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.
- Task
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.
- Related task
11l
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
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
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
a2n=: (+#)@ NB. add 2^n
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
Task examples:
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
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]];
def task:
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 \($v).\n" );
task- Output:
As for #Wren.
Julia
const multiplicationtable = [
0 1 2 3 4 5 6 7 8 9;
1 2 3 4 0 6 7 8 9 5;
2 3 4 0 1 7 8 9 5 6;
3 4 0 1 2 8 9 5 6 7;
4 0 1 2 3 9 5 6 7 8;
5 9 8 7 6 0 4 3 2 1;
6 5 9 8 7 1 0 4 3 2;
7 6 5 9 8 2 1 0 4 3;
8 7 6 5 9 3 2 1 0 4;
9 8 7 6 5 4 3 2 1 0]
const permutationtable = [
0 1 2 3 4 5 6 7 8 9;
1 5 7 6 2 8 3 0 9 4;
5 8 0 3 7 9 6 1 4 2;
8 9 1 6 0 4 3 5 2 7;
9 4 5 3 1 2 6 8 7 0;
4 2 8 6 5 7 3 9 0 1;
2 7 9 3 8 0 6 4 1 5;
7 0 4 6 9 1 3 2 5 8]
const inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]
"""
verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)
Calculate the Verhoeff checksum over `n`.
Terse mode or with single argument: return true if valid (last digit is a correct check digit).
If checksum mode, return the expected correct checksum digit.
If validation mode, return true if last digit checks correctly.
"""
function verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)
verbose && println("\n", validate ? "Validation" : "Check digit",
" calculations for '$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]
if not validate: digits.add 0
var val = n
while val != 0:
digits.add val mod 10
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( $int.chars < 8 );
}
- Output:
Checkdigit calculation for 236: i ni p(i, ni) c 0 0 0 0 1 6 3 3 2 3 3 1 3 2 1 2 Checkdigit: 3 Validation calculation for 2363: i ni p(i, ni) c 0 3 3 3 1 6 3 1 2 3 3 4 3 2 1 0 Checkdigit: correct Validation calculation for 2369: i ni p(i, ni) c 0 9 9 9 1 6 3 6 2 3 3 8 3 2 1 7 Checkdigit: incorrect Checkdigit calculation for 12345: i ni p(i, ni) c 0 0 0 0 1 5 8 8 2 4 7 1 3 3 6 7 4 2 5 2 5 1 2 4 Checkdigit: 1 Validation calculation for 123451: i ni p(i, ni) c 0 1 1 1 1 5 8 9 2 4 7 2 3 3 6 8 4 2 5 3 5 1 2 0 Checkdigit: correct Validation calculation for 123459: i ni p(i, ni) c 0 9 9 9 1 5 8 1 2 4 7 8 3 3 6 2 4 2 5 7 5 1 2 5 Checkdigit: incorrect Checkdigit calculation for 123456789012: Checkdigit: 0 Validation calculation for 1234567890120: Checkdigit: correct Validation calculation for 1234567890129: Checkdigit: incorrect
V (Vlang)
const d = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0],
]
const inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]
const p = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
[5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
[9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
[2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
[7, 0, 4, 6, 9, 1, 3, 2, 5, 8],
]
fn verhoeff(ss string, validate bool, table bool) int {
mut s:= ss
if table {
mut t := "Check digit"
if validate {
t = "Validation"
}
println("$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
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.