Overview

Floating-point arithmetic is notorious for its subtle edge cases and rounding errors. When working on critical systems that rely on precise floating-point calculations, ensuring correct rounding modes is essential. That’s why I developed dReal-clang-tidy, a C++ static analysis tool that validates floating-point rounding mode preconditions.

The Challenge

Traditional static analysis tools often struggle with:

• Understanding complex floating-point semantics
• Validating rounding mode requirements across function boundaries
• Detecting logical contradictions in floating-point constraints
• Providing actionable feedback to developers

Technical Approach

The solution leverages several cutting-edge technologies:

LLVM Integration

By building on top of LLVM’s Abstract Syntax Tree (AST) infrastructure, dReal-clang-tidy can:

• Parse C++ code at the compiler level
• Extract semantic information about floating-point operations
• Integrate seamlessly with existing build systems

Graph-Based Solver

The core innovation is the use of a graph-based solver that:

• Represents floating-point constraints as a directed graph
• Propagates rounding mode requirements through the call graph
• Identifies contradictions using constraint satisfaction techniques
• Generates minimal counterexamples when violations are found

Structured Output

The tool generates comprehensive JSON reports that include:

• Precise source locations of violations
• Constraint propagation chains
• Suggested fixes
• Confidence metrics

Real-World Impact

This tool has been deployed in production codebases where floating-point precision is critical, helping catch bugs that would have been nearly impossible to find through traditional testing methods.

Key Takeaways

1. Compiler Technology is Powerful: LLVM provides an incredible foundation for building sophisticated analysis tools
2. Graph Algorithms Matter: Representing constraints as graphs enables efficient analysis at scale
3. Usability is Key: Even the most sophisticated tool is useless if developers can’t understand its output

Future Directions

I’m exploring extensions including:

• Support for GPU floating-point operations
• Integration with formal verification tools
• Machine learning-based suggestion improvements

Check out the project on GitHub!