Verhoeff algorithm: Difference between revisions
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{{
;Description
The [https://en.wikipedia.org/wiki/Verhoeff_algorithm 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.
Line 19:
* [[Damm algorithm]]
<br><br>
=={{header|11l}}==
{{trans|Python}}
<syntaxhighlight lang="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)</syntaxhighlight>
{{out}}
The same as in Python.
=={{header|C}}==
<syntaxhighlight lang="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;
}</syntaxhighlight>
{{out}}
<pre>
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.
</pre>
=={{header|C++}}==
<syntaxhighlight lang="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;
}
}
}
</syntaxhighlight>
{{ out }}
<pre>
The same as the Wren example.
</pre>
=={{header|FreeBASIC}}==
{{trans|Wren}}
<syntaxhighlight lang="vbnet">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</syntaxhighlight>
{{out}}
<pre>Same as Wren entry.</pre>
=={{header|F_Sharp|F#}}==
<syntaxhighlight lang="fsharp">
// 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}"
</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|Go}}==
{{trans|Wren}}
<
import "fmt"
Line 98 ⟶ 569:
}
}
}</
{{out}}
Line 104 ⟶ 575:
Identical to Wren example
</pre>
=={{header|J}}==
Implementation:
<syntaxhighlight lang="j">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</syntaxhighlight>
Task examples:
<syntaxhighlight lang="j"> 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 │
</syntaxhighlight>
=={{header|Java}}==
<syntaxhighlight lang="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;
}
</syntaxhighlight>
{{ out }}
<pre>
The same as the Wren example.
</pre>
=={{header|jq}}==
{{trans|Wren}}
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
<syntaxhighlight lang="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</syntaxhighlight>
{{out}}
As for [[#Wren]].
=={{header|Julia}}==
<
0 1 2 3 4 5 6 7 8 9;
1 2 3 4 0 6 7 8 9 5;
Line 131 ⟶ 846:
"""
verhoeffchecksum(n::Integer, validate=true, terse=true, verbose=false)
Calculate the Verhoeff checksum over `n`.
Terse mode or with
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)
Line 158 ⟶ 875:
verhoeffchecksum(args...)
end
</
=={{header|Nim}}==
<
const
Line 242 ⟶ 959:
discard verhoeff(10 * n + 9, true)
except ValueError:
echo getCurrentExceptionMsg()</
{{out}}
Line 302 ⟶ 1,019:
Check digit validation was successful for 1234567890120.
Check digit validation failed for 1234567890129.</pre>
=={{header|Perl}}==
<syntaxhighlight lang="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";
}</syntaxhighlight>
{{out}}
<pre>
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
</pre>
=={{header|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).
<!--<
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #7060A8;">tagset</span><span style="color: #0000FF;">(</span><span style="color: #000000;">9</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)},</span>
Line 367 ⟶ 1,179:
<span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">verhoeff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]&</span><span style="color: #008000;">'9'</span><span style="color: #0000FF;">,</span><span style="color: #004600;">true</span><span style="color: #0000FF;">,</span><span style="color: #000000;">show_workings</span><span style="color: #0000FF;">)!=</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<!--</
{{out}}
<pre>
Line 436 ⟶ 1,248:
The validation for `1234567890129` is incorrect
</pre>
=={{header|Python}}==
<syntaxhighlight lang="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)
</syntaxhighlight>{{out}}Output same as Wren example.
=={{header|Raku}}==
Generate the tables rather than hard coding, They're not all that complex.
<syntaxhighlight lang="raku"
@d[$_][^5].=rotate($_), @d[$_][5..*].=rotate($_) for 1..4;
push @d: [@d[$_].reverse] for flat 1..4, 0;
Line 486 ⟶ 1,361:
validate $check, :verbose( $int.chars < 8 );
validate +($check.chop ~ 9), :verbose( $int.chars < 8 );
}</
{{out}}
<pre>Checkdigit calculation for 236:
Line 550 ⟶ 1,425:
Validation calculation for 1234567890129:
Checkdigit: incorrect</pre>
=={{header|V (Vlang)}}==
{{trans|Go}}
<syntaxhighlight lang="go">const d = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 2, 3, 4, 0, 6, 7, 8, 9, 5],
[2, 3, 4, 0, 1, 7, 8, 9, 5, 6],
[3, 4, 0, 1, 2, 8, 9, 5, 6, 7],
[4, 0, 1, 2, 3, 9, 5, 6, 7, 8],
[5, 9, 8, 7, 6, 0, 4, 3, 2, 1],
[6, 5, 9, 8, 7, 1, 0, 4, 3, 2],
[7, 6, 5, 9, 8, 2, 1, 0, 4, 3],
[8, 7, 6, 5, 9, 3, 2, 1, 0, 4],
[9, 8, 7, 6, 5, 4, 3, 2, 1, 0],
]
const inv = [0, 4, 3, 2, 1, 5, 6, 7, 8, 9]
const p = [
[0, 1, 2, 3, 4, 5, 6, 7, 8, 9],
[1, 5, 7, 6, 2, 8, 3, 0, 9, 4],
[5, 8, 0, 3, 7, 9, 6, 1, 4, 2],
[8, 9, 1, 6, 0, 4, 3, 5, 2, 7],
[9, 4, 5, 3, 1, 2, 6, 8, 7, 0],
[4, 2, 8, 6, 5, 7, 3, 9, 0, 1],
[2, 7, 9, 3, 8, 0, 6, 4, 1, 5],
[7, 0, 4, 6, 9, 1, 3, 2, 5, 8],
]
fn verhoeff(ss string, validate bool, table bool) int {
mut s:= ss
if table {
mut t := "Check digit"
if validate {
t = "Validation"
}
println("$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")
}
}
}</syntaxhighlight>
{{out}}
<pre>
Identical to Wren example
</pre>
=={{header|Wren}}==
{{libheader|Wren-fmt}}
<
var d = [
Line 608 ⟶ 1,566:
System.print("\nThe validation for '%(stc)' is %(v ? "correct" : "incorrect").\n")
}
}</
{{out}}
| |||