Interval Difference Analyzer

Overview

Analyze differences in program intervals (variable value ranges) between two versions of a program to detect behavioral changes, identify potential bugs, and guide testing efforts.

Core Workflow

1. Setup Program Versions

Prepare both program versions for analysis:

OLD_VERSION=/path/to/old/program
NEW_VERSION=/path/to/new/program
TEST_SUITE=/path/to/tests  # Optional

2. Extract Intervals

Extract interval information from both versions:

python scripts/interval_analyzer.py \
    --program $OLD_VERSION \
    --output old_intervals.json

python scripts/interval_analyzer.py \
    --program $NEW_VERSION \
    --output new_intervals.json

3. Compare Intervals

Compare intervals and identify differences:

python scripts/compare_intervals.py \
    --old old_intervals.json \
    --new new_intervals.json \
    --output interval_diff_report.json

4. Review Report

Examine the generated report for:

• Added intervals (new variables or wider ranges)
• Removed intervals (deleted variables or narrower ranges)
• Modified intervals (changed bounds)
• Behavioral implications
• Testing recommendations

What Are Program Intervals?

Program intervals represent the possible ranges of values that variables can take during program execution.

Example:

def calculate_discount(price, discount_rate):
    # Intervals:
    # price: [0, 10000]
    # discount_rate: [0.0, 1.0]
    # discount: [0, 10000]
    discount = price * discount_rate
    return discount

Why intervals matter:

• Detect overflow/underflow risks
• Identify boundary condition changes
• Validate numeric computation correctness
• Guide test case generation

Interval Extraction Methods

Method 1: Static Analysis

Analyze code to infer possible value ranges without execution.

Method 2: Dynamic Analysis

Execute program with test inputs and observe actual ranges.

Method 3: Abstract Interpretation

Use abstract domains to compute sound interval approximations.

Interval Comparison

Identifying Added Intervals

Pattern: New variables or wider ranges in new version

Implications:

• New computation paths
• Potential new bugs
• Requires new tests

Identifying Removed Intervals

Pattern: Deleted variables or narrower ranges in new version

Implications:

• Simplified computation
• Reduced intermediate state
• May affect debugging

Identifying Modified Intervals

Pattern: Changed bounds for existing variables

Example:

# Old version: age: [0, 120]
# New version: age: [0, 150]  # Widened!

Implications:

• Relaxed constraints
• May accept invalid inputs
• Requires validation testing

Behavioral Change Detection

Overflow/Underflow Detection

Check if new intervals exceed type bounds.

Example:

# Old: result: [0, 1000000] ✓ Safe (int32)
# New: result: [0, 10000000000] ✗ Overflow risk!

Precision Loss Detection

Check if new intervals lose precision.

Example:

# Old: result: [0.0, 100.0] (float)
# New: result: [0, 100] (int) - precision loss!

Boundary Condition Changes

Check if interval boundaries change critically.

Example:

# Old: index: [0, 99]
# New: index: [-1, 99]  # Negative index possible!

Testing Recommendations

Priority Levels

Critical: Test immediately

• Overflow/underflow risks
• Negative indices
• Division by zero
• Type mismatches

High: Test soon

• Widened intervals
• Boundary changes
• Precision loss

Medium: Test when convenient

• Narrowed intervals (safer)
• Removed intermediate variables

Low: Optional testing

• Cosmetic changes
• Unchanged intervals

Test Case Generation

Generate test cases targeting interval boundaries:

# Interval: x: [0, 100]
test_cases = [0, 1, 50, 99, 100]

# For modified interval: [0, 100] → [0, 150]
additional_tests = [101, 125, 149, 150]

Report Format

The analyzer generates a comprehensive JSON report:

{
  "summary": {
    "total_intervals_old": 45,
    "total_intervals_new": 48,
    "added_intervals": 5,
    "removed_intervals": 2,
    "modified_intervals": 8
  },
  "differences": [
    {
      "type": "modified",
      "variable": "age",
      "old_interval": "[0, 120]",
      "new_interval": "[0, 150]",
      "severity": "high",
      "implications": ["Accepts wider range"],
      "testing_priority": "high",
      "suggested_tests": [121, 135, 149, 150]
    }
  ],
  "recommendations": [
    "Test modified intervals with boundary values",
    "Verify no overflow in calculations"
  ]
}

Integration with Test Suites

Validate Intervals with Tests

Run existing tests and verify intervals:

python scripts/validate_intervals.py \
    --program $NEW_VERSION \
    --intervals new_intervals.json \
    --test-suite $TEST_SUITE

Generate Tests from Intervals

Automatically generate tests for interval boundaries:

python scripts/generate_interval_tests.py \
    --intervals interval_diff_report.json \
    --output generated_tests.py

Best Practices

1. Use both static and dynamic analysis: Combine for better coverage
2. Focus on critical intervals: Prioritize safety-critical variables
3. Test boundary values: Always test interval bounds
4. Document intentional changes: Mark expected interval modifications
5. Automate analysis: Integrate into CI/CD pipeline

Resources

• references/interval_analysis.md: Detailed interval analysis techniques
• references/abstract_interpretation.md: Abstract interpretation theory
• scripts/interval_analyzer.py: Main interval extraction tool
• scripts/compare_intervals.py: Interval comparison engine
• scripts/validate_intervals.py: Test suite validation
• scripts/generate_interval_tests.py: Test case generator