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# Lab for Automated Reasoning and Analysis LARA

# Exercises on Code generation and Dataflow analysis

## Exercise 1 (Warm up): Bytecode generation

Translate the following function to JVM instructions.

def middle(small: Int, big: Int): Int = { val mid = small + (big - small) / 2 return mid }

## Exercise 2: Branch Instruction

- Translate the for-loop and if-condition to
*branch*instructions. You can keep all the other statements in . You can also assume that the for loop is translated into the corresponding while loop. - Now convert the following code fragments to byte code:
- loop stopping condition from line 3
- if-statement condition on line 4
- line 7

1: def bubblesort( xs : Array[Int]) : Array[Int] = { 2: for( i <- 0 until (xs.length - 1)) 3: for( j <- 0 until (xs.length - i - 1)) 4: if( xs(j) > xs(j+1)) { 5: var tmp = xs(j) 6: xs(j) = xs(j + 1) 7: xs(j + 1) = tmp 8: } 9: xs 10:}

The JVM instructions for getting the length of the array in the local slot x are

1: aload_x 2: arraylength

and the instruction to access the ith element of the array xs, i.e. xs(i) is

1: aload_x 2: iload_y 3: iaload

where x is the slot of the array and y the slot of the index i.

## Exercise 3: Range analysis

Draw the control-flow graph for the following program.

x := 0; while (x < 10) { x := x + 3; } if (x >= 0) { if (x <= 15) { a[x]=7; // made sure index is within range } else { // v1 error; } } else { // v2 error; }

Run range analysis that maintains an interval for at each program point in the control flow graph. Assume that the ranges that the integers can take are [-128, 127] for simplicity, i.e. all intervals within this range are allow, for instance [-1, 3].

What are the fixpoint values at program points marked and ?

## Exercise 4: Live variables analysis

The GCD of two numbers can be computed using the Euclid algorithm.

We can implement the GCD algorithm with temporary variables as the following.

x1 := a x2 := b Start: if x2 = 0 jump Done x3 := x1 % x2 x1 := x2 x2 := x3 jump Start Done: return x1

- Construct the control-flow graph
- Determine the set of live variables before and after the execution of each instruction.