Available expressions analysis in Compiler Design - Mini Project: Build & Apply

Available Expressions Analysis

📖 Scenario: You are working on a simple compiler optimization task. You want to find expressions in a program that have already been computed and whose values are still available at certain points in the program. This helps avoid repeating calculations and speeds up the program.

🎯 Goal: Build a step-by-step analysis to identify available expressions at each point in a simple control flow graph (CFG) of a program.

📋 What You'll Learn

Create a control flow graph with basic blocks and their expressions

Define the set of all expressions in the program

Compute the available expressions at the entry and exit of each block

Complete the analysis by applying the data flow equations

💡 Why This Matters

🌍 Real World

Available expressions analysis is used in compilers to optimize code by reusing previously computed expressions, reducing redundant calculations and improving performance.

💼 Career

Understanding data flow analysis techniques like available expressions is essential for compiler developers, performance engineers, and software developers working on code optimization.

1

Create the control flow graph data structure

Create a dictionary called cfg representing the control flow graph with these exact entries: 'B1': ['a + b', 'c * d'], 'B2': ['a + b', 'e - f'], and 'B3': ['c * d', 'g + h'].

Compiler Design

# Create the control flow graph dictionary called cfg
# Your code here

Need a hint?

Use a Python dictionary with block names as keys and lists of expressions as values.

2

Define the universal set of expressions

Create a set called all_expr that contains all unique expressions from all blocks in cfg.

Compiler Design

cfg = {
    'B1': ['a + b', 'c * d'],
    'B2': ['a + b', 'e - f'],
    'B3': ['c * d', 'g + h']
}

# Create the set all_expr with all unique expressions
# Your code here

Need a hint?

Use a loop over cfg keys and update a set with expressions from each block.

3

Initialize available expressions at entry and exit

Create two dictionaries called avail_in and avail_out with keys as block names from cfg. Initialize avail_in for all blocks to the empty set, and avail_out for all blocks to the set of expressions in that block.

Compiler Design

cfg = {
    'B1': ['a + b', 'c * d'],
    'B2': ['a + b', 'e - f'],
    'B3': ['c * d', 'g + h']
}

all_expr = set()
for block in cfg:
    all_expr.update(cfg[block])

# Initialize avail_in and avail_out dictionaries
# Your code here

Need a hint?

Use dictionary comprehensions to create avail_in and avail_out.

4

Apply data flow equations to update available expressions

Given the control flow graph edges edges = {'B1': ['B2', 'B3'], 'B2': ['B3'], 'B3': []}, update avail_in and avail_out by applying the available expressions data flow equations once: for each block, set avail_in[block] to the intersection of avail_out of its predecessors, and set avail_out[block] to the union of cfg[block] and avail_in[block]. Assume avail_in of entry block 'B1' is empty set.

Compiler Design

cfg = {
    'B1': ['a + b', 'c * d'],
    'B2': ['a + b', 'e - f'],
    'B3': ['c * d', 'g + h']
}

all_expr = set()
for block in cfg:
    all_expr.update(cfg[block])

avail_in = {block: set() for block in cfg}
avail_out = {block: set(cfg[block]) for block in cfg}

edges = {'B1': ['B2', 'B3'], 'B2': ['B3'], 'B3': []}

# Update avail_in and avail_out using data flow equations
# Your code here

Need a hint?

First find predecessors of each block, then update avail_in as intersection of avail_out of predecessors, and avail_out as union of block expressions and avail_in.