## Overview

`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.

## Arithmetic

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.

## Operators

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

## Conversion

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 `BigInt`

s from `string`

s, 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.

## Serialization

`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`

.

## Properties

`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.

## History

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. |