Studio 11: Control yourself

You can access the repository for this studio here.

Introduction

Last week we looked at the basic operation of assembly: how you can load values into registers, how to apply basic math and logic operations to values, and how to break code into interoperable functions.

Now we look at the thing that makes computers special: using data to control the flow of execution (the ability to make decisions that control the instructions that are executed or repeated).

Objectives

By the end of this studio, you should:

  • know how to compare two values in assembly,
  • know how to use the result of a comparison to branch in your program (i.e., control the “flow” of the program by potentially “branching off” to different instructions),
  • know how to translate C-style loops into assembly, and
  • know how to translate almost any C into assembly.

There are a lot of very important topics today. Let’s get started.

Compares are nondestructive.

The key to control flow is the ability to compare values. AVR assembly language includes a compare instruction: cp. Let’s use it.

  1. Set up your repository. We have written a bare bones project, CSE132-studio11/studio11/programControl (very creatively named). In it are assembly stubs for four functions. Let’s start by writing lessThan().

  2. If you carefully review most loops or if-statements you’ll notice that they nearly always use a relational operator, like ==, !=, <, <=, etc. These operators produce a boolean value based on the relationalship between values: are they the same? are they different? does the first come before the second? is the first either before or the same as the second? etc.

    In AVR assembly the most general way to do relative comparison is the compare instruction, cp. (cp is the only instruction needed today, but there are other instructions used for comparisons: tst, cpi and cpc. As you may guess from the names, cpi and cpc ork much like cp).

    The compare instruction cp Rd, Rr takes two registers and subtracts them: Rd - Rr. The result is thrown away, but the processor sets the various flags properly. The flags are just individual bits in a special register called called sreg, which stands for “status register”. We don’t usually care about the integer value of sreg, but it may be helpful to understand how the individual bits of sreg may be used by decision making instructions (branching instructions). You may have noticed that the printRegs function prints a line that looks like:

     sreg: C=0 Z=1 N=0 V=0 S=0 H=0 T=0 I=1
     

    This shows the individual bits contained in sreg, which are named with letters that denote their meaning:

    • Z: the zero flag, true if the result is 0.
    • C: the carry flag, true if there was an operational carry.
    • N: the negative flag, true if the result is considered negative (if it’s interpreted as a signed number).
    • V: the overflow flag, true if there was overflow.
    • S: equivalent to N XOR V, the signed overflow flag
    • H: the half-carry flag, true if the low nibble carried from the high.

    Once you do a cp between two registers these flags are set appropriately. Try using cp to compare the arguments passed into the lessThan function and use printRegs to print the register contents immediately after the cp. (You may want to review “What registers are used by the C compiler?”) How are the flags set for each of the test cases in testLessThan()? What happens when you change the order of the registers used by cp?

    We don’t expect you to be too familiar with each of the flags because most of the time you don’t have to care about them, as you’ll see in a minute.

Jumping around (branching)

Assembly languages usually move sequentially, mindlessly executing one line after another.

Assembly languages control program “flow”—how the program executes different code depending on the situation—by jumping and branching.

For example, the command jmp takes as its argument a label, which is just a name for a location with the program, and then jumps from the jmp command to that label without executing any of the code in between. You can jump forwards or backwards to any location in your assembly code merely by placing a label at the location you want to go and jumping there.

	jmp myLabel
	nop ; this code will be skipped;
	    ; The jmp instruction  "jumps" 
	    ; right to the "myLabel" line
	    ...
myLabel:
	nop ; this code runs right after jmp

Labels are used to “label” the locations of many things in a program. Soon you’ll be completing the lessThan() function and the name lessThan: is just a label for the function’s instructions.

The jmp type of instruction is sometimes called an unconditional jump or unconditional branch because it always jumps (also called branching). This is in contrast to instructions that may skip to a different label depending on some condition.

Conditional branches jump based on the current status of the CPU’s flags, like the zero bit and all the other sreg flags set by the cp instruction. For example, breq branches if and only if the zero flag is set. Remember that the cp does subtraction and sets the flags based on the result. If (and only if) the two values are equal, the result will be zero, which will cause the Z flag to be true. By clever use of the cp and br** instructions (where ** is two letters, like lt or ge), you can write comparisons for any type of boolean or mathematical tests (<, <=, ==, etc.).

Most of the time you do not need to be clever or pay attention to the flags at all because AVR assembly has convenient branch commands for most mathematical operations and includes a cheat sheet for all logical comparisons (Section 3 / page 21 of the AVR manual). Using the various branch commands (like brne, brlt), you can do various tests between registers, like Rd != Rr or Rd < Rr.

Just like a jmp, a branch command takes a label as an argument. Unlike jmp though, the branches depend on a condition. If the condition is true they will jump to the label. Otherwise they will continue to the next instruction. For example:

	cp r18, r20 ; compare r18 and r20
	brne myLabel
	nop ; this code runs if r18 and r20 are equal (i.e. r18==r20)
myLabel:
	nop ; this code runs in either case

Notice that the logic above is reverse of how you might typically think. In pre-condition control structures (if-statements, while-loops, for-loops) assembly language uses logic exactly the opposite of what you may do in C or Java. It jumps to avoid the instructions that follow.

Complete the lessThan() in assembly commands to return 1 if a is less than b (if r24 is less than r22) and 0 otherwise. Make sure the results in programControl.ino make sense. Notice that it uses signed 8-bit integers.

The following pseudo-code shows the basic structure using C, but you need to create an equivalent assembly language version (normally this is what the compiler does for you!):

bool lessThanPseudocode(int8_t a, int8_t b) {
	// Yes, we know this is bad programming form
	// you should just `return (a < b);`
	// but we're illustrating a point here, ok?
	if(a < b) {
		return 1;
	} else {
		return 0;
	}
}

After completing lessThan(), complete a comparable lessThanOrEqualUnsigned() that uses unsigned 8-bit integers. A test function (testLessThanOrEqualUnsigned()) has already been created for you. Uncomment both the function and the call to it in setup() to test your work.

Agan, here’s C “pseudo code” of the basic logic:

bool lessThanOrEqualUnsignedPseudocode(byte a, byte b) {
    // Note that a & b are bytes here, not int8_t.
	if(a <= b) {
		return 1;
	} else {
		return 0;
	}
}

Get in the loop.

The lessThan code can be thought of as, basically, an if statement. If a was greater than b, return 1, else 0. Loops in C can be thought of in the same way. A while loop might look like this:

byte i = 0;
while(i < 5) {
	// code
	i++;
}

But you can also use labels and unconditional jumps (gotos) in C to write it with an if-statement (C can have labels, just like assembly, but people prefer not to use them. In fact, using them in places where another control structure can be used is a very bad practice. One of the great pioneering computer scientists, Edsger Dijkstra, even wrote an article titled Go To Considered Harmful):

byte i = 0;
loopBegin:
	if(i >= 5) {
		goto loopEnd;
	}
	// code
	i++;
	goto loopBegin;
loopEnd:
	// end

Since you should already be comfortable writing if statements in assembly, you should now be able to write while loops in assembly (and for loops, too).

  1. We would like to implement multiplication of two numbers as a loop using addition. Again, here’s some C-like Pseuso-code that may help you design the assembly language code:

     byte slowMultiplyPseudocode(byte a, byte b) {
         byte sum = 0;
         byte counter = 0;
         while(counter < a) {
             sum += b;
             counter++;
         }
         return sum;
     }
    

    It turns out that there is a multiply instruction in AVR, but we’ve never been a fan of doing things the easy way in this class. Implement slowMultiply with add using the above algorithm. You will need to use additional registers for your counter and sum (no need to actually allocate memory for them, keeping them in registers is fine).

    We do not care about overflow, and you’re only multiplying bytes, so no carries either. Also note that this is an unsigned multiply.

    Write and test this function by calling it in programControl.ino.

  2. Just to prove once and for all that you understand program control, we want you to implement exponentiation in a similar way. Sure, you could just call your new multiply function the correct number of times (in a loop), but that’s no fun. Write slowExponent to calculate exponents using addition. Here’s the pseudo-code for an implementation:

     byte slowExponentPseudocode(byte a, byte power) {
         byte sum = 1;
         byte i = 0;
         while(i < power) {
             byte innerSum = 0;
             byte j = 0;
             while(j < a) {
                 innerSum += sum;
                 j++;
             }
             sum = innerSum;
             i++;
         }
         return sum;
     }
    

    Again, the test code has been written for your and just needs to be uncommented to run.

  3. Once you’ve completed all that, you should, at least theoretically, be able to translate any C code into assembly with all the AVR you’ve learned in the past two weeks. You are now a compiler!

    You may spend time working on your assignments.

    Notice that throughout this studio, we often first wrote out programs in C before translating them to assembly. C is a more expressive language, so it’s often easier to write out what you want to do first and then directly translate it to assembly. This may be a good way to complete your assembly assignments: understand what you are trying to do, line by line in C, and then implement the assembly. This let’s you separate mentally the algorithms you want to implement and the assembly boilerplate you have to write.

Debugging

In addition to the printRegs() function from the previous assignment, the studio also contains a file called asmMacros.S. This file includes macros. A macro is a set of assembly language instructions that can be added to a file in place of a simple name. This file defines two two macros, one named print and another named printAReg. When either word is used assembly.S, many instructions will be inserted in place of the name. As the names imply, they are intended to print out things, which may help you debug your code.

print is for printing single words or groups of words. To print a single word, print WORD. To print multiple words, print [MULTIPLE WORDS], which will print the brackets and the words within. Note that print does not work well with symbols, like =.

printAReg will print the contents of a single register. For example, pringAReg 22 will print r22 = 0xXX. Note that it prints the value in hex and only the number is used for the register (22 rather than r22).

These macros and printRegs can be used to study how individual values change as your assembly code executes.

Demo

When done, your code should run all test cases without error. It should look something like this:

 *** Starting program...
 *** lessThan() *** 
4 < 6 is 1
6 < 4 is 0
4 < 4 is 0
-4 < 6 is 1
4 < -6 is 0
-4 < -4 is 0
-3 < -4 is 0
-4 < -3 is 1
127 < -128 is 0
-128 < 127 is 1
 *** lessThanOrEqualUnsigned() *** 
4 <= 6 is 1
6 <= 4 is 0
4 <= 4 is 1
5 <= 255 is 1
255 <= 5 is 0
128 <= 127 is 0
127 <= 128 is 1
0 <= 0 is 1
250 <= 250 is 1
 *** slowMultiply() *** 
4 * 6 is 24
6 * 4 is 24
4 * 4 is 16
1 * 255 is 255
6 * 40 is 240
200 * 1 is 200
1 * 200 is 200
0 * 0 is 0
0 * 1 is 0
1 * 0 is 0
 *** slowExponent() *** 
4 ^ 2 is 16
2 ^ 4 is 16
3 ^ 2 is 9
3 ^ 3 is 27
6 ^ 2 is 36
1 ^ 210 is 1
1 ^ 0 is 1
0 ^ 1 is 0
8 ^ 2 is 64
3 ^ 5 is 243
2 ^ 7 is 128
Ended setup!

Key Concepts

  • Assembly
    • Compare
      • cp
    • Flags
    • Jumping and Branching
      • jmp
      • brlt, brne, etc.
    • Loops
    • Mimicking Control Structures from C (Ex: if-statements, if-else statements, loops, etc.)