Finding if an array is ordered

I recently wrote a quick code to find if a numeric array is ordered i.e sorted in a ascending or descending order. I needed it to check a sort algorithm I had written. The problem is that the following code has a worst-case running time of O(N). Can we make the running time logarithmic.

/* orderedArray.php */

define("ORDER_ASC", 1);
define("ORDER_DSC", 0);

function is_array_ordered($array, $sort_order)
{
    $i=0;
    $total_elements = count($array);
    
    if($sort_order == ORDER_ASC)
    {
        //Check for ascending order
        while($total_elements > 1)
        {
            if($array[$i] < $array[$i+1]) 
            {
                $i++;
                $total_elements--;
            }
            else
            {
                return false;
            }
        }
    }
    elseif($sort_order == ORDER_DSC)
    {
        //Check for descending order
        while($total_elements > 1)
        {
            if($array[$i] > $array[$i+1]) 
            {
                $i++;
                $total_elements--;
            }
            else
            {
                return false;
            }
        }
    }
    
    return true;
}

The unit test for the same is given below.

include 'PHPUnit/Framework.php';
include 'orderedArray.php';

class ArrayTest extends PHPUnit_Framework_TestCase
{
    public function testArrayOrder()
    {
        // Ascending
        $test_array = array(0,1,2,3,4,6,7,8,9,10);
        $this->assertEquals(is_array_ordered($test_array, ORDER_ASC), true);
        
        $test_array = array(10,9,8,7,6,5,4,3,2,1,0);
        $this->assertEquals(is_array_ordered($test_array, ORDER_ASC), false);
        
        $test_array = array(0,1,2,3,4,6,7,8,9,10,1);
        $this->assertEquals(is_array_ordered($test_array, ORDER_ASC), false);
        
        $test_array = array(1,0,1,2,3,4,6,7,8,9,10);
        $this->assertEquals(is_array_ordered($test_array, ORDER_ASC), false);
        
        
        // Descending
        $test_array = array(10,9,8,7,6,5,4,3,2,1,0);
        $this->assertEquals(is_array_ordered($test_array, ORDER_DSC), true);
        
        $test_array = array(0,1,2,3,4,6,7,8,9,10);
        $this->assertEquals(is_array_ordered($test_array, ORDER_DSC), false);
        
        $test_array = array(10,9,8,7,6,5,4,3,2,1,0,1);
        $this->assertEquals(is_array_ordered($test_array, ORDER_DSC), false);
        
        $test_array = array(1,10,9,8,7,6,5,4,3,2,1,0);
        $this->assertEquals(is_array_ordered($test_array, ORDER_DSC), false);
        
    }
}