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  • >> Sean: We've done a series of hardware videos with Dr Bagley about various different

  • parts of CPUs, and things like this. And one of the things he'd mentioned during

  • one of the videos is something that I believe you want to tell us a bit more

  • about -- the Wheeler Jump ? >> DFB: Yes the Wheeler Jump David Wheeler [a]

  • very very talented computer scientist. An excellent lateral thinker. I didn't know

  • him very well; I knew him very slightly. Maybe met him four or five times but you

  • just had to be impressed that he, as a computer pioneer, had to grapple with the

  • fact that very early computers did not have enough registers in their CPUs.

  • >> Sean: Registers are just like tiny bits of memory? >> DFB: Yeah! tiny bits of memory, but within the

  • central processor unit. They could be built of much faster technology than

  • main memory, so typically, you know, like with the ARM chip at user level, you'd

  • end up with 16 general-purpose registers. One or two of those might be set aside

  • to use for all sorts of useful things. And one of the useful things was the

  • idea of -- you're running through your program -- you want to jump into a subroutine to

  • calculate a sine, or to print out "Hello World", or something like that. You don't

  • want it to be running linearly on your program you want to jump into it and

  • jump back out of it again. So you could use it several times in your program

  • from several different places. You could jump in and jump back out. Now David

  • Wheeler is credited with this idea of inventing the subroutine and say[ing] "Well,

  • yeah, when people want to calculate sine of something they don't want to have to

  • replicate, in their program, the coding for sine in six different places". It might

  • make it go faster - and of course some of you will know that if you write macros

  • you can force it [to create in-line code] to do that. [You] sacrifice a lot more code for faster speed But no, to

  • keep it clean you basically say "I want this piece of code to be separate but

  • "jumpable into" and "jump back outable from", back to where you came from.

  • So, before you jump in, at the moment of the jump, you've got to say "Where am i coming

  • from? Whose responsibility is it to remember

  • that? And in modern CPUs you would have a link register of some sort that

  • remembers. You didn't have that in the very early days. But, boy, did it [soon] dawn on them

  • that you needed it! So if you didn't have a link register how on earth were you

  • going to get into, and out of, your subroutine? So let's say you're coming

  • from 70 shall we say - location 70 - something like that? Right, now, on this

  • particular occasion therefore - when you get back out of that subroutine - you

  • don't want to go back to 70 itself because you'd end up in an endless loop

  • of jumping back into yourself you want to go to the instruction just beyond 70.

  • But you want to get back out! You want to remember 70 [and] add -- depending on the

  • architecture -- you add 1, 2, 4 ... depending. whetherWhen it's a byte machine, a word machine,

  • whatever. But you add a small number on to that address and say: "That's where I

  • want to get back to -- the instruction after where I jumped from". >> Sean: And the

  • problem is that you've got nowhere tosave [it]? >> DFB: Well, on modern machines [address] 70 would be

  • saved in a link register, maybe [on the ARM chip] register number 14, or something.

  • You say: "Jump to subroutine". The moment you say it, it automatically

  • remembers where you're jumping from and puts it in the link register. So when you

  • want to come back out you say: "ere I am, on this architecture, where's my link

  • register? Number 14?. Let's look at its content. Oh! it says "70" and I'm on a

  • 32-bit machine with 4 bytes to the word so that's ... I want to jump 4 beyond 70".

  • Or if it's, y' know, like EDSAC it might be 1 or 2 beyond. But you want to

  • just jump back to where you came from, slightly adjusted, with a little amount

  • added. And it is that link register that saves you from going insane. Now back in

  • the early days of David Wheeler and this EDSAC machine he had to do this for ...

  • Oh golly! I wish I had an extra register but I haven't

  • Wat register have I got, that's in use all the time, that might - if I'm very careful -

  • serve me all right. And the answer is - the Arithmetic Accumulator.

  • Every time you loaded a number into the accumulator, or did some arithmetic, the

  • answer stays in the accumulator. OK, so here's the deal: we're going to use the

  • arithmetic accumulator as the means of remembering where we came from. So here

  • you are at location 70, in the early EDSAC machine, what do you have to do ...

  • >> Sean: So, you have to add 70 to 0, or something? >> DFB: Yes! Basically "yes"! You're jumping

  • from 70 -- OK 70 has got to be in the accumulator at the moment of jump -- and

  • then you do an unconditional branch instruction to get to the start of the

  • subroutine. Fine! But you wake up in that subroutine your

  • first job is to preserve your link to get back! You must NOT do any arithmetic

  • - because you [might] feel like it. Duty calls! You must save off your return link

  • somewhere safe! Right?! Because, if you don't, you won't be able to get back.

  • But you have no spare ... >> Sean: So we've got nowhere to save .... >> DFB: ... no spare registers to save it

  • Yeah! you might think so, but how about this: suppose at the bottom of your

  • subroutine there is a branch instruction, a dummy one, which is basically going to

  • say branch, or jump, back to where I came from. But "where I came from"

  • must be a literal correct address. And in the accumulator is 70. So what you that

  • have to do is - knowing the length of your subroutine and its addresses and knowing

  • where the return instruction is planted as a dummy - you've basically got to turn

  • 70 into 72, 74, whatever it is, to make it go back to the next instruction after

  • where you came from. And you must literally plant that instruction and -

  • shock! horror! - overwrite your own program code at the bottom of this subroutine, so

  • that the dummy jump, which has probably got zeros left in it by now, becomes jump

  • back to location 72, shall we say. But you are actually

  • altering memory. Now can you imagine if that goes wrong, how to debug a program

  • that's trampling all over itself and jumping back to the wrong address! you

  • know >> Sean: Code gets altered all the time, right?! Can you give us some sense of how

  • sacrosanct these lines of code are when it's running? >> DFB: Well, code may seem to alter

  • itself all the time but it's usually altering itself by manipulating

  • registers in the CPU not physically overwriting memory in your main memory store.

  • >> Sean: So it's OK to obviously change the value for variables, and and all of

  • that, but actually changing those lines of code should be .... >> DFB: Changing variables is

  • fine. That's data. You're allowed to change data. What you're not allowed to

  • do is to treat a program-instruction bit pattern as if it was just a piece of

  • data and to patch something on top of it Now you can do this on Z80 chips,

  • I've tried doing it! If you go to very simple chips there's no protection

  • mechanisms. They'll let you do anything you want and you just hang yourself! Fine.

  • More advanced chips, now, and particularly operating systems make use of this, give

  • you an ability to mark which pieces of memory are read-only and are not to be

  • overwritten. And that way you can stay fairly sane.

  • Although you've left behind a polluted piece of code saying "jump back to 72" the

  • next time you come into this routine - maybe having jumped from 256, shall we

  • say, you've now got to remember 256six in the accumulator. The moment you

  • get in there you adjust it ever so slightly to come back to 258,

  • or whatever it is, and you plant that instruction to overwrite the jump back

  • to 72 which is still there, literally inside your code. So, every single call

  • you make into that subroutine the link back has to overwrite whatever

  • usage you had before and plant it in exactly the right place to get back. You

  • can see now why the moment EDSAC II came along - all of a sudden this had link

  • registers. All of this early experience just showed the pioneers

  • what the next generation of machinery had to have. And that's how the

  • importance of link registers became obvious. It will have occured to you of

  • course, Sean, I think I've got this right, that doing it the day David Wheeler way

  • with a Wheeler Junp, right, you successively at the end of your routine

  • of writing back and patching it with your address you need to get back to,

  • That's fine and it'll work. But what does that NOT enable you to do? Begins with an "R". omen

  • >> Sean: A further ... recursion oh yeah! >> DFB: One of thereasons for wanting a more general

  • mechanism for doing it is [that] you can't do recursion with the Wheeler method

  • because you've only got one place in memory, at the end of the subroutine,

  • where you patch back a new return address. What you need with recursion is

  • to have *several* return addresses all waiting to be used

  • queued up ... no not queued up ... stacked up on tha stack. So, that's the other thing.

  • >> Sean: Recursion is obviously a very particular special case but does this Wheeler Jump

  • not even allow you to do branches in branches? >> DFB: Oh! you can do that. Yes, yes, you

  • can do that but but actually having, y'know a thing call itself, since you've

  • textually only got one copy of the routine, just one, you're not able to

  • replicate the text in any way, there's no ability to do that. You can only damage

  • that one return address, just the one. That means that the next realization from

  • being a pioneer is my golly we've gotta be able to do recursion. My golly we need

  • more general-purpose registers and all this kind of stuff. And oh! also,

  • wouldn't it be nice to put a marker on memory saying: "Don't let anybody over-write

  • this!" And actually have it hardware- imposed not just by people's good nature.

>> Sean: We've done a series of hardware videos with Dr Bagley about various different

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ウィーラージャンプ - コンピュータマニア (Wheeler Jump - Computerphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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