Merge sort in JavaScript

I implemented this merge sort in JS and noticed that for random integer numbers it's a lot faster than the build in sort functions of all the browsers I tested (Chrome, FF, IE).
Does anyone have an idea why that is? Also, is there a way to make my code even faster?

function bubbleSort(f, a, start, end) {
    end--;
    while(end > start) {
        for(var i = start; i  0) {a[i] = y; a[i+1] = x;}
        }
        end--;
    }
}

function merge(f, a, start, a2, start2, mid, end) {
    var i = start, i1 = start2, i2 = mid;
    while(i1 = mid) {
        i1 = i2;
        mid = end;
    }
    while(i1 < mid) {
        a[i++] = a2[i1++];
    }
};

function _mergeSort(f, a1, a2, start, end) {
    var mid;
    if(end - start < 2) return;
    if(end - start < 8) { bubbleSort(f, a1, start, end); return; }
    mid = Math.floor((start + end)/2);
    _mergeSort(f, a2, a1, start, mid);
    _mergeSort(f, a2, a1, mid, end);
    merge(f, a1, start, a2, start, mid, end);
};

function mergeSort(f, a) {
    var a2 = a.slice();
    _mergeSort(f, a, a2, 0, a.length);
};

Here is some JSFiddle site to test the code
http://jsfiddle.net/mxbppLu0/
In Chrome I get the biggest difference (1.4 vs. 3 seconds for 10 million numbers)

You define the comparison function like this:

function(a, b) { return a - b }

and then you use it like this:

if (f(x, y)  0) { ... }

This is a bit tedious. It would be more intuitive like this:

function(a, b) { return a <= b }

and use it like this:

if (f(x, y)) { ... }
if (!f(x, y)) { ... }

Why is it faster?

I don't know, but as @Flambino commented:


I browsed around the V8 source code and the sort function does a lot of stuff, namely handling sorting of non-array objects, arrays with "holes", and similar cases. All of that before actually sorting anything. I have no idea what exactly is causing the slowdown, but, as mentioned, there's just a lot of stuff going on there. Their implementation is also sorting in-place, which could be a contributing factor. But I honestly haven't dug that deeply

How to make it faster?

Changing the comparison function like this:

function(a, b) { return a < b }

and the bubble sort condition to use 6 instead of 8 (in if (end - start < 6) { ...), together, often yielded faster result in my test runs, but not always, and I don't think that means anything.

The bottom line: I don't know...

Naming and formatting

The code would be more readable if you improved some of the names. For example renaming a and a2 to part1 and part2, respectively. Or even arr1 and arr2. It would make them look more like arrays, instantly.

This may be a matter of taste, but instead of this:

var x = a[i], y = a[i+1];
if(f(x, y) > 0) {a[i] = y; a[i+1] = x;}

I would find this slightly more readable:

var x = a[i];
var y = a[i + 1];
if (f(x, y) > 0) {
    a[i] = y;
    a[i + 1] = x;
}

StackExchange Code Review Q#59599, answer score: 4