WIFI: LA Central Library?

DOWNTOWN LOS ANGELES — I just noticed that the Central Library website lists wifi in their computer center. I can't seem to find, though, if the coverage is specific to the computer center or if it covers the entire library. I could really use a good place to go with the laptop; all the cool ones I've been to are far from downtown. Something outside, like the coverage that should someday blanket Pershing Square, would be excellent.