Generate unique number within range (0 – X), keeping a history to prevent duplicates

This should do it:

function makeRandomRange(x) {
    var used = new Array(x),
        exhausted = false;
    return function getRandom() {
        var random = Math.floor(Math.random() * x);
        if (exhausted) {
            return random;
        } else {
            for (var i=0; i<x; i++) {
                random = (random + 1) % x;
                if (random in used)
                    continue;
                used[random] = true;
                return random;
            }
            // no free place found
            exhausted = true;
            used = null; // free memory
            return random;
        }
    };
}

Usage:

var generate = makeRandomRange(20);

var x1 = generate(),
    x2 = generate(),
    ...

---

Although it works, it has no good performance when the x-th random is generated – it searches the whole list for a free place. This algorithm, a step-by-step Fisher–Yates shuffle, from the question Unique (non-repeating) random numbers in O(1)?, will perform better:

function makeRandomRange(x) {
    var range = new Array(x),
        pointer = x;
    return function getRandom() {
        pointer = (pointer-1+x) % x;
        var random = Math.floor(Math.random() * pointer);
        var num = (random in range) ? range[random] : random;
        range[random] = (pointer in range) ? range[pointer] : pointer;
        return range[pointer] = num;
    };
}

(Demo at jsfiddle.net)

Extended version which does only generate one “group” of unique numbers:

function makeRandomRange(x) {
    var range = new Array(x),
        pointer = x;
    return function getRandom() {
        if (range) {
            pointer--;
            var random = Math.floor(Math.random() * pointer);
            var num = (random in range) ? range[random] : random;
            range[random] = (pointer in range) ? range[pointer] : pointer;
            range[pointer] = num;
            if (pointer <= 0) { // first x numbers had been unique
                range = null; // free memory;
            }
            return num;
        } else {
            return Math.floor(Math.random() * x);
        }
    };
}

(Demo)