As I can see BigInteger is a ValueType, as much as I know, a ValueType must have a maximum size of 16 bytes.
No, that's not true. It's a conventional limit, but it's entirely feasible for a value type to take more than that. For example:
public struct Foo {
private readonly int a, b, c, d, e; // Look ma, 20 bytes!
}
However, I strongly suspect that BigInteger
actually includes a reference to a byte array:
public struct BigInteger {
private readonly byte[] data;
// Some other fields...
}
(Moslem Ben Dhaou's answer shows one current implementation using int
and uint[]
, but of course the details of this are intentionally hidden.)
So the value of a BigInteger
can still be small, but it can refer to a big chunk of memory - and if there isn't enough memory to allocate what's required when you perform some operation, you'll get an exception.
How could it store such big values, as big as double.MaxValue + double.MaxValue ?
Well BigInteger
is for integers, so I wouldn't particularly want to use it for anything to do with double
... but fundamentally the limitations are going to be around how much memory you've got and the size of array the CLR can cope with. In reality, you'd be talking about enormous numbers before actually hitting the limit for any specific number - but if you have gazillions of smaller numbers, that obviously has large memory requirements too.