Snapchat·Software Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jun 2026Remote

Summary

Snapchat systems interview that went deep into numerical methods for trig functions, specifically how you'd take a working sin(x) and actually make it production-grade. More math-heavy than I expected for what I thought was a software engineering role.

Questions Asked (1)

You have a working sin(x) implementation written from scratch. Walk through how you would optimize it for production use, covering range reduction, polynomial approximation strategies, lookup tables, and SIMD vectorization. What are the trade-offs between speed, accuracy, and memory?

Technical Trade-offsSystem DesignAlgorithms & Data Structures

Author's notes

This was the whole interview basically.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the accuracy and performance requirements, then systematically address each optimization area: range reduction, polynomial approximation, lookup tables, and SIMD. For each, explain the technique, its impact on speed/accuracy/memory, and the trade-offs involved. Conclude by discussing how you would measure and validate the optimized implementation.

Pro tip: Emphasize that optimization must be driven by profiling and accuracy requirements; premature optimization can lead to subtle bugs. Mention that for production, you'd also consider edge cases like NaN/Inf and denormal inputs.

1. Clarify Requirements and Constraints

Ask about the required accuracy (e.g., ULP), performance targets, input range, and hardware. This determines the optimization strategy.

2. Range Reduction

Explain how to reduce the input to a small interval (e.g., [-π/4, π/4]) using periodicity and symmetry. Discuss techniques like Cody-Waite or Payne-Hanek for large arguments.

3. Polynomial Approximation

Choose between minimax, Chebyshev, or Taylor polynomials. Discuss degree selection, coefficient storage, and evaluation methods (Horner, Estrin).

4. Lookup Tables and SIMD

Describe using lookup tables for coarse approximation or to assist range reduction. Explain how to vectorize with SIMD (e.g., AVX, NEON) for parallel evaluation.

5. Trade-offs and Validation

Summarize trade-offs: speed vs accuracy vs memory. Discuss testing against a reference implementation and benchmarking.

Key Points to Mention

Range reduction: Cody-Waite for moderate arguments, Payne-Hanek for huge arguments; use of fused multiply-add (FMA) for accuracy.
Polynomial approximation: minimax polynomials minimize maximum error; Chebyshev nodes for near-optimal; Horner's method for evaluation but Estrin for parallelism.
Lookup tables: trade memory for speed; can store coefficients or precomputed values; interpolation for accuracy.
SIMD vectorization: process multiple inputs in parallel; use intrinsics; handle remainder loops; consider gather/scatter for tables.
Trade-offs: higher accuracy often requires more computation or memory; SIMD increases speed but may reduce portability; tables increase memory but reduce computation.
Validation: compare against high-precision reference (e.g., MPFR); measure ULP error; benchmark on target hardware.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.