My first instinct was Taylor series and I went with that, which is fine for small x but I didn't think about range reduction until they pushed back.
Start by explaining the mathematical foundation (Taylor series or range reduction) and then implement a clean, correct solution. After that, discuss optimization techniques like range reduction, iterative term computation, and early termination, and finally cover production hardening such as input validation, edge cases, and performance considerations.
Pro tip: Demonstrate awareness of floating-point precision issues and the trade-off between accuracy and performance; mention that for production, you might use a lookup table or polynomial approximation (e.g., minimax) instead of Taylor series for better efficiency.
Ask about the expected input range, required accuracy (epsilon), performance constraints, and whether the function will be used in a real-time system. This shows you think about the context before coding.
Select a method like Taylor series, range reduction with polynomial approximation, or CORDIC. Explain why you chose it, considering accuracy, performance, and simplicity.
Write a clean, correct implementation. For Taylor series, compute terms iteratively until the term is below epsilon. Include range reduction to improve convergence and accuracy.
Discuss optimizations: reduce the input range using periodicity, use iterative term computation to avoid recomputing factorials, and consider using a fixed number of terms based on epsilon.
Address edge cases (NaN, infinity, very large inputs), handle floating-point errors, add input validation, and consider thread safety and numerical stability. Discuss testing strategies.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.