www.nand2tetris.org
Building a Modern Computer From First Principles
Virtual Machine
Part I: Stack Arithmetic
Where we are at:
Assembler Chapter 6
H.L. Language
&
Operating Sys.
abstract interface
Compiler
Chapters 10 - 11
VM Translator
Chapters 7 - 8
Computer Architecture
Chapters 4 - 5
Gate Logic
Chapters 1 - 3 Electrical
Engineering
Physics Virtual
Machine
abstract interface
Software hierarchy
Assembly Language
abstract interface
Hardware hierarchy
Machine Language
abstract interface
Hardware Platform
abstract interface
Chips &
Logic Gates
abstract interface
Human Thought
Abstract design
Chapters 9, 12
Motivation
class Main { static int x;
function void main() {
// Inputs and multiplies two numbers var int a, b, x;
let a = Keyboard.readInt(“Enter a number”);
let b = Keyboard.readInt(“Enter a number”);
let x = mult(a,b);
return;
} }
// Multiplies two numbers.
function int mult(int x, int y) { var int result, j;
let result = 0; let j = y;
while ~(j = 0) {
let result = result + x;
let j = j – 1;
}
return result;
} }
Jack code (example)
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
...
Hack code
Compilation models
. . .
requires n m translators
hardware platform 2 hardware
platform 1
hardware platform m
. . .
language 1 language 2 language n
direct compilation:
.
. . .
hardware platform 2 hardware
platform 1
hardware platform m
. . .
language 1 language 2 language n
intermediate language
requires n + m translators
2-tier compilation:
Two-tier compilation:
First stage: depends only on the details of the source language
Second stage: depends only on the details of the target language.
The big picture
. . .
RISC
Intermediate code
other digital platforms, each equipped RISC
machine language
Hack
Hack machine language CISC
machine language
CISC
. . .
a high-levelwritten in languageAny
. . .
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
. . .
The intermediate code: The interface between the 2 compilation stages
Must be sufficiently general to support many
<high-level language, machine-language>
pairs
Can be modeled as the language of an abstract virtual machine (VM)
Can be implemented in several different ways.
Focus of this lecture
(yellow):
. . .
RISC machine
VM language
other digital platforms, each equipped with its VM implementation RISC
machine language
computerHack
Hack machine language CISC
machine language
CISC machine
. . .
a high-levelwritten in languageAny computer
. . .
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
. . .
1, 2, 3, 4, 5, 6 7, 8
9, 10, 11, 12 Book chapters and Course projects:
(this and the next lecture)
Virtual machines
A virtual machine (VM) is an emulation of a particular (real or hypothetical) computer system.
System virtual machine (full virtualization VMs): a complete substitute for the targeted real machine and a level of
functionality required for the execution of a complete operating system, e.g., VirtualBox.
Virtual machines
A virtual machine (VM) is an emulation of a particular (real or hypothetical) computer system.
System virtual machine (full virtualization VMs): a complete substitute for the targeted real machine and a level of
functionality required for the execution of a complete operating system, e.g., VirtualBox.
Process virtual machine: designed to execute a single computer
program by providing an abstracted and platform-independent program execution environment, e.g., Java virtual machine (JVM).
The VM model and language
Perspective:
From here till the end of the next lecture we describe the VM model used in the Hack-Jack platform
Other VM models (like Java’s JVM/JRE and .NET’s IL/CLR) are similar in spirit, but differ in scope and details.
The VM model and language
Several different ways to think about the notion of a virtual machine:
Abstract software engineering view:
the VM is an interesting abstraction that makes sense in its own right (a hypothetical machine closer to high-level language, but could still be built easily. Sometimes, no need to worry about how to implement it in hardware.)
Practical software engineering view:
the VM code layer enables “managed code” (e.g. enhanced security)
Pragmatic compiler writing view:
a VM architecture makes writing a compiler much easier (as we’ll see later in the course)
Opportunistic empire builder view:
a VM architecture allows writing high-level code once and have it run on many target platforms with little or no modification.
Hack virtual machine
Arithmetic / Boolean commands add
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
Goal: Specify and implement a VM model and language:
Our game plan: (a) describe the VM abstraction (3 types of instructions) (b) propose how to implement it over the Hack platform.
The stack
The stack:
A classical LIFO data structure
Elegant and powerful
Several hardware / software implementation options.
The stack
The stack:
A classical LIFO data structure
Elegant and powerful
Several hardware / software implementation options.
Several flavors: next empty/available, upward/downward
push(x)
stack[top]=x;
top++;
pop()
top‐‐;
return stack[top];
peek(), empty()
What is the stack good for?
Stack can be used for evaluating arithmetic expressions
Expression: 5 * (6+2) – 12/4
Infix
Prefix
Postfix
Stack is also good for implementing function call structures, such as subroutines, local variables and recursive calls. Will discuss it later.
Our VM model is stack-oriented
All operations are done on a stack
Data is saved in several separate memory segments
All the memory segments behave the same
One of the memory segments m is called static, and we will use it (as an arbitrary example) in the following examples:
Data types
Our VM model features a single 16-bit data type that can be used as:
an integer value (16-bit 2’s complement: ‐32768, ... , 32767)
a Boolean value (0 and ‐1, standing for true and false)
a pointer (memory address)
Memory access operations
(before)
push static 2
(after)
Evaluation of arithmetic expressions
// z=(2‐x)‐(y+5) push 2
push x sub push y push 5 add sub pop z
VM code (example) (suppose that
x refers to static 0, y refers to static 1, z refers to static 2)
Evaluation of Boolean expressions
// (x<7) or (y=8) push x
push 7 lt
push y push 8 eq
or
VM code (example) (suppose that
x refers to static 0, y refers to static 1)
(actually true and false
are stored as 0 and ‐1, respectively)
Arithmetic and Boolean commands in the VM language
(wrap-up)A VM program is designed to provide an interim abstraction of a program written in some high-level language.
Modern OO languages normally feature the following variable kinds:
Class level:
Static variables (class-level variables)
Private variables (aka “object variables” / “fields” / “properties”) Method level:
Local variables
Argument variables
When translated into the VM language,
The static, private, local and argument variables are mapped by the
compiler on the four memory segments static, this, local, argument In addition, there are four additional memory segments, whose role will
The VM’s Memory segments
Memory segments and memory access commands
Memory access VM commands:
pop memorySegment index
push memorySegment index
Where memorySegment is static, this, local, argument, that, constant, pointer, or temp
And index is a non-negative integer
The VM abstraction includes 8 separate memory segments named:
static, this, local, argument, that, constant, pointer, temp
As far as VM programming commands go, all memory segments look and behave the same
To access a particular segment entry, use the following generic syntax:
(In all our code examples thus far, memorySegment was static)
The different roles of the eight memory segments will become relevant when we’ll talk about the compiler
At the VM abstraction level, all memory segments are treated the same way.
VM programming
VM programs are normally written by compilers, not by humans However, compilers are written by humans ...
In order to write or optimize a compiler, it helps to first
understand the spirit of the compiler’s target language – the VM language
So, we’ll now see an example of a VM program
VM programming
The example includes three new VM commands:
function functionSymbol // function declaration
label labelSymbol // label declaration
if‐goto labelSymbol // pop x
// if x=true, jump to execute the // command after labelSymbol
// else proceed to execute the next // command in the program
For example, to effect if (x > n) goto loop, we can use the following VM commands:
push x push n gt
if‐goto loop // Note that x, n, and the truth value // were removed from the stack.
function mult (x,y) { int result, j;
result = 0;
j = y;
while ~(j = 0) {
result = result + x;
j = j ‐ 1;
}
return result;
}
High-level code
function mult(x,y) push 0
pop result push y
pop j label loop
push j push 0 eq
if‐goto end push result push x
add
pop result push j
push 1 sub pop j
goto loop label end
VM code (first approx.)
function mult 2 push constant 0 pop local 0 push argument 1 pop local 1 label loop
push local 1 push constant 0 eq
if‐goto end push local 0 push argument 0 add
pop local 0 push local 1 push constant 1 sub
pop local 1 goto loop label end VM code
...
loop:
if (j=0) goto end result=result+x j=j‐1
goto loop end:
...
Pseudo code
function mult (x,y) { int result, j;
result = 0;
j = y;
while ~(j = 0) {
result = result + x;
j = j ‐ 1;
}
return result;
}
High-level code
function mult(x,y) push 0
pop result push y
pop j label loop
push j push 0 eq
if‐goto end push result push x
add
pop result push j
push 1 sub pop j
goto loop label end
push result VM code (first approx.)
function mult 2 push constant 0 pop local 0 push argument 1 pop local 1 label loop
push local 1 push constant 0 eq
if‐goto end push local 0 push argument 0 add
pop local 0 push local 1 push constant 1 sub
pop local 1 goto loop label end
push local 0 VM code
VM programming:
multiple functions Compilation: A Jack application is a set of 1 or more class files (just like .java files).
When we apply the Jack compiler to these files, the compiler
creates a set of 1 or more .vm files (just like .class files). Each method in the Jack app is translated into a VM function written in the VM language
Thus, a VM file consists of one or more VM functions.
VM programming:
multiple functions Execution: At any given point of time, only one VM function is executing (the
“current function”), while 0 or more functions are waiting for it to terminate (the functions up the “calling hierarchy”)
For example, a main function starts running; at some point we may reach the command call factorial, at which point the factorial function starts running;
then we may reach the command call mult, at which point the mult function starts running, while both main and factorial are waiting for it to terminate
The stack: a global data structure, used to save and restore the
resources (memory segments) of all the VM functions up the calling hierarchy (e.g. main and factorial). The tip of this stack if the working stack of the current function (e.g. mult).
VM programming:
multiple functions (files)VM programming:
multiple functions (memory)Handling array
int foo() { // some language, not Jack int bar[10];
...
bar[2] = 19;
}
Handling array
Alternative push local 0 pop pointer 1
push constant 19
pop that 2
Handling objects
Class Ball { // some language, not Jack int x, y, radius, color;
int SetR(int r) {radius = r;}
}
Ball b;
b.SetR(10);
Handling objects
Lecture plan
Summary: Hack VM has the following instructions and eight memory segments.
Method: (a) specify the abstraction (stack, memory segments, commands) Arithmetic / Boolean commands
add 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
Implementation of VM on Hack
Each VM instruction must be translated into a set of Hack assembly code
VM segments need to be realized on the host memory
Implementation
VM implementation options:
Emulator-based (e.g. emulate the VM model using Java)
Translator-based (e. g. translate VM programs into the Hack machine language)
Hardware-based (realize the VM model using dedicated memory and registers)
Two well-known translator-based implementations:
JVM: Javac translates Java programs into bytecode;
The JVM translates the bytecode into
the machine language of the host computer
CLR: C# compiler translates C# programs into IL code;
The CLR translated the IL code into
the machine language of the host computer.
Software implementation: VM emulator
(part of the course software suite)VM implementation on the Hack platform (memory)
The stack: a global data structure, used to save and restore the resources of all the VM
functions up the calling hierarchy.
The tip of this stack if the working stack of the current function
static, constant, temp, pointer:
Global memory segments, all functions see the same four segments
local,argument,this,that:
these segments are local at the function level;
each function sees its own, private copy of each one of these four segments
The challenge:
represent all these logical constructs on the same single physical address space -- the host RAM.
Host
RAM
VM implementation on the Hack platform (memory)
Basic idea: the mapping of the stack and the global segments on the RAM is easy (fixed);
the mapping of the function-level segments is dynamic, using pointers
The stack: mapped on RAM[256 ... 2047];
The stack pointer is kept in RAM address SP static: mapped on RAM[16 ... 255];
each segment reference static i appearing in a VM file named f is compiled to the assembly language symbol f.i (recall that the assembler further maps such symbols to the RAM, from address 16 onward)
local,argument,this,that: these method-level segments are mapped somewhere from address 2048 onward, in an area called “heap”. The base addresses of these segments are kept in RAM addresses LCL, ARG, THIS, and THAT. Access to the i-th entry of any of these segments is
implemented by accessing RAM[segmentBase + i]
constant: a truly a virtual segment:
access to constant i is implemented by supplying the constant i.
pointer: discussed later.
Statics
3
12
. . .
4 5
14 15 0 1
13 2 THIS THAT SP LCL ARG
TEMP
255
. . .
16 General
purpose
2047
. . .256
2048
Stack
. . . Heap
Host
RAM
VM implementation on the Hack platform (memory)
Statics
3
12
. . .
4 5
14 15 0 1
13 2 THIS THAT SP LCL ARG
TEMP
255
. . .
16 General
purpose
2047
. . .256
2048
Stack
. . . Heap
Host RAM
Practice exercises
Now that we know how the memory segments are mapped on the host RAM, we can write Hack
commands that realize the various VM commands.
for example, let us write the Hack code that implements the following VM commands:
push constant 1
pop static 7 (suppose it appears in a VM file named f)
push constant 5
add
pop local 2
eq
Tips:
1.The implementation of any one of these VM commands requires several Hack assembly commands involving pointer arithmetic
(using commands like A=M)
2. If you run out of registers (you have only two ...),
VM implementation on the Hack platform (translator)
push constant 1
@1 D=A
@SP A=M M=D
@SP M=M+1
add
@SP AM=M‐1 D+M A=A‐1 M=M+D
pop local 2
@LCL D=M
@2 D=D+A
@R15 M=D
@SP AM=M‐1 D=M
@R15 A=M M=D
Perspective
In this lecture we began the process of building a compiler
Modern compiler architecture:
Front-end (translates from a high-level language to a VM language)
Back-end (translates from the VM language to the machine language of some target hardware platform)
Brief history of virtual machines:
1970’s: p-Code
1990’s: Java’s JVM
2000’s: Microsoft .NET
A full blown VM implementation typically also includes a common software library (can be viewed as a mini, portable OS).
. . .
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
compilerSome Some Other
compiler compiler
. . .
Some language . . .
The big picture
JVM
Java
Java compiler
JRE
CLR
C#
C# compiler
.NET base class library
VM
Jack
Jack compiler
Mini OS
7, 8
9
10, 11
12
(Book chapters and Course projects)
