}

        // compute the scale and rescale values
        final double scale;
        final double rescale;
        if (max > LARGE_THRESH) {
            scale = SCALE_DOWN;
            rescale = SCALE_UP;
        } else if (max < SAFE_SCALE_UP_THRESH) {
            scale = SCALE_UP;
            rescale = SCALE_DOWN;
        } else {
            scale = 1d;
            rescale = 1d;
        }

        // initialise sum and compensation using scaled x
        final double sx = xabs * scale;
        double sum = sx * sx;
        double comp = DD.twoSquareLow(sx, sum);

        // add scaled y
        final double sy = yabs * scale;
        final double py = sy * sy;
        comp += DD.twoSquareLow(sy, py);
        final double sumPy = sum + py;
        comp += DD.twoSumLow(sum, py, sumPy);
        sum = sumPy;