 2, 6, 8, 7, 0}, _
{4, 2, 8, 6, 5, 7, 3, 9, 0, 1}, _
{2, 7, 9, 3, 8, 0, 6, 4, 1, 5}, _
{7, 0, 4, 6, 9, 1, 3, 2, 5, 8} }

Function Verhoeff(s As String, validate As Integer, table As Integer) As Integer
Dim As Integer c, le, k, ni, pi
If table Then
Print
Print Iif(validate, "Validation", "Check digit") & " calculations for '" & s & "':"
Print !"\n i  ni  p[i,ni]  c\n------------------"
End If
If Not validate Then s = s & "0"
c = 0
le = Len(s) - 1
For k = le To 0 Step -1
ni = Asc(Mid(s, k + 1, 1)) - 48
pi = p((le - k) Mod 8, ni)
c = d(c, pi)
If table Then Print Using "##  #      #     #"; le - k; ni; pi; c
Next k
If table And Not validate Then Print !"\ninv[" & c & "] = " & inv(c)
Return Iif(Not validate, inv(c), c = 0)
End Function

Type miTipo
s As String
b As Boolean
End Type
Dim sts(2) As miTipo
sts(0).s = "236"          : sts(0).b = True
sts(1).s = "12345"        : sts(1).b = True
sts(2).s = "123456789012" : sts(2).b = False

Dim As Integer i, j, v , c
For i = 0 To 2
c = Verhoeff(sts(i).s, False, sts(i).b)
Print Using !"\nThe check digit for '&' is '&'"; sts(i).s; c
Dim stc(1) As String = {Left(sts(i).s, Len(sts(i).s)-1) & Str(c), Left(sts(i).s, Len(sts(i).s)-1) & "9"}
For j = 0 To Ubound(stc)
v = Verhoeff(stc(j), True, sts(i).b)
Print Using !"\nThe validation for '&' is "; stc(j);
Print Iif (v, "correct", "incorrect"); "."
Next j
Print
Next i

Sleep
```
Output:
`Same as Wren entry.`

## F#

```// Verhoeff algorithm. Nigel Galloway: August 26th., 2021
let d,inv,p=let d=[|0;1;2;3;4;5;6;7;8;9;1;2;3;4;0;6;7;8;9;5;2;3;4;0;1;7;8;9;5;6;3;4;0;1;2;8;9;5;6;7;4;0;1;2;3;9;5;6;7;8;5;9;8;7;6;0;4;3;2;1;6;5;9;8;7;1;0;4;3;2;7;6;5;9;8;2;1;0;4;3;8;7;6;5;9;3;2;1;0;4;9;8;7;6;5;4;3;2;1;0|]
let p=[|0;1;2;3;4;5;6;7;8;9;1;5;7;6;2;8;3;0;9;4;5;8;0;3;7;9;6;1;4;2;8;9;1;6;0;4;3;5;2;7;9;4;5;3;1;2;6;8;7;0;4;2;8;6;5;7;3;9;0;1;2;7;9;3;8;0;6;4;1;5;7;0;4;6;9;1;3;2;5;8|]
let inv=[|0;4;3;2;1;5;6;7;8;9|] in (fun n g->d.[10*n+g]),(fun g->inv.[g]),(fun n g->p.[10*(n%8)+g])
let fN g=Seq.unfold(fun(i,g,l)->if i=0I then None else let ni=int(i%10I) in let l=d l (p g ni) in Some((ni,l),(i/10I,g+1,l)))(g,0,0)
let csum g=let _,g=Seq.last(fN g) in inv g
let printTable g=printfn \$"Work Table for %A{g}\n i  nᵢ  p[i,nᵢ] c\n--------------"; fN g|>Seq.iteri(fun i (n,g)->printfn \$"%d{i}  %d{n}      %d{p i n}    %d{g}")
printTable 2360I
printfn \$"\nThe CheckDigit for 236 is %d{csum 2360I}\n"
printTable 2363I
printfn \$"\nThe assertion that 2363 is valid is %A{csum 2363I=0}\n"
printTable 2369I
printfn \$"\nThe assertion that 2369 is valid is %A{csum 2369I=0}\n"
printTable 123450I
printfn \$"\nThe CheckDigit for 12345 is %d{csum 123450I}\n"
printTable 123451I
printfn \$"\nThe assertion that 123451 is valid is %A{csum 123451I=0}\n"
printTable 123459I
printfn \$"\nThe assertion that 123459 is valid is %A{csum 123459I=0}"
printfn \$"The CheckDigit for 123456789012 is %d{csum 1234567890120I}"
printfn \$"The assertion that 1234567890120 is valid is %A{csum 1234567890120I=0}"
printfn \$"The assertion that 1234567890129 is valid is %A{csum 1234567890129I=0}"
```
Output:
```Work Table for 2360
i  nᵢ  p[i,nᵢ] c
--------------
0  0      0    0
1  6      3    3
2  3      3    1
3  2      1    2

The CheckDigit for 236 is 3

Work Table for 2363
i  nᵢ  p[i,nᵢ] c
--------------
0  3      3    3
1  6      3    1
2  3      3    4
3  2      1    0

The assertion that 2363 is valid is true

Work Table for 2369
i  nᵢ  p[i,nᵢ] c
--------------
0  9      9    9
1  6      3    6
2  3      3    8
3  2      1    7

The assertion that 2369 is valid is false

Work Table for 123450
i  nᵢ  p[i,nᵢ] c
--------------
0  0      0    0
1  5      8    8
2  4      7    1
3  3      6    7
4  2      5    2
5  1      2    4

The CheckDigit for 12345 is 1

Work Table for 123451
i  nᵢ  p[i,nᵢ] c
--------------
0  1      1    1
1  5      8    9
2  4      7    2
3  3      6    8
4  2      5    3
5  1      2    0

The assertion that 123451 is valid is true

Work Table for 123459
i  nᵢ  p[i,nᵢ] c
--------------
0  9      9    9
1  5      8    1
2  4      7    8
3  3      6    2
4  2      5    7
5  1      2    5

The assertion that 123459 is valid is false
The CheckDigit for 123456789012 is 0
The assertion that 1234567890120 is valid is true
The assertion that 1234567890129 is valid is false
```

## Go

Translation of: Wren
```package main

import "fmt"

var d = [][]int{
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
{1, 2, 3, 4, 0, 6, 7, 8, 9, 5},
{2, 3, 4, 0, 1, 7, 8, 9, 5, 6},
{3, 4, 0, 1, 2, 8, 9, 5, 6, 7},
{4, 0, 1, 2, 3, 9, 5, 6, 7, 8},
{5, 9, 8, 7, 6, 0, 4, 3, 2, 1},
{6, 5, 9, 8, 7, 1, 0, 4, 3, 2},
{7, 6, 5, 9, 8, 2, 1, 0, 4, 3},
{8, 7, 6, 5, 9, 3, 2, 1, 0, 4},
{9, 8, 7, 6, 5, 4, 3, 2, 1, 0},
}

var inv = []int{0, 4, 3, 2, 1, 5, 6, 7, 8, 9}

var p = [][]int{
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
{1, 5, 7, 6, 2, 8, 3, 0, 9, 4},
{5, 8, 0, 3, 7, 9, 6, 1, 4, 2},
{8, 9, 1, 6, 0, 4, 3, 5, 2, 7},
{9, 4, 5, 3, 1, 2, 6, 8, 7, 0},
{4, 2, 8, 6, 5, 7, 3, 9, 0, 1},
{2, 7, 9, 3, 8, 0, 6, 4, 1, 5},
{7, 0, 4, 6, 9, 1, 3, 2, 5, 8},
}

func verhoeff(s string, validate, table bool) interface{} {
if table {
t := "Check digit"
if validate {
t = "Validation"
}
fmt.Printf("%s calculations for '%s':\n\n", t, s)
fmt.Println(" i  nᵢ  p[i,nᵢ]  c")
fmt.Println("------------------")
}
if !validate {
s = s + "0"
}
c := 0
le := len(s) - 1
for i := le; i >= 0; i-- {
ni := int(s[i] - 48)
pi := p[(le-i)%8][ni]
c = d[c][pi]
if table {
fmt.Printf("%2d  %d      %d     %d\n", le-i, ni, pi, c)
}
}
if table && !validate {
fmt.Printf("\ninv[%d] = %d\n", c, inv[c])
}
if !validate {
return inv[c]
}
return c == 0
}

func main() {
ss := []string{"236", "12345", "123456789012"}
ts := []bool{true, true, false, true}
for i, s := range ss {
c := verhoeff(s, false, ts[i]).(int)
fmt.Printf("\nThe check digit for '%s' is '%d'\n\n", s, c)
for _, sc := range []string{s + string(c+48), s + "9"} {
v := verhoeff(sc, true, ts[i]).(bool)
ans := "correct"
if !v {
ans = "incorrect"
}
fmt.Printf("\nThe validation for '%s' is %s\n\n", sc, ans)
}
}
}
```
Output:
```Identical to Wren example
```

## J

Implementation:

```cyc=: | +/~@i.   NB. cyclic group, order y
ac=:  |(+-/~@i.) NB. anticyclic group, order y
di=: (cyc,.cyc a2n),((ac a2n),.ac)

D=:   di 5
INV=: ,I.0=D
P=: {&(C.1 5 8 9 4 2 7 0;3 6)^:(i.8) i.10

verhoeff=: {{
c=. 0
for_N. |.10 #.inv y do.
c=. D{~<c,P{~<(8|N_index),N
end.
}}

traceverhoeff=: {{
r=. EMPTY
c=. 0
for_N. |.10 #.inv y do.
c0=. c
c=. D{~<c,p=.P{~<(j=.8|N_index),N
r=. r, c,p,j,N_index,N,c0
end.
labels=. cut 'cᵢ p[i,nᵢ] i nᵢ n cₒ'
1 1}.}:~.":labels,(<;._1"1~[:*/' '=])' ',.":r
}}

checkdigit=: INV {~ verhoeff@*&10
valid=: 0 = verhoeff
```

```   checkdigit 236 12345 123456789012
3 1 0
valid 2363
1
valid 123451
1
valid 1234567890120
1
valid 2369
0
valid 123459
0
valid 1234567890129
0
traceverhoeff 2363
cᵢ│p[i,nᵢ]│i│nᵢ│n│cₒ│
──┼───────┼─┼──┼─┼──┤
3 │3      │0│0 │3│0 │
1 │3      │1│1 │6│3 │
4 │3      │2│2 │3│1 │
0 │1      │3│3 │2│4 │
traceverhoeff 123451
cᵢ│p[i,nᵢ]│i│nᵢ│n│cₒ│
──┼───────┼─┼──┼─┼──┤
1 │1      │0│0 │1│0 │
9 │8      │1│1 │5│1 │
2 │7      │2│2 │4│9 │
8 │6      │3│3 │3│2 │
3 │5      │4│4 │2│8 │
0 │2      │5│5 │1│3 │
```

## Java

```import java.util.Arrays;
import java.util.List;

public class VerhoeffAlgorithm {

public static void main(String[] args) {
initialise();

List<List<Object>> tests = List.of(
List.of( "236", true ), List.of( "12345", true ), List.of( "123456789012", false ) );

for ( List<Object> test : tests ) {
Object object = verhoeffChecksum((String) test.get(0), false, (boolean) test.get(1));
System.out.println("The check digit for " + test.get(0) + " is " + object + "\n");

for ( String number : List.of( test.get(0) + String.valueOf(object), test.get(0) + "9" ) ) {
object = verhoeffChecksum(number, true, (boolean) test.get(1));
String result = (boolean) object ? "correct" : "incorrect";
System.out.println("The validation for " + number + " is " + result + ".\n");
}
}
}

private static Object verhoeffChecksum(String number, boolean doValidation, boolean doDisplay) {
if ( doDisplay ) {
String calculationType = doValidation ? "Validation" : "Check digit";
System.out.println(calculationType + " calculations for " + number + "\n");
System.out.println(" i  ni  p[i, ni]  c");
System.out.println("-------------------");
}

if ( ! doValidation ) {
number += "0";
}

int c = 0;
final int le = number.length() - 1;
for ( int i = le; i >= 0; i-- ) {
final int ni = number.charAt(i) - '0';
final int pi = permutationTable.get((le - i) % 8).get(ni);
c = multiplicationTable.get(c).get(pi);

if ( doDisplay ) {
System.out.println(String.format("%2d%3d%8d%6d\n", le - i, ni, pi, c));
}
}

if ( doDisplay && ! doValidation ) {
System.out.println("inverse[" + c + "] = " + inverse.get(c) + "\n");
}

return doValidation ? c == 0 : inverse.get(c);
}

private static void initialise() {
multiplicationTable = List.of(
List.of( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ),
List.of( 1, 2, 3, 4, 0, 6, 7, 8, 9, 5 ),
List.of( 2, 3, 4, 0, 1, 7, 8, 9, 5, 6 ),
List.of( 3, 4, 0, 1, 2, 8, 9, 5, 6, 7 ),
List.of( 4, 0, 1, 2, 3, 9, 5, 6, 7, 8 ),
List.of( 5, 9, 8, 7, 6, 0, 4, 3, 2, 1 ),
List.of( 6, 5, 9, 8, 7, 1, 0, 4, 3, 2 ),
List.of( 7, 6, 5, 9, 8, 2, 1, 0, 4, 3 ),
List.of( 8, 7, 6, 5, 9, 3, 2, 1, 0, 4 ),
List.of( 9, 8, 7, 6, 5, 4, 3, 2, 1, 0 )
);

inverse = Arrays.asList( 0, 4, 3, 2, 1, 5, 6, 7, 8, 9 );

permutationTable = List.of(
List.of( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ),
List.of( 1, 5, 7, 6, 2, 8, 3, 0, 9, 4 ),
List.of( 5, 8, 0, 3, 7, 9, 6, 1, 4, 2 ),
List.of( 8, 9, 1, 6, 0, 4, 3, 5, 2, 7 ),
List.of( 9, 4, 5, 3, 1, 2, 6, 8, 7, 0 ),
List.of( 4, 2, 8, 6, 5, 7, 3, 9, 0, 1 ),
List.of( 2, 7, 9, 3, 8, 0, 6, 4, 1, 5 ),
List.of( 7, 0, 4, 6, 9, 1, 3, 2, 5, 8 )
);
}

private static List<List<Integer>> multiplicationTable;
private static List<Integer> inverse;
private static List<List<Integer>> permutationTable;

}
```
Output:
```The same as the Wren example.
```

## jq

Translation of: Wren
Works with: jq

Works with gojq, the Go implementation of jq

```def lpad(\$len): tostring | (\$len - length) as \$l | (" " * \$l)[:\$l] + .;

def d: [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
];

def inv: [0, 4, 3, 2, 1, 5, 6, 7, 8, 9];

def p: [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
[5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
[9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
[2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
[7, 0, 4, 6, 9, 1, 3, 2, 5, 8]
];

# Output: an object: {emit, c}
def verhoeff(\$s; \$validate; \$table):

{emit:
(if \$table then
["\(if \$validate then "Validation" else "Check digit" end) calculations for '\(\$s)':\n",
" i  nᵢ  p[i,nᵢ]  c",
"------------------"]
else []
end),
s: (if \$validate then \$s else \$s + "0" end),
c: 0 }
| ((.s|length) - 1) as \$le
| reduce range(\$le; -1; -1) as \$i (.;
(.s[\$i:\$i+1]|explode[] - 48) as \$ni
| (p[(\$le-\$i) % 8][\$ni]) as \$pi
| .c = d[.c][\$pi]
| if \$table
then .emit += ["\(\$le-\$i|lpad(2))  \(\$ni)      \(\$pi)     \(.c)"]
else .
end )
| if \$table and (\$validate|not)
then .emit += ["\ninv[\(.c)] = \(inv[.c])"]
else .
end
| .c = (if \$validate then (.c == 0) else inv[.c] end);

def sts: [
["236", true],
["12345", true],
["123456789012", false]];

sts[]
| . as \$st
| verhoeff(\$st[0]; false; \$st[1]) as {c: \$c, emit: \$emit}
| \$emit[],
"\nThe check digit for '\(\$st[0])' is '\(\$c)'\n",
( (\$st[0] + (\$c|tostring)), (\$st[0] + "9")
| . as \$stc
| verhoeff(\$stc; true; \$st[1]) as {emit: \$emit, c: \$v}
| (if \$v then "correct" else "incorrect" end) as \$v
| \$emit[],
"\nThe validation for '\(\$stc)' is \(\$v).\n" );

Output:

As for #Wren.

## Julia

```const multiplicationtable = [
0  1  2  3  4  5  6  7  8  9;
1  2  3  4  0  6  7  8  9  5;
2  3  4  0  1  7  8  9  5  6;
3  4  0  1  2  8  9  5  6  7;
4  0  1  2  3  9  5  6  7  8;
5  9  8  7  6  0  4  3  2  1;
6  5  9  8  7  1  0  4  3  2;
7  6  5  9  8  2  1  0  4  3;
8  7  6  5  9  3  2  1  0  4;
9  8  7  6  5  4  3  2  1  0]

const permutationtable = [
0  1  2  3  4  5  6  7  8  9;
1  5  7  6  2  8  3  0  9  4;
5  8  0  3  7  9  6  1  4  2;
8  9  1  6  0  4  3  5  2  7;
9  4  5  3  1  2  6  8  7  0;
4  2  8  6  5  7  3  9  0  1;
2  7  9  3  8  0  6  4  1  5;
7  0  4  6  9  1  3  2  5  8]

const inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

"""
verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)

Calculate the Verhoeff checksum over `n`.
Terse mode or with single argument: return true if valid (last digit is a correct check digit).
If checksum mode, return the expected correct checksum digit.
If validation mode, return true if last digit checks correctly.
"""
function verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)
verbose && println("\n", validate ? "Validation" : "Check digit",
" calculations for '\$n':\n\n", " i  nᵢ  p[i,nᵢ]  c\n------------------")
# transform number list
c, dig = 0, reverse(digits(validate ? n : 10 * n))
for i in length(dig):-1:1
ni = dig[i]
p = permutationtable[(length(dig) - i) % 8 + 1, ni + 1]
c = multiplicationtable[c + 1, p + 1]
verbose && println(lpad(length(dig) - i, 2), "  \$ni      \$p    \$c")
end
verbose && !validate && println("\ninv(\$c) = \$(inv[c + 1])")
!terse && println(validate ? "\nThe validation for '\$n' is \$(c == 0 ?
"correct" : "incorrect")." : "\nThe check digit for '\$n' is \$(inv[c + 1]).")
return validate ? c == 0 : inv[c + 1]
end

for args in [(236, false, false, true), (2363, true, false, true), (2369, true, false, true),
(12345, false, false, true), (123451, true, false, true), (123459, true, false, true),
(123456789012, false, false), (1234567890120, true, false), (1234567890129, true, false)]
verhoeffchecksum(args...)
end
```
Output:

Same as Wren example.

## Nim

```import strformat

const

D = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]]

Inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

P = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
[5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
[9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
[2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
[7, 0, 4, 6, 9, 1, 3, 2, 5, 8]]

type Digit = 0..9

proc verhoeff[T: SomeInteger](n: T; validate, verbose = false): T =
## Compute or validate a check digit.
## Return the check digit if computation or the number with the check digit
## removed if validation.
## If not in verbose mode, an exception is raised if validation failed.

doAssert n >= 0, "Argument must not be negative."

# Extract digits.
var digits: seq[Digit]
var val = n
while val != 0:
val = val div 10

if verbose:
echo if validate: &"Check digit validation for {n}:" else: &"Check digit computation for {n}:"
echo " i  ni  p(i, ni)  c"

# Compute c.
var c = 0
for i, ni in digits:
let p = P[i mod 8][ni]
c = D[c][p]
if verbose: echo &"{i:2}   {ni}     {p}      {c}"

if validate:
if verbose:
let verb = if c == 0: "is" else: "is not"
echo &"Validation {verb} successful.\n"
elif c != 0:
raise newException(ValueError, &"Check digit validation failed for {n}.")
result = n div 10

else:
result = Inv[c]
if verbose: echo &"The check digit for {n} is {result}.\n"

for n in [236, 12345]:
let d = verhoeff(n, false, true)
discard verhoeff(10 * n + d, true, true)
discard verhoeff(10 * n + 9, true, true)

let n = 123456789012
let d = verhoeff(n)
echo &"Check digit for {n} is {d}."
discard verhoeff(10 * n + d, true)
echo &"Check digit validation was successful for {10 * n + d}."
try:
discard verhoeff(10 * n + 9, true)
except ValueError:
echo getCurrentExceptionMsg()
```
Output:
```Check digit computation for 236:
i  ni  p(i, ni)  c
0   0     0      0
1   6     3      3
2   3     3      1
3   2     1      2
The check digit for 236 is 3.

Check digit validation for 2363:
i  ni  p(i, ni)  c
0   3     3      3
1   6     3      1
2   3     3      4
3   2     1      0
Validation is successful.

Check digit validation for 2369:
i  ni  p(i, ni)  c
0   9     9      9
1   6     3      6
2   3     3      8
3   2     1      7
Validation is not successful.

Check digit computation for 12345:
i  ni  p(i, ni)  c
0   0     0      0
1   5     8      8
2   4     7      1
3   3     6      7
4   2     5      2
5   1     2      4
The check digit for 12345 is 1.

Check digit validation for 123451:
i  ni  p(i, ni)  c
0   1     1      1
1   5     8      9
2   4     7      2
3   3     6      8
4   2     5      3
5   1     2      0
Validation is successful.

Check digit validation for 123459:
i  ni  p(i, ni)  c
0   9     9      9
1   5     8      1
2   4     7      8
3   3     6      2
4   2     5      7
5   1     2      5
Validation is not successful.

Check digit for 123456789012 is 0.
Check digit validation was successful for 1234567890120.
Check digit validation failed for 1234567890129.```

## Perl

```#!/usr/bin/perl

use strict; # https://rosettacode.org/wiki/Verhoeff_algorithm
use warnings;

my @inv = qw(0 4 3 2 1 5 6 7 8 9);

my @d = map [ split ], split /\n/, <<END;
0 	1 	2 	3 	4 	5 	6 	7 	8 	9
1 	2 	3 	4 	0 	6 	7 	8 	9 	5
2 	3 	4 	0 	1 	7 	8 	9 	5 	6
3 	4 	0 	1 	2 	8 	9 	5 	6 	7
4 	0 	1 	2 	3 	9 	5 	6 	7 	8
5 	9 	8 	7 	6 	0 	4 	3 	2 	1
6 	5 	9 	8 	7 	1 	0 	4 	3 	2
7 	6 	5 	9 	8 	2 	1 	0 	4 	3
8 	7 	6 	5 	9 	3 	2 	1 	0 	4
9 	8 	7 	6 	5 	4 	3 	2 	1 	0
END

my @p = map [ split ], split /\n/, <<END;
0 	1 	2 	3 	4 	5 	6 	7 	8 	9
1 	5 	7 	6 	2 	8 	3 	0 	9 	4
5 	8 	0 	3 	7 	9 	6 	1 	4 	2
8 	9 	1 	6 	0 	4 	3 	5 	2 	7
9 	4 	5 	3 	1 	2 	6 	8 	7 	0
4 	2 	8 	6 	5 	7 	3 	9 	0 	1
2 	7 	9 	3 	8 	0 	6 	4 	1 	5
7 	0 	4 	6 	9 	1 	3 	2 	5 	8
END

my \$debug;

sub generate
{
local \$_ = shift() . 0;
my \$c = my \$i = 0;
my (\$n, \$p);
\$debug and print "i ni d(c,p(i%8,ni)) c\n";
while( length )
{
\$c = \$d[ \$c ][ \$p = \$p[ \$i % 8 ][ \$n = chop ] ];
\$debug and printf "%d%3d%7d%10d\n", \$i, \$n, \$p, \$c;
\$i++;
}
return \$inv[ \$c ];
}

sub validate { shift =~ /(\d+)(\d)/ and \$2 == generate(\$1) }

for ( 236, 12345, 123456789012 )
{
print "testing \$_\n";
\$debug = length() < 6;
my \$checkdigit = generate(\$_);
print "check digit for \$_ is \$checkdigit\n";
\$debug = 0;
for my \$cd ( \$checkdigit, 9 )
{
print "\$_\$cd is ", validate(\$_ . \$cd) ? '' : 'not ', "valid\n";
}
print "\n";
}
```
Output:
```testing 236
i ni d(c,p(i%8,ni)) c
0  0      0         0
1  6      3         3
2  3      3         1
3  2      1         2
check digit for 236 is 3
2363 is valid
2369 is not valid

testing 12345
i ni d(c,p(i%8,ni)) c
0  0      0         0
1  5      8         8
2  4      7         1
3  3      6         7
4  2      5         2
5  1      2         4
check digit for 12345 is 1
123451 is valid
123459 is not valid

testing 123456789012
check digit for 123456789012 is 0
1234567890120 is valid
1234567890129 is not valid

```

## Phix

The tables were generated in case 1-based index versions of them would help, tbh, but in the end I didn't even try that, aka start with tagset(10).

```with javascript_semantics
sequence d = {tagset(9,0)},
inv = tagset(9,0),
p = {tagset(9,0)}
for i=1 to 4 do d = append(d,extract(d[\$],{2,3,4,5,1,7,8,9,10,6})) end for
for i=5 to 8 do d = append(d,reverse(d[-4])) end for
d = append(d,reverse(d[1]))
inv[2..5] = reverse(inv[2..5])
for i=1 to 7 do p = append(p,extract(p[\$],{2,6,8,7,3,9,4,1,10,5})) end for

-- alternatively, if you prefer:
--constant d = {{0,1,2,3,4,5,6,7,8,9},
--              {1,2,3,4,0,6,7,8,9,5},
--              {2,3,4,0,1,7,8,9,5,6},
--              {3,4,0,1,2,8,9,5,6,7},
--              {4,0,1,2,3,9,5,6,7,8},
--              {5,9,8,7,6,0,4,3,2,1},
--              {6,5,9,8,7,1,0,4,3,2},
--              {7,6,5,9,8,2,1,0,4,3},
--              {8,7,6,5,9,3,2,1,0,4},
--              {9,8,7,6,5,4,3,2,1,0}},
--        inv = {0,4,3,2,1,5,6,7,8,9},
--         p = {{0,1,2,3,4,5,6,7,8,9},
--              {1,5,7,6,2,8,3,0,9,4},
--              {5,8,0,3,7,9,6,1,4,2},
--              {8,9,1,6,0,4,3,5,2,7},
--              {9,4,5,3,1,2,6,8,7,0},
--              {4,2,8,6,5,7,3,9,0,1},
--              {2,7,9,3,8,0,6,4,1,5},
--              {7,0,4,6,9,1,3,2,5,8}}

function verhoeff(string n, bool validate=false, show_workings=false)
string {s,t} = iff(validate?{n,"Validation"}:{n&'0',"Check digit"})
if show_workings then
printf(1,"%s calculations for `%s`:\n", {t, n})
printf(1," i  ni  p(i,ni)  c\n")
printf(1,"------------------\n")
end if
integer c = 0
for i=1 to length(s) do
integer ni = s[-i]-'0',
pi = p[remainder(i-1,8)+1][ni+1]
c = d[c+1][pi+1]
if show_workings then
printf(1,"%2d  %d      %d     %d\n", {i-1, ni, pi, c})
end if
end for
integer ch = inv[c+1]+'0'
string r = iff(validate?iff(c=0?"":"in")&"correct"
:"`"&ch&"`")
printf(1,"The %s for `%s` is %s\n\n",{lower(t),n,r})
return ch
end function

constant tests = {"236", "12345", "123456789012"}
for i=1 to length(tests) do
bool show_workings = (i<=2)
integer ch = verhoeff(tests[i],false,show_workings)
assert(verhoeff(tests[i]&ch,true,show_workings)=='0')
assert(verhoeff(tests[i]&'9',true,show_workings)!='0')
end for
```
Output:
```Check digit calculations for `236`:
i  ni  p(i,ni)  c
------------------
0  0      0     0
1  6      3     3
2  3      3     1
3  2      1     2
The check digit for `236` is `3`

Validation calculations for `2363`:
i  ni  p(i,ni)  c
------------------
0  3      3     3
1  6      3     1
2  3      3     4
3  2      1     0
The validation for `2363` is correct

Validation calculations for `2369`:
i  ni  p(i,ni)  c
------------------
0  9      9     9
1  6      3     6
2  3      3     8
3  2      1     7
The validation for `2369` is incorrect

Check digit calculations for `12345`:
i  ni  p(i,ni)  c
------------------
0  0      0     0
1  5      8     8
2  4      7     1
3  3      6     7
4  2      5     2
5  1      2     4
The check digit for `12345` is `1`

Validation calculations for `123451`:
i  ni  p(i,ni)  c
------------------
0  1      1     1
1  5      8     9
2  4      7     2
3  3      6     8
4  2      5     3
5  1      2     0
The validation for `123451` is correct

Validation calculations for `123459`:
i  ni  p(i,ni)  c
------------------
0  9      9     9
1  5      8     1
2  4      7     8
3  3      6     2
4  2      5     7
5  1      2     5
The validation for `123459` is incorrect

The check digit for `123456789012` is `0`

The validation for `1234567890120` is correct

The validation for `1234567890129` is incorrect
```

## Python

```MULTIPLICATION_TABLE = [
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
(1, 2, 3, 4, 0, 6, 7, 8, 9, 5),
(2, 3, 4, 0, 1, 7, 8, 9, 5, 6),
(3, 4, 0, 1, 2, 8, 9, 5, 6, 7),
(4, 0, 1, 2, 3, 9, 5, 6, 7, 8),
(5, 9, 8, 7, 6, 0, 4, 3, 2, 1),
(6, 5, 9, 8, 7, 1, 0, 4, 3, 2),
(7, 6, 5, 9, 8, 2, 1, 0, 4, 3),
(8, 7, 6, 5, 9, 3, 2, 1, 0, 4),
(9, 8, 7, 6, 5, 4, 3, 2, 1, 0),
]

INV = (0, 4, 3, 2, 1, 5, 6, 7, 8, 9)

PERMUTATION_TABLE = [
(0, 1, 2, 3, 4, 5, 6, 7, 8, 9),
(1, 5, 7, 6, 2, 8, 3, 0, 9, 4),
(5, 8, 0, 3, 7, 9, 6, 1, 4, 2),
(8, 9, 1, 6, 0, 4, 3, 5, 2, 7),
(9, 4, 5, 3, 1, 2, 6, 8, 7, 0),
(4, 2, 8, 6, 5, 7, 3, 9, 0, 1),
(2, 7, 9, 3, 8, 0, 6, 4, 1, 5),
(7, 0, 4, 6, 9, 1, 3, 2, 5, 8),
]

def verhoeffchecksum(n, validate=True, terse=True, verbose=False):
"""
Calculate the Verhoeff checksum over `n`.
Terse mode or with single argument: return True if valid (last digit is a correct check digit).
If checksum mode, return the expected correct checksum digit.
If validation mode, return True if last digit checks correctly.
"""
if verbose:
print(f"\n{'Validation' if validate else 'Check digit'}",\
f"calculations for {n}:\n\n i  nᵢ  p[i,nᵢ]   c\n------------------")
# transform number list
c, dig = 0, list(str(n if validate else 10 * n))
for i, ni in enumerate(dig[::-1]):
p = PERMUTATION_TABLE[i % 8][int(ni)]
c = MULTIPLICATION_TABLE[c][p]
if verbose:
print(f"{i:2}  {ni}      {p}    {c}")

if verbose and not validate:
print(f"\ninv({c}) = {INV[c]}")
if not terse:
print(f"\nThe validation for '{n}' is {'correct' if c == 0 else 'incorrect'}."\
if validate else f"\nThe check digit for '{n}' is {INV[c]}.")
return c == 0 if validate else INV[c]

if __name__ == '__main__':

for n, va, t, ve in [
(236, False, False, True), (2363, True, False, True), (2369, True, False, True),
(12345, False, False, True), (123451, True, False, True), (123459, True, False, True),
(123456789012, False, False, False), (1234567890120, True, False, False),
(1234567890129, True, False, False)]:
verhoeffchecksum(n, va, t, ve)
```
Output:

Output same as Wren example.

## Raku

Generate the tables rather than hard coding, They're not all that complex.

```my @d = [^10] xx 5;
@d[\$_][^5].=rotate(\$_), @d[\$_][5..*].=rotate(\$_) for 1..4;
push @d: [@d[\$_].reverse] for flat 1..4, 0;

my @i = 0,4,3,2,1,5,6,7,8,9;

my %h = flat (0,1,5,8,9,4,2,7,0).rotor(2 =>-1).map({.[0]=>.[1]}), 6=>3, 3=>6;
my @p = [^10],;
@p.push: [@p[*-1].map: {%h{\$_}}] for ^7;

sub checksum (Int \$int where * ≥ 0, :\$verbose = True ) {
my @digits = \$int.comb;
say "\nCheckdigit calculation for \$int:";
say " i  ni  p(i, ni)  c" if \$verbose;
my (\$i, \$p, \$c) = 0 xx 3;
say " \$i   0      \$p     \$c" if \$verbose;
for @digits.reverse {
++\$i;
\$p = @p[\$i % 8][\$_];
\$c = @d[\$c; \$p];
say "{\$i.fmt('%2d')}   \$_      \$p     \$c" if \$verbose;
}
say "Checkdigit: {@i[\$c]}";
+(\$int ~ @i[\$c]);
}

sub validate (Int \$int where * ≥ 0, :\$verbose = True) {
my @digits = \$int.comb;
say "\nValidation calculation for \$int:";
say " i  ni  p(i, ni)  c" if \$verbose;
my (\$i, \$p, \$c) = 0 xx 3;
for @digits.reverse {
\$p = @p[\$i % 8][\$_];
\$c = @d[\$c; \$p];
say "{\$i.fmt('%2d')}   \$_      \$p     \$c" if \$verbose;
++\$i;
}
say "Checkdigit: {'in' if \$c}correct";
}

## TESTING

for 236, 12345, 123456789012 -> \$int {
my \$check = checksum \$int, :verbose( \$int.chars < 8 );
validate \$check, :verbose( \$int.chars < 8 );
validate +(\$check.chop ~ 9), :verbose( \$int.chars < 8 );
}
```
Output:
```Checkdigit calculation for 236:
i  ni  p(i, ni)  c
0   0      0     0
1   6      3     3
2   3      3     1
3   2      1     2
Checkdigit: 3

Validation calculation for 2363:
i  ni  p(i, ni)  c
0   3      3     3
1   6      3     1
2   3      3     4
3   2      1     0
Checkdigit: correct

Validation calculation for 2369:
i  ni  p(i, ni)  c
0   9      9     9
1   6      3     6
2   3      3     8
3   2      1     7
Checkdigit: incorrect

Checkdigit calculation for 12345:
i  ni  p(i, ni)  c
0   0      0     0
1   5      8     8
2   4      7     1
3   3      6     7
4   2      5     2
5   1      2     4
Checkdigit: 1

Validation calculation for 123451:
i  ni  p(i, ni)  c
0   1      1     1
1   5      8     9
2   4      7     2
3   3      6     8
4   2      5     3
5   1      2     0
Checkdigit: correct

Validation calculation for 123459:
i  ni  p(i, ni)  c
0   9      9     9
1   5      8     1
2   4      7     8
3   3      6     2
4   2      5     7
5   1      2     5
Checkdigit: incorrect

Checkdigit calculation for 123456789012:
Checkdigit: 0

Validation calculation for 1234567890120:
Checkdigit: correct

Validation calculation for 1234567890129:
Checkdigit: incorrect```

## V (Vlang)

Translation of: Go
```const d = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0],
]

const inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

const p = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
[5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
[9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
[2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
[7, 0, 4, 6, 9, 1, 3, 2, 5, 8],
]

fn verhoeff(ss string, validate bool, table bool) int {
mut s:= ss
if table {
mut t := "Check digit"
if validate {
t = "Validation"
}
println("\$t calculations for '\$s':\n")
println(" i  nᵢ  p[i,nᵢ]  c")
println("------------------")
}
if !validate {
s = s + "0"
}
mut c := 0
le := s.len - 1
for i := le; i >= 0; i-- {
ni := int(s[i] - 48)
pi := p[(le-i)%8][ni]
c = d[c][pi]
if table {
println("\${le-i:2}  \$ni      \$pi     \$c")
}
}
if table && !validate {
println("\ninv[\$c] = \${inv[c]}")
}
if !validate {
return inv[c]
}
return int(c == 0)
}

fn main() {
ss := ["236", "12345", "123456789012"]
ts := [true, true, false, true]
for i, s in ss {
c := verhoeff(s, false, ts[i])
println("\nThe check digit for '\$s' is '\$c'\n")
for sc in [s + c.str(), s + "9"] {
v := verhoeff(sc, true, ts[i])
mut ans := "correct"
if v==0 {
ans = "incorrect"
}
println("\nThe validation for '\$sc' is \$ans\n")
}
}
}
```
Output:
```Identical to Wren example
```

## Wren

Library: Wren-fmt
```import "./fmt" for Fmt

var d = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0]
]

var inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]

var p = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
[5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
[9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
[2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
[7, 0, 4, 6, 9, 1, 3, 2, 5, 8]
]

var verhoeff = Fn.new { |s, validate, table|
if (table) {
System.print("%(validate ? "Validation" : "Check digit") calculations for '%(s)':\n")
System.print(" i  nᵢ  p[i,nᵢ]  c")
System.print("------------------")
}
if (!validate) s = s + "0"
var c = 0
var le = s.count - 1
for (i in le..0) {
var ni = s[i].bytes[0] - 48
var pi = p[(le-i) % 8][ni]
c = d[c][pi]
if (table) Fmt.print("\$2d  \$d      \$d     \$d", le-i, ni, pi, c)
}
if (table && !validate) System.print("\ninv[%(c)] = %(inv[c])")
return !validate ? inv[c] : c == 0
}

var sts = [["236", true], ["12345", true], ["123456789012", false]]
for (st in sts) {
var c = verhoeff.call(st[0], false, st[1])
System.print("\nThe check digit for '%(st[0])' is '%(c)'\n")
for (stc in [st[0] + c.toString, st[0] + "9"]) {
var v = verhoeff.call(stc, true, st[1])
System.print("\nThe validation for '%(stc)' is %(v ? "correct" : "incorrect").\n")
}
}
```
Output:
```Check digit calculations for '236':

i  nᵢ  p[i,nᵢ]  c
------------------
0  0      0     0
1  6      3     3
2  3      3     1
3  2      1     2

inv[2] = 3

The check digit for '236' is '3'

Validation calculations for '2363':

i  nᵢ  p[i,nᵢ]  c
------------------
0  3      3     3
1  6      3     1
2  3      3     4
3  2      1     0

The validation for '2363' is correct.

Validation calculations for '2369':

i  nᵢ  p[i,nᵢ]  c
------------------
0  9      9     9
1  6      3     6
2  3      3     8
3  2      1     7

The validation for '2369' is incorrect.

Check digit calculations for '12345':

i  nᵢ  p[i,nᵢ]  c
------------------
0  0      0     0
1  5      8     8
2  4      7     1
3  3      6     7
4  2      5     2
5  1      2     4

inv[4] = 1

The check digit for '12345' is '1'

Validation calculations for '123451':

i  nᵢ  p[i,nᵢ]  c
------------------
0  1      1     1
1  5      8     9
2  4      7     2
3  3      6     8
4  2      5     3
5  1      2     0

The validation for '123451' is correct.

Validation calculations for '123459':

i  nᵢ  p[i,nᵢ]  c
------------------
0  9      9     9
1  5      8     1
2  4      7     8
3  3      6     2
4  2      5     7
5  1      2     5

The validation for '123459' is incorrect.

The check digit for '123456789012' is '0'

The validation for '1234567890120' is correct.

The validation for '1234567890129' is incorrect.
```