If you, like so many travelers of the western world, including your humble Author, have considered traveling to the Middle East, but were uncertain about the question of whether it is necessary to pack toilet paper, and if it is, then how much should be packed, the Author hopes to answer your questions on that subject once and for all.
The short answer is, no.
To expostulate a little further:
In the Author's limited travels, so far confined to the airport in Dubai, a 5-star hotel in downtown Riyadh, and a modern, recently built office building, the Author has found that toilet paper is in generous supply. Whether this condition also applies to less urban parts of Saudi Arabia or other countries in the Middle East, the Author is humbly unable to answer.
To go into the question much further, one comes up against the larger issue of whether there are any of "life's necessities" that the western traveler should consider packing when traveling to this distant and exotic location.
There is in fact one vital necessity that the Author highly recommends packing, something that is indisputably necessary to those of us accustomed to western mores and traditions, though, unexpectedly, something that it seems the natives of these parts and many of the inhabitants who hail from other Muslim lands do not seem to need at all.
That necessity is air ... oxygen ... something to breath.
Upon descending from the airplane at King Khalid International Airport and attempting to inhale for the first time in Riyadh, one is immediately struck, rather forcefully, by the lack of oxygen in the air. There seem to be many varieties of particulate ranging from sand to cigarette smoke to diesel exhaust available for inhalation. But these various particles displace the oxygen and associated gases that one becomes accustomed to, living in the West. Surprisingly, the natives and other residents seem to be perfectly adapted to inhaling this atmosphere, to the extent that they often add to it by smoking large numbers of cigarettes while gathered in groups.
Therefore, the Author suggests, Gentle Reader, that you consider packing several oxygen tanks and a portable fan powered air filter with a washable/reusable filter element. This will assuredly make your visit to Riyadh far more pleasant and may even enable you to return to your home, when that happy day comes after long travels, where your feet feel the familiar earth beneath them and your eyes feast on the happy sights of pleasant memory, alive.