[javascript] Using jQuery to compare two arrays of Javascript objects

I found this discussion because I needed a way to deep compare arrays and objects. Using the examples here, I came up with the following (broken up into 3 methods for clarity):

jQuery.extend({
    compare : function (a,b) {
        var obj_str = '[object Object]',
            arr_str = '[object Array]',
            a_type  = Object.prototype.toString.apply(a),
            b_type  = Object.prototype.toString.apply(b);

            if ( a_type !== b_type) { return false; }
            else if (a_type === obj_str) {
                return $.compareObject(a,b);
            }
            else if (a_type === arr_str) {
                return $.compareArray(a,b);
            }
            return (a === b);
        }
});

jQuery.extend({
    compareArray: function (arrayA, arrayB) {
        var a,b,i,a_type,b_type;
        // References to each other?
        if (arrayA === arrayB) { return true;}

        if (arrayA.length != arrayB.length) { return false; }
        // sort modifies original array
        // (which are passed by reference to our method!)
        // so clone the arrays before sorting
        a = jQuery.extend(true, [], arrayA);
        b = jQuery.extend(true, [], arrayB);
        a.sort(); 
        b.sort();
        for (i = 0, l = a.length; i < l; i+=1) {
            a_type = Object.prototype.toString.apply(a[i]);
            b_type = Object.prototype.toString.apply(b[i]);

            if (a_type !== b_type) {
                return false;
            }

            if ($.compare(a[i],b[i]) === false) {
                return false;
            }
        }
        return true;
    }
});

jQuery.extend({
    compareObject : function(objA,objB) {

        var i,a_type,b_type;

        // Compare if they are references to each other 
        if (objA === objB) { return true;}

        if (Object.keys(objA).length !== Object.keys(objB).length) { return false;}
        for (i in objA) {
            if (objA.hasOwnProperty(i)) {
                if (typeof objB[i] === 'undefined') {
                    return false;
                }
                else {
                    a_type = Object.prototype.toString.apply(objA[i]);
                    b_type = Object.prototype.toString.apply(objB[i]);

                    if (a_type !== b_type) {
                        return false; 
                    }
                }
            }
            if ($.compare(objA[i],objB[i]) === false){
                return false;
            }
        }
        return true;
    }
});

Testing

var a={a : {a : 1, b: 2}},
    b={a : {a : 1, b: 2}},
    c={a : {a : 1, b: 3}},
    d=[1,2,3],
    e=[2,1,3];

console.debug('a and b = ' + $.compare(a,b)); // a and b = true
console.debug('b and b = ' + $.compare(b,b)); // b and b = true
console.debug('b and c = ' + $.compare(b,c)); // b and c = false
console.debug('c and d = ' + $.compare(c,d)); // c and d = false
console.debug('d and e = ' + $.compare(d,e)); // d and e = true

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