# Part II: Program Control

## Full text

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www.nand2tetris.org

Building a Modern Computer From First Principles

## Virtual Machine

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### . . .

RISC

VM language

other digital platforms, each equipped RISC

machine language

Hack

Hack machine language CISC

machine language

CISC

### . . .

a high-levelwritten in language

Any

### . . .

VM implementation

over CISC platforms

VM imp.

over RISC platforms

VM imp.

over the Hack platform VM

emulator Some Other

language

Jack language

compilerSome Some Other compiler

compilerJack

Some

language

### . . .

Chapters 1-6

Chapters 7-8

Chapters 9-13

A Java-based emulator is included in the course software suite

Implemented in Projects 7-8

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### The VM language

Goal: Complete the specification and implementation of the VM model and language

Method: (a) specify the abstraction (model’s constructs and commands) (b) propose how to implement it over the Hack platform.

sub neg eq gt lt and or not

Memory access commands

pop x (pop into x, which is a variable) push y (y being a variable or a constant)

Program flow commands

label     (declaration) goto      (label)

if‐goto   (label)

Function calling commands

function  (declaration) call (a function) return (from a function)

Chapter 7 Chapter 8

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### The compilation challenge

class Main { static int x;

function void main() {

// Inputs and multiplies two numbers var int a, b, c;

let a = Keyboard.readInt(“Enter a number”);

let b = Keyboard.readInt(“Enter a number”);

let c = Keyboard.readInt(“Enter a number”);

let x = solve(a,b,c);

return;

} }

// Solves a quadratic equation (sort of) function int solve(int a, int b, int c) {

var int x;

if (~(a = 0))

x=(‐b+sqrt(b*b–4*a*c))/(2*a);

else

x=‐c/b;

return x;

} }

Source code (high-level language)

Our ultimate goal:

Translate high-level programs into

executable code.

Compiler

0000000000010000 1110111111001000 0000000000010001 1110101010001000 0000000000010000 1111110000010000 0000000000000000 1111010011010000 0000000000010010 1110001100000001 0000000000010000 1111110000010000 0000000000010001 0000000000010000 1110111111001000 0000000000010001 1110101010001000 0000000000010000 1111110000010000 0000000000000000 1111010011010000 0000000000010010 1110001100000001 0000000000010000 1111110000010000 0000000000010001

...

Target code

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### The compilation challenge / two-tier setting

if (~(a = 0))

x = (‐b+sqrt(b*b–4*a*c))/(2*a) else

x = ‐c/b  Jack source code

push a push 0 eq

if‐goto elseLabel push b

neg push b push b call mult push 4 push a call mult push c call mult call sqrt add

push 2 push a call mult div

pop x

goto contLable elseLabel:

push c neg push b call div pop x contLable:

Compiler

VM (pseudo) code

0000000000010000 1110111111001000 0000000000010001 1110101010001000 0000000000010000 1111110000010000 0000000000000000 1111010011010000 0000000000010010 1110001100000001 0000000000010000 1111110000010000 0000000000010001 0000000000010000 1110111111001000 0000000000010001 1110101010001000 0000000000010000 1111110000010000 0000000000000000 1111010011010000 0000000000010010 1110001100000001 0000000000010000 1111110000010000 0000000000010001 0000000000010010 1110001100000001 ...

VM translator

Machine code

### the desired semantics.

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// Computes x = (‐b + sqrt(b^2 ‐4*a*c)) / 2*a if (~(a = 0))

x = (‐b + sqrt(b * b – 4 * a * c)) / (2 * a) else

x = ‐ c / b

Typical compiler’s source code input:

### The compilation challenge

arithmetic expressions function call and

return logic Boolean

expressions program flow logic

(branching)

### In a two-tier compilation model, the overall translation challenge is broken between a front-end compilation stage and a subsequent back-

end translation stage

### arithmetic / Boolean expressions and program flow / function calling

(previous lecture) (previous lecture)

(this lecture) (this lecture)

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### Lecture plan

sub neg eq gt lt and or not

Memory access commands

pop x (pop into x, which is a variable) push y (y being a variable or a constant)

Program flow commands

label     (declaration) goto      (label)

if‐goto   (label)

Function calling commands

function  (declaration) call (a function) return (from a function) Chapter 7

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### Program flow commands in the VM language

How to translate these abstractions into assembly?

Simple: label declarations and goto directives can be effected directly by assembly commands

More to the point: given any one of these three VM commands, the VM Translator must emit one or

more assembly commands that effects the same semantics on the Hack platform

label c    // label declaration

// VM command following the label c if‐goto c // pops the topmost stack element;

// if it’s not zero, jumps to the

// VM command following the label c In the VM language, the program flow abstraction is delivered using three commands:

VM code example:

function mult 1 push constant 0 pop local 0

label loop

push argument 0  push constant 0 eq

if‐goto end

push argument 0 push 1

sub

pop argument 0 push argument 1 push local 0 add

pop local 0 goto loop label end

push local 0

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### Lecture plan

sub neg eq gt lt and or not

Memory access commands

pop x (pop into x, which is a variable) push y (y being a variable or a constant)

Program flow commands

label     (declaration) goto      (label)

if‐goto   (label)

Function calling commands

function  (declaration) call (a function) return (from a function) previous

lecture

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### The challenge: implement this abstraction, i.e. allow the program control to flow effortlessly between one subroutine to the other

// Compute x = (‐b + sqrt(b^2 ‐4*a*c)) / 2*a if (~(a = 0))

x = (‐b + sqrt(b * b – 4 * a * c)) / (2 * a) else

x = ‐ c / b

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### Subroutines in the VM language

function mult 1 push constant 0

pop local 0 // result (local 0) = 0 label loop

push argument 0  push constant 0 eq

if‐goto end // if arg0==0, jump to end push argument 0

push 1 sub

pop argument 0  // arg0‐‐

push argument 1 push local 0 add

pop local 0  // result += arg1 goto loop

label end

push local 0  // push result return

Called code, aka “callee” (example) ...

// computes (7 + 2) * 3 ‐ 5  push constant 7

push constant 3 call mult

push constant 5 sub

...

Calling code, aka “caller” (example)

VM subroutine call-and-return commands

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### The following scenario happens

The caller pushes the necessary arguments and call callee

### The space of callee’s local variables is allocated

The callee executes what it is supposed to do

The callee removes all arguments and pushes the result to the stack

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### Stack as the facility for subroutines

function a call b call c  ...

function b call c call d ...

function c call d ...

function d ...

code flow stack

start a start b

start c start d end d end c start d end d end b start c

start d end d end c end a

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### A: Because it simplifies the VM implementation (later).

function g nVars // here starts a function called g,

// which has nVars local variables

call g nArgs // invoke function g for its effect;

// nArgs arguments have already been pushed // onto the stack

return // terminate execution and return control // to the caller

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### Function call-and-return conventions

function mult 1 push constant 0

pop local 0 // result (local 0) = 0 label loop

...         // rest of code omitted label end

push local 0  // push result return

called function aka “callee” (example) function demo 3

...

push constant 7 push constant 2 add

push constant 3 call mult

...

Calling function

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### Function call-and-return conventions

function mult 1 push constant 0

pop local 0 // result (local 0) = 0 label loop

...         // rest of code omitted label end

push local 0  // push result return

called function aka “callee” (example) function demo 3

...

push constant 7 push constant 2 add

push constant 3 call mult

...

Calling function

Call-and-return programming convention

The caller must push the necessary argument(s), call the callee, and wait for it to return

Before the callee terminates (returns), it must push a return value

At the point of return, the callee’s resources are recycled, the caller’s state is re-instated, execution continues from the command just after the call

Caller’s net effect: the arguments were replaced by the return value (just like with primitive commands)

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### Function call-and-return conventions

function mult 1 push constant 0

pop local 0 // result (local 0) = 0 label loop

...         // rest of code omitted label end

push local 0  // push result return

called function aka “callee” (example) function demo 3

...

push constant 7 push constant 2 add

push constant 3 call mult

...

Calling function

Behind the scene

Recycling and re-instating subroutine resources and states is a major headache

Some agent (either the VM or the compiler) should manage it behind the scene “like magic”

In our implementation, the magic is VM / stack-based, and is considered a great CS gem.

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### The function-call-and-return protocol

The caller’s view:

 Before calling a function g, I must push onto the stack as many arguments as needed by g

 Next, I invoke the function using the command call g nArgs

 After g returns:

 The arguments that I pushed before the call have disappeared from the stack, and a return value (that always exists) appears at the top of the stack

 All my memory segments (local, argument, this, that, pointer) are the same as before the call.

Blue = VM function writer’s responsibility

Black = black box magic, delivered by the VM implementation

Thus, the VM implementation writer must worry about the “black operations” only.

function g nVars call g nArgs return

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### The function-call-and-return protocol

 When I start executing, my argument segment has been initialized with actual argument values passed by the caller

 My local variables segment has been allocated and initialized to zero

 The static segment that I see has been set to the static segment of the VM file to which I belong, and the working stack that I see is empty

 Before exiting, I must push a value onto the stack and then use the command return.

The callee’s (g ‘s) view:

function g nVars call g nArgs return

Blue = VM function writer’s responsibility

Black = black box magic, delivered by the VM implementation

Thus, the VM implementation writer must worry about the “black operations” only.

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When function f calls function g, the VM implementation must:

Save the return address within f ‘s code:

the address of the command just after the call

Save the virtual segments of f

Allocate, and initialize to 0, as many local variables as needed by g

Set the local and argument segment pointers of g

Transfer control to g.

When g terminates and control should return to f, the VM implementation must:

Clear g ’s arguments and other junk from the stack

Restore the virtual segments of f

Transfer control back to f

Q: How should we make all this work “like magic”?

A: We’ll use the stack cleverly.

### The function-call-and-return protocol: the VM implementation view

function g nVars call g nArgs return

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### The implementation of the VM’s stack on the host Hack RAM

Global stack:

the entire RAM area dedicated for holding the stack

Working stack:

The stack that the current function sees

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### The implementation of the VM’s stack on the host Hack RAM

At any point of time, only one function (the current function) is executing; other functions may be waiting up the calling chain

irrelevant to the current function

The current function sees only the working stack, and has access only to its memory segments

The rest of the stack holds the frozen states of all the functions up the calling hierarchy.

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call g nArgs

### command

Implementation: If the VM is implemented as a program that translates VM code into assembly code, the

// In the course of implementing the code of f

// (the caller), we arrive to the command call g nArgs.

// we assume that nArgs arguments have been pushed // onto the stack. What do we do next?

// We generate a symbol, let’s call it returnAddress;

// Next, we effect the following logic:

push returnAddress // saves the return address push LCL       // saves the LCL of f

push ARG       // saves the ARG of f push THIS      // saves the THIS of f push THAT      // saves the THAT of f ARG = SP‐nArgs‐5   // repositions SP for g LCL = SP       // repositions LCL for g goto g       // transfers control to g returnAddress:       // the generated symbol

call g nArgs

None of this code is executed yet ...

At this point we are just generating code (or simulating the VM code on some platform)

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function g nVars

### command

argument nArgs-1 ARG

saved THIS saved ARG saved returnAddress

saved LCL

local 0 local 1

### . . .

local nVars-1 argument 0 argument 1

### . . .

frames of all the functions up the calling chain

LCL

SP

saved THAT

Implementation: If the VM is implemented as a program that translates VM code into assembly code, the

translator must emit the above logic in assembly.

function g nVars

// to implement the command function g nVars, // we effect the following logic:

g:

repeat nVars times:

push 0

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return

### command

Implementation: If the VM is implemented as a program that translates VM code into assembly code, the

// In the course of implementing the code of g, // we arrive to the command return.

// We assume that a return value has been pushed  // onto the stack.

// We effect the following logic:

frame = LCL      // frame is a temp. variable retAddr = *(frame‐5) // retAddr is a temp. variable

*ARG = pop       // repositions the return value // for the caller

SP=ARG+1       // restores the caller’s SP THAT = *(frame‐1)    // restores the caller’s THAT THIS = *(frame‐2)    // restores the caller’s THIS ARG = *(frame‐3)     // restores the caller’s ARG LCL = *(frame‐4)     // restores the caller’s LCL goto retAddr // goto returnAddress

return

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### Example: factorial

function fact (n) { int result, j;

result = 1;

j = 1;

while ((j=j+1) <= n) {  result = result * j;

}

return result;

}

High-level code function fact(n) push 0

pop result push 1

pop j label loop

pop j push n gt

if‐goto end push result push j

mult

pop result goto loop label end

push result return

VM code (first approx.)

...

loop:

if ((j=j+1) > n) goto end result=result*j

goto loop end:

...

Pseudo code

function fact 2 push constant 0 pop local 0

push constant 1 pop local 1

label loop

push constant 1 push local 1 add

pop local 1

push argument 0 gt

if‐goto end push local 0 push local 1 call mult 2 pop local 0

goto loop label end

push local 0 return

VM code

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function p ...

push constant 4 call fact 1

...

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### Example: factorial

function fact (n) { int r;

if (n!=1)

r = n * fact(n‐1);

else

r = 1;

return r;

}

High-level code function fact(n)    push n

push 1 eq

if‐goto else push n

push 1 sub

fact push n mult pop r

goto cont label else

push 1 pop r label cont

push r return

VM code (first approx.)

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### Example: factorial

function fact (n) { int r;

if (n!=1)

r = n * fact(n‐1);

else

r = 1;

return r;

}

High-level code function fact(n)    push n

push 1 eq

if‐goto else push n

push 1 sub

fact push n mult

goto cont label else

push 1 label cont

return

VM code (first approx.) VM code

function fact 1    push argument 0 push constant 1 eq

if‐goto else push argument 0 push constant 1 sub

call fact 1

push argument 0 call mult 2

goto cont label else

push constant 1 label cont

return

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### Calling stack for fact(4)

stack

frame fact(4) function fact (n) {

int r;

if (n!=1)

r = n * fact(n‐1);

else

r = 1;

return r;

}

High-level code

frame fact(3) frame fact(2) frame fact(1)

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### Calling stack for fact(4)

stack

frame fact(4) function fact (n) {

int r;

if (n!=1)

r = n * fact(n‐1);

else

r = 1;

return r;

}

High-level code

frame fact(3) frame fact(2) frame mult(2,1)

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### Calling stack for fact(4)

stack

frame fact(4) function fact (n) {

int r;

if (n!=1)

r = n * fact(n‐1);

else

r = 1;

return r;

}

High-level code

frame fact(3) frame mult(3,2)

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### Calling stack for fact(4)

stack

frame fact(4) function fact (n) {

int r;

if (n!=1)

r = n * fact(n‐1);

else

r = 1;

return r;

}

High-level code

frame mult(4,6)

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### Bootstrapping

SP = 256        // initialize the stack pointer to 0x0100

A high-level jack program (aka application) is a set of class files.

By a Jack convention, one class must be called Main, and this class must have at least one function, called main.

The contract: when we tell the computer to execute a Jack program, the function Main.main starts running

Implementation:

 After the program is compiled, each class file is translated into a .vm file

 The operating system is also implemented as a set of .vm files (aka

“libraries”)

that co-exist alongside the program’s .vm files

One of the OS libraries, called Sys.vm, includes a method called init.

The Sys.init function starts with some OS initialization code (we’ll deal with this later, when we discuss the OS), then it does call Main.main

 Thus, to bootstrap, the VM implementation has to effect (e.g. in assembly), the following operations:

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### Code mobility: Internet, cloud

. . .

VM language

RISC machine

language Hack

CISC machine

language . . . a high-levelwritten in

language

. . .

VM implementation

over CISC platforms

VM imp.

over RISC

platforms emulatorVM Translator

Some Other

language Jack

Some

compiler Some Other

compiler compiler

. . .

Some

language . . .

Benefits of managed code:

Security

Array bounds, index checking, …

Etc.

VM Cons

 Performance.

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### simple compilers

. . .

VM language

RISC machine

language Hack

CISC machine

language . . . a high-levelwritten in

language

. . .

VM implementation

over CISC platforms

VM imp.

over RISC

platforms emulatorVM Translator

Some Other

language Jack

Some

compiler Some Other

compiler compiler

. . .

Some

language . . .

Benefits of managed code:

Security

Array bounds, index checking, …

Etc.

VM Cons

 Performance.

Updating...

## References

Related subjects :