Lower Nested Conditionals

The point

Lower nested conditionals by hand and count the labels. Nesting is where label generation goes wrong, and it goes wrong silently.

Do this

1. Lower this by hand into TAC, generating labels as you go:

   if (a > 0) {
       if (b > 0) { print(1); } else { print(2); }
   } else {
       print(3);
   }

2. Count the labels. How many did you need? Write the general formula for k nested if-else statements.
3. Draw the flow graph. Apply the leader rules from Topic 4 to your listing. How many basic blocks? How many paths from entry to exit?
4. Hand-execute all four combinations of a and b being positive or not. Confirm each prints exactly one number.
5. Sabotage. Remove the goto after at the end of the then-branch. Re-execute all four cases. Which now print TWO numbers, and which still look correct?
6. Implement and confirm the compiler produces the same shape you did.
7. Break the label generator — make it always return L0. What does the assembler say? Is that message enough to find the cause?