Scientific Computing Property-Based Test Harness Generator

Role: Principal Research Software Engineer specializing in Numerical Stability and Scientific Computing.

Context

• Target mathematical function: {{target_math_function}}
• Invariants and algebraic properties: {{mathematical_invariants}}
• Floating-point precision target: {{floating_point_precision}}
• Testing framework and language: {{framework_language}}
• Edge-case domains and boundaries: {{edge_case_domains}}
• Failure tolerance threshold: {{failure_tolerance_threshold}}

Task

Develop an end-to-end property-based testing script that rigorously verifies mathematical invariants, edge-case handling, and numerical precision stability across extreme dynamic ranges for scientific research synthesis algorithms.

Method

1. Parse {{target_math_function}} against the formal mathematical invariants defined in {{mathematical_invariants}}.
2. Define parameter sampling strategies in {{framework_language}} to cover {{edge_case_domains}}, including denormalized numbers, infinities, and NaN boundaries.
3. Formulate metamorphic relations and invariant properties as parameterized test assertions.
4. Implement numerical stability assertion checks enforcing {{floating_point_precision}} limits with ULP (Unit in the Last Place) comparison logic.
5. Structure shrinkers and custom generators to isolate the minimal failing inputs when invariants break.
6. Inject bounded perturbation tests to evaluate error propagation under {{failure_tolerance_threshold}}.
7. Embed automated report logging capturing failure distributions, seed reproducibility, and floating-point condition numbers.

Constraints

• Generated code MUST compile and run directly within {{framework_language}} without placeholder implementations.
• Numerical comparisons MUST NOT rely on raw equality (==) for floating-point calculations; explicit epsilon or ULP bounds are mandatory.
• Include explicit setup fixtures, parameterized strategy generators, and tear-down harnesses.
• Inline documentation MUST explain the mathematical rationale behind every property assertion.

Output format

Provide a single executable test script organized into:

1. Strategy and Custom Generator Definitions
2. Precision Comparator Utility Functions
3. Parametric Property Assertion Test Cases (minimum 4 distinct property tests)
4. Execution Harness with Reproducible Seed Configuration

Self-review

• Ensure all properties in {{mathematical_invariants}} map to distinct test functions.
• Verify that {{floating_point_precision}} bounds use correct tolerance tolerances.
• Confirm no mock imports or pseudo-code exist in the script.