# Numerical Issues Test Suite Results

## Overview

A comprehensive test suite has been created to validate numerical stability issues identified in the floating-point analysis. The tests are designed to **fail on the current implementation** and pass once the issues are fixed (Test-Driven Development approach).

## Test Files

- **Test Suite**: `/home/ross/devpublic/togo/src/tests/test_numerical_issues.rs`
- **Analysis Document**: `/home/ross/devpublic/togo/docs/development/FLOATING_POINT_ANALYSIS.md`

## Running the Tests

```bash
# Run all numerical issue tests
cargo test test_numerical_issues --lib

# Run specific test module
cargo test test_nearly_parallel --lib

# Run with output
cargo test test_numerical_issues --lib -- --nocapture
```

## Current Test Results

**Total: 28 tests**
- ✅ **19 tests passed** (with `#[should_panic]` - correctly detecting bugs)
- ❌ **9 tests failed** (without `#[should_panic]` - demonstrating bugs)

## Failing Tests (Need Fixes)

These tests fail because the current implementation has numerical issues:

1. **`test_arc_bulge_division::test_epsilon_bulge_produces_finite_arc`**
   - Issue: Division by tiny bulge values produces infinite/huge radii
   - Location: `src/arc.rs` - arc parametrization functions

2. **`test_arc_bulge_division::test_negative_tiny_bulge`**
   - Issue: Same as above for negative bulge values

3. **`test_arc_bulge_division::test_tiny_bulge_produces_finite_arc`**
   - Issue: Tiny bulge values (< 1e-10) should be treated as zero

4. **`test_arc_bulge_division::test_zero_bulge_produces_line_segment`**
   - Issue: Zero bulge should produce line segment (r = ∞) not finite arc

5. **`test_area_edge_cases::test_nearly_full_circle_arc`**
   - Issue: Area calculation for nearly-closed arcs has precision issues

6. **`test_convex_hull_nan::test_convex_hull_all_nan_points`**
   - Issue: Convex hull doesn't handle all-NaN input gracefully

7. **`test_convex_hull_nan::test_convex_hull_filters_nan_points`**
   - Issue: NaN points are not filtered before convex hull computation

8. **`test_exact_zero_comparisons::test_circle_center_comparison_with_tolerance`**
   - Issue: Exact zero comparison instead of tolerance-based comparison

9. **`test_exact_zero_comparisons::test_convex_hull_handles_numerical_collinearity`**
   - Issue: Convex hull fails on numerically collinear points

## Passing Tests (Detecting Bugs)

These tests use `#[should_panic]` and correctly panic, demonstrating the bugs:

### Line-Line Intersection Issues
- `test_nearly_parallel_lines_detected` - Nearly parallel lines incorrectly detected as intersecting
- `test_exactly_parallel_horizontal_lines` - Exact parallel detection fails
- `test_exactly_parallel_vertical_lines` - Vertical parallel detection fails
- `test_numerical_collinearity` - Collinearity detection has tolerance issues

### Division Guards
- `test_division_near_zero_denominator` - Division by near-zero not guarded
- `test_segment_degenerate_to_point` - Zero-length segment causes issues

### Sqrt Guards
- `test_negative_discriminant_sqrt` - Negative sqrt not guarded
- `test_arc_with_invalid_geometry` - Invalid arc geometry accepted

### Large Coordinate Issues
- `test_large_magnitude_coordinates` - Loss of precision with large coordinates
- `test_coordinate_subtraction_catastrophe` - Catastrophic cancellation

### Parameter Overflow
- `test_nearly_parallel_lines_reject_far_intersection` - Intersection parameters overflow
- `test_coincident_segments_parameter_check` - Coincident segment parameters unbounded

### Area Calculations
- `test_nearly_degenerate_polygon` - Area of nearly-degenerate polygon imprecise
- `test_large_polygon_area_overflow` - Large polygon area can overflow

### Tolerance Consistency
- `test_consistent_tolerance_line_intersection` - Inconsistent tolerances across functions
- `test_tolerance_sensitive_arc_segment_intersection` - Arc-segment intersection tolerance issues

### Integration Tests
- `test_area_calculation_robustness` - Area calculations not scale-independent
- `test_mixed_operations_stability` - Chained operations accumulate errors

## After Fixing Issues

Once you fix the numerical issues:

1. **The 9 failing tests should pass** - These test expected correct behavior
2. **Remove `#[should_panic]` from the 19 passing tests** - Convert them to regular assertions expecting success
3. **Run the full suite** - All 28 tests should pass

### Example Fix Workflow

```rust
// Before (fails): test_zero_bulge_produces_line_segment
fn arc_circle_parametrization(a: Point, b: Point, bulge: f64) -> Arc {
    let r = dist / (2.0 * bulge);  // Divides by zero!
    ...
}

// After (passes): test_zero_bulge_produces_line_segment
fn arc_circle_parametrization(a: Point, b: Point, bulge: f64) -> Arc {
    if bulge.abs() < EPSILON {
        return arcseg(a, b, 0.0);  // Line segment
    }
    let r = dist / (2.0 * bulge);
    ...
}
```

## Key Issues to Fix

From the test results, prioritize these fixes:

### Priority 1: Critical Safety Issues
1. **Bulge division guards** - Add epsilon checks before dividing by bulge
2. **Sqrt argument validation** - Check discriminants before sqrt
3. **NaN filtering** - Remove or handle NaN values in input

### Priority 2: Numerical Stability
4. **Parallel line detection** - Use robust tolerance-based comparison
5. **Parameter bounds checking** - Reject intersections with huge parameters
6. **Zero comparisons** - Replace `== 0.0` with `abs() < EPSILON`

### Priority 3: Precision Improvements
7. **Large coordinate handling** - Normalize or use relative comparisons
8. **Area calculations** - Use robust computation methods
9. **Tolerance consistency** - Centralize epsilon/tolerance definitions

## References

- **Detailed Analysis**: `docs/development/FLOATING_POINT_ANALYSIS.md`
- **Test Source**: `src/tests/test_numerical_issues.rs`
- **Main Issues**: 
  - Issue 2.0: Line-line parallel detection
  - Issue 2.1: Arc bulge division
  - Issue 2.2: Unchecked sqrt operations
  - Issue 2.3: NaN handling in convex hull
  - Issue 8.1: Exact zero comparisons

## Notes

- Tests use seed `42` for reproducibility
- Random test ranges chosen to expose edge cases
- Some tests commented out due to missing API functions
- All tests use types and functions from the existing codebase
