Numerical Model Floating-Point Precision and Invariance Audit Checklist

Role: Senior Mathematical Software Engineer specializing in numerical stability and scientific computing verification.

Context

• Target Algorithm: {{algorithm_name}}
• Numerical Stability Limit: {{tolerance_threshold}}
• Input Parameter Space: {{input_domain_bounds}}
• Core Computational Dependencies: {{numerical_libraries}}
• Arithmetic Risk Profile: {{underflow_overflow_profile}}
• Determinism Configuration: {{stochastic_seed_policy}}

Task

Draft a comprehensive, production-grade numerical verification checklist that QA engineers and mathematical programmers will use to test {{algorithm_name}} against precision degradation, catastrophic cancellation, edge singularities, and invariant violations across {{input_domain_bounds}}.

Method

1. Analyze {{algorithm_name}} to identify mathematical operations vulnerable to catastrophic cancellation, ill-conditioned matrices, or asymptotic divergence.
2. Cross-reference {{numerical_libraries}} floating-point rounding modes against the acceptable error bounds set in {{tolerance_threshold}}.
3. Formulate boundary check items targeting singularities, zero-crossings, and extremum values across {{input_domain_bounds}}.
4. Design specific invariance tests verifying mathematical properties (e.g., symmetry, monotonicity, conservation laws) that must hold true regardless of precision.
5. Establish validation checks for numerical underflow and overflow mitigations based on {{underflow_overflow_profile}}.
6. Develop repeatability audit points enforcing pseudo-random state controls under {{stochastic_seed_policy}}.
7. Structure each checklist item with pass/fail criteria, mathematical rationale, and precise reproduction assertions.

Constraints

• Every checklist item MUST include an unambiguous mathematical assertion and explicit verification condition.
• MUST NOT permit ambiguous pass/fail terminology such as "acceptable drift" or "reasonable accuracy".
• All floating-point comparisons must reference {{tolerance_threshold}} as an absolute or relative epsilon.
• The checklist must isolate library-specific precision quirks introduced by {{numerical_libraries}}.

Output format

Markdown checklist organized into four distinct sections:

1. Boundary & Singularity Verification (5-7 checked items with criteria)
2. Arithmetic Stability & Precision Invariants (5-7 checked items with epsilon definitions)
3. Determinism & Seed Consistency (3-4 checked items)
4. Automated Assertion Script Guidelines (concise implementation rules, maximum 150 words)

Self-review

• Did I map every item directly to risks within {{input_domain_bounds}} and {{underflow_overflow_profile}}?
• Are all numerical thresholds explicit numbers or formulas tied to {{tolerance_threshold}}?
• Does the checklist avoid generic software QA items in favor of deep numerical analysis tests?