Operating Systems
Elements of Computing Systems, Nisan & Schocken, MIT Press www.idc.ac.il/tecs
www.nand2tetris.org
Building a Modern Computer From First Principles
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
Jack revisited
/** Computes the average of a sequence of integers. */
class Main {
function void main() { var Array a;
var int length;
var int i, sum;
let length = Keyboard.readInt(”How many numbers? ”);
let a = Array.new(length); // Constructs the array let i = 0;
while (i < length) {
let a[i] = Keyboard.readInt(”Enter the next number: ”);
let sum = sum + a[i];
let i = i + 1;
}
do Output.printString(”The average is: ”);
do Output.printInt(sum / length);
do Output.println();
return;
}
/** Computes the average of a sequence of integers. */
class Main {
function void main() { var Array a;
var int length;
var int i, sum;
let length = Keyboard.readInt(”How many numbers? ”);
let a = Array.new(length); // Constructs the array let i = 0;
while (i < length) {
let a[i] = Keyboard.readInt(”Enter the next number: ”);
let sum = sum + a[i];
let i = i + 1;
}
do Output.printString(”The average is: ”);
do Output.printInt(sum / length);
do Output.println();
return;
}
Jack revisited
Typical OS functions
Language extensions / standard library
Mathematical operations (abs, sqrt, ...)
Abstract data types (String, Date, ...)
Output functions
(printChar, printString ...)
Input functions
(readChar, readLine ...)
Graphics functions
(drawPixel, drawCircle, ...)
And more ...
System-oriented services
Memory management (objects, arrays, ...)
I/O device drivers
Mass storage
File system
Multi-tasking
UI management (shell / windows)
Security
Communications
And more ...
The Jack OS
Math : Provides basic mathematical operations;
String : Implements the String type and string-related operations;
Array : Implements the Array type and array-related operations;
Output : Handles text output to the screen;
Screen : Handles graphic output to the screen;
Keyboard : Handles user input from the keyboard;
Memory : Handles memory operations;
Sys : Provides some execution-related services.
Jack OS API
class Math {
function void init() function int abs(int x)
function int multiply(int x, int y) function int divide(int x, int y) function int min(int x, int y) function int max(int x, int y) function int sqrt(int x)
}
Class String {
constructor String new(int maxLength) method void dispose()
method int length()
method char charAt(int j)
method void setCharAt(int j, char c) method String appendChar(char c)
method void eraseLastChar() method int intValue()
method void setInt(int j) function char backSpace() function char doubleQuote() function char newLine() }
Class Array {
function Array new(int size) method void dispose()
}
class Output {
function void moveCursor(int i, int j) function void printChar(char c)
function void printString(String s) function void printInt(int i)
function void println() function void backSpace() }
Class Screen {
function void clearScreen()
function void setColor(boolean b)
function void drawPixel(int x, int y) function void drawLine(int x1, int y1,
int x2, int y2)
function void drawRectangle(int x1, int y1, int x2, int y2) function void drawCircle(int x, int y, int r) }
class Memory {
function int peek(int address)
function void poke(int address, int value) function Array alloc(int size)
function void deAlloc(Array o) }
Class Keyboard {
function char keyPressed() function char readChar()
function String readLine(String message) function int readInt(String message) }
Class Sys {
function void halt():
function void error(int errorCode)
function void wait(int duration)
A typical OS:
Is modular and scalable
Empowers programmers (language extensions)
Empowers users (file system, GUI, ...)
Closes gaps between software and hardware
Runs in “protected mode”
Typically written in some high level language
Typically grows gradually, assuming more and more functions
Must be efficient.
Efficiency
We have to implement various operations on n -bit binary numbers ( n = 16, 32, 64, ...).
For example, consider multiplication
Naïve algorithm: to multiply x*y: { for i = 1 ... y do sum = sum + x } Run-time is proportional to y
In a 64-bit system, y can be as large as 2 64.
Multiplications can take years to complete
Algorithms that operate on n -bit inputs can be either:
Naïve: run-time is proportional to the value of the n -bit inputs
Good: run-time is proportional to n, the input’s size.
Run-time: proportional to n
Can be implemented in SW or HW
Division: similar idea.
Example I: multiplication
Example II: square root
The square root function has two convenient properties:
It’s inverse function is computed easily
Monotonically increasing
Functions that have these two properties can be computed by binary search:
Number of loop iterations is bounded by n/2, thus the run-time is O(n).
Complexity
Complexity
Donald Knuth 高德納
Born in 1938
Author of “The Art of Computer Programming”
《美國科學家》(American Scientist)雜誌曾將該書與愛因斯坦 的《相對論》、狄拉克的《量子力學》、理查·費曼的《量子電 動力學》等書並列為20世紀最重要的12本物理科學類專論書之 一。
Creator of Tex and metafont
Turing Award, 1974
$2.56 check
Math operations (in the Jack OS)
class Math {
function void init() function int abs(int x)
function int multiply(int x, int y) function int divide(int x, int y) function int min(int x, int y) function int max(int x, int y) function int sqrt(int x)
}
class Math { class String {
class Array { class Output {
class Screen { class Memory {
class Keyboard { class Sys {
function (…)
… }
The remaining functions are simple to implement.
String processing ( in the Jack OS)
Class String {
constructor String new(int maxLength) method void dispose()
method int length()
method char charAt(int j)
method void setCharAt(int j, char c) method String appendChar(char c)
method void eraseLastChar() method int intValue()
method void setInt(int j) function char backSpace() function char doubleQuote() function char newLine()
class Math { class String {
class Array { class Output {
class Screen { class Memory {
class Keyboard { class Sys {
function (…)
… }
Single digit ASCII conversions
asciiCode(digit) == digit + 48
digit(asciiCode) == asciiCode - 48
SingleDigit–to-character conversions: done
Number–to-string conversions:
Converting a number to a string
Memory management ( in the Jack OS )
class Memory {
function int peek(int address)
function void poke(int address, int value) function Array alloc(int size)
function void deAlloc(Array o) }
class Math { class String {
class Array { class Output {
class Screen { class Memory {
class Keyboard { class Sys {
function (…)
… }
The data structure that this algorithm manages is a single pointer: free.
Memory management (naive)
When a program constructs (destructs) an object, the OS has to allocate (de-allocate) a RAM block on the heap:
alloc(size): returns a reference to a free RAM block of size size
deAlloc(object): recycles the RAM block that object refers to
Memory management (improved)
Peek and poke
class Memory {
function int peek(int address)
function void poke(int address, int value) function Array alloc(int size)
function void deAlloc(Array o) }
Implementation: based on our ability to exploit exotic casting in Jack:
Graphics primitives ( in the Jack OS )
Class Screen {
function void clearScreen()
function void setColor(boolean b)
function void drawPixel(int x, int y)
function void drawLine(int x1, int y1, int x2, int y2) function void drawRectangle(int x1, int y1,int x2, int y2) function void drawCircle(int x, int y, int r)
}
class Math { class String {
class Array { class Output {
class Screen { class Memory {
class Keyboard { class Sys {
function (…)
… }
Memory-mapped screen
Pixel drawing
Implementation: using poke(address,value)
screen program
application physical
refresh mechanism screen
driver
part of the part of the
Image representation: bitmap versus vector graphics
Bitmap file: 00100, 01010,01010,10001,11111,10001,00000, . . .
Vector graphics file: drawLine(2,0,0,5), drawLine(2,0,4,5), drawLine(1,4,3,4)
Pros and cons of each method.
(0,0)
vector bitmap
pixel
Vector graphics: basic operations
drawPixel(x,y)
drawCircle(x,y,r)
drawLine(x1,y1,x2,y2)
drawRectangle(x1,y1,x2,y2)
1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 7 8 9 10 11 12 13 0
drawLine(0,3,0,11)
drawRectangle(1,3,5,9) drawLine(1,12,2,12) drawLine(3,10,3,11) drawLine(6,4,6,9) drawLine(7,0,7,12) drawLine(8,1,8,12)
(Primitive operation)
drawTriangle(x1,y1,x2,y2,x3,y3) etc. (a few more similar operations) 1
2 3 . . .
0 1 2 3 . . . 0
Screen =
grid of pixels
How to draw a line?
drawLine(x1,y1,x2,y2)
Basic idea: drawLine is implemented through a sequence of drawPixel operations
Challenge 1: which pixels should be drawn ?
Challenge 2: how to draw the line
fast?
Simplifying assumption: the line that we are asked to draw goes north-east.
Line Drawing
Given: drawLine(x1,y1,x2,y2)
Notation: x=x1, y=y1, dx=x2-x1, dy=y2-y1
Using the new notation:
We are asked to draw a line between (x,y) and (x+dx,y+dy)
set (a,b) = (0,0)
while there is more work to do drawPixel(x+a,y+b)
decide if you want to go right, or up if you decide to go right, set a=a+1;
if you decide to go up, set b=b+1
set (a,b) = (0,0)
while (a ≤ dx) and (b ≤ dy) drawPixel(x+a,y+b)
decide if you want to go right, or up if you decide to go right, set a=a+1;
if you decide to go up, set b=b+1 dx
dy
Line Drawing algorithm
drawLine(x,y,x+dx,y+dy) set (a,b) = (0,0)
while (a ≤ dx) and (b ≤ dy) drawPixel(x+a,y+b)
decide if you want to go right, or up if you decide to go right, set a=a+1;
if you decide to go up, set b=b+1
drawLine(x,y,x+dx,y+dy) set (a,b) = (0,0)
while (a ≤ dx) and (b ≤ dy) drawPixel(x+a,y+b) if b/a > dy/dx set a=a+1
else set b=b+1
costy
Line Drawing algorithm, optimized
b/a > dy/dx is the same as a*dy < b*dx Define diff = a*dy – b*dx
Let’s take a close look at this diff:
1.
b/a > dy/dx is the same as diff < 0
2.
When we set (a,b)=(0,0), diff = 0
3.
When we set a=a+1, diff goes up by dy When we set b=b+1, diff goes down by dx drawLine(x,y,x+dx,y+dy)
set (a,b) = (0,0)
while (a ≤ dx) and (b ≤ dy) drawPixel(x+a,y+b) if b/a > dy/dx set a=a+1
else set b=b+1
drawLine(x,y,x+dx,y+dy) set (a,b) = (0,0), diff = 0 while (a ≤ dx) and (b ≤ dy)
drawPixel(x+a,y+b)
if diff < 0 set a=a+1, diff = diff + dx else set b=b+1, diff = diff - dy
Motivation
When you draw polygons, e.g. in animation or video, you need to draw millions of lines
Therefore, drawLine must be ultra fast
Division is a very slow operation
Addition is ultra fast (hardware based)
Circle drawing
The screen
origin (0,0)
is at the top
left.
An anecdote about efficiency and design
… Jobs obsessed about the look of what would appear on the screen. One day Bill Atkinson burst into his office all excited. He had just come up with a brilliant algorithm that could draw circles onscreen quickly. The math for making circles usually required calculating square roots, which the Motorola 68000 microprocessor didn’t support.
But Atkinson did a workaround based on the fact that the sum of a sequence of odd numbers produces a sequence of perfect squares (e.g. 1 + 3 = 4, 1 + 3 + 5 = 9, etc.)
When Atkinson fired up his demo, everyone was
impressed except Jobs. “Well, circles are nice,” he said,
“but how about drawing rectangles with rounded
corners?”
To do vector graphics (e.g. display a PPT file), you have to draw polygons
To draw polygons, you need to draw lines
To draw lines, you need to divide
Division can be
re-expressed as multiplication
Multiplication can be reduced to addition
Addition is easy.
To sum up (vector graphics)…
Ivan Sutherland
Born in 1938
PhD dissertation on Sketchpad (3D demo), 1963 one of the most influential computer programs ever written. This work was seminal in Human-Computer Interaction, Graphics and Graphical User Interfaces (GUIs), Computer Aided Design (CAD), and
contraint/object-oriented programming.
TX-2 computer (built circa 1958) on which the software ran was built from discrete transistors (not integrated circuits -it was room-sized) and contained just 64K of 36-bit words (~272k bytes).
PhD advisor: Claude Shannon
Father of computer graphics
Turing Award, 1988
Character output primitives ( in the Jack OS )
class Output {
function void moveCursor(int i, int j) function void printChar(char c)
function void printString(String s) function void printInt(int i)
function void println() function void backSpace() }
class Math { class String {
class Array { class Output {
class Screen { class Memory {
class Keyboard { class Sys {
function (…)
… }
Character output
Given display: a physical screen, say 256 rows by 512 columns
We can allocate an 11 by 8 grid for each character
Hence, our output package should manage a 23 lines by 64 characters screen
Font: each displayable character must have an agreed-upon bitmap
In addition, we have to manage a “cursor”.
class Output {
static Array charMaps;
function void initMap() {
let charMaps = Array.new(127);
// Assign a bitmap for each character
do Output.create(32,0,0,0,0,0,0,0,0,0,0,0); // space do Output.create(33,12,30,30,30,12,12,0,12,12,0,0); // ! do Output.create(34,54,54,20,0,0,0,0,0,0,0,0); // “ do Output.create(35,0,18,18,63,18,18,63,18,18,0,0); // # ...
do Output.create(48,12,30,51,51,51,51,51,30,12,0,0); // 0 do Output.create(49,12,14,15,12,12,12,12,12,63,0,0); // 1 do Output.create(50,30,51,48,24,12,6,3,51,63,0,0); // 2 . . .
do Output.create(65,0,0,0,0,0,0,0,0,0,0,0); // A ** TO BE FILLED **
do Output.create(66,31,51,51,51,31,51,51,51,31,0,0); // B do Output.create(67,28,54,35,3,3,3,35,54,28,0,0); // C . . .
return;
}
Font implementation ( in the Jack OS )
// Creates a character map array
function void create(int index, int a, int b, int c, int d, int e, int f, int g, int h, int i, int j, int k) { var Array map;
let map = Array.new(11);
let charMaps[index] = map;
let map[0] = a;
let map[1] = b;
let map[2] = c;
...
let map[10] = k;
return; }
Keyboard primitives ( in the Jack OS )
Class Keyboard {
function char keyPressed() function char readChar()
function String readLine(String message) function int readInt(String message) }
class Math { class String {
class Array { class Output {
class Screen { class Memory {
class Keyboard { class Sys {
function (…)
… }