CheckDigits.Net 2.0.0

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#r "nuget: CheckDigits.Net, 2.0.0"

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// Install CheckDigits.Net as a Cake Addin
#addin nuget:?package=CheckDigits.Net&version=2.0.0

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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.

Future Algorithms

Is there an algorithm that you would like to see included in CheckDigits.Net? Use the "Contact owners" link on https://www.nuget.org/packages/CheckDigits.Net and let us know. Or contribute to the CheckDigits.Net repository: https://github.com/KnowledgeForwardSolutions/CheckDigits.Net

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
- v1.0.0-alpha
- v1.0.0
- v1.1.0
- v2.0.0

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 (.Net 8)

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.

Previous .Net 7 benchmarks available at https://github.com/KnowledgeForwardSolutions/CheckDigits.Net/blob/main/Documentation/DotNet7Benchmarks.md

Benchmark Details

BenchmarkDotNet v0.13.10, Windows 11 (10.0.22621.2715/22H2/2022Update/SunValley2) Intel Core i7-8700K CPU 3.70GHz (Coffee Lake), 1 CPU, 12 logical and 6 physical cores .NET SDK 8.0.100 [Host] : .NET 8.0.0 (8.0.23.53103), X64 RyuJIT AVX2 DefaultJob : .NET 8.0.0 (8.0.23.53103), X64 RyuJIT AVX2

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	5.381 ns	0.1181 ns	0.1105 ns	-
Damm	140662	11.121 ns	0.0850 ns	0.0796 ns	-
Damm	140662538	16.117 ns	0.1801 ns	0.1684 ns	-
Damm	140662538042	20.952 ns	0.2006 ns	0.1675 ns	-
Damm	140662538042551	25.882 ns	0.2047 ns	0.1915 ns	-
Damm	140662538042551028	31.169 ns	0.2748 ns	0.2436 ns	-
Damm	140662538042551028265	37.167 ns	0.7315 ns	0.6843 ns	-

ISO/IEC 706 11,10	140	6.355 ns	0.0509 ns	0.0476 ns	-
ISO/IEC 706 11,10	140662	10.266 ns	0.0631 ns	0.0590 ns	-
ISO/IEC 706 11,10	140662538	12.386 ns	0.0982 ns	0.0919 ns	-
ISO/IEC 706 11,10	140662538042	15.053 ns	0.1208 ns	0.1130 ns	-
ISO/IEC 706 11,10	140662538042551	18.437 ns	0.1473 ns	0.1378 ns	-
ISO/IEC 706 11,10	140662538042551028	22.820 ns	0.1971 ns	0.1843 ns	-
ISO/IEC 706 11,10	140662538042551028265	26.027 ns	0.1479 ns	0.1384 ns	-

ISO/IEC 706 11-2	140	4.241 ns	0.0141 ns	0.0132 ns	-
ISO/IEC 706 11-2	140662	8.603 ns	0.0292 ns	0.0259 ns	-
ISO/IEC 706 11-2	140662538	11.325 ns	0.0451 ns	0.0400 ns	-
ISO/IEC 706 11-2	140662538042	14.259 ns	0.0477 ns	0.0423 ns	-
ISO/IEC 706 11-2	140662538042551	16.991 ns	0.1129 ns	0.1000 ns	-
ISO/IEC 706 11-2	140662538042551028	14.592 ns	0.0717 ns	0.0636 ns	-
ISO/IEC 706 11-2	140662538042551028265	22.463 ns	0.1754 ns	0.1555 ns	-

ISO/IEC 706 97-10	140	6.887 ns	0.0739 ns	0.0692 ns	-
ISO/IEC 706 97-10	140662	10.281 ns	0.1422 ns	0.1330 ns	-
ISO/IEC 706 97-10	140662538	13.230 ns	0.1022 ns	0.0956 ns	-
ISO/IEC 706 97-10	140662538042	16.044 ns	0.1452 ns	0.1358 ns	-
ISO/IEC 706 97-10	140662538042551	18.855 ns	0.1708 ns	0.1426 ns	-
ISO/IEC 706 97-10	140662538042551028	22.542 ns	0.2155 ns	0.2016 ns	-
ISO/IEC 706 97-10	140662538042551028265	25.380 ns	0.2038 ns	0.1906 ns	-

Luhn	140	5.678 ns	0.0561 ns	0.0497 ns	-
Luhn	140662	10.488 ns	0.0978 ns	0.0915 ns	-
Luhn	140662538	14.572 ns	0.1481 ns	0.1237 ns	-
Luhn	140662538042	18.432 ns	0.1437 ns	0.1122 ns	-
Luhn	140662538042551	22.530 ns	0.2081 ns	0.1947 ns	-
Luhn	140662538042551028	19.954 ns	0.2879 ns	0.2693 ns	-
Luhn	140662538042551028265	30.808 ns	0.5542 ns	0.5184 ns	-

Modulus10_13	140	4.845 ns	0.0532 ns	0.0498 ns	-
Modulus10_13	140662	8.806 ns	0.1316 ns	0.1167 ns	-
Modulus10_13	140662538	11.743 ns	0.1881 ns	0.1760 ns	-
Modulus10_13	140662538042	12.224 ns	0.0869 ns	0.0813 ns	-
Modulus10_13	140662538042551	17.971 ns	0.1486 ns	0.1317 ns	-
Modulus10_13	140662538042551028	21.347 ns	0.1666 ns	0.1558 ns	-
Modulus10_13	140662538042551028265	24.085 ns	0.1882 ns	0.1761 ns	-

Modulus10_1	140	3.865 ns	0.0509 ns	0.0476 ns	-
Modulus10_1	140662	5.566 ns	0.0775 ns	0.0725 ns	-
Modulus10_1	140662538	7.337 ns	0.0871 ns	0.0815 ns	-

Modulus10_2	140	4.541 ns	0.0420 ns	0.0372 ns	-
Modulus10_2	140662	6.142 ns	0.0614 ns	0.0513 ns	-
Modulus10_2	140662538	7.874 ns	0.0784 ns	0.0733 ns	-

Modulus11	140	6.740 ns	0.0600 ns	0.0562 ns	-
Modulus11	140662	10.089 ns	0.0851 ns	0.0796 ns	-
Modulus11	140662538	13.288 ns	0.0696 ns	0.0651 ns	-

Verhoeff	140	9.926 ns	0.0724 ns	0.0642 ns	-
Verhoeff	140662	17.185 ns	0.0629 ns	0.0558 ns	-
Verhoeff	140662538	24.601 ns	0.0843 ns	0.0747 ns	-
Verhoeff	140662538042	32.311 ns	0.6764 ns	0.8307 ns	-
Verhoeff	140662538042551	40.603 ns	0.1477 ns	0.1309 ns	-
Verhoeff	140662538042551028	48.069 ns	0.1373 ns	0.1218 ns	-
Verhoeff	140662538042551028265	55.524 ns	0.1693 ns	0.1501 ns	-

General Alphabetic Algorithms

Algorithm Name	Value	Mean	Error	StdDev	Allocated
ISO/IEC 7064 MOD 27,26	EGR	6.915 ns	0.0760 ns	0.0711 ns	-
ISO/IEC 7064 MOD 27,26	EGRNML	9.448 ns	0.0751 ns	0.0627 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOC	14.985 ns	0.0798 ns	0.0707 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECU	14.329 ns	0.0699 ns	0.0619 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIK	17.069 ns	0.0676 ns	0.0599 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWW	19.291 ns	0.0719 ns	0.0600 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWWVVO	26.171 ns	0.0983 ns	0.0871 ns	-

ISO/IEC 7064 MOD 661-26	EGR	6.994 ns	0.0361 ns	0.0282 ns	-
ISO/IEC 7064 MOD 661-26	EGRNML	10.143 ns	0.0711 ns	0.0594 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOC	13.182 ns	0.0760 ns	0.0674 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECU	16.399 ns	0.0647 ns	0.0605 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIK	20.300 ns	0.0949 ns	0.0887 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWW	22.779 ns	0.0896 ns	0.0838 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWWVVO	27.412 ns	0.1551 ns	0.1450 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	10.603 ns	0.0421 ns	0.0329 ns	-
AlphanumericMod97_10	U7y8SX	18.684 ns	0.0887 ns	0.0786 ns	-
AlphanumericMod97_10	U7y8SXrC0	27.203 ns	0.1398 ns	0.1239 ns	-
AlphanumericMod97_10	U7y8SXrC0O3S	33.243 ns	0.1609 ns	0.1427 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4I	42.317 ns	0.2219 ns	0.1853 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQ	46.321 ns	0.2685 ns	0.2242 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQF4M	51.706 ns	0.1936 ns	0.1811 ns	-

ISO/IEC 7064 MOD 1271-36	U7Y	9.381 ns	0.0675 ns	0.0599 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SX	13.931 ns	0.0701 ns	0.0621 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0	17.402 ns	0.0820 ns	0.0727 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3S	22.540 ns	0.0591 ns	0.0524 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4I	27.310 ns	0.1040 ns	0.0922 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQ	32.300 ns	0.1056 ns	0.0936 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQF4M	35.724 ns	0.1192 ns	0.0995 ns	-

ISO/IEC 7064 MOD 37-2	U7Y	7.391 ns	0.0347 ns	0.0324 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SX	11.461 ns	0.0774 ns	0.0724 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0	15.736 ns	0.0734 ns	0.0686 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3S	19.804 ns	0.0717 ns	0.0671 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4I	23.759 ns	0.0894 ns	0.0836 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQ	33.503 ns	0.1415 ns	0.1324 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQF4M	38.716 ns	0.1444 ns	0.1280 ns	-

ISO/IEC 7064 MOD 37,36	U7Y	7.937 ns	0.0461 ns	0.0385 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SX	12.423 ns	0.0516 ns	0.0482 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0	16.474 ns	0.0991 ns	0.0927 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3S	20.351 ns	0.3404 ns	0.2843 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4I	24.541 ns	0.1335 ns	0.1183 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQ	30.263 ns	0.1079 ns	0.0956 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQF4M	35.554 ns	0.1783 ns	0.1668 ns	-

NOID Check Digit	11404/2h9	8.473 ns	0.0361 ns	0.0337 ns	-
NOID Check Digit	11404/2h9tqb	12.857 ns	0.0650 ns	0.0576 ns	-
NOID Check Digit	11404/2h9tqbxk6	16.108 ns	0.0807 ns	0.0755 ns	-
NOID Check Digit	11404/2h9tqbxk6rw7	19.350 ns	0.1326 ns	0.1240 ns	-
NOID Check Digit	11404/2h9tqbxk6rw7dwm	25.295 ns	0.0684 ns	0.0571 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	22.20 ns	0.108 ns	0.096 ns	-
IBAN	GB00WEST12345698765432	37.50 ns	0.316 ns	0.280 ns	-
IBAN	SC00MCBL01031234567890123456USD	54.90 ns	0.559 ns	0.467 ns	-

ISIN	AU0000XVGZA	27.01 ns	0.071 ns	0.066 ns	-
ISIN	GB000263494	20.26 ns	0.098 ns	0.091 ns	-
ISIN	US037833100	19.10 ns	0.144 ns	0.135 ns	-

VIN	1G8ZG127_WZ157259	21.46 ns	0.078 ns	0.073 ns	-
VIN	1HGEM212_2L047875	20.74 ns	0.131 ns	0.123 ns	-
VIN	1M8GDM9A_KP042788	20.89 ns	0.076 ns	0.071 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	5.413 ns	0.1208 ns	0.1187 ns	-
Damm	1406622	10.189 ns	0.1256 ns	0.1049 ns	-
Damm	1406625388	15.553 ns	0.2573 ns	0.2406 ns	-
Damm	1406625380422	20.646 ns	0.1639 ns	0.1533 ns	-
Damm	1406625380425518	25.791 ns	0.2073 ns	0.1939 ns	-
Damm	1406625380425510280	30.905 ns	0.2570 ns	0.2278 ns	-
Damm	1406625380425510282654	37.264 ns	0.2827 ns	0.2644 ns	-

ISO/IEC 7064 MOD 11,10	1409	6.567 ns	0.0645 ns	0.0572 ns	-
ISO/IEC 7064 MOD 11,10	1406623	11.212 ns	0.0784 ns	0.0695 ns	-
ISO/IEC 7064 MOD 11,10	1406625381	14.277 ns	0.0848 ns	0.0708 ns	-
ISO/IEC 7064 MOD 11,10	1406625380426	18.457 ns	0.0729 ns	0.0682 ns	-
ISO/IEC 7064 MOD 11,10	1406625380425514	20.652 ns	0.0946 ns	0.0884 ns	-
ISO/IEC 7064 MOD 11,10	1406625380425510286	25.927 ns	0.0780 ns	0.0730 ns	-
ISO/IEC 7064 MOD 11,10	1406625380425510282657	29.294 ns	0.1947 ns	0.1822 ns	-

ISO/IEC 7064 MOD 11-2	140X	5.319 ns	0.0585 ns	0.0488 ns	-
ISO/IEC 7064 MOD 11-2	1406628	9.415 ns	0.1067 ns	0.0998 ns	-
ISO/IEC 7064 MOD 11-2	1406625380	11.886 ns	0.0424 ns	0.0397 ns	-
ISO/IEC 7064 MOD 11-2	1406625380426	15.054 ns	0.1373 ns	0.1284 ns	-
ISO/IEC 7064 MOD 11-2	1406625380425511	18.343 ns	0.1774 ns	0.1482 ns	-
ISO/IEC 7064 MOD 11-2	140662538042551028X	15.708 ns	0.1594 ns	0.1491 ns	-
ISO/IEC 7064 MOD 11-2	1406625380425510282651	22.860 ns	0.0759 ns	0.0634 ns	-

ISO/IEC 7064 MOD 97-10	14066	6.683 ns	0.0606 ns	0.0537 ns	-
ISO/IEC 7064 MOD 97-10	14066262	9.404 ns	0.0898 ns	0.0840 ns	-
ISO/IEC 7064 MOD 97-10	14066253823	12.522 ns	0.1327 ns	0.1241 ns	-
ISO/IEC 7064 MOD 97-10	14066253804250	15.676 ns	0.1332 ns	0.1246 ns	-
ISO/IEC 7064 MOD 97-10	14066253804255112	18.960 ns	0.2592 ns	0.2298 ns	-
ISO/IEC 7064 MOD 97-10	14066253804255102853	22.186 ns	0.2068 ns	0.1935 ns	-
ISO/IEC 7064 MOD 97-10	14066253804255102826587	24.965 ns	0.5259 ns	0.4919 ns	-

Luhn	1404	7.787 ns	0.0630 ns	0.0589 ns	-
Luhn	1406628	11.274 ns	0.0995 ns	0.0931 ns	-
Luhn	1406625382	16.513 ns	0.2051 ns	0.1818 ns	-
Luhn	1406625380421	19.712 ns	0.1856 ns	0.1736 ns	-
Luhn	1406625380425514	23.241 ns	0.1690 ns	0.1581 ns	-
Luhn	1406625380425510285	27.301 ns	0.2171 ns	0.1813 ns	-
Luhn	1406625380425510282651	32.255 ns	0.2482 ns	0.2321 ns	-

Modulus10_13	1403	5.844 ns	0.0538 ns	0.0503 ns	-
Modulus10_13	1406627	9.622 ns	0.1128 ns	0.1055 ns	-
Modulus10_13	1406625385	12.078 ns	0.1033 ns	0.0966 ns	-
Modulus10_13	1406625380425	16.629 ns	0.3109 ns	0.2908 ns	-
Modulus10_13	1406625380425518	19.143 ns	0.1654 ns	0.1547 ns	-
Modulus10_13	1406625380425510288	18.478 ns	0.1429 ns	0.1336 ns	-
Modulus10_13	1406625380425510282657	26.205 ns	0.1747 ns	0.1634 ns	-

Modulus10_1	1401	3.168 ns	0.0427 ns	0.0399 ns	-
Modulus10_1	1406628	4.805 ns	0.0789 ns	0.0738 ns	-
Modulus10_1	1406625384	7.102 ns	0.1677 ns	0.1647 ns	-

Modulus10_2	1406	3.313 ns	0.0394 ns	0.0368 ns	-
Modulus10_2	1406627	4.892 ns	0.0527 ns	0.0493 ns	-
Modulus10_2	1406625389	6.557 ns	0.0890 ns	0.0833 ns	-

Modulus11	1406	5.127 ns	0.0476 ns	0.0422 ns	-
Modulus11	1406625	6.844 ns	0.1128 ns	0.1000 ns	-
Modulus11	1406625388	8.112 ns	0.0454 ns	0.0425 ns	-

Verhoeff	1401	12.043 ns	0.0532 ns	0.0472 ns	-
Verhoeff	1406625	19.670 ns	0.1123 ns	0.1050 ns	-
Verhoeff	1406625388	27.181 ns	0.1446 ns	0.1353 ns	-
Verhoeff	1406625380426	34.401 ns	0.1227 ns	0.1024 ns	-
Verhoeff	1406625380425512	41.722 ns	0.1302 ns	0.1154 ns	-
Verhoeff	1406625380425510285	49.574 ns	0.2021 ns	0.1792 ns	-
Verhoeff	1406625380425510282655	58.037 ns	1.1438 ns	1.1746 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	7.274 ns	0.0623 ns	0.0552 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLU	10.292 ns	0.0467 ns	0.0436 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCB	14.444 ns	0.0622 ns	0.0582 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUA	18.226 ns	0.1115 ns	0.0988 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKA	21.802 ns	0.1181 ns	0.1047 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWWY	25.724 ns	0.0692 ns	0.0647 ns	-
ISO/IEC 7064 MOD 27,26	EGRNMLJOCECUJIKNWWVVOQ	29.716 ns	0.1309 ns	0.1224 ns	-

ISO/IEC 7064 MOD 661-26	EGRSE	6.263 ns	0.0179 ns	0.0167 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLDR	10.339 ns	0.0777 ns	0.0726 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCCK	13.633 ns	0.0456 ns	0.0427 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUZJ	16.896 ns	0.0641 ns	0.0568 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKFQ	20.183 ns	0.0823 ns	0.0729 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWWQN	23.412 ns	0.0979 ns	0.0915 ns	-
ISO/IEC 7064 MOD 661-26	EGRNMLJOCECUJIKNWWVVORC	26.679 ns	0.1163 ns	0.0971 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	10.741 ns	0.0950 ns	0.0793 ns	-
AlphanumericMod97_10	U7y8SX89	19.366 ns	0.1097 ns	0.0972 ns	-
AlphanumericMod97_10	U7y8SXrC087	28.522 ns	0.2386 ns	0.2232 ns	-
AlphanumericMod97_10	U7y8SXrC0O3S38	35.760 ns	0.1844 ns	0.1724 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4I27	44.344 ns	0.0969 ns	0.0810 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQ54	49.380 ns	0.1968 ns	0.1744 ns	-
AlphanumericMod97_10	U7y8SXrC0O3Sc4IHYQF4M21	57.042 ns	0.1509 ns	0.1260 ns	-

ISO/IEC 7064 MOD 1271-36	U7YM0	8.068 ns	0.0306 ns	0.0271 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXOR	13.625 ns	0.0857 ns	0.0760 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0FI	17.588 ns	0.0977 ns	0.0914 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SX4	20.950 ns	0.0567 ns	0.0503 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4I9D	24.208 ns	0.0451 ns	0.0400 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQYI	31.207 ns	0.1850 ns	0.1731 ns	-
ISO/IEC 7064 MOD 1271-36	U7Y8SXRC0O3SC4IHYQF4M44	33.292 ns	0.0991 ns	0.0828 ns	-

ISO/IEC 7064 MOD 37-2	U7YZ	6.713 ns	0.0368 ns	0.0326 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXV	10.742 ns	0.0440 ns	0.0412 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0E	14.103 ns	0.0575 ns	0.0538 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SU	18.156 ns	0.0843 ns	0.0747 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IB	21.720 ns	0.0729 ns	0.0682 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQG	26.040 ns	0.1465 ns	0.1370 ns	-
ISO/IEC 7064 MOD 37-2	U7Y8SXRC0O3SC4IHYQF4MF	29.839 ns	0.0916 ns	0.0812 ns	-

ISO/IEC 7064 MOD 37,36	U7YW	8.697 ns	0.0715 ns	0.0669 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SX8	13.124 ns	0.0772 ns	0.0722 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0E	17.682 ns	0.0633 ns	0.0529 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SR	23.219 ns	0.2057 ns	0.1924 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IT	24.299 ns	0.1017 ns	0.0902 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQD	27.938 ns	0.1244 ns	0.0971 ns	-
ISO/IEC 7064 MOD 37,36	U7Y8SXRC0O3SC4IHYQF4MP	32.631 ns	0.1183 ns	0.1049 ns	-

NOID Check Digit	11404/2h9m	12.579 ns	0.0894 ns	0.0837 ns	-
NOID Check Digit	11404/2h9tqb0	16.119 ns	0.0622 ns	0.0551 ns	-
NOID Check Digit	11404/2h9tqbxk6d	20.225 ns	0.0792 ns	0.0740 ns	-
NOID Check Digit	11404/2h9tqbxk6rw74	24.573 ns	0.1188 ns	0.1111 ns	-
NOID Check Digit	11404/2h9tqbxk6rw7dwmz	30.319 ns	0.0998 ns	0.0833 ns	-

Value Specific Algorithms

Algorithm Name	Value	Mean	Error	StdDev	Allocated
ABA RTN	111000025	10.830 ns	0.0650 ns	0.0580 ns	-
ABA RTN	122235821	10.400 ns	0.1880 ns	0.1570 ns	-
ABA RTN	325081403	10.310 ns	0.0610 ns	0.0570 ns	-

IBAN	BE71096123456769	20.090 ns	0.1710 ns	0.1600 ns	-
IBAN	GB82WEST12345698765432	34.960 ns	0.2120 ns	0.1880 ns	-
IBAN	SC74MCBL01031234567890123456USD	51.580 ns	0.2410 ns	0.2130 ns	-

ISAN	C594660A8B2E5D22X6DDA3272E	54.400 ns	0.1940 ns	0.1810 ns	-
ISAN	D02C42E954183EE2Q1291C8AEO	51.210 ns	0.2820 ns	0.2640 ns	-
ISAN	E9530C32BC0EE83B269867B20F	46.700 ns	0.1390 ns	0.1300 ns	-

ISAN (Formatted)	ISAN C594-660A-8B2E-5D22-X	45.420 ns	0.1530 ns	0.1360 ns	-
ISAN (Formatted)	ISAN D02C-42E9-5418-3EE2-Q	44.310 ns	0.2520 ns	0.2360 ns	-
ISAN (Formatted)	ISAN E953-0C32-BC0E-E83B-2	50.080 ns	0.2070 ns	0.1840 ns	-
ISAN (Formatted)	ISAN C594-660A-8B2E-5D22-X-6DDA-3272-E	64.650 ns	0.3200 ns	0.3000 ns	-
ISAN (Formatted)	ISAN D02C-42E9-5418-3EE2-Q-1291-C8AE-O	65.820 ns	0.3030 ns	0.2840 ns	-
ISAN (Formatted)	ISAN E953-0C32-BC0E-E83B-2-6986-7B20-F	64.220 ns	0.3640 ns	0.3400 ns	-

ISIN	AU0000XVGZA3	25.520 ns	0.1260 ns	0.1170 ns	-
ISIN	GB0002634946	19.150 ns	0.1290 ns	0.1140 ns	-
ISIN	US0378331005	19.110 ns	0.1400 ns	0.1310 ns	-

NHS	4505577104	11.280 ns	0.0360 ns	0.0340 ns	-
NHS	5301194917	11.270 ns	0.0400 ns	0.0360 ns	-
NHS	9434765919	11.270 ns	0.0450 ns	0.0430 ns	-

NPI	1122337797	14.490 ns	0.0490 ns	0.0440 ns	-
NPI	1234567893	14.530 ns	0.0800 ns	0.0710 ns	-
NPI	1245319599	14.520 ns	0.0890 ns	0.0830 ns	-

VIN	1G8ZG127XWZ157259	21.120 ns	0.1160 ns	0.1080 ns	-
VIN	1HGEM21292L047875	20.920 ns	0.0770 ns	0.0690 ns	-
VIN	1M8GDM9AXKP042788	21.050 ns	0.0940 ns	0.0830 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)
NcdAlgorithm (NOID Check Digit)

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, Validate method ~18% improvement, TryCalculateCheckDigit method ~21% improvement

v2.0.0

Updated to .Net 8.0

Average performance improvement for .Net 8.0 across all algorithms: Validate method ~8% improvement, TryCalculateCheckDigit method ~4.9% improvement

Detailed benchmark results for .Net 7 vs .Net 8 located at https://github.com/KnowledgeForwardSolutions/CheckDigits.Net/blob/main/Documentation/DotNet7_DotNet8_PerformanceComparision.md

Product	Compatible and additional computed target framework versions.
.NET	net8.0 is compatible. 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.

Compatible target framework(s)

Included target framework(s) (in package)

Learn more about Target Frameworks and .NET Standard.

net8.0
- 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
2.3.1	1,055	5/15/2024
2.3.0	90	5/14/2024
2.2.0	8,528	1/25/2024
2.1.0	228	12/5/2023
2.0.0	162	11/21/2023
1.1.0	147	11/18/2023
1.0.0	165	10/26/2023
1.0.0-alpha	116	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)
* NcdAlgorithm (NOID Check Digit)

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, Validate method ~18% improvement, TryCalculateCheckDigit method ~21% improvement

v2.0.0

Updated to .Net 8.0

Average performance improvement for .Net 8.0 across all algorithms:
Validate method ~8% improvement, TryCalculateCheckDigit method ~4.9% improvement

CheckDigits.Net 2.0.0

CheckDigits.Net

Future Algorithms

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