CheckDigits.Net 1.1.0

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// Install CheckDigits.Net as a Cake Addin
#addin nuget:?package=CheckDigits.Net&version=1.1.0

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CheckDigits.Net

CheckDigits.Net brings together in one library an extensive collection of different check digit algorithms. CheckDigits.Net has the goal that each algorithm supported be optimized, be resilient to malformed input and that memory allocations be minimized or eliminated completely. Benchmarks for each algorithm are provided to demonstrate performance over a range of values and the memory allocation (if any).

Benchmarks have shown that the optimized versions of the algorithms in CheckDigits.Net are up to 10X-50X faster than those in popular Nuget packages.

Check Digit Overview
ISO/IEC 7064 Algorithms
Supported Algorithms
Value/Identifier Types and Associated Algorithms
Using CheckDigits.Net
Algorithm Descriptions
Benchmarks
Release History/Release Notes

Check Digit Overview

Check digits are a useful tool for detecting human transcription errors. By embedding a check digit in a piece of information it is possible to detect common data entry errors early, often before performing more extensive and time consuming processing.

Typical errors that can be detected by check digit algorithms include:

Single digit transcription errors (any single digit in a value being entered incorrectly).
Two digit transposition errors (two adjacent digits being swapped, i.e. ab → ba).
Twin errors (two identical digits being replaced by another pair, i.e. aa → bb).
Two digit jump transpositions (two digits separated by one position being swapped, i.e. abc → cba).
Jump twin errors (two identical digits separated by one position being replaced by another pair, i.e. aba → cbc).

Check digit algorithms attempt to balance detection capabilities with the cost in execution time and/or the complexity to implement.

Note also that if a value has a valid check digit, it does not imply that the value is valid, only that the value was transcribed correctly. There may be other requirements that are specific to the type of value that could cause a value with a valid check digit to be considered incorrect/invalid.

ISO/IEC 7064 Algorithms

The ISO/IEC 7064 standard defines a family of algorithms capable of detecting a broad range of errors including all single character transcription errors as well as all or nearly all two character transposition errors, two character jump transposition errors, circular shift errors and double transcription errors (two separate single transcription errors in a single value). The algorithms are suitable for numeric strings, alphabetic strings, alphanumeric strings and can be extended to handle custom character domains beyond ASCII alphanumeric characters.

ISO/IEC 7064 algorithms fall into different categories. Pure system algorithms use a single modulus value and a radix value and can generate one or two check characters, depending on the algorithm. If a pure system algorithm generates a single check character, the check character produced will either be one of the valid input characters or a single supplementary character that is only valid as a check digit. Hybrid system algorithms use two modulus values, M and M+1, and generate a single check character that will be one of the valid input characters.

While CheckDigits.Net provides optimized implementations of all of the algorithms defined in the ISO/IEC 7064 standard, the standard is flexible enough to support the creation of algorithms for custom alphabets. For example, Annex B of the ISO/IEC 7064 standard demonstrates the creation of a system for the Danish alphabet which includes three additional characters.

CheckDigits.Net includes three classes to support custom alphabets:

Iso7064PureSystemSingleCharacterAlgorithm (generates a single check character, including a supplementary character)
Iso7064PureSystemDoubleCharacterAlgorithm (generates two check characters)
Iso7064HybridSystemAlgorithm (generates a single check character)

Refer to Using CheckDigits.Net for more information about using these classes.

The ISO/IEC 7064:2003 standard is available at https://www.iso.org/standard/31531.html

Supported Algorithms

ABA RTN (Routing Transit Number) Algorithm
Alphanumeric MOD 97-10 Algorithm
Damm Algorithm
IBAN (International Bank Account Number) Algorithm
ISAN (International Standard Audiovisual Number) Algorithm
ISIN (International Securities Identification Number) Algorithm
ISO/IEC 7064 MOD 11,10 Algorithm
ISO/IEC 7064 MOD 11-2 Algorithm
ISO/IEC 7064 MOD 1271-36 Algorithm
ISO/IEC 7064 MOD 27,26 Algorithm
ISO/IEC 7064 MOD 37-2 Algorithm
ISO/IEC 7064 MOD 37-36 Algorithm
ISO/IEC 7064 MOD 661-26 Algorithm
ISO/IEC 7064 MOD 97-10 Algorithm
Luhn Algorithm
Modulus10_1 Algorithm
Modulus10_2 Algorithm
Modulus10_13 Algorithm (UPC/EAN/ISBN-13/etc.)
Modulus11 Algorithm (ISBN-10/ISSN/etc.)
NHS (UK National Health Service) Algorithm
NOID Check Digit Algorithm
NPI (US National Provider Identifier) Algorithm
Verhoeff Algorithm
VIN (Vehicle Identification Number) Algorithm

Value/Identifier Types and Associated Algorithms

Value/Identifier Type	Algorithm
ABA Routing Transit Number	ABA RTN Algorithm
CA Social Insurance Number	Luhn Algorithm
CAS Registry Number	Modulus10 Algorithm
Credit card number	Luhn Algorithm
EAN-8	Modulus10_13 Algorithm
EAN-13	Modulus10_13 Algorithm
Global Release Identifier	ISO/IEC 7064 MOD 37-36 Algorithm
GTIN-8	Modulus10_13 Algorithm
GTIN-12	Modulus10_13 Algorithm
GTIN-13	Modulus10_13 Algorithm
GTIN-14	Modulus10_13 Algorithm
IBAN	IBAN Algorithm
IMEI	Luhn Algorithm
IMO Number	Modulus10 Algorithm
ISAN	ISAN Algorithm
ISBN-10	Modulus11 Algorithm
ISBN-13	Modulus10_13 Algorithm
ISBT Donation Identification Number	ISO/IEC 7064 MOD 37-2 Algorithm
ISIN	ISIN Algorithm
ISMN	Modulus10_13 Algorithm
ISNI	ISO/IEC 7064 MOD 11-2 Algorithm
ISSN	Modulus11 Algorithm
Legal Entity Identifier	Alphanumeric MOD 97-10 Algorithm
UK National Health Service Number	NHS Algorithm
US National Provider Identifier	NPI Algorithm
SSCC	Modulus10_13 Algorithm
Vehicle Identification Number	VIN Algorithm
Universal Loan Identifier	Alphanumeric MOD 97-10 Algorithm
UPC-A	Modulus10_13 Algorithm
UPC-E	Modulus10_13 Algorithm

Using CheckDigits.Net

Add a reference to CheckDigits.Net to your project.

Obtain an instance of the desired check digit algorithm. Either create an instance by using new AlgorithmXyz() or using the static Algorithms class to get a lazily instantiated singleton instance of the desired algorithm.

Calculate a check digit for a value by invoking the TryCalculateCheckDigit method.

Validate a value that contains a check digit by invoking the Validate method.

Examples:

using CheckDigits.Net;

// Create a new instance of the Luhn algorithm.
var algorithm = new LuhnAlgorithm();

// Get a lazily instantiated singleton instance of the Luhn algorithm.
var lazy = Algorithms.Luhn;


// Calculate the check digit for a value that does not already contain a check digit.
var newValue = "123456789012345";
var successful = algorithm.TryCalculateCheckDigit(newValue, out var checkDigit);  // Returns true; checkDigit will equal '2'

// Validate a value that contains a check digit.
var toValidate = "1234567890123452";
var isValid = lazy.Validate(toValidate);    // Returns true

Custom Alphabets for ISO 7064

The three classes that allow the use of custom alphabets are:

Iso7064PureSystemSingleCharacterAlgorithm (generates a single check character, including a supplementary character)
Iso7064PureSystemDoubleCharacterAlgorithm (generates two check characters)
Iso7064HybridSystemAlgorithm (generates a single check character)

To use one of these classes you must first create an instance of a class that implements IAlphabet or ISupplementalCharacterAlphabet. Then you create an instance of the desired generic ISO 7064 class, supplying the algorithm details (including the alphabet) to the class constructor.

The custom Danish alphabet check algorithm covered in Annex B of the ISO/IEC 7064 standard, uses a pure system algorithm that generates two check characters and has a modulus = 29 and radix = 2.

Danish Alphabet Example

public class DanishAlphabet : IAlphabet
{
   // Additional characters:
   // diphthong AE (\u00C6) has value 26
   // slashed O (\u00D8) has value 27
   // A with diaeresis (\u00C4) has value 28
   private const String _validCharacters = "ABCDEFGHIJKLMNOPQRSTUVWXYZ\u00C6\u00D8\u00C4";

   public Int32 CharacterToInteger(Char ch)
      => ch switch
      {
         var x when x >= 'A' && x <= 'Z' => x - 'A',
         '\u00C6' => 26,
         '\u00D8' => 27,
         '\u00C4' => 28,
         _ => -1
      };

   public Char IntegerToCheckCharacter(Int32 checkDigit) => _validCharacters[checkDigit];
}

var checkAlgorithm = new Iso7064PureSystemDoubleCharacterAlgorithm(
    "Danish", 
    "Danish, modulus = 29, radix = 2", 
    29, 
    2, 
    new DanishAlphabet());

// Calculate the check digit for Danish word for sister (uses slashed O instead of i)
var str = "S\u00D8STER";
var successful = checkAlgorithm.TryCalculateCheckDigits(str, out var firstChar, out var secondChar);    // Returns true, firstChar = 'D', secondChar = 'A'


// Validate a value containing check digit(s).
var isValid = checkAlgorithm.Validate("S\u00D8STERDA");     // Returns true

Interfaces

A check digit algorithm is a class that implements two different interfaces. Every algorithm implements ICheckDigitAlgorithm which has properties for getting the algorithm name and algorithm description and a Validate method that accepts a string and returns a boolean value that indicates if the string contains a valid check digit.

Check digit algorithms that use a single character also implement ISingleCheckDigitAlgorithm which has a TryCalculateCheckDigit method that accepts a string value and an out parameter which will contain the calculated check digit or '\0' if it was not possible to calculate the check digit. TryCalculateCheckDigit also returns a boolean value that indicates if the check digit was calculated or not. Mal-formed input such as a null value, an empty string, a string of incorrect length or a string that contains characters that are not valid for the algorithm will return false instead of throwing an exception.

Check digit algorithms that use two character check digits also implement IDoubleCheckDigitAlgorithm. This interface has a TryCalculateCheckDigits method that has two output parameters, one for each check digit.

Note that ISingleCheckDigitAlgorithm and IDoubleCheckDigitAlgorithm are not implemented for algorithms for government issued identifiers (for example, UK NHS numbers and US NPI numbers) or values issued by a single authority (such as ABA Routing Transit Numbers).

The IAlphabet and ISupplementalCharacterAlphabet interfaces are used for ISO/IEC 7064 algorithms with custom alphabets. IAlphabet has two methods: CharacterToInteger, which maps a character in the value being processed to its integer equivalent and IntegerToCheckCharacter which maps a calculated check digit to its character equivalent. ISupplementalCharacterAlphabet extends IAlphabet by adding the CheckCharacterToInteger method which maps a check character to its integer equivalent. ISupplementalCharacterAlphabet is only used by Iso7064PureSystemSingleCharacterAlgorithm.

Algorithm Descriptions

ABA RTN Algorithm

Description

The American Bankers Association (ABA) Routing Transit Number (RTN) algorithm is a modulus 10 algorithm that uses weights 3, 7 and 1. The algorithm can detect all single digit transcription errors and most two digit transposition errors except those where the transposed digits differ by 5 (i.e. 1 ↔ 6, 2 ↔ 7, etc.).

The ABA RTN algorithm only supports validation of check digits and does support calculation of check digits.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - ninth digit
Value length - 9 characters
Class name - AbaRtnAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/ABA_routing_transit_number#Check_digit

Alphanumeric MOD 97-10 Algorithm

Description

The Alphanumeric MOD 97-10 algorithm uses a variation of the ISO/IEC 7064 MOD 97-10 algorithm where alphabetic characters (A-Z) are mapped to integers (10-35) before calculating the check digit. The algorithm is case insensitive and lowercase letters are mapped to their uppercase equivalent before conversion to integers.

Details

Valid characters - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit size - two characters
Check digit value - decimal digits ('0' - '9')
Check digit location - assumed to be the trailing (right-most) characters when validating
Class name - AlphanumericMod97_10Algorithm

Common Applications

Legal Entity Identifier (LEI)
Universal Loan Identifier (ULI)

Links

Wikipedia: https://en.wikipedia.org/wiki/Legal_Entity_Identifier

https://www.govinfo.gov/content/pkg/CFR-2016-title12-vol8/xml/CFR-2016-title12-vol8-part1003-appC.xml

Damm Algorithm

Description

The Damm algorithm was first described by H. Michael Damm in 2004. It is similar to the Verhoeff algorithm in that it can detect all single digit transcription errors and all two digit transposition errors and that it uses a precomputed table instead of modulus operations to calculate the check digit. Unlike the Verhoeff algorithm, the Damm algorithm uses a single quasigroup table of order 10 instead of the multiple tables used by Verhoeff. The implementation of the Damm algorithm provided by CheckDigits.Net uses the table generated from the quasigroup specified on page 111 of Damm's doctoral dissertation.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - DammAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/Damm_algorithm

IBAN Algorithm

Description

The IBAN (International Bank Account Number) algorithm uses a variation of the ISO/IEC 7064 MOD 97-10 algorithm where alphabetic characters (A-Z) are mapped to integers (10-35) before calculating the check digit. Additionally, the first four characters (2 character country code and 2 decimal check digits) are moved to the end of the string before calculating the check digit.

Note that this implementation only confirms that the length of the value is sufficient to calculate the check digits (min length = 5) and that check digit characters in positions 3 & 4 are valid for the string. All other IBAN checks (the leading two characters indicating a valid country code, the check digit positions only contain digits, maximum length, country specific check digits contained in account number, etc.) are left to the application developer.

Details

Valid characters - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit size - two characters
Check digit value - decimal digits ('0' - '9')
Check digit location - character positions 3 & 4 (1-based) when validating
Value minimum length - 5
Class name - IbanAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/International_Bank_Account_Number

ISAN Algorithm

Description

The ISAN (International Standard Audiovisual Number) algorithm uses a variation of the ISO/IEC 7064 MOD 37,36 algorithm and can have either one or two check characters. A full ISAN value consists of 12 hexadecimal digits for the "root" segment, 4 hexadecimal digits for the "episode" segment, an alphanumeric check character calculated for the 16 characters of the root/episode segments and optionally, 8 hexadecimal digits for the version segment and an alphanumeric check character calculated for the 24 characters of the root/episode/version segments. Per https://www.isan.org/docs/isan_check_digit_calculation_v2.0.pdf, both check characters must be correct if the value includes a version segment.

CheckDigits.Net can validate either unformatted ISAN values consisting only of hexadecimal digits and alphanumeric check characters or ISAN values that have been formatted for human readability.

To validate unformatted root+version ISAN values, use the Validate method. The Validate method only checks 26 character unformatted ISAN root+version values. (To check 17 character root/episode only ISAN values, use the ISO/IEC 7064 MOD 37,36 algorithm directly.)

To validate formatted ISAN values, either root/episode values or root/episode/version values, use the ValidateFormatted method. The ValidateFormatted method will check both the format of the value ("ISAN " prefix plus dash characters that separate the value into 4 character groups) and the check character(s) in the value.

An example formatted root/episode ISAN value is ISAN 0000-0000-C36D-002B-K. An example formatted root/episode/version ISAN value is ISAN 0000-0000-C36D-002B-K-0000-0000-E.

Details

Valid characters - hexadecimal characters ('0' - '9', 'A' - 'F')
Check digit size - one character
Check digit value - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit location - the 17th non-format character (and the 26th non-format character for root+version values)
Class name - IsanAlgorithm

Links

https://en.wikipedia.org/wiki/International_Standard_Audiovisual_Number https://www.isan.org/docs/isan_check_digit_calculation_v2.0.pdf https://web.isan.org/public/en/search

ISIN Algorithm

Description

The ISIN (International Securities Identification Number) algorithm uses a variation of the Luhn algorithm and has all of the capabilities of the Luhn algorithm, including the ability to detect all single digit (or character) transcription errors and most two digit transposition errors except 09 → 90 and vice versa.

The algorithm has significant weaknesses. Transpositions of two letters cannot be detected. Additionally, transpositions of a digit character and the letters B, M or X cannot be detected (because B is converted to 11, M to 22 and X to 33 and when combined with another digit, the result is a jump transposition that the Luhn algorithm cannot detect).

Details

Valid characters - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Value length - 12
Class name - IsinAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/International_Securities_Identification_Number

ISO/IEC 7064 MOD 11,10 Algorithm

The ISO/IEC 7064 MOD 11,10 algorithm is a hybrid system algorithm (with M = 10 and M+1 = 11) that is suitable for use with numeric strings. It generates a single check character that is a decimal digit.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - Iso7064Mod11_10Algorithm

ISO/IEC 7064 MOD 11-2 Algorithm

The ISO/IEC 7064 MOD 11-2 algorithm is a pure system algorithm (with modulus 11 and radix 2) that is suitable for use with numeric strings. It generates a single check character that is either a decimal digit or a supplementary 'X' character.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - either decimal digit ('0' - '9') or an uppercase 'X'
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - Iso7064Mod11_2Algorithm

Common Applications

International Standard Name Identifier (ISNI)

ISO/IEC 7064 MOD 1271-36 Algorithm

The ISO/IEC 7064 MOD 1271-36 algorithm is a pure system algorithm (with modulus 1271 and radix 36) that is suitable for use with alphanumeric strings. It generates two check alphanumeric characters.

Details

Valid characters - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit size - two characters
Check digit value - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit location - assumed to be the trailing (right-most) characters when validating
Class name - Iso7064Mod1271_36Algorithm

ISO/IEC 7064 MOD 27,26 Algorithm

The ISO/IEC 7064 MOD 27,26 algorithm is a hybrid system algorithm (with M = 26 and M+1 = 27) that is suitable for use with alphabetic strings. It generates a single check character that is an alphabetic character.

Details

Valid characters - alphabetic characters ('A' - 'Z')
Check digit size - one character
Check digit value - alphabetic characters ('A' - 'Z')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - Iso7064Mod27_26Algorithm

ISO/IEC 7064 MOD 37-2 Algorithm

The ISO/IEC 7064 MOD 37-2 algorithm is a pure system algorithm (with modulus 37 and radix 2) that suitable for use with alphanumeric strings. It generates a single check character that is either an alphanumeric character or a supplementary '*' character.

Details

Valid characters - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit size - one character
Check digit value - either decimal digit ('0' - '9', 'A' - 'Z') or an asterisk '*'
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - Iso7064Mod37_2Algorithm

ISO/IEC 7064 MOD 37,36 Algorithm

The ISO/IEC 7064 MOD 37,36 algorithm is a hybrid system algorithm (with M = 36 and M+1 = 37) that is suitable for use with alphanumeric strings. It generates a single check character that is an alphanumeric character.

Details

Valid characters - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit size - one character
Check digit value - alphanumeric characters ('0' - '9', 'A' - 'Z')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - Iso7064Mod37_36Algorithm

Common Applications

Global Release Identifier (GRid)

Common Applications

International Society of Blood Transfusion (ISBT) Donation Identification Numbers

ISO/IEC 7064 MOD 661-26 Algorithm

The ISO/IEC 7064 MOD 661-26 algorithm is a pure system algorithm (with modulus 661 and radix 26) that is suitable for use with alphabetic strings. It generates two check alphabetic characters.

Details

Valid characters - alphabetic characters ('A' - 'Z')
Check digit size - two characters
Check digit value - alphabetic characters ('A' - 'Z')
Check digit location - assumed to be the trailing (right-most) characters when validating
Class name - Iso7064Mod661_26Algorithm

ISO/IEC 7064 MOD 97-10 Algorithm

The ISO/IEC 7064 MOD 97-10 algorithm is a pure system algorithm (with modulus 97 and radix 210) that is suitable for use with numeric strings. It generates a two numeric check digits.

Note: the ISO/IEC 7064 MOD 97-10 algorithm is the basis of a number of check digit algorithms that first map alphabetic characters to numbers between 10 and 35. Examples include International Bank Account Numbers (IBAN) and Universal Loan Identifiers (ULI). However this implementation is limited to values containing only decimal digits. Other algorithms will handle values like IBAN and ULI and perform the mapping of alphabetic characters internally.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - two characters
Check digit value - decimal digits ('0' - '9')
Check digit location - assumed to be the trailing (right-most) characters when validating
Class name - Iso7064Mod97_10Algorithm

Luhn Algorithm

Description

The Luhn algorithm is a modulus 10 algorithm that was developed in 1960 by Hans Peter Luhn. It can detect all single digit transcription errors and most two digit transposition errors except 09 → 90 and vice versa. It can also detect most twin errors (i.e. 11 ↔ 44) except 22 ↔ 55, 33 ↔ 66 and 44 ↔ 77.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - LuhnAlgorithm

Common Applications

Credit card numbers
International Mobile Equipment Identity (IMEI) numbers
Canadian Social Insurance Number (SIN)

Links

Wikipedia: https://en.wikipedia.org/wiki/Luhn_algorithm

Modulus10_1 Algorithm

The Modulus10 algorithm uses modulus 10 and each digit is weighted by its position in the value, starting with weight 1 for the right-most non-check digit character.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - either decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Max length - 9 characters when generating a check digit; 10 characters when validating
Class name - Modulus10_1Algorithm

Common Applications

Chemical Abstracts Service (CAS) Registry Number

Links

Wikipedia: https://en.wikipedia.org/wiki/CAS_Registry_Number

Modulus10_2 Algorithm

The Modulus10 algorithm uses modulus 10 and each digit is weighted by its position in the value, starting with weight 2 for the right-most non-check digit character.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - either decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Max length - 9 characters when generating a check digit; 10 characters when validating
Class name - Modulus10_2Algorithm

Common Applications

International Maritime Organization (IMO) Number

Links

Wikipedia: https://en.wikipedia.org/wiki/IMO_number

Modulus10_13 Algorithm

Description

The Modulus10_13 algorithm is a widely used modulus 10 algorithm that uses weights 1 and 3 (odd positions have weight 3, even positions have weight 1). It can detect all single digit transcription errors and ~80% of two digit transposition errors (except where the transposed digits have a difference of 5, i.e. 1 ↔ 6, 2 ↔ 7, etc.). The algorithm cannot detect two digit jump transpositions.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - Modulus10_13Algorithm

Common Applications

Global Trade Item Number (GTIN-8, GTIN-12, GTIN-13, GTIN-14)
International Article Number/European Article Number (EAN-8, EAN-13)
International Standard Book Number, starting January 1, 2007 (ISBN-13)
International Standard Music Number (ISMN)
Serial Shipping Container Code (SSCC)
Universal Product Code (UPC-A, UPC-E)

Links

Wikipedia: https://en.wikipedia.org/wiki/Universal_Product_Code#Check_digit_calculation https://en.wikipedia.org/wiki/International_Article_Number#Calculation_of_checksum_digit

Modulus11 Algorithm

Description

The Modulus11 algorithm uses modulus 11 and each digit is weighted by its position in the value, starting from the right-most digit. Prior to the existence of the Verhoeff algorithm and the Damm algorithm it was popular because it was able to detect two digit transposition errors while using only a single character. However, because it used modulus 11, the check digit could not be a single decimal digit. Commonly an 'X' character was used when the modulus operation resulted in a value of 10. This meant that identifiers that used the Modulus11 algorithm could not be stored as numbers and instead must be strings.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - either decimal digit ('0' - '9') or an uppercase 'X'
Check digit location - assumed to be the trailing (right-most) character when validating
Max length - 9 characters when generating a check digit; 10 characters when validating
Class name - Modulus11Algorithm

Common Applications

International Standard Book Number, prior to January 1, 2007 (ISBN-10)
International Standard Serial Number (ISSN)

Links

Wikipedia: https://en.wikipedia.org/wiki/ISBN#ISBN-10_check_digits https://en.wikipedia.org/wiki/ISSN

NHS Algorithm

Description

UK National Health Service (NHS) identifiers use a variation of the Modulus 11 algorithm. However, instead of generating 11 possible values for the check digit, the NHS algorithm does not allow a remainder of 10 (the 'X' character used by the Modulus 11 algorithm). Any possible NHS number that would generate a remainder of 10 is not allowed and those numbers are not issued. This means that the check digit for a NHS number remains '0' - '9'. The NHS algorithm retains all error detecting capabilities of the Modulus 11 algorithm (detecting all single digit transcription errors and all two digit transposition errors).

The NHS algorithm only supports validation of check digits and does support calculation of check digits.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Value length - 10 characters
Class name - NhsAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/NHS_number#Format,_number_ranges,_and_check_characters https://www.datadictionary.nhs.uk/attributes/nhs_number.html

NOID Check Digit Algorithm

Description

The NOID (Nice Opaque Identifier) Check Digit Algorithm is used by systems that deal with persistent identifiers (for example, ARK (Archival Resource Key) identifiers). The algorithm can detect single character transcription errors and two character transposition errors for values that are less than 29 characters in length. If the value is 29 character in length or greater then the algorithm is slightly less capable. The algorithm operates on lower case betanumeric characters (i.e. alphanumeric characters, minus vowels, including 'y', and the letter 'l'). The use of betanumeric characters reduces the likelihood that an identifier would equal a recognizable word or that the digits 0 or 1 could be confused for the letters 'o' or 'l'.

Details

Valid characters - betanumeric characters ('0123456789bcdfghjkmnpqrstvwxz')
Check digit size - one character
Check digit value - betanumeric characters ('0123456789bcdfghjkmnpqrstvwxz')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - NcdAlgorithm

Links

https://metacpan.org/dist/Noid/view/noid#NOID-CHECK-DIGIT-ALGORITHM

NPI Algorithm

Description

US National Provider Identifiers (NPI) use the Luhn algorithm to calculate the check digit located in the trailing (right-most) position. However, before calculating, the value is prefixed with a constant "80840" and the check digit is calculated using the entire 15 digit string. The resulting check digit has all the capabilities of the base Luhn algorithm (detecting all single digit transcription errors and most two digit transposition errors except 09 → 90 and vice versa as well as most twin errors (i.e. 11 ↔ 44) except 22 ↔ 55, 33 ↔ 66 and 44 ↔ 77.

(You can create and validate NPI check digits using the standard Luhn algorithm by first prefixing your value with "80840". However, CheckDigits.Net's implementation of the NPI algorithm handles the prefix internally and without allocating an extra string.)

The NPI algorithm only supports validation of check digits and does support calculation of check digits.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Value length - 10 characters
Class name - NpiAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/National_Provider_Identifier

Verhoeff Algorithm

Description

The Verhoeff algorithm was the first algorithm using a single decimal check digit that was capable of detecting all single digit transcription errors and all two digit transposition errors. It was first described by Jacobus Verhoeff in 1969. Prior to Verhoeff it was believed that it was not possible to define an algorithm that used a single decimal check digit that could detect both all single digit transcription errors and all two digit transposition errors. Verhoeff's algorithm does not use modulus operations and instead uses a dihedral group (typically implemented as a set of lookup tables). Additionally, Verhoeff's algorithm can detect many, though not all, twin errors, two digit jump transpositions and jump twin errors.

Details

Valid characters - decimal digits ('0' - '9')
Check digit size - one character
Check digit value - decimal digit ('0' - '9')
Check digit location - assumed to be the trailing (right-most) character when validating
Class name - VerhoeffAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/Verhoeff_algorithm

VIN Algorithm

Description

The VIN (Vehicle Identification Number) algorithm is used on the VIN of vehicles sold in North America (US and Canada). The check digit is the 9th character of the 17 character value. Upper-case alphabetic characters (except 'I', 'O' and 'Q') are allowed in the value and must be transliterated to integer values before weighting, summing and calculating sum modulus 11.

Details

Valid characters - decimal digits ('0' - '9') and upper case letters ('A' - 'Z'), excluding 'I', 'O' and 'Q'
Check digit size - one character
Check digit value - either decimal digit ('0' - '9') or an uppercase 'X'
Check digit location - 9th character of 17
Length - 17 characters
Class name - VinAlgorithm

Links

Wikipedia: https://en.wikipedia.org/wiki/Vehicle_identification_number#Check-digit_calculation

Benchmarks

The methodology for the general algorithms is to generate values for the benchmarks by taking substrings of lengths 3, 6, 9, etc. from the same randomly generated source string. For the TryCalculateCheckDigit or TryCalculateCheckDigits methods the substring is used as is. For the Validate method benchmarks the substring is appended with the check character or characters that make the test value valid for the algorithm being benchmarked.

For value specific algorithms, three separate values that are valid for the algorithm being benchmarked are used.

TryCalculateCheckDigit/TryCalculateCheckDigits Methods

General Numeric Algorithms

Note that the Modulus10_1, Modulus10_2 and Modulus11 algorithms have a maximum length of 10 (including the check digit) for values being validated so their benchmarks do not cover lengths greater than 10.

Algorithm Name	Value	Mean	Error	StdDev	Allocated
Damm	140	4.949 ns	0.1024 ns	0.0908 ns	-
Damm	140662	8.825 ns	0.0712 ns	0.0666 ns	-
Damm	140662538	14.690 ns	0.2001 ns	0.1774 ns	-
Damm	140662538042	19.815 ns	0.1659 ns	0.1471 ns	-
Damm	140662538042551	24.766 ns	0.1932 ns	0.1713 ns	-
Damm	140662538042551028	29.666 ns	0.1946 ns	0.1725 ns	-
Damm	140662538042551028265	35.442 ns	0.5445 ns	0.5093 ns	-

ISO/IEC 706 11,10	140	7.461 ns	0.0557 ns	0.0465 ns	-
ISO/IEC 706 11,10	140662	10.676 ns	0.0782 ns	0.0731 ns	-
ISO/IEC 706 11,10	140662538	14.477 ns	0.1290 ns	0.1144 ns	-
ISO/IEC 706 11,10	140662538042	18.263 ns	0.2106 ns	0.1970 ns	-
ISO/IEC 706 11,10	140662538042551	21.087 ns	0.1063 ns	0.0942 ns	-
ISO/IEC 706 11,10	140662538042551028	23.131 ns	0.2303 ns	0.2042 ns	-
ISO/IEC 706 11,10	140662538042551028265	24.776 ns	0.1663 ns	0.1474 ns	-

ISO/IEC 706 11-2	140	6.268 ns	0.1064 ns	0.0995 ns	-
ISO/IEC 706 11-2	140662	10.061 ns	0.1256 ns	0.1175 ns	-
ISO/IEC 706 11-2	140662538	13.671 ns	0.2918 ns	0.2730 ns	-
ISO/IEC 706 11-2	140662538042	17.033 ns	0.1795 ns	0.1679 ns	-
ISO/IEC 706 11-2	140662538042551	20.707 ns	0.2469 ns	0.2189 ns	-
ISO/IEC 706 11-2	140662538042551028	24.420 ns	0.1823 ns	0.1616 ns	-
ISO/IEC 706 11-2	140662538042551028265	27.453 ns	0.1923 ns	0.1799 ns	-

ISO/IEC 706 97-10	140	6.853 ns	0.1224 ns	0.1085 ns	-
ISO/IEC 706 97-10	140662	10.487 ns	0.1345 ns	0.1258 ns	-
ISO/IEC 706 97-10	140662538	15.189 ns	0.1493 ns	0.1247 ns	-
ISO/IEC 706 97-10	140662538042	18.234 ns	0.1331 ns	0.1180 ns	-
ISO/IEC 706 97-10	140662538042551	21.893 ns	0.3501 ns	0.3275 ns	-
ISO/IEC 706 97-10	140662538042551028	25.735 ns	0.2219 ns	0.2076 ns	-
ISO/IEC 706 97-10	140662538042551028265	28.758 ns	0.1250 ns	0.0976 ns	-

Luhn	140	7.013 ns	0.1099 ns	0.1028 ns	-
Luhn	140662	10.537 ns	0.1623 ns	0.1518 ns	-
Luhn	140662538	13.909 ns	0.1060 ns	0.0991 ns	-
Luhn	140662538042	17.530 ns	0.1428 ns	0.1266 ns	-
Luhn	140662538042551	21.001 ns	0.2169 ns	0.2029 ns	-
Luhn	140662538042551028	24.310 ns	0.2837 ns	0.2654 ns	-
Luhn	140662538042551028265	27.940 ns	0.2464 ns	0.2184 ns	-

Modulus10_13	140	6.798 ns	0.1453 ns	0.1359 ns	-
Modulus10_13	140662	10.110 ns	0.2074 ns	0.1940 ns	-
Modulus10_13	140662538	12.569 ns	0.1022 ns	0.0853 ns	-
Modulus10_13	140662538042	16.103 ns	0.1472 ns	0.1229 ns	-
Modulus10_13	140662538042551	18.845 ns	0.2321 ns	0.2171 ns	-
Modulus10_13	140662538042551028	22.300 ns	0.1369 ns	0.1214 ns	-
Modulus10_13	140662538042551028265	25.200 ns	0.2025 ns	0.1795 ns	-

Modulus10_1	140	4.139 ns	0.0645 ns	0.0603 ns	-
Modulus10_1	140662	5.800 ns	0.0984 ns	0.0920 ns	-
Modulus10_1	140662538	7.435 ns	0.0742 ns	0.0620 ns	-

Modulus10_2	140	3.952 ns	0.0486 ns	0.0431 ns	-
Modulus10_2	140662	5.621 ns	0.1259 ns	0.1178 ns	-
Modulus10_2	140662538	7.305 ns	0.0875 ns	0.0776 ns	-

Modulus11	140	4.415 ns	0.0479 ns	0.0400 ns	-
Modulus11	140662	6.528 ns	0.1075 ns	0.1005 ns	-
Modulus11	140662538	7.811 ns	0.1584 ns	0.1945 ns	-

Verhoeff	140	10.665 ns	0.1498 ns	0.1402 ns	-
Verhoeff	140662	18.160 ns	0.0953 ns	0.0796 ns	-
Verhoeff	140662538	25.813 ns	0.1021 ns	0.0853 ns	-
Verhoeff	140662538042	33.391 ns	0.3761 ns	0.2936 ns	-
Verhoeff	140662538042551	40.823 ns	0.2580 ns	0.2413 ns	-
Verhoeff	140662538042551028	48.616 ns	0.4191 ns	0.3921 ns	-
Verhoeff	140662538042551028265	56.447 ns	0.5107 ns	0.4777 ns	-

General Alphabetic Algorithms

Algorithm Name	Value	Mean	Error	StdDev	Allocated
ISO/IEC 7064 MOD 27,26	EGR	7.323 ns	0.0744 ns	0.0660 ns	-
ISO/IEC 7064 MOD 27,26	EGRNML	10.075 ns	0.0852 ns	0.0711 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOC	13.165 ns	0.1768 ns	0.1567 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECU	16.666 ns	0.1215 ns	0.1137 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIK	20.371 ns	0.1702 ns	0.1508 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWW	22.317 ns	0.1799 ns	0.1682 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWWVVO	25.042 ns	0.1730 ns	0.1533 ns	-

ISO/IEC 7064 MOD 661-26	EGR	6.285 ns	0.1391 ns	0.1161 ns	-
ISO/IEC 7064 MOD 661-26	EGRNML	9.172 ns	0.1611 ns	0.1507 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOC	11.706 ns	0.0904 ns	0.0755 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECU	16.000 ns	0.1052 ns	0.0932 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIK	20.669 ns	0.2951 ns	0.2616 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWW	23.121 ns	0.2003 ns	0.1874 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWWVVO	27.655 ns	0.0923 ns	0.0771 ns	-

General Alphanumeric Algorithms

Note that the values used for the NOID Check Digit algorithm do not include lengths 3 or 6 so that benchmarks are not run on purely numeric strings.

Algorithm Name	Value	Mean	Error	StdDev	Allocated
AlphanumericMod97_10	U7y	10.957 ns	0.1313 ns	0.1229 ns	-
AlphanumericMod97_10	U7y8SX	20.110 ns	0.1744 ns	0.1632 ns	-
AlphanumericMod97_10	U7y8SXrC0	27.565 ns	0.4840 ns	0.4528 ns	-
AlphanumericMod97_10	U7y8SXrC0O3S	36.799 ns	0.2212 ns	0.2069 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4I	43.957 ns	0.3136 ns	0.2933 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQ	53.902 ns	0.3897 ns	0.3645 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQF4M	60.975 ns	0.4534 ns	0.4241 ns	-

ISO/IEC 7064 MOD 1271-36	U7Y	7.775 ns	0.1203 ns	0.1125 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SX	11.586 ns	0.0878 ns	0.0821 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0	16.392 ns	0.1493 ns	0.1324 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3S	19.021 ns	0.1470 ns	0.1375 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4I	23.149 ns	0.1528 ns	0.1429 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQ	27.458 ns	0.1873 ns	0.1752 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQF4M	32.253 ns	0.3277 ns	0.3066 ns	-

ISO/IEC 7064 MOD 37-2	U7Y	7.287 ns	0.0465 ns	0.0388 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SX	11.315 ns	0.0584 ns	0.0547 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0	15.624 ns	0.1161 ns	0.1086 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3S	20.231 ns	0.1653 ns	0.1546 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4I	24.034 ns	0.2066 ns	0.1831 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQ	28.953 ns	0.1903 ns	0.1589 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQF4M	32.639 ns	0.4190 ns	0.3919 ns	-

ISO/IEC 7064 MOD 37,36	U7Y	7.197 ns	0.0649 ns	0.0608 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SX	10.884 ns	0.1312 ns	0.1227 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0	15.222 ns	0.1170 ns	0.1038 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3S	19.103 ns	0.1590 ns	0.1488 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4I	24.701 ns	0.1302 ns	0.1218 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQ	28.522 ns	0.3561 ns	0.3157 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQF4M	33.024 ns	0.1466 ns	0.1300 ns	-

NOID Check Digit	11404/2h9	10.701 ns	0.0572 ns	0.0535 ns	-
NOID Check Digit	11404/2h9tqb	16.175 ns	0.1153 ns	0.1022 ns	-
NOID Check Digit	11404/2h9tqbxk6	19.212 ns	0.1336 ns	0.1250 ns	-
NOID Check Digit	11404/2h9tqbxk6rw7	22.600 ns	0.1498 ns	0.1328 ns	-
NOID Check Digit	11404/2h9tqbxk6rw7dwm	28.120 ns	0.1829 ns	0.1711 ns	-

Value Specific Algorithms

Note: ABA RTN, NHS and NPI algorithms do not support calculation of check digits, only validation of values containing check digits.

Algorithm Name	Value	Mean	Error	StdDev	Allocated
IBAN	BE00096123456769	35.28 ns	0.211 ns	0.197 ns	-
IBAN	GB00WEST12345698765432	52.85 ns	0.645 ns	0.571 ns	-
IBAN	SC00MCBL01031234567890123456USD	74.39 ns	0.522 ns	0.463 ns	-

ISIN	AU0000XVGZA	29.73 ns	0.588 ns	0.550 ns	-
ISIN	GB000263494	23.10 ns	0.253 ns	0.237 ns	-
ISIN	US037833100	23.02 ns	0.264 ns	0.247 ns	-

VIN	1G8ZG127_WZ157259	41.17 ns	0.607 ns	0.568 ns	-
VIN	1HGEM212_2L047875	40.46 ns	0.332 ns	0.277 ns	-
VIN	1M8GDM9A_KP042788	41.28 ns	0.769 ns	0.719 ns	-

Validate Method

General Numeric Algorithms

All algorithms use a single check digit except ISO/IEC 7064 MOD 97-10 which uses two check digits.

Algorithm Name	Value	Mean	Error	StdDev	Allocated
Damm	1402	6.130 ns	0.1318 ns	0.1233 ns	-
Damm	1406622	10.398 ns	0.1068 ns	0.0999 ns	-
Damm	1406625388	15.985 ns	0.2725 ns	0.2549 ns	-
Damm	1406625380422	21.212 ns	0.2268 ns	0.2122 ns	-
Damm	1406625380425518	26.353 ns	0.1993 ns	0.1864 ns	-
Damm	1406625380425510280	31.554 ns	0.3449 ns	0.3226 ns	-
Damm	1406625380425510282654	37.529 ns	0.2162 ns	0.1917 ns	-

ISO/IEC 7064 MOD 11,10	1409	7.648 ns	0.1277 ns	0.1195 ns	-
ISO/IEC 7064 MOD 11,10	1406623	11.939 ns	0.1648 ns	0.1541 ns	-
ISO/IEC 7064 MOD 11,10	1406625381	16.038 ns	0.1963 ns	0.1836 ns	-
ISO/IEC 7064 MOD 11,10	1406625380426	20.212 ns	0.2354 ns	0.2202 ns	-
ISO/IEC 7064 MOD 11,10	1406625380425514	24.405 ns	0.2345 ns	0.2194 ns	-
ISO/IEC 7064 MOD 11,10	1406625380425510286	28.210 ns	0.2072 ns	0.1730 ns	-
ISO/IEC 7064 MOD 11,10	1406625380425510282657	32.046 ns	0.1599 ns	0.1248 ns	-

ISO/IEC 7064 MOD 11-2	140X	5.999 ns	0.0537 ns	0.0476 ns	-
ISO/IEC 7064 MOD 11-2	1406628	9.602 ns	0.1235 ns	0.1156 ns	-
ISO/IEC 7064 MOD 11-2	1406625380	13.766 ns	0.2956 ns	0.3163 ns	-
ISO/IEC 7064 MOD 11-2	1406625380426	16.767 ns	0.3326 ns	0.2949 ns	-
ISO/IEC 7064 MOD 11-2	1406625380425511	20.032 ns	0.2177 ns	0.2037 ns	-
ISO/IEC 7064 MOD 11-2	140662538042551028X	24.437 ns	0.1978 ns	0.1850 ns	-
ISO/IEC 7064 MOD 11-2	1406625380425510282651	27.452 ns	0.2728 ns	0.2552 ns	-

ISO/IEC 7064 MOD 97-10	14066	7.052 ns	0.0363 ns	0.0303 ns	-
ISO/IEC 7064 MOD 97-10	14066262	10.809 ns	0.1203 ns	0.1125 ns	-
ISO/IEC 7064 MOD 97-10	14066253823	15.062 ns	0.2334 ns	0.2184 ns	-
ISO/IEC 7064 MOD 97-10	14066253804250	18.767 ns	0.1066 ns	0.0945 ns	-
ISO/IEC 7064 MOD 97-10	14066253804255112	22.839 ns	0.2047 ns	0.1815 ns	-
ISO/IEC 7064 MOD 97-10	14066253804255102853	25.885 ns	0.1921 ns	0.1703 ns	-
ISO/IEC 7064 MOD 97-10	14066253804255102826587	29.362 ns	0.3131 ns	0.2928 ns	-

Luhn	1404	7.285 ns	0.1008 ns	0.0943 ns	-
Luhn	1406628	11.476 ns	0.2376 ns	0.2106 ns	-
Luhn	1406625382	14.897 ns	0.1170 ns	0.1037 ns	-
Luhn	1406625380421	19.188 ns	0.2519 ns	0.2356 ns	-
Luhn	1406625380425514	22.925 ns	0.2653 ns	0.2482 ns	-
Luhn	1406625380425510285	27.039 ns	0.3149 ns	0.2945 ns	-
Luhn	1406625380425510282651	30.417 ns	0.3339 ns	0.3123 ns	-

Modulus10_13	1403	7.743 ns	0.0618 ns	0.0548 ns	-
Modulus10_13	1406627	11.071 ns	0.1356 ns	0.1269 ns	-
Modulus10_13	1406625385	14.656 ns	0.1905 ns	0.1689 ns	-
Modulus10_13	1406625380425	19.068 ns	0.2373 ns	0.2103 ns	-
Modulus10_13	1406625380425518	22.867 ns	0.4330 ns	0.3839 ns	-
Modulus10_13	1406625380425510288	26.763 ns	0.3102 ns	0.2901 ns	-
Modulus10_13	1406625380425510282657	29.478 ns	0.2864 ns	0.2391 ns	-

Modulus10_1	1401	4.642 ns	0.1087 ns	0.1017 ns	-
Modulus10_1	1406628	6.595 ns	0.1182 ns	0.1048 ns	-
Modulus10_1	1406625384	8.193 ns	0.0861 ns	0.0763 ns	-

Modulus10_2	1406	5.222 ns	0.0586 ns	0.0489 ns	-
Modulus10_2	1406627	7.420 ns	0.1605 ns	0.1340 ns	-
Modulus10_2	1406625389	9.537 ns	0.1169 ns	0.1093 ns	-

Modulus11	1406	6.240 ns	0.0799 ns	0.0709 ns	-
Modulus11	1406625	8.356 ns	0.0805 ns	0.0753 ns	-
Modulus11	1406625388	9.767 ns	0.1164 ns	0.1089 ns	-

Verhoeff	1401	13.822 ns	0.0920 ns	0.0815 ns	-
Verhoeff	1406625	22.863 ns	0.1531 ns	0.1432 ns	-
Verhoeff	1406625388	32.046 ns	0.3094 ns	0.2584 ns	-
Verhoeff	1406625380426	41.280 ns	0.4174 ns	0.3700 ns	-
Verhoeff	1406625380425512	50.391 ns	0.5977 ns	0.5591 ns	-
Verhoeff	1406625380425510285	58.905 ns	0.8780 ns	0.7332 ns	-
Verhoeff	1406625380425510282655	67.668 ns	0.7107 ns	0.6648 ns	-

General Alphabetic Algorithms

ISO/IEC 7064 MOD 27,26 uses a single check character. ISO/IEC 7064 MOD 661-26 uses two check characters.

Algorithm Name	Value	Mean	Error	StdDev	Allocated
ISO/IEC 7064 MOD 27,26	EGRS	7.528 ns	0.1329 ns	0.1243 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLU	11.776 ns	0.1623 ns	0.1439 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCB	16.419 ns	0.2130 ns	0.1779 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUA	20.097 ns	0.1830 ns	0.1712 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKA	24.309 ns	0.2585 ns	0.2291 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWWY	28.131 ns	0.2375 ns	0.2106 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWWVVOQ	32.378 ns	0.2915 ns	0.2727 ns	-

ISO/IEC 7064 MOD 661-26	EGRSE	7.655 ns	0.0919 ns	0.0860 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLDR	11.261 ns	0.1051 ns	0.0983 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCCK	15.377 ns	0.2277 ns	0.2018 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUZJ	18.679 ns	0.2463 ns	0.2304 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKFQ	22.296 ns	0.1711 ns	0.1429 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWWQN	26.118 ns	0.2422 ns	0.2147 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWWVVORC	29.567 ns	0.6012 ns	0.6433 ns	-

General Alphanumeric Algorithms

AlphanumericMod97_10 algorithm and ISO/IEC 7064 MOD 1271-36 uses two check characters. ISO/IEC 7064 MOD 37-2, ISO/IEC 7064 MOD 37,36 and NOID Check Digit algorithms use a single check character.

Note also that the values used for the NOID Check Digit algorithm do not include lengths 3 or 6 so that benchmarks are not run on purely numeric strings.

Algorithm Name	Value	Mean	Error	StdDev	Allocated
AlphanumericMod97_10	U7y46	12.354 ns	0.0603 ns	0.0534 ns	-
AlphanumericMod97_10	U7y8SX89	20.738 ns	0.0957 ns	0.0799 ns	-
AlphanumericMod97_10	U7y8SXrC087	28.463 ns	0.2733 ns	0.2423 ns	-
AlphanumericMod97_10	U7y8SXrC0O3S38	36.453 ns	0.2528 ns	0.2365 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4I27	44.678 ns	0.2166 ns	0.2026 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQ54	54.195 ns	0.3931 ns	0.3677 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQF4M21	61.407 ns	0.3487 ns	0.3262 ns	-

ISO/IEC 7064 MOD 1271-36	U7YM0	8.423 ns	0.0587 ns	0.0549 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXOR	13.001 ns	0.1098 ns	0.1028 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0FI	17.476 ns	0.1368 ns	0.1279 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SX4	21.074 ns	0.1622 ns	0.1517 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4I9D	26.002 ns	0.2291 ns	0.2143 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQYI	30.088 ns	0.2033 ns	0.1803 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQF4M44	33.630 ns	0.2810 ns	0.2346 ns	-

ISO/IEC 7064 MOD 37-2	U7YZ	7.013 ns	0.0817 ns	0.0764 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXV	11.281 ns	0.1002 ns	0.0837 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0E	15.225 ns	0.1731 ns	0.1619 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SU	19.720 ns	0.1730 ns	0.1618 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IB	24.069 ns	0.2132 ns	0.1994 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQG	28.596 ns	0.2424 ns	0.2267 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQF4MF	32.949 ns	0.2376 ns	0.2223 ns	-

ISO/IEC 7064 MOD 37,36	U7YW	8.342 ns	0.0490 ns	0.0434 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SX8	12.235 ns	0.1005 ns	0.0940 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0E	16.822 ns	0.1493 ns	0.1323 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SR	20.733 ns	0.1190 ns	0.0994 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IT	25.913 ns	0.2772 ns	0.2593 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQD	30.133 ns	0.3057 ns	0.2860 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQF4MP	35.250 ns	0.2788 ns	0.2608 ns	-

NOID Check Digit	11404/2h9m	13.725 ns	0.0985 ns	0.0873 ns	-
NOID Check Digit	11404/2h9tqb0	19.307 ns	0.1813 ns	0.1607 ns	-
NOID Check Digit	11404/2h9tqbxk6d	23.805 ns	0.1584 ns	0.1482 ns	-
NOID Check Digit	11404/2h9tqbxk6rw74	28.676 ns	0.3153 ns	0.2795 ns	-
NOID Check Digit	11404/2h9tqbxk6rw7dwmz	33.666 ns	0.3178 ns	0.2973 ns	-

Value Specific Algorithms

Algorithm Name	Value	Mean	Error	StdDev	Allocated
ABA RTN	111000025	8.862 ns	0.1623 ns	0.1518 ns	-
ABA RTN	122235821	8.692 ns	0.1737 ns	0.1624 ns	-
ABA RTN	325081403	8.684 ns	0.1237 ns	0.1157 ns	-

IBAN	BE71096123456769	22.310 ns	0.2240 ns	0.1980 ns	-
IBAN	GB82WEST12345698765432	34.930 ns	0.3060 ns	0.2870 ns	-
IBAN	SC74MCBL01031234567890123456USD	51.930 ns	0.8720 ns	0.7730 ns	-

ISAN	C594660A8B2E5D22X6DDA3272E	57.740 ns	0.7840 ns	0.6950 ns	-
ISAN	D02C42E954183EE2Q1291C8AEO	54.680 ns	0.7400 ns	0.6560 ns	-
ISAN	E9530C32BC0EE83B269867B20F	54.830 ns	0.6520 ns	0.5780 ns	-

ISAN (Formatted)	ISAN C594-660A-8B2E-5D22-X	49.680 ns	0.5080 ns	0.4750 ns	-
ISAN (Formatted)	ISAN D02C-42E9-5418-3EE2-Q	49.640 ns	0.3700 ns	0.3460 ns	-
ISAN (Formatted)	ISAN E953-0C32-BC0E-E83B-2	47.750 ns	0.4370 ns	0.4090 ns	-
ISAN (Formatted)	ISAN C594-660A-8B2E-5D22-X-6DDA-3272-E	71.010 ns	0.9400 ns	0.8790 ns	-
ISAN (Formatted)	ISAN D02C-42E9-5418-3EE2-Q-1291-C8AE-O	69.900 ns	0.9790 ns	0.8680 ns	-
ISAN (Formatted)	ISAN E953-0C32-BC0E-E83B-2-6986-7B20-F	71.490 ns	0.9130 ns	0.8540 ns	-

ISIN	AU0000XVGZA3	25.624 ns	0.2618 ns	0.2449 ns	-
ISIN	GB0002634946	21.148 ns	0.2497 ns	0.2335 ns	-
ISIN	US0378331005	21.139 ns	0.3062 ns	0.2865 ns	-

NHS	4505577104	11.933 ns	0.1477 ns	0.1309 ns	-
NHS	5301194917	11.898 ns	0.1416 ns	0.1324 ns	-
NHS	9434765919	11.917 ns	0.1627 ns	0.1522 ns	-

NPI	1122337797	15.106 ns	0.2468 ns	0.2309 ns	-
NPI	1234567893	14.986 ns	0.0968 ns	0.0808 ns	-
NPI	1245319599	15.067 ns	0.2008 ns	0.1878 ns	-

VIN	1G8ZG127XWZ157259	40.107 ns	0.3094 ns	0.2743 ns	-
VIN	1HGEM21292L047875	40.206 ns	0.2919 ns	0.2438 ns	-
VIN	1M8GDM9AXKP042788	40.266 ns	0.5329 ns	0.4985 ns	-

Release History/Release Notes

v1.0.0-alpha

Initial limited release. Included algorithms:

ABA RTN (Routing Transit Number) Algorithm
Damm Algorithm
ISIN (International Securities Identification Number) Algorithm
Luhn Algorithm
Modulus10_1 Algorithm
Modulus10_2 Algorithm
Modulus10_13 Algorithm (UPC/EAN/ISBN-13/etc.)
Modulus11 Algorithm (ISBN-10/ISSN/etc.)
NHS (UK National Health Service) Algorithm
NPI (US National Provider Identifier) Algorithm
Verhoeff Algorithm
VIN (Vehicle Identification Number) Algorithm

v1.0.0

Initial release. Additional included algorithms

ISO/IEC 7064 MOD 11,10
ISO/IEC 7064 MOD 11-2
ISO/IEC 7064 MOD 1271-36
ISO/IEC 7064 MOD 27,26
ISO/IEC 7064 MOD 37-2
ISO/IEC 7064 MOD 37,36
ISO/IEC 7064 MOD 661-26
ISO/IEC 7064 MOD 97-10

v1.1.0

Additional included algorithms

AlphanumericMod97_10Algorithm
IbanAlgorithm
IsanAlgorithm (including ValidateFormatted method)

Performance increases for:

ISO/IEC 7064 MOD 1271-36, Validate method ~18% improvement
ISO/IEC 7064 MOD 37-2, Validate method ~17% improvement, TryCalculateCheckDigit method ~20% improvement
ISO/IEC 7064 MOD 37-36, ValidateMethod ~18% improvement, TryCalculateCheckDigit method ~21% improvement

Product	Compatible and additional computed target framework versions.
.NET	net7.0 is compatible. net7.0-android was computed. net7.0-ios was computed. net7.0-maccatalyst was computed. net7.0-macos was computed. net7.0-tvos was computed. net7.0-windows was computed. net8.0 was computed. net8.0-android was computed. net8.0-browser was computed. net8.0-ios was computed. net8.0-maccatalyst was computed. net8.0-macos was computed. net8.0-tvos was computed. net8.0-windows was computed.

Product

.NET

Compatible target framework(s)

Included target framework(s) (in package)

Learn more about Target Frameworks and .NET Standard.

net7.0
- No dependencies.

NuGet packages

This package is not used by any NuGet packages.

GitHub repositories

This package is not used by any popular GitHub repositories.

Version	Downloads	Last updated
2.2.0	1,829	1/25/2024
2.1.0	207	12/5/2023
2.0.0	140	11/21/2023
1.1.0	124	11/18/2023
1.0.0	137	10/26/2023
1.0.0-alpha	98	10/14/2023

1.0.0-alpha

Initial limited release. Included algorithms:
* ABA RTN (Routing Transit Number) Algorithm
* Damm Algorithm
* ISIN (International Securities Identification Number) Algorithm
* Luhn Algorithm
* Modulus10_1 Algorithm
* Modulus10_2 Algorithm
* Modulus10_13 Algorithm (UPC/EAN/ISBN-13/etc.)
* Modulus11 Algorithm (ISBN-10/ISSN/etc.)
* NHS (UK National Health Service) Algorithm
* NPI (US National Provider Identifier) Algorithm
* Verhoeff Algorithm
* VIN (Vehicle Identification Number) Algorithm

1.0.0

Initial release. Additional included algorithms
* ISO/IEC 7064 MOD 11,10
* ISO/IEC 7064 MOD 11-2
* ISO/IEC 7064 MOD 1271-36
* ISO/IEC 7064 MOD 27,26
* ISO/IEC 7064 MOD 37-2
* ISO/IEC 7064 MOD 37,36
* ISO/IEC 7064 MOD 661-26
* ISO/IEC 7064 MOD 97-10

## v1.1.0
Additional included algorithms
* AlphanumericMod97_10Algorithm
* IbanAlgorithm
* IsanAlgorithm (including ValidateFormatted method)

Performance increases for:
* ISO/IEC 7064 MOD 1271-36, Validate method ~18% improvement
* ISO/IEC 7064 MOD 37-2, Validate method ~17% improvement, TryCalculateCheckDigit method ~20% improvement
* ISO/IEC 7064 MOD 37-36, ValidateMethod ~18% improvement, TryCalculateCheckDigit method ~21% improvement

CheckDigits.Net 1.1.0

CheckDigits.Net

Table of Contents

Check Digit Overview

ISO/IEC 7064 Algorithms

Supported Algorithms

Value/Identifier Types and Associated Algorithms

Using CheckDigits.Net

Interfaces

Algorithm Descriptions

ABA RTN Algorithm

Description

Details

Links

Alphanumeric MOD 97-10 Algorithm

Description

Details

Common Applications

Links

Damm Algorithm

Description

Details

Links

IBAN Algorithm

Description

Details

Links

ISAN Algorithm

Description

Details

Links

ISIN Algorithm

Description

Details

Links

ISO/IEC 7064 MOD 11,10 Algorithm

Details

ISO/IEC 7064 MOD 11-2 Algorithm

Details

Common Applications

ISO/IEC 7064 MOD 1271-36 Algorithm

Details

ISO/IEC 7064 MOD 27,26 Algorithm

Details

ISO/IEC 7064 MOD 37-2 Algorithm

Details

ISO/IEC 7064 MOD 37,36 Algorithm

Details

Common Applications

Common Applications

ISO/IEC 7064 MOD 661-26 Algorithm

Details

ISO/IEC 7064 MOD 97-10 Algorithm

Details

Luhn Algorithm

Description

Details

Common Applications

Links

Modulus10_1 Algorithm

Details

Common Applications

Links

Modulus10_2 Algorithm

Details

Common Applications

Links

Modulus10_13 Algorithm

Description

Details

Common Applications

Links

Modulus11 Algorithm

Description

Details

Common Applications

Links

NHS Algorithm

Description

Details