Binary floating point summation accurate to full precision in JavaScript

gistfile1.js

// Read this first: http://code.activestate.com/recipes/393090/

function sum(ar) {
    var c = ar.length;
    var s = 0;
    for (var i = 0; i < c; i++) {
        s += ar[i];
    }
    return s;
}

function msum(ar) {
    var partials = [], x, y, j, k, i, tmp, hi, lo;

    for (j = 0; j < ar.length; j++) {
        x = ar[j];
        i = 0;
        for (k = 0; k < partials.length; k++) {
            y = partials[k];

            if (Math.abs(x) < Math.abs(y)) {
                tmp = x;
                x = y;
                y = tmp;
            }

            hi = x + y;
            lo = y - (hi - x);
            if (lo) {
                partials[i] = lo;
                i++;
            }
            x = hi;
        }
        if (partials.length > i) {
            partials.length = i;
        }
        partials.push(x);
    }

    var sum = 0.0;
    for (i = 0; i < partials.length; i++) {
        sum += partials[i];
    }

    return sum;
}


console.log('3 =', msum([1,2]), '=', sum([1,2]))
console.log('6 =', msum([1,2,3]), '=', sum([1,2,3]))
console.log('10 =', msum([1,2,3,4]), '=', sum([1,2,3,4]))

var a = [], i;
for (i = 0; i < 10000; i++) a.push(1, 1e100, 1, -1e100);
console.log('2 =', msum([1, 1e100, 1, -1e100]), '=', sum([1, 1e100, 1, -1e100]));
console.log('20000 =', msum(a), '=', sum(a));

Example output:

3 = 3 = 3
6 = 6 = 6
10 = 10 = 10
2 = 2 = 0
20000 = 20000 = 0