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Currently I am borrowing java.math.BigInteger from the J# libraries as described here. Having never used a library for working with large integers before, this seems slow, on the order of 10 times slower, even for ulong length numbers. Does anyone have any better (preferably free) libraries, or is this level of performance normal?

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nice link. A couple of gems there. –  Mitch Wheat Oct 7 '08 at 0:34
Only problem is that they require the J# redistributables to be installed. The fact that J# is all but dead (it wasn't in VS 2008 atleast) probably doesn't help with promoting that. –  Matthew Scharley Oct 7 '08 at 0:39
J# is just to facilitate the migration of existing Java projects to .NET. I definitely wouldn't incorporate any of its libraries into a new project. –  MusiGenesis Oct 7 '08 at 1:44
possible duplicate of [How can I represent a very large integer in .NET? ](stackoverflow.com/questions/25375/…) –  Roger Pate May 26 '10 at 22:27
@Roger: I'd rather close the other, as this one has more up to information attached to it. –  Matthew Scharley May 27 '10 at 8:14
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11 Answers

up vote 50 down vote accepted

MS is going to introduce System.Numerics.BigInteger class in .NET 4.0

Until then, look at IntX class.

IntX is an arbitrary precision integers library written in pure C# 2.0 with fast - O(N * log N) - multiplication/division algorithms implementation. It provides all the basic operations on integers like addition, multiplication, comparing, bitwise shifting etc.

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For the record, The System.Numerics assembly is not referenced by default in new projects, so this needs to be added before BigInteger can be used. –  romkyns Dec 5 '10 at 16:45
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F# also ships with one. You can get it at Microsoft.FSharp.Math.

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The System.Numerics.BigInteger class in .NET 4.0 is based on Microsoft.SolverFoundation.Common.BigInteger from Microsoft Research.

The Solver Foundation's BigInteger class looks very performant. I am not sure about which license it is released under, but you can get it here (download and install Solver Foundation and find the Microsoft.Solver.Foundation.dll).

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I reckon you could optimize the implementation if you perform all the operations on BigInts that are going to return results smaller than a native type (Eg. int64) on the native types and only deal with the big array if you are going to overflow.

edit This implementation on codeproject, seems only 7 times slower ... But with the above optimization you could get it to perform almost identically to native types for small numbers.

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I believe the J# library uses Byte's internally, it has a ToByteArray() function atleast, and no other ToArray() function. This might be an idea if I wanted to roll my own, I'm not too thrilled with that idea either though. –  Matthew Scharley Oct 7 '08 at 0:37
What size data are you working with, in general? Will stuff overflow the Int64 size on a regular basis, or is it an exception? –  Sam Saffron Oct 7 '08 at 0:44
I'm doing it mostly on a case by case basis, setting it to BigInt when I run into an overflow with a checked{} block. If it does that once, then there's a pretty good chance it'll do it repeatedly and often. –  Matthew Scharley Oct 7 '08 at 0:58
monoxide, I don't think it will be easy to get this to perform much faster than the implementation on codeproject for large numbers. –  Sam Saffron Oct 7 '08 at 1:35
Like I said in my original post, I've never used a BigInteger implementation before, so I wouldn't know what sort of performance they get. That was more the question I was asking. Damn, I still want to roll my own as an intellectual excercise now though :( –  Matthew Scharley Oct 7 '08 at 2:13
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Here are several implementations of BigInteger in C#. I've used Mono's BigInteger implementation, works pretty fast (I've used it in CompactFramework)

Bouncy Castle


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I'm not sure about the performance, but IronPython also has a BigInteger class. It is in the Microsoft.Scripting.Math namespace.

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This may sound like a strange suggestion, but have you tested the decimal type to see how fast it works?

The decimal range is ±1.0 × 10^−28 to ±7.9 × 10^28, so it may still not be large enough, but it is larger than a ulong.

There was supposed to be a BigInteger class in .NET 3.5, but it got cut.

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Yes, I saw that anouncement when originally looking for a BigInt library. Makes me sad. Oh well. –  Matthew Scharley Oct 7 '08 at 0:34
You would have to be careful - using a decimal might cause rounding issues. –  Blorgbeard Oct 7 '08 at 0:40
Decimal doesn't cause rounding errors. It's not floating point. –  Kibbee Oct 7 '08 at 0:57
Decimal only tries to minimize errors due to rounding. It is not immune to rounding. msdn.microsoft.com/en-us/library/system.decimal.aspx –  Robert Paulson Oct 7 '08 at 1:48
Decimal is a floating point type. It's just that it's a floating decimal point instead of a floating binary point. See pobox.com/~skeet/csharp/decimal.html I wouldn't expect rounding issues if all values are integers within the appropriate range though. –  Jon Skeet Oct 7 '08 at 6:10
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Yes, it will be slow, and 10x difference is about what I'd expect. BigInt uses an array to represent an arbitrary length, and all the operations have to be done manually (as opposed to most math which can be done directly with the CPU)

I don't even know if hand-coding it in assembly will give you much of a performance gain over 10x, that's pretty damn close. I'd look for other ways to optimize it--sometimes depending on your math problem there are little tricks you can do to make it quicker.

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I used Biginteger at a previous job. I don't know what kind of performance needs you have. I did not use it in a performance-intensive situation, but never had any problems with it.

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This won't help you, but there was supposed to be a BigInteger class in .Net 3.5; it got cut, but from statements made at PDC, it will be in .Net 4.0. They apparently have spent a lot of time optimizing it, so the performance should be much better than what you're getting now.

Further, this question is essentially a duplicate of http://stackoverflow.com/questions/25375/how-can-i-represent-a-very-large-integer-in-net

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BigInteger is in 3.5 but its an internal class. ;) Its there just not ready for prime time. –  Ray Booysen Jan 31 '09 at 13:25
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See the answers in this thread. You will need to use one of the third-party big integer libraries/classes available or wait for C# 4.0 which will include a native BigInteger datatype.

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