Summary

Nic Taylor surveys historical and practical approximations to the two-parameter arctangent function atan2, explaining why similar formulas recur and how to find a fast, accurate floating-point approximation. The article shows how to derive, implement, and benchmark branchless polynomial/rational approximations and gives optimization tips for real-time DSP use.

Key Takeaways

• Evaluate accuracy vs. performance trade-offs for several atan2 approximations using error metrics and timing tests
• Derive and implement a branchless polynomial/rational approximation suitable for floating-point atan2
• Benchmark candidate approximations against standard library atan2 on target hardware to quantify speedups and accuracy loss
• Optimize implementations using platform techniques (e.g., bit tricks, reduced conditionals, or SIMD) and adapt them for constrained environments

Who Should Read This

DSP engineers and software developers working on real-time signal processing, FFT-based phase estimation, communications or radar systems who need faster atan2 with known accuracy trade-offs.

Still RelevantIntermediate

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