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, 8 Mar 2010 CPOL
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A general-purpose unbounded integer implementation


BigInt is a general-purpose unbounded integer implementation consistent with C# and .NET numeric type conventions: it's an immutable ValueType, implements IComparable<BigInt>, IEquatable<BigInt>, and IConvertable interfaces, and supplies arithmetic operators and various implicit and explicit conversion operators.

To date, there are very few options available for C# .NET developers in need of "Big" numbers. Chew Keong TAN's C# BigInteger[^] is very fast, but specialized for cryptology at the neglect of memory considerations (implemented with a constant length Array, memory is quickly exhausted, and performance degraded when the length is set even moderately high). Microsoft's J# BigInteger[^] is also available, but is awkward to use (reference type, no operators, Camel-case), and also requires distributing the J# runtime with your applications.

BigInt is implemented with a LinkedList<byte> in base-10. Hence, memory consumption and performance are not as optimal as may be achieved with an Array in a higher base. That being said, BigInt is reasonably performing and light enough on memory that it should be suitable for many applications.


Standard pencil and paper algorithms are implemented for addition, subtraction, multiplication, and division. Hence, addition and subtraction yield m + n complexity where m and n are the number of digits in each operand, respectively. And multiplication and division are order m * n. Multiplication uses mutation internally for performance gains (the addition steps are accumulated in the result with AddTo, sparing repeated large memory allocation we'd otherwise incur for temporary states).

Common Algorithms

Beyond basic arithmetic, several common algorithms are provided for BigInt including min, max, mod, pow, and truncated square root, to name a few.


All binary and unary operators traditionally associated with numeric types are provided; however, bitwise operations and operators have yet to be implemented.


To avoid redundancy, while risking incompatibility across all .NET languages, we refrain from using non-default constructors as a method of conversion to BigInt; instead, we rely on implicit conversion operators for lossless conversions from numeric .NET System types, and explicit conversion operators for other useful types. BigInt.Parse and BigInt.TryParse are preferable methods for constructing BigInts from strings, but we also make an exception and implement an explicit string to BigInt conversion operator to accommodate Enumerable.Cast<string>(BigInt). In addition, several lossy explicit conversion operators paralleling IConvertable are provided for conversion from BigInt to other types.


BigInt is suitable for both binary and XML serialization. Marked with the Serializable attribute, only the private fields of BigInt (digits and isneg) participate in binary serialization, as is appropriate. Default XML serialization, whereby public fields and properties are serialized, is wholly inappropriate; therefore, we implement the IXmlSerializable interface, representing the BigInt via BigInt.ToString for WriteXml, and deserializing via BigInt.Parse for ReadXml.


Divisors, ProperDivisors, DigitsLeftToRight, and DigitsRightToLeft are implemented as object streams (IEnumerable<BigInt>) and were selected for their ability to describe fundamental aspects of integers. The first two expose the integer intrinsics. The latter support manipulating integers on the structural level. A PrimeFactorization property is pending implementation.

Big Calculator

The sample application provided is driven by BigInt's static Eval method. Eval can parse and evaluate many simple binary and unary BigInt expressions. Eval / BigCalculator may be extended in the future to support processing complex expression trees and typical calculator features such as variable assignment.

BigCalculator screen shot


Version Date Description
1.00 May 10, 2009 First release
1.01 May 11, 2009 Improved performance of Pow by using exponentiation by squaring. Improved performance of Gcd (and therefore Lcm) by using the Euclidean algorithm.
Modified Range to accept reverse ranges.
1.02 May 16, 2009 Fixed remainder bug.
1.03 May 17, 2009 Improved division memory usage.


This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)


About the Author

Stephen Swensen

United States United States
I'm developing Unquote, a library for writing unit test assertions as F# quoted expressions:

I am working through Project Euler with F#:

I participate in Stack Overflow:

Comments and Discussions

Generaldivision in o(n+m) Pinmemberlaurv8-Feb-10 5:00 
GeneralRe: division in o(n+m) PinmemberStephen Swensen10-Feb-10 23:05 
NewsFastest BigInt for C# PinmemberSquat15-Sep-09 21:23 
GeneralRe: Fastest BigInt for C# [modified] PinmemberStephen Swensen16-Sep-09 6:13 
GeneralRe: Fastest BigInt for C# PinmemberSquat2-Oct-09 2:07 
GeneralIncorrect Remainder PinmemberShaikk15-May-09 9:34 
GeneralRe: Incorrect Remainder PinmemberStephen Swensen15-May-09 9:45 
GeneralRe: Incorrect Remainder PinmemberStephen Swensen16-May-09 11:03 
GeneralWhy not use a fast multiplication algorithm PinmemberZTransform15-May-09 5:11 
GeneralRe: Why not use a fast multiplication algorithm PinmemberStephen Swensen15-May-09 5:25 
GeneralC# 4.0 big ints Pinmemberdarrellp14-May-09 11:12 
GeneralRe: C# 4.0 big ints PinmemberStephen Swensen14-May-09 15:50 
GeneralNo performance nor Memory consumption is minimized at all PinmemberGabriel 212-May-09 18:12 
GeneralRe: No performance nor Memory consumption is minimized at all PinmemberStephen Swensen17-May-09 4:47 
QuestionPerformance? Pinmembertorial12-May-09 7:40 
AnswerRe: Performance? PinmemberStephen Swensen12-May-09 16:24 
GeneralYou can increase performance if you use some larger base, for example 1024 PinmemberVadim Shtayura11-May-09 22:33 
GeneralRe: You can increase performance if you use some larger base, for example 1024 PinmemberSteve Hansen12-May-09 1:51 
GeneralRe: You can increase performance if you use some larger base, for example 1024 PinmemberStephen Swensen12-May-09 16:09 
Thanks for your valuable insight.

I have been planning on looking into switching to a larger base, but starting with base-10 allowed me to get off the ground more quickly and also made debugging and algorithm visualization easier during initial design and development!

Addressing your other points:

1) I chose to store BigInt digits in a LinkedList rather than an Array for a number reasons, one being that it's more natural to use in many cases (e.g. we can't always reasonably figure out the exact number of digits we require upfront for the result of a computation like addition). Also, having run a few quick tests, on my computer (32-bit Intel Core 2 Duo CPU @ 2.00 GHz x 2, 2.00 GB RAM) it takes about 15 ticks to allocate and assign an Array of length 1000000 and about 200 ticks to allocate and assign a LinkedList of length 1000000. The Array is clearly superior, but the LinkedList isn’t bad either! That being said, your point is well taken and I have contemplated gutting my implementation to use an Array.

2) It’s certainly undesirable but not a show stopper in my estimation. To put my claim to memory conservation in context, the only other publicly available c#/.net unbounded integer implementation I've found (C# BigInteger Class[^]) is specialized for cryptography and uses a static constant length Array, leading to definite memory exhaustion when pushed high for doing something like computing 20000! with a memorization based factorial implementation.
GeneralRe: You can increase performance if you use some larger base, for example 1024 Pinmemberdarrellp14-May-09 11:20 
GeneralRe: You can increase performance if you use some larger base, for example 1024 PinmemberStephen Swensen14-May-09 16:41 
GeneralRe: You can increase performance if you use some larger base, for example 1024 PinmemberUtah Luxury15-Mar-10 18:21 
GeneralRe: You can increase performance if you use some larger base, for example 1024 PinmemberStephen Swensen16-Mar-10 6:37 
GeneralFirst release PinmemberStephen Swensen11-May-09 19:24 
GeneralRe: First release PinmvpDaveyM6912-May-09 4:09 

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