# Boundary Analysis
Boundary analysis identifies the exact input values where an operation's behavior changes qualitatively.
## What Is a Boundary?
A boundary is an input value that sits at the edge of an equivalence class. Off-by-one errors, overflow, underflow, and mask mishandling cluster at boundaries.
## Common Boundary Patterns
| Unsigned wrap | `0`, `1`, `u32::MAX - 1`, `u32::MAX` |
| Signed reinterpretation | `0`, `0x7FFFFFFF` (i32::MAX), `0x80000000` (i32::MIN) |
| Shift/rotate | `0`, `1`, `31`, `32`, `33` |
| Division/modulo | Divisor `0`, `1`, dividend `0`, `u32::MAX` |
| Bit extraction/insertion | Offset `0`, `31`, count `0`, `1`, `31` |
| Boolean/logical | `0`, `1`, `u32::MAX` (non-zero) |
## Registry Requirement
Every `OpSpec` must list every boundary value reachable by its signature. The conformance suite must run each one. Missing a boundary is a coverage gap even if millions of random tests pass.
## Coverage Metric
```text
boundary_coverage = covered_boundary_values / total_declared_boundary_values
```
100% boundary coverage is required for a complete conformance claim.