The Elements of Computing Systems: Building a Modern Computer from First Principles (43 page)
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Authors: Noam Nisan,Shimon Schocken
BOOK: The Elements of Computing Systems: Building a Modern Computer from First Principles
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We don’t provide specific guidelines on how to develop the code generation features of the compiler, though the examples spread throughout the chapter are quite instructive. Instead, we provide a set of six application programs designed to unit-test these features incrementally. We strongly suggest to test your compiler on these programs in the given order. This way, you will be implicitly guided to build the compiler’s code generation capabilities in stages, according to the demands of each test program.
The Operating System
The Jack OS—the subject of chapter 12—was written in the Jack language. The source OS code was then translated (by an error-free Jack compiler) into a set of VM files, collectively known as the Jack OS. Each time we want to run an application program on the VM emulator, we must load into the emulator not only the application’s .vm files, but also all the OS .vm files. This way, when an application-level VM function calls some OS-level VM function, they will find each other in the same environment.
The Jack OS—the subject of chapter 12—was written in the Jack language. The source OS code was then translated (by an error-free Jack compiler) into a set of VM files, collectively known as the Jack OS. Each time we want to run an application program on the VM emulator, we must load into the emulator not only the application’s .vm files, but also all the OS .vm files. This way, when an application-level VM function calls some OS-level VM function, they will find each other in the same environment.
Testing Method
Normally, when you compile a program and run into some problems, you conclude that the program is screwed up and proceed to debug it. In this project the setting is exactly the opposite. All the test programs that we supply are error-free. Therefore, if their compilation yields any errors, it’s the compiler that you have to fix, not the test programs. For each test program, we recommend going through the following routine:
Normally, when you compile a program and run into some problems, you conclude that the program is screwed up and proceed to debug it. In this project the setting is exactly the opposite. All the test programs that we supply are error-free. Therefore, if their compilation yields any errors, it’s the compiler that you have to fix, not the test programs. For each test program, we recommend going through the following routine:
1. Copy all the supplied OS .vm files from tools/OS into the program directory, together with the supplied . jack file(s) comprising the test program.
2. Compile the program directory using your compiler. This operation should compile only the .jack files in the directory, which is exactly what we want.
3. If there are any compilation errors, fix your compiler and return to step 2 (note that all the supplied test programs are error-free).
4. At this point, the program directory should contain one .vm file for each source . jack file, as well as all the supplied OS .vm files. If this is not the case, fix your compiler and return to step 2.
5. Execute the translated VM program in the VM Emulator, loading the entire directory and using the “no animation” mode. Each one of the six test programs contains specific execution guidelines, as listed here.
6. If the program behaves unexpectedly or some error message is displayed by the VM emulator, fix your compiler and return to step 2.
Test Programs
We supply six test programs. Each program is designed to gradually unit-test specific language handling capabilities of your compiler.
Seven
This program computes the value of (3*2)+1 and prints the result at the top left of the screen. To test whether your compiler has translated the program correctly, run the translated code in the VM emulator and make sure that it displays 7 correctly. Purpose: Tests how your compiler handles a simple program containing an arithmetic expression with integer constants (without variables), a do statement, and a return statement.
This program computes the value of (3*2)+1 and prints the result at the top left of the screen. To test whether your compiler has translated the program correctly, run the translated code in the VM emulator and make sure that it displays 7 correctly. Purpose: Tests how your compiler handles a simple program containing an arithmetic expression with integer constants (without variables), a do statement, and a return statement.
Decimal-to-Binary Conversion
This program converts a 16-bit decimal number into its binary representation. The program takes a decimal number from RAM [8000], converts it to binary, and stores the individual bits in RAM [8001..8016] (each location will contain 0 or 1). Before the conversion starts, the program initializes RAM [8001..8016] to -1. To test whether your compiler has translated the program correctly, load the translated code into the VM emulator and go through the following routine:
This program converts a 16-bit decimal number into its binary representation. The program takes a decimal number from RAM [8000], converts it to binary, and stores the individual bits in RAM [8001..8016] (each location will contain 0 or 1). Before the conversion starts, the program initializes RAM [8001..8016] to -1. To test whether your compiler has translated the program correctly, load the translated code into the VM emulator and go through the following routine:
■ Put (interactively) a 16-bit decimal value in RAM[8000].
■ Run the program for a few seconds, then stop its execution.
■ Check (interactively) that RAM[8001..8016] contain the correct results, and that none of them contains -1.
Purpose:
Tests how your compiler handles all the procedural elements of the Jack language, namely, expressions (without arrays or method calls), functions, and all the language statements. The program does not test the handling of methods, constructors, arrays, strings, static variables, and field variables.
Tests how your compiler handles all the procedural elements of the Jack language, namely, expressions (without arrays or method calls), functions, and all the language statements. The program does not test the handling of methods, constructors, arrays, strings, static variables, and field variables.
Square Dance
This program is a trivial interactive “game” that enables moving a black square around the screen using the keyboard’s four arrow keys. While moving, the size of the square can be increased and decreased by pressing the “z” and “x” keys, respectively. To quit the game, press the “q” key. To test if your compiler has translated the program correctly, run the translated code in the VM emulator and make sure that it works according to this description. Purpose: Tests how your compiler handles the object-oriented constructs of the Jack language: constructors, methods, fields and expressions that include method calls. It does not test the handling of static variables.
This program is a trivial interactive “game” that enables moving a black square around the screen using the keyboard’s four arrow keys. While moving, the size of the square can be increased and decreased by pressing the “z” and “x” keys, respectively. To quit the game, press the “q” key. To test if your compiler has translated the program correctly, run the translated code in the VM emulator and make sure that it works according to this description. Purpose: Tests how your compiler handles the object-oriented constructs of the Jack language: constructors, methods, fields and expressions that include method calls. It does not test the handling of static variables.
Average
This program computes the average of a user-supplied sequence of integers. To test if your compiler has translated the program correctly, run the translated code in the VM emulator and follow the instructions displayed on the screen. Purpose: Tests how your compiler handles arrays and strings.
This program computes the average of a user-supplied sequence of integers. To test if your compiler has translated the program correctly, run the translated code in the VM emulator and follow the instructions displayed on the screen. Purpose: Tests how your compiler handles arrays and strings.
Pong
A ball is moving randomly on the screen, bouncing off the screen “walls.” The user can move a small bat horizontally by pressing the keyboard’s left and right arrow keys. Each time the bat hits the ball, the user scores a point and the bat shrinks a little, to make the game harder. If the user misses and the ball hits the bottom horizontal line, the game is over. To test whether your compiler has translated this program correctly, run the translated code in the VM emulator and play the game (make sure to score some points, to test the part of the program that displays the score on the screen). Purpose: Provides a complete test of how your compiler handles objects, including the handling of static variables.
A ball is moving randomly on the screen, bouncing off the screen “walls.” The user can move a small bat horizontally by pressing the keyboard’s left and right arrow keys. Each time the bat hits the ball, the user scores a point and the bat shrinks a little, to make the game harder. If the user misses and the ball hits the bottom horizontal line, the game is over. To test whether your compiler has translated this program correctly, run the translated code in the VM emulator and play the game (make sure to score some points, to test the part of the program that displays the score on the screen). Purpose: Provides a complete test of how your compiler handles objects, including the handling of static variables.
Complex Arrays
Performs five complex calculations using arrays. For each such calculation, the program prints on the screen the expected result versus the actual result (as performed by the compiled program). To test whether your compiler has translated the program correctly, run the translated code in the VM emulator and make sure that the actual results are identical to the expected results. Purpose: Tests how your compiler handles complex array references and expressions.
Performs five complex calculations using arrays. For each such calculation, the program prints on the screen the expected result versus the actual result (as performed by the compiled program). To test whether your compiler has translated the program correctly, run the translated code in the VM emulator and make sure that the actual results are identical to the expected results. Purpose: Tests how your compiler handles complex array references and expressions.
12
Operating System
Civilization progresses by extending the number of operations that we can perform without
thinking about them.
—Alfred North Whitehead,
Introduction to Mathematics
(1911)
Introduction to Mathematics
(1911)
In previous chapters of this book, we described and built the hardware architecture of a computer platform, called Hack, and the software hierarchy that makes it usable. In particular, we introduced an object-based language, called Jack, and described how to write a compiler for it. Other high-level programming languages can be specified on top of the Hack platform, each requiring its own compiler.
The last major interface missing in this puzzle is an operating system (OS). The OS is designed to close gaps between the computer’s hardware and software systems, and to make the overall computer more accessible to programmers and users. For example, in order to render the text “Hello World” on our computer’s screen, several hundred pixels must be drawn at specific screen locations. This can be done by consulting the hardware specification and writing code that puts the necessary bits in the RAM-resident screen memory map. Obviously, high-level programmers expect something better than that. They want to use a command like printString(“Hello World”) and let someone else worry about the details. And that’s where the operating system enters the picture.
Throughout this chapter, the term operating system is used rather loosely. In fact, the OS services that we describe comprise an operating system in a very minimal fashion, aiming at (i) encapsulating various hardware-specific services in a software-friendly way, and (ii) extending high-level languages with various functions and abstract data types. The dividing line between an operating system in this sense and a standard language library is not very clear. Indeed, some modern languages, most notably Java, tend to pack many classic operating system services like GUI management, memory management, and multitasking in its standard software library, along with many language extensions.
Following this pattern, the collection of services that we specify and build in this chapter can be viewed as a combination of a simple OS and a standard library for the Jack language. This OS is packaged as a collection of Jack classes, each providing a set of related services via Jack subroutine calls. The resulting OS has many features resembling those of industrial strength operating systems, but it still lacks numerous OS features such as process handling, disk management, communications, and more.
Operating systems are usually written in a high-level language and compiled into binary form, just like any other program. Our OS is no exception—it can be written completely in Jack. Yet unlike other programs written in high-level languages, the operating system code must be aware of the hardware platform on which it runs. In other words, in order to hide the gory hardware details from the application programmer, the OS programmer must write code that manipulates these details directly (a task that requires access to the hardware documentation). Conveniently, this can be done using the Jack language. As we observe in this chapter, Jack was defined with sufficient “lowness” in it, permitting an intimate closeness to the hardware when needed.
The chapter starts with a relatively long Background section, describing key algorithms normally used to implement basic operating system services. These include mathematical functions, string operations, memory management, handling text and graphics output to the screen, and handling inputs from the keyboard. This algorithmic introduction is followed by a Specification section, providing the complete API of the Jack OS, and an Implementation section, describing how to build the OS using the classic algorithms presented earlier. As usual, the final Project section provides all the necessary project materials for gradual construction and unit-testing the entire OS presented in the chapter.
The chapter provides two key lessons, one in software engineering and one in computer science. First, we complete the construction of the high-level language, compiler, and operating system trio. Second, since operating system services must execute efficiently, we pay attention to running time considerations. The result is an elegant series of algorithms, each being a computer science gem.
12.1 Background12.1.1 Mathematical Operations
Computer systems must support mathematical operations like addition, multiplication, and division. Normally, addition is implemented in hardware, at the ALU level, as we have done in chapter 3. Other operations like multiplication and division can be handled by either hardware or software, depending on the computer’s cost/performance requirements. This section shows how multiplication, division, and square root operations can be implemented efficiently in software, at the OS level. We note in passing that hardware implementations of these mathematical operations can be based on the same algorithms presented here.
Efficiency First
Mathematical algorithms operate on
n
-bit binary numbers, with typical computer architectures having
n
= 16, 32, or 64. As a rule, we seek algorithms whose running time is proportional (or at least polynomial) in this parameter n. Algorithms whose running time is proportional to the value of
n
-bit numbers are unacceptable, since these values are exponential in n. For example, suppose we implement the multiplication operation
x
·
y
using the repeated addition algorithm for i = 1 ... y {
result
= result +
x
}. Well, the problem is that in a 64-bit computer,
y
can be greater than 18,000,000,000,000,000,000, implying that this naïve algorithm may run for years even on the fastest computers. In sharp contrast, the running time of the multiplication algorithm that we present below is proportional not to the multiplicands’ value, which may be as large as 2
n
, but rather to n. Therefore, it will require only
c·n
elementary operations for any pair of multiplicands, where c is a small constant representing the number of elementary operations performed in each loop iteration.
Mathematical algorithms operate on
n
-bit binary numbers, with typical computer architectures having
n
= 16, 32, or 64. As a rule, we seek algorithms whose running time is proportional (or at least polynomial) in this parameter n. Algorithms whose running time is proportional to the value of
n
-bit numbers are unacceptable, since these values are exponential in n. For example, suppose we implement the multiplication operation
x
·
y
using the repeated addition algorithm for i = 1 ... y {
result
= result +
x
}. Well, the problem is that in a 64-bit computer,
y
can be greater than 18,000,000,000,000,000,000, implying that this naïve algorithm may run for years even on the fastest computers. In sharp contrast, the running time of the multiplication algorithm that we present below is proportional not to the multiplicands’ value, which may be as large as 2
n
, but rather to n. Therefore, it will require only
c·n
elementary operations for any pair of multiplicands, where c is a small constant representing the number of elementary operations performed in each loop iteration.
We use the standard “Big-Oh” notation,
O
(
n
), to describe the running time of algorithms. Readers who are not familiar with this notation can simply read
O
(
n
) as “in the order of magnitude of
n
.” With that in mind, we now turn to present an efficient multiplication
x · y
algorithm for
n
-bit numbers whose running time is
O
(
n
) rather than
O
(
x
) or
O
(
y
), which are exponentially larger.
O
(
n
), to describe the running time of algorithms. Readers who are not familiar with this notation can simply read
O
(
n
) as “in the order of magnitude of
n
.” With that in mind, we now turn to present an efficient multiplication
x · y
algorithm for
n
-bit numbers whose running time is
O
(
n
) rather than
O
(
x
) or
O
(
y
), which are exponentially larger.
Multiplication
Consider the standard multiplication method taught in elementary school. To compute 356 times 27, we line up the two numbers one on top of the other. Next, we multiply each digit of 356 by 7. Next, we “shift to the left” one position, and multiply each digit of 356 by 2. Finally, we sum up the columns and obtain the result. The binary version of this technique—figure 12.1—follows exactly the same logic.
Consider the standard multiplication method taught in elementary school. To compute 356 times 27, we line up the two numbers one on top of the other. Next, we multiply each digit of 356 by 7. Next, we “shift to the left” one position, and multiply each digit of 356 by 2. Finally, we sum up the columns and obtain the result. The binary version of this technique—figure 12.1—follows exactly the same logic.
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