Translating C to C: Control Structures

The ultimate goal

The C programming language like all modern programming languages has three basic types on control structures: sequence, selection, and iteration.

The sequence control structure is the statement block. A collection of statements inside curly braces, { and }. The selection control structures are if, if else, and switch. The iteration control structures are while, do while, and for. All of these control structures are common to C, C++, and Java.

C and C++ also support the goto which can be used to make a transfer to a labeled statement along with break and select statements which can alter the execution of iterative statements. Java does not have a goto, but it does support the use of labels with the break and select which can result in goto-like code.

Most C/C++/Java programmers realize that the for can be easily rewritten using a while and that a select can be replaced with a series of if then statements.

We’re going to do something similar, but more drastic, in this handout. We are going to replace all the control structures of C using the goto and three very simple versions of the if statement:
        if (τ == 0) goto λ ;
or
        if (τ != 0) goto λ ;
        goto λ ;
where τ is an integer variable and λ is a label generated during the translation process.

The real ultimate goal

Of course, the real goal is to translate C into a machine or assembly language. To do that, we eventually need to learn how to allocate storage, evaluate exressions, and call functions.

But let’s forget that for now. Let’s only worry about translating
        if (τ == 0) goto λ ;
to an assembly language.

Well, than one isn’t hard. First we need to test if τ is zero or not. Generally this can be done by using a machine instructions that loads τ and then sets something like a Z bit. In the PIC processor, this can be done with the MOV instruction.

Once the Z bit is set on the PIC, we can use either
        BRA    Z,λ
or
        BRA    NZ,λ
On an Intel computer, we would use an instruction similar to
        je     λ

Processors with “skip” instructions, such as smaller PICs, will need a two instruction sequence. The second instruction performs the branch and the first instruction decides it the second should be skipped.

     btsc   SR,Z        ;; skip the next instruction if Z is clear
     goto   λ

The if statement

The if statement has the following form where statement represents the body of the if statement.

if (expression)
  statement

This statement can be transformed into a sequence of C statements similar to the following:

  int τ = expression ;
  if (τ == 0) goto λ ;
  statement
λ :

If this code segment, τ a C variable that is uniquely generated for the purpose of this translation. In this handout, we are using Greek letters, sometimes suffixed with unique integers for this purpose. Similarly, λ represents a uniguely generated location name for a location.

A nested example

These rules must be applied recursively to translate a program. Suppose we have been asked to translate the following more complex C if statement.

if (n % 4 == 0) {
  ++julianLeap ;
  if (n % 400 == 0 || n % 100 != 0) {
    ++gregorianLeap ;
  }
}

In this case, two unique data variables, τ1 and τ2, along with two unique labels, λ1 and λ2, would be needed.

The translated code would look something like the following.

  τ1 = ( n % 4 == 0 ) ;
  if (τ1 == 0) goto λ1 ;
  ++julianLeap ;
  τ2 = ( n % 400 == 0 || n % 100 != 0 ) ;
  if (τ2 == 0) goto λ2 ;
  ++gregorianLeap ;
λ2 :
λ1 :

Notice how the inner if is translated inside the outer if.

Anything else?

The if else can be translated by adding two labels in the code. For example, consider the following rather abstract C code.

if (expression)
  statement1
else
  statement2

It could be transformed as follows:

  int τ = expression ;
  if (τ == 0) goto λ1 ;
  statement1
  goto λ2 ;
λ1 :
  statement2
λ2 :

So the following example

if (a > b)
  m = a ;
else
  m = b ;

would be changed to

  int τ = (a > b) ;
  if (τ == 0) goto λ1 ;
  m = a ;
  goto λ2 ;
λ1 :
  m = b ;
λ2 :

The switch

The switch statement isn’t pretty, so you can’t expect its transformation to be easily explained. However, the switch can be viewed as series of if choices which select the target code for each choice. The break statements are replaced with goto’s to the end of the switch.

Let’s do an example using the following silly C code.

switch (sizeNum) {
case '0':
case '1':
  sizeChar = 's' ;
  break ;
case '2':
  sizeChar = 'm' ;
  break ;
default:
  sizeChar = 'l' ;
}

This can expressed switch-less as:

  if (sizeNum == 1 || sizeNum == 2)
    goto λ1 ;
  else if (sizeNum == 3)
    goto λ2 ;
  else
    goto λ3 ;

λ1:
  sizeChar = 's' ;
  goto λ4 ;

λ2:
  sizeChar = 'm' ;
  goto λ4 ;

λ3:
  sizeChar = 'l' ;

λ4:

Iterative statements

Translating the while isn’t hard. The code begins with a test that evaluates the continuation condition and exits the loop if it is false. At the end of the loop is a goto back to the beginning.

Consider the following abstract loop

while (expression)
  statement

It can be translated into if controlled code as:

λ1:
  if (! expression) goto λ2;
  statement
  goto λ1:
λ2:

However, many compilers generate the following because it makes the loop a tad faster.

goto λ2
λ1:
  statement
λ2:
  if (expression) goto λ1 ;

Fortunately for us, the for is often described using the while. Thus a for statement like the following:

for(init ; condition ; increment)
  statement

Can be translated into the following while statement. Be sure to put the increment after the for statement.

init ;
while(condition) {
  statement
  increment ;
}

And thus the following two sections of C code do the same.

for(i=0 ; i<10 ; ++i)
  sum = sum + i ;

i=0 ;
while(i<10) {
  sum = sum + i ;
  ++i ;
}

We’re going to leave the while do as an exercise to the reader. It’s really not hard. Just make the test at the end of the loop rather than the beginning.

Taking a break or continueing

If a break statement is used inside a loop statement, it needs to replaced by a goto that leaves the loop, without performing any of the tests for continuing the loop.

If a continue statement is used inside a while statement, it needs to replaced by a goto that braches to the beginning of the the loop. In this case, the tests for continuing the loop must be performed. A continue within a for statement should be replaced to a goto to the code where the for loop increment statement is performed.