Verhoeff algorithm
- 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
Go
<lang 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)
}
}
}</lang>
- Output:
Identical to Wren example
Julia
<lang 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]
"""
Calculate the Verhoeff checksum over `n`. 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, 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])")
return validate ? c == 0 : inv[c + 1]
end
println("\nThe check digit for '236' is $(verhoeffchecksum(236, false, true)).") println("\nThe validation for '2363' is ", verhoeffchecksum(2363, true, true) ?
"correct" : "incorrect", ".")
println("\nThe validation for '2369' is ", verhoeffchecksum(2369, true, true) ?
"correct" : "incorrect", ".")
println("\nThe check digit for '12345' is $(verhoeffchecksum(12345, false, true)).") println("\nThe validation for '123451' is ", verhoeffchecksum(123451, true, true) ?
"correct" : "incorrect", ".")
println("\nThe validation for '123459' is ", verhoeffchecksum(123459, true, true) ?
"correct" : "incorrect", ".")
println("\nThe check digit for '123456789012' is $(verhoeffchecksum(123456789012, false)).") println("\nThe validation for '1234567890120' is ",
verhoeffchecksum(1234567890120, true) ? "correct." : "incorrect.")
println("\nThe validation for '1234567890129' is ",
verhoeffchecksum(1234567890129, true) ? "correct." : "incorrect.")
</lang>
- Output:
Same as Wren example.
Nim
<lang 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()</lang>
- 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.
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
Raku
Generate the tables rather than hard coding, They're not all that complex.
<lang perl6>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 );
}</lang>
- 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
Wren
<lang ecmascript>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")
}
}</lang>
- 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.