CheckDigits.Net 2.2.0

.NET 8.0 .NET Standard 2.0 
dotnet add package CheckDigits.Net --version 2.2.0
NuGet\Install-Package CheckDigits.Net -Version 2.2.0
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<PackageReference Include="CheckDigits.Net" Version="2.2.0" />
For projects that support PackageReference, copy this XML node into the project file to reference the package. 
paket add CheckDigits.Net --version 2.2.0
#r "nuget: CheckDigits.Net, 2.2.0"
#r directive can be used in F# Interactive and Polyglot Notebooks. Copy this into the interactive tool or source code of the script to reference the package. 
// Install CheckDigits.Net as a Cake Addin
#addin nuget:?package=CheckDigits.Net&version=2.2.0

// Install CheckDigits.Net as a Cake Tool
#tool nuget:?package=CheckDigits.Net&version=2.2.0

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

Table of Contents

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

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_1 Algorithm
Credit card number Luhn Algorithm
CUSIP CUSIP 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_2 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
SEDOL SEDOL Algorithm
Shipping Container Number ISO 6346 Algorithm
SSCC Modulus10_13 Algorithm
Universal Loan Identifier Alphanumeric MOD 97-10 Algorithm
UK National Health Service Number NHS Algorithm
UPC-A Modulus10_13 Algorithm
UPC-E Modulus10_13 Algorithm
US National Provider Identifier NPI Algorithm
Vehicle Identification Number VIN 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

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)

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

CUSIP Algorithm

Description

The CUSIP (Committee on Uniform Security Identification Procedures) algorithm is used for nine character alphanumeric codes that identify North American financial securities. The algorithm has similarities with both the Luhn algorithm and the ISIN algorithm.

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

Details
  • Valid characters - alphanumeric characters ('0' - '9', 'A' - 'Z') plus '*', '@' and '#'
  • 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 - CusipAlgorithm

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

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

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

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

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

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

ISO 6346 Algorithm

The ISO 6346 algorithm is used for eleven character shipping container numbers.

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 - 11
  • Class name - Iso6346Algorithm

Wikipedia: https://en.wikipedia.org/wiki/ISO_6346

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)

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

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

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)

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)

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

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

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

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

SEDOL Algorithm

Description

The SEDOL (Stock Exchange Daily Official List) algorithm is used for seven character alphanumeric codes that identify financial securities in the United Kingdom and Ireland.

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

Details
  • Valid characters - alphanumeric characters, excluding vowels ('0' - '9', 'BCDFGHJKLMNPQRSTVWXYZ')
  • 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 - 7 characters
  • Class name - SedolAlgorithm

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

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

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

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 4.525 ns 0.0571 ns 0.0506 ns -
Damm 140662 5.477 ns 0.0170 ns 0.0142 ns -
Damm 140662538 8.315 ns 0.0803 ns 0.0712 ns -
Damm 140662538042 11.993 ns 0.0355 ns 0.0332 ns -
Damm 140662538042551 16.354 ns 0.3389 ns 0.3170 ns -
Damm 140662538042551028 19.487 ns 0.0783 ns 0.0654 ns -
Damm 140662538042551028265 23.192 ns 0.0936 ns 0.0781 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 6.674 ns 0.1106 ns 0.1035 ns -
Luhn 140662 9.396 ns 0.0575 ns 0.0538 ns -
Luhn 140662538 14.913 ns 0.0464 ns 0.0434 ns -
Luhn 140662538042 14.981 ns 0.0720 ns 0.0638 ns -
Luhn 140662538042551 20.813 ns 0.1534 ns 0.1435 ns -
Luhn 140662538042551028 22.434 ns 0.1459 ns 0.1365 ns -
Luhn 140662538042551028265 27.432 ns 0.1217 ns 0.1138 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 8.358 ns 0.1062 ns 0.0941 ns -
Verhoeff 140662 12.916 ns 0.0614 ns 0.0544 ns -
Verhoeff 140662538 17.835 ns 0.1126 ns 0.0998 ns -
Verhoeff 140662538042 22.727 ns 0.1362 ns 0.1274 ns -
Verhoeff 140662538042551 27.473 ns 0.1085 ns 0.0961 ns -
Verhoeff 140662538042551028 32.246 ns 0.1009 ns 0.0842 ns -
Verhoeff 140662538042551028265 37.262 ns 0.1306 ns 0.1090 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, CUSIP, NHS, NPI and SEDOL 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 -
ISO 6346 CSQU305438 16.74 ns 0.216 ns 0.202 ns -
ISO 6346 MSKU907032 16.22 ns 0.078 ns 0.069 ns -
ISO 6346 TOLU473478 16.22 ns 0.135 ns 0.113 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.

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 1402 3.825 ns 0.0240 ns 0.0213 ns -
Damm 1406622 6.032 ns 0.0244 ns 0.0216 ns -
Damm 1406625388 9.435 ns 0.0801 ns 0.0750 ns -
Damm 1406625380422 13.104 ns 0.0813 ns 0.0760 ns -
Damm 1406625380425518 16.887 ns 0.1718 ns 0.1523 ns -
Damm 1406625380425510280 20.558 ns 0.1472 ns 0.1377 ns -
Damm 1406625380425510282654 24.074 ns 0.1599 ns 0.1495 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 6.671 ns 0.0366 ns 0.0305 ns -
Luhn 1406628 8.910 ns 0.0483 ns 0.0377 ns -
Luhn 1406625382 12.273 ns 0.0815 ns 0.0763 ns -
Luhn 1406625380421 14.002 ns 0.0486 ns 0.0431 ns -
Luhn 1406625380425514 18.127 ns 0.2873 ns 0.2687 ns -
Luhn 1406625380425510285 19.739 ns 0.1725 ns 0.1613 ns -
Luhn 1406625380425510282651 23.388 ns 0.1535 ns 0.1435 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 9.365 ns 0.0523 ns 0.0489 ns -
Verhoeff 1406625 14.769 ns 0.0841 ns 0.0656 ns -
Verhoeff 1406625388 20.334 ns 0.1164 ns 0.1089 ns -
Verhoeff 1406625380426 25.942 ns 0.1319 ns 0.1234 ns -
Verhoeff 1406625380425512 31.425 ns 0.1170 ns 0.0977 ns -
Verhoeff 1406625380425510285 36.982 ns 0.1119 ns 0.0935 ns -
Verhoeff 1406625380425510282655 42.288 ns 0.1756 ns 0.1642 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 -
CUSIP 037833100 16.500 ns 0.1990 ns 0.1760 ns -
CUSIP 38143VAA7 13.020 ns 0.0830 ns 0.0770 ns -
CUSIP 91282CJL6 12.850 ns 0.0630 ns 0.0530 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 -
ISO 6346 CSQU3054383 14.970 ns 0.0350 ns 0.0280 ns -
ISO 6346 MSKU9070323 14.890 ns 0.0930 ns 0.0870 ns -
ISO 6346 TOLU4734787 14.840 ns 0.0980 ns 0.0870 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 -
SEDOL 3134865 12.290 ns 0.1440 ns 0.1200 ns -
SEDOL B0YQ5W0 12.180 ns 0.0630 ns 0.0560 ns -
SEDOL BRDVMH9 12.220 ns 0.0800 ns 0.0710 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

v2.1.0

Additional included algorithms

  • CUSIP Algorithm
  • ISO 6346 Algorithm
  • SEDOL Algorithm

Performance increases for:

  • Luhn Algorithm, Validate method ~15% improvement over .Net 7, TryCalculateCheckDigit method ~27% improvement over .Net 7 (Luhn algorithm originally saw a slight performance decrease when switching from .Net 7 to .Net 8. This release addresses that performance decrease.)
  • Damm Algorithm, Validate and TryCalculateCheckDigit methods ~30% improvement
  • Verhoeff Algorithm, Validate method ~20% improvement, TryCalculateCheckDigit method ~30% improvement
Product Compatible and additional computed target framework versions.
.NET net5.0 was computed.  net5.0-windows was computed.  net6.0 was computed.  net6.0-android was computed.  net6.0-ios was computed.  net6.0-maccatalyst was computed.  net6.0-macos was computed.  net6.0-tvos was computed.  net6.0-windows was computed.  net7.0 was computed.  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 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. 
.NET Core netcoreapp2.0 was computed.  netcoreapp2.1 was computed.  netcoreapp2.2 was computed.  netcoreapp3.0 was computed.  netcoreapp3.1 was computed. 
.NET Standard netstandard2.0 is compatible.  netstandard2.1 was computed. 
.NET Framework net461 was computed.  net462 was computed.  net463 was computed.  net47 was computed.  net471 was computed.  net472 was computed.  net48 was computed.  net481 was computed. 
MonoAndroid monoandroid was computed. 
MonoMac monomac was computed. 
MonoTouch monotouch was computed. 
Tizen tizen40 was computed.  tizen60 was computed. 
Xamarin.iOS xamarinios was computed. 
Xamarin.Mac xamarinmac was computed. 
Xamarin.TVOS xamarintvos was computed. 
Xamarin.WatchOS xamarinwatchos was computed. 
Compatible target framework(s)
Included target framework(s) (in package)
Learn more about Target Frameworks and .NET Standard.

  • .NETStandard 2.0

  • 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
2.2.0 1,712 1/25/2024
2.1.0 205 12/5/2023
2.0.0 138 11/21/2023
1.1.0 122 11/18/2023
1.0.0 135 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)
* 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

## v2.1.0

Additional included algorithms
* CUSIP Algorithm
* ISO 6346 Algorithm
* SEDOL Algorithm

Performance increases for:
* Luhn Algorithm, Validate method ~15% improvement over .Net 7, TryCalculateCheckDigit method ~27% improvement over .Net 7
 (Luhn algorithm originally saw a slight performance decrease when switching from .Net 7 to .Net 8. This release addresses that performance decrease.)
* Damm Algorithm, Validate and TryCalculateCheckDigit methods ~30% improvement
* Verhoeff Algorithm, Validate method ~20% improvement, TryCalculateCheckDigit method ~30% improvement

## v2.2.0

Support for netstandard2.0

Thanks to Steff Beckers for this addition