How to implement infinity in Java?

Question

Does Java have anything to represent infinity for every numerical data type? How is it implemented such that I can do mathematical operations with it?

E.g.

int myInf = infinity; //However it is done
myInf + 5; //returns infinity
myInf*(-1); //returns negative infinity

I have tried using very large numbers, but I want a proper, easy solution.

Answer 1

double supports Infinity

double inf = Double.POSITIVE_INFINITY;
System.out.println(inf + 5);
System.out.println(inf - inf); // same as Double.NaN
System.out.println(inf * -1); // same as Double.NEGATIVE_INFINITY

prints

Infinity
NaN
-Infinity

note: Infinity - Infinity is Not A Number.

Answer 2

A generic solution is to introduce a new type. It may be more involved, but it has the advantage of working for any type that doesn't define its own infinity.

If T is a type for which lteq is defined, you can define InfiniteOr<T> with lteq something like this:

class InfiniteOr with type parameter T:
    field the_T of type null-or-an-actual-T
    isInfinite()
        return this.the_T == null
    getFinite():
        assert(!isInfinite());
        return this.the_T
    lteq(that)
        if that.isInfinite()
            return true
        if this.isInfinite()
            return false
        return this.getFinite().lteq(that.getFinite())

I'll leave it to you to translate this to exact Java syntax. I hope the ideas are clear; but let me spell them out anyways.

The idea is to create a new type which has all the same values as some already existing type, plus one special value which—as far as you can tell through public methods—acts exactly the way you want infinity to act, e.g. it's greater than anything else. I'm using null to represent infinity here, since that seems the most straightforward in Java.

If you want to add arithmetic operations, decide what they should do, then implement that. It's probably simplest if you handle the infinite cases first, then reuse the existing operations on finite values of the original type.

There might or might not be a general pattern to whether or not it's beneficial to adopt a convention of handling left-hand-side infinities before right-hand-side infinities or vice versa; I can't tell without trying it out, but for less-than-or-equal (lteq) I think it's simpler to look at right-hand-side infinity first. I note that lteq is not commutative, but add and mul are; maybe that is relevant.

Note: coming up with a good definition of what should happen on infinite values is not always easy. It is for comparison, addition and multiplication, but maybe not subtraction. Also, there is a distinction between infinite cardinal and ordinal numbers which you may want to pay attention to.