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C#: Decimal -> Largest integer that can be stored exactly

I've been looking at the decimal type for some possible programming fun in the near future, and would like to use it a a bigger integer than an Int64. One key point is that I need to find out the largest integer that I can store safely into the decimal (without losing precision); I say this, because apparently it uses some floating point in there, and as programmers, we all know the love that only floating point can give us.
So, does anyone know the largest int I can shove in there?
And on a separate note, does anyone have any experience playing with arrays of longs / ints? It's for the project following this one.
Thanks,
-R

decimal works differently to float and double - it always has enough information to store as far as integer precision, as the maximum exponent is 28 and it has 28-29 digits of precision. You may be interested in my articles on decimal floating point and binary floating point on .NET to look at the differences more closely.
So you can store any integer in the range [decimal.MinValue, decimal.MaxValue] without losing any precision.
If you want a wider range than that, you should use BigInteger as Fredrik mentioned (assuming you're on .NET 4, of course... I believe there are 3rd party versions available for earlier versions of .NET).

If you want to deal with big integers, you might want to look into the BigInteger type.
From the documentation:
Represents an arbitrarily large signed integer

double minus double giving precision problems

I have come across a precision issue with double in .NET I thought this only applied to floats but now I see that double is a float.
double test = 278.97 - 90.46;
Debug.WriteLine(test) //188.51000000000005
//correct answer is 188.51
What is the correct way to handle this? Round? Lop off the unneeded decimal places?

Use the decimal data type. "The Decimal value type is appropriate for financial calculations requiring large numbers of significant integral and fractional digits and no round-off errors."

This happens in many languages and stems from the fact that we cannot usually store doubles or floats precisely in digital hardware. For a detailed explanation of how doubles, floats, and all other floating point values are often stored, look at the various IEEE specs described on wikipedia. For example: http://en.wikipedia.org/wiki/Double_precision
Of course there are other formats, such as fixed-point format. But this imprecision is in most languages, and why you often need to use epsilon tests instead of equality tests when using doubles in conditionals (i.e. abs(x - y) <= 0.0001 instead of x == y).
How you deal with this imprecision is up to you, and depends on your application.

Why is System.Math and for example MathNet.Numerics based on double?

All the methods in System.Math takes double as parameters and returns parameters. The constants are also of type double. I checked out MathNet.Numerics, and the same seems to be the case there.
Why is this? Especially for constants. Isn't decimal supposed to be more exact? Wouldn't that often be kind of useful when doing calculations?

This is a classic speed-versus-accuracy trade off.
However, keep in mind that for PI, for example, the most digits you will ever need is 41.
The largest number of digits of pi
that you will ever need is 41. To
compute the circumference of the
universe with an error less than the
diameter of a proton, you need 41
digits of pi †. It seems safe to
conclude that 41 digits is sufficient
accuracy in pi for any circle
measurement problem you're likely to
encounter. Thus, in the over one
trillion digits of pi computed in
2002, all digits beyond the 41st have
no practical value.
In addition, decimal and double have a slightly different internal storage structure. Decimals are designed to store base 10 data, where as doubles (and floats), are made to hold binary data. On a binary machine (like every computer in existence) a double will have fewer wasted bits when storing any number within its range.
Also consider:
System.Double 8 bytes Approximately ±5.0e-324 to ±1.7e308 with 15 or 16 significant figures
System.Decimal 12 bytes Approximately ±1.0e-28 to ±7.9e28 with 28 or 29 significant figures
As you can see, decimal has a smaller range, but a higher precision.

No, - decimals are no more "exact" than doubles, or for that matter, any type. The concept of "exactness", (when speaking about numerical representations in a compuiter), is what is wrong. Any type is absolutely 100% exact at representing some numbers. unsigned bytes are 100% exact at representing the whole numbers from 0 to 255. but they're no good for fractions or for negatives or integers outside the range.
Decimals are 100% exact at representing a certain set of base 10 values. doubles (since they store their value using binary IEEE exponential representation) are exact at representing a set of binary numbers.
Neither is any more exact than than the other in general, they are simply for different purposes.
To elaborate a bit furthur, since I seem to not be clear enough for some readers...
If you take every number which is representable as a decimal, and mark every one of them on a number line, between every adjacent pair of them there is an additional infinity of real numbers which are not representable as a decimal. The exact same statement can be made about the numbers which can be represented as a double. If you marked every decimal on the number line in blue, and every double in red, except for the integers, there would be very few places where the same value was marked in both colors.
In general, for 99.99999 % of the marks, (please don't nitpick my percentage) the blue set (decimals) is a completely different set of numbers from the red set (the doubles).
This is because by our very definition for the blue set is that it is a base 10 mantissa/exponent representation, and a double is a base 2 mantissa/exponent representation. Any value represented as base 2 mantissa and exponent, (1.00110101001 x 2 ^ (-11101001101001) means take the mantissa value (1.00110101001) and multiply it by 2 raised to the power of the exponent (when exponent is negative this is equivilent to dividing by 2 to the power of the absolute value of the exponent). This means that where the exponent is negative, (or where any portion of the mantissa is a fractional binary) the number cannot be represented as a decimal mantissa and exponent, and vice versa.
For any arbitrary real number, that falls randomly on the real number line, it will either be closer to one of the blue decimals, or to one of the red doubles.

Decimal is more precise but has less of a range. You would generally use Double for physics and mathematical calculations but you would use Decimal for financial and monetary calculations.
See the following articles on msdn for details.
Double
http://msdn.microsoft.com/en-us/library/678hzkk9.aspx
Decimal
http://msdn.microsoft.com/en-us/library/364x0z75.aspx

Seems like most of the arguments here to "It does not do what I want" are "but it's faster", well so is ANSI C+Gmp library, but nobody is advocating that right?
If you particularly want to control accuracy, then there are other languages which have taken the time to implement exact precision, in a user controllable way:
http://www.doughellmann.com/PyMOTW/decimal/
If precision is really important to you, then you are probably better off using languages that mathematicians would use. If you do not like Fortran then Python is a modern alternative.
Whatever language you are working in, remember the golden rule:
Avoid mixing types...
So do convert a and b to be the same before you attempt a operator b

If I were to hazard a guess, I'd say those functions leverage low-level math functionality (perhaps in C) that does not use decimals internally, and so returning a decimal would require a cast from double to decimal anyway. Besides, the purpose of the decimal value type is to ensure accuracy; these functions do not and cannot return 100% accurate results without infinite precision (e.g., irrational numbers).

Neither Decimal nor float or double are good enough if you require something to be precise. Furthermore, Decimal is so expensive and overused out there it is becoming a regular joke.
If you work in fractions and require ultimate precision, use fractions. It's same old rule, convert once and only when necessary. Your rounding rules too will vary per app, domain and so on, but sure you can find an odd example or two where it is suitable. But again, if you want fractions and ultimate precision, the answer is not to use anything but fractions. Consider you might want a feature of arbitrary precision as well.
The actual problem with CLR in general is that it is so odd and plain broken to implement a library that deals with numerics in generic fashion largely due to bad primitive design and shortcoming of the most popular compiler for the platform. It's almost the same as with Java fiasco.
double just turns out to be the best compromise covering most domains, and it works well, despite the fact MS JIT is still incapable of utilising a CPU tech that is about 15 years old now.
[piece to users of MSDN slowdown compilers]

Double is a built-in type. Is is supported by FPU/SSE core (formerly known as "Math coprocessor"), that's why it is blazingly fast. Especially at multiplication and scientific functions.
Decimal is actually a complex structure, consisting of several integers.

How deal with the fact that most decimal fractions cannot be accurately represented in binary?

So, we know that fractions such as 0.1, cannot be accurately represented in binary base, which cause precise problems (such as mentioned here: Formatting doubles for output in C#).
And we know we have the decimal type for a decimal representation of numbers... but the problem is, a lot of Math methods, do not supporting decimal type, so we have convert them to double, which ruins the number again.
so what should we do?

Oh, what should we do about the fact that most decimal fractions cannot be represented in binary? or for that matter, that binary fractions cannot be represented in Decimal ?
or, even, that an infinity (in fact, a non-countable infinity) of real numbers in all bases cannot be accurately represented in any computerized system??
nothing! To recall an old cliche, You can get close enough for government work... In fact, you can get close enough for any work... There is no limit to the degree of accuracy the computer can generate, it just cannot be infinite, (which is what would be required for a number representation scheme to be able to represent every possible real number)
You see, for every number representation scheme you can design, in any computer, it can only represent a finite number of distinct different real numbers with 100.00 % accuracy. And between each adjacent pair of those numbers (those that can be represented with 100% accuracy), there will always be an infinity of other numbers that it cannot represent with 100% accuracy.

so what should we do?
We just keep on breathing. It really isn't a structural problem. We have a limited precision but usually more than enough. You just have to remember to format/round when presenting the numbers.
The problem in the following snippet is with the WriteLine(), not in the calculation(s):
double x = 6.9 - 10 * 0.69;
Console.WriteLine("x = {0}", x);
If you have a specific problem, th post it. There usually are ways to prevent loss of precision. If you really need >= 30 decimal digits, you need a special library.

Keep in mind that the precision you need, and the rounding rules required, will depend on your problem domain.
If you are writing software to control a nuclear reactor, or to model the first billionth of a second of the universe after the big bang (my friend actually did that), you will need much higher precision than if you are calculating sales tax (something I do for a living).
In the finance world, for example, there will be specific requirements on precision either implicitly or explicitly. Some US taxing jurisdictions specify tax rates to 5 digits after the decimal place. Your rounding scheme needs to allow for that much precision. When much of Western Europe converted to the Euro, there was a very specific approach to rounding that was written into law. During that transition period, it was essential to round exactly as required.
Know the rules of your domain, and test that your rounding scheme satisfies those rules.

I think everyone implying:
Inverting a sparse matrix? "There's an app for that", etc, etc
Numerical computation is one well-flogged horse. If you have a problem, it was probably put to pasture before 1970 or even much earlier, carried forward library by library or snippet by snippet into the future.

you could shift the decimal point so that the numbers are whole, then do 64 bit integer arithmetic, then shift it back. Then you would only have to worry about overflow problems.

And we know we have the decimal type
for a decimal representation of
numbers... but the problem is, a lot
of Math methods, do not supporting
decimal type, so we have convert them
to double, which ruins the number
again.
Several of the Math methods do support decimal: Abs, Ceiling, Floor, Max, Min, Round, Sign, and Truncate. What these functions have in common is that they return exact results. This is consistent with the purpose of decimal: To do exact arithmetic with base-10 numbers.
The trig and Exp/Log/Pow functions return approximate answers, so what would be the point of having overloads for an "exact" arithmetic type?

How to fix precision of variable

In c#
double tmp = 3.0 * 0.05;
tmp = 0.15000000000000002
This has to do with money. The value is really $0.15, but the system wants to round it up to $0.16. 0.151 should probably be rounded up to 0.16, but not 0.15000000000000002
What are some ways I can get the correct numbers (ie 0.15, or 0.16 if the decimal is high enough).

Use a fixed-point variable type, or a base ten floating point type like Decimal. Floating point numbers are always somewhat inaccurate, and binary floating point representations add another layer of inaccuracy when they convert to/from base two.

Money should be stored as decimal, which is a floating decimal point type. The same goes for other data which really is discrete rather than continuous, and which is logically decimal in nature.
Humans have a bias to decimal for obvious reasons, so "artificial" quantities such as money tend to be more appropriate in decimal form. "Natural" quantities (mass, height) are on a more continuous scale, which means that float/double (which are floating binary point types) are often (but not always) more appropriate.

In Patterns of Enterprise Application Architecture, Martin Fowler recommends using a Money abstraction
http://martinfowler.com/eaaCatalog/money.html
Mostly he does it for dealing with Currency, but also precision.
You can see a little of it in this Google Book search result:
http://books.google.com/books?id=FyWZt5DdvFkC&pg=PT520&lpg=PT520&dq=money+martin+fowler&source=web&ots=eEys-C_vdA&sig=jckdxgMLSRJtGDYZtcbYST1ak8M&hl=en&sa=X&oi=book_result&resnum=6&ct=result

'decimal' type was designed especially for this

A decimal data type would work well and is probably your choice.
However, in the past I've been able to do this in an optimized way using fixed point integers. It's ideal for high performance computations where decimal bogs down and you can't have the small precision errors of float.
Start with, say an Int32, and split in half. First half is whole number portion, second half is fractional portion. You get 16-bits of signed integer plus 16 bits of fractional precision. e.g. 1.5 as an 16:16 fixed point would be represented as 0x00018000. Or, alter the distribution of bits to suit your needs.
Fixed point numbers can generally be added/sub/mul/div like any other integer, with a little bit of work around mul/div to avoid overflows.

What you faced is a rounding problem, which I had mentioned earlier in another post
Can I use “System.Currency” in .NET?
And refer to this as well Rounding