Pynchonesque Dialect in Inherent Vice?

Inherent Vice

Thomas Pynchon

(Image from Wikipedia)

I could easily have become one of those Pynchon addicts. No, not the sort that he writes about. The kind that get addicted to reading his books. I read Gravity's Rainbow when I was a senior in college way back in the 1970s and got blown away by its complexity. I also found it very funny. I went on to read nearly each of his other works but never found any of the others quite as entertaining . . . until now. Inherent Vice is a very different type of Pynchon novel. It has all the same features, of course -- the drugs, the paranoia, the weirdly named characters -- but they fit together in a different way. A gestalt thing, I suppose, with the whole being greater than the sum of its parts.

But I'm not yet up to doing any literary analysis of the book. I just have a tangential query stemming from the following freaky dialogue between a hippie named Denis (pronounced with a long "e," as in Venus) and the main character, Doc Sportello, who's also a hippie but works (if you can call it that) as a private investigator:

"So Doc, I'm up on Duncrest, you know the drugstore there, and like I noticed their sign, 'Drug'? 'Store'? Okay? Walked past it a thousand times, never really saw it -- Drug, Store! man, far out, so I went in and Smilin Steve was at the counter and I said, like, 'Yes, hi, I'd like some drugs, please?' -- oh, here, finish this up if you want."

"Thanks, all's 'at'll do 's just burn my lip."

Without being of a certain place and time (of America and of the sixties), a reader would likely find this dialogue rather difficult to follow. Denis's part of the conversation is perhaps not too hard. You only have to know that "far out" means something like "wow" . . . but what does Doc Sportello's reply mean? What has Denis just offered him? For someone who remembers the sixties, it's pretty clear. Denis has just offered Doc the butt end of a marijuana cigarette, only to have the offer turned down and the reason given. "Thanks" here means "Thanks, but no thanks," and the reason supplied by Doc is that the butt end is so short that the still burning marijuana cigarette is too little to get him high but just enough to burn his lip. In plainer English:

"Thanks, all that will do is just burn my lip."

Okay, that's clarified for anyone who might have been unsure. Now comes your turn to help me out. Here's my merely tangential query:

What does the "s" in "all's" mean?

Is it a contraction of "is," mistakenly carried over from the "all is" of, for example, "all's well"?

I don't dispute the fact that the expression used by Pynchon exists. I've also used the form "All's that'll do is . . ."

But where does the "s" come from?