Question

For the issue of the floating precision, I defined my custom compare function for floating numbers:

bool cmp(double a, double b)
{
    if(abs(a - b) <= eps) return false;
    return a < b;
}

Then I call sort on some array of floating numbers. I’ve heard that some bad compare function will cause the sort to segment fault. I just wondering will cmp work correctly for sort? On one hand, cmp satisfied the associating rule. But on the other hand, cmp(x - eps, x) == false && cmp(x, x + eps) == false doesn’t mean cmp(x - eps, x + eps) == false.

I didn’t use sort directly on floating numbers because what I want to sort is pair<double, double>.
For example:

(1,2), (2,1), (2.000000001, 0)

I’d like to consider 2 and 2.000000001 as the same and expect the result to be:

(1,2), (2.000000001, 0), (2,1)

Answer 1

std::sort requires a comparer that defines a strict weak ordering. This means, among other things, that the following condition must be met:

• We define two items, a and b, to be equivalent (a === b) if !cmp(a, b) && !cmp(b, a)
• Equivalence is transitive: a === b && b === c => a === c

As you already say in your question, your function cmp() does not meet these conditions, so you cannot use your function in std::sort(). Not only the result of the algorithm will be unpredictable, which is bad unless you are actually looking for this unpredictability (cf. randomize): if you have a few values that are very close to each other, such that any of them compare true with some, but false with some others, the algorithm might enter an infinite loop.

So the answer is no, you cannot use your function cmp() in std::sort() unless you want to risk your program freezing.