How to determine if two rectangles overlap

// Assuming that x1,y1 and x2,y2 give the upper left and
// lower right coordinates of the rectangles (respectively).
function rectangles_dont_intersect(Ax1,Ay1,Ax2,Ay2,Bx1,By1,Bx2,By2) {
  return (Ax1 < Bx2) && (Ax2 > Bx1) && (Ay1 < By1) && (Ay2 > By2);
}

function rectangles_intersect(Ax1,Ay1,Ax2,Ay2,Bx1,By1,Bx2,By2) {
  return !rectangles_dont_intersect(Ax1,Ay1,Ax2,Ay2,Bx1,By1,Bx2,By2);
}