# Float Comparison Reified and int_lin_ne Implementation

**Date**: January 2025  
**Selen Version**: v0.9.1+  
**Status**: ✅ **COMPLETE**

---

## Overview

This document describes the implementation of:
1. **6 Float Comparison Reified Constraints** - Conditional constraints for float variables
2. **int_lin_ne Constraint** - Integer linear not-equal constraint

These features complete the remaining gaps in Selen's FlatZinc support for P1 features.

---

## Part 1: Float Comparison Reified Constraints

### Implemented Methods (6 total)

All six float comparison reified constraints have been implemented:

#### 1. `float_eq_reif`

**Signature:**
```rust
pub fn float_eq_reif(&mut self, x: VarId, y: VarId, b: VarId)
```

**Purpose:** Posts reified equality: `b ⇔ (x = y)` for float variables.

**Example:**
```rust
let x = model.float(0.0, 10.0);
let y = model.float(0.0, 10.0);
let b = model.bool();
model.float_eq_reif(x, y, b);
// Now b is 1 if and only if x = y
```

---

#### 2. `float_ne_reif`

**Signature:**
```rust
pub fn float_ne_reif(&mut self, x: VarId, y: VarId, b: VarId)
```

**Purpose:** Posts reified not-equal: `b ⇔ (x ≠ y)` for float variables.

**Example:**
```rust
let x = model.float(0.0, 10.0);
let y = model.float(0.0, 10.0);
let b = model.bool();
model.float_ne_reif(x, y, b);
// Now b is 1 if and only if x ≠ y
```

---

#### 3. `float_lt_reif`

**Signature:**
```rust
pub fn float_lt_reif(&mut self, x: VarId, y: VarId, b: VarId)
```

**Purpose:** Posts reified less-than: `b ⇔ (x < y)` for float variables.

**Example:**
```rust
let x = model.float(0.0, 10.0);
let y = model.float(0.0, 10.0);
let b = model.bool();
model.float_lt_reif(x, y, b);
// Now b is 1 if and only if x < y
```

---

#### 4. `float_le_reif`

**Signature:**
```rust
pub fn float_le_reif(&mut self, x: VarId, y: VarId, b: VarId)
```

**Purpose:** Posts reified less-or-equal: `b ⇔ (x ≤ y)` for float variables.

**Example:**
```rust
let x = model.float(0.0, 10.0);
let y = model.float(0.0, 10.0);
let b = model.bool();
model.float_le_reif(x, y, b);
// Now b is 1 if and only if x ≤ y
```

---

#### 5. `float_gt_reif`

**Signature:**
```rust
pub fn float_gt_reif(&mut self, x: VarId, y: VarId, b: VarId)
```

**Purpose:** Posts reified greater-than: `b ⇔ (x > y)` for float variables.

**Example:**
```rust
let x = model.float(0.0, 10.0);
let y = model.float(0.0, 10.0);
let b = model.bool();
model.float_gt_reif(x, y, b);
// Now b is 1 if and only if x > y
```

---

#### 6. `float_ge_reif`

**Signature:**
```rust
pub fn float_ge_reif(&mut self, x: VarId, y: VarId, b: VarId)
```

**Purpose:** Posts reified greater-or-equal: `b ⇔ (x ≥ y)` for float variables.

**Example:**
```rust
let x = model.float(0.0, 10.0);
let y = model.float(0.0, 10.0);
let b = model.bool();
model.float_ge_reif(x, y, b);
// Now b is 1 if and only if x ≥ y
```

---

### Key Design Decisions

#### 1. Leverage Existing Infrastructure

All float reified comparison methods **delegate to existing integer reified constraints:**

```rust
pub fn float_eq_reif(&mut self, x: VarId, y: VarId, b: VarId) {
    self.props.int_eq_reif(x, y, b);  // Reuses int_eq_reif!
}
```

**Rationale:** Selen's reified comparison propagators (`IntEqReif`, `IntLtReif`, etc.) are already **type-agnostic** at the VarId level. They work correctly with both integer and float variables because:
- Comparison operations (==, <, <=, etc.) work the same for both types
- Domain propagation uses the same logic regardless of whether domains are integer or float intervals
- No float-specific propagation needed

**Benefits:**
- ✅ Minimal code (6 one-line wrapper methods)
- ✅ Reuses well-tested propagators
- ✅ No new constraint types to debug
- ✅ Consistent behavior with integer versions

#### 2. FlatZinc Specification Compliance

These methods match **FlatZinc specification Section 4.2.2** for float comparison reified constraints:

| FlatZinc Builtin | Selen Method | Status |
|------------------|--------------|--------|
| `float_eq_reif` | `float_eq_reif()` | ✅ |
| `float_ne_reif` | `float_ne_reif()` | ✅ |
| `float_lt_reif` | `float_lt_reif()` | ✅ |
| `float_le_reif` | `float_le_reif()` | ✅ |
| `float_gt_reif` | `float_gt_reif()` | ✅ |
| `float_ge_reif` | `float_ge_reif()` | ✅ |

**Result:** Zelen can now compile FlatZinc float reified constraints **without decomposition**.

---

### Test Suite: Float Comparison Reified

**Location:** `tests/test_float_comparison_reif.rs` - 16 comprehensive tests

#### Test Categories

**Equality Tests (3 tests):**
- `test_float_eq_reif_true` - Force b=1, verify x=y
- `test_float_eq_reif_false` - Force b=0, verify x≠y
- `test_float_eq_reif_inference_to_true` - Fixed x=y, infer b=1

**Not-Equal Tests (2 tests):**
- `test_float_ne_reif_true` - Force b=1, verify x≠y
- `test_float_ne_reif_false` - Force b=0, verify x=y

**Less-Than Tests (3 tests):**
- `test_float_lt_reif_true` - Force b=1, verify x<y
- `test_float_lt_reif_false` - Force b=0, verify x≥y
- `test_float_lt_reif_inference` - Fixed x<y, infer b=1

**Less-or-Equal Tests (2 tests):**
- `test_float_le_reif_true` - Force b=1, verify x≤y
- `test_float_le_reif_false` - Force b=0, verify x>y

**Greater-Than Tests (2 tests):**
- `test_float_gt_reif_true` - Force b=1, verify x>y
- `test_float_gt_reif_false` - Force b=0, verify x≤y

**Greater-or-Equal Tests (2 tests):**
- `test_float_ge_reif_true` - Force b=1, verify x≥y
- `test_float_ge_reif_false` - Force b=0, verify x<y
- `test_float_ge_reif_inference` - Fixed x≥y, infer b=1

**Combined Test (1 test):**
- `test_float_reif_combined` - Multiple reified constraints (x<y and y<z)

#### Test Results

```bash
cargo test --test test_float_comparison_reif
```

**Output:**
```
running 16 tests
test test_float_eq_reif_true ... ok
test test_float_eq_reif_false ... ok
test test_float_eq_reif_inference_to_true ... ok
test test_float_ne_reif_true ... ok
test test_float_ne_reif_false ... ok
test test_float_lt_reif_true ... ok
test test_float_lt_reif_false ... ok
test test_float_lt_reif_inference ... ok
test test_float_le_reif_true ... ok
test test_float_le_reif_false ... ok
test test_float_gt_reif_true ... ok
test test_float_gt_reif_false ... ok
test test_float_ge_reif_true ... ok
test test_float_ge_reif_false ... ok
test test_float_ge_reif_inference ... ok
test test_float_reif_combined ... ok

test result: ok. 16 passed; 0 failed; 0 ignored
```

**Status:** ✅ All 16 tests passing

---

## Part 2: Integer Linear Not-Equal Constraint

### Implemented Method

#### `int_lin_ne`

**Signature:**
```rust
pub fn int_lin_ne(&mut self, coefficients: &[i32], variables: &[VarId], constant: i32)
```

**Purpose:** Posts linear not-equal constraint: `sum(coefficients[i] * variables[i]) ≠ constant`.

**Example:**
```rust
let x = model.int(0, 10);
let y = model.int(0, 10);
let z = model.int(0, 10);

// x + y + z ≠ 15
model.int_lin_ne(&[1, 1, 1], &[x, y, z], 15);
```

**With Coefficients:**
```rust
// 2*x + 3*y - z ≠ 10
model.int_lin_ne(&[2, 3, -1], &[x, y, z], 10);
```

---

### Implementation Details

The implementation follows the **exact same pattern** as `int_lin_eq` and `int_lin_le`:

```rust
pub fn int_lin_ne(&mut self, coefficients: &[i32], variables: &[VarId], constant: i32) {
    // Handle mismatched lengths
    if coefficients.len() != variables.len() {
        self.props.equals(Val::ValI(0), Val::ValI(1));  // Unsatisfiable
        return;
    }

    // Handle empty arrays
    if variables.is_empty() {
        self.props.not_equals(Val::ValI(0), Val::ValI(constant));
        return;
    }

    // Create scaled variables: coeffs[i] * vars[i]
    let scaled_vars: Vec<VarId> = coefficients
        .iter()
        .zip(variables.iter())
        .map(|(&coeff, &var)| self.mul(var, Val::ValI(coeff)))
        .collect();

    // Create sum of all scaled variables
    let sum_var = self.sum(&scaled_vars);

    // Post not-equal constraint: sum ≠ constant
    self.props.not_equals(sum_var, Val::ValI(constant));
}
```

**Key Points:**
- Reuses existing `mul()` and `sum()` methods
- Uses existing `not_equals` propagator
- Handles edge cases (empty arrays, mismatched lengths)
- Consistent with `int_lin_eq` and `int_lin_le` implementations

---

### Test Suite: int_lin_ne

**Location:** `tests/test_int_lin_ne.rs` - 13 comprehensive tests

#### Test Categories

**Basic Tests (4 tests):**
- `test_int_lin_ne_basic` - Simple x + y ≠ 6
- `test_int_lin_ne_with_coefficients` - Weighted sum 2*x + 3*y ≠ 12
- `test_int_lin_ne_negative_coefficients` - Mixed coefficients 2*x - y ≠ 5
- `test_int_lin_ne_three_variables` - Three variables x + y + z ≠ 6

**Propagation Tests (2 tests):**
- `test_int_lin_ne_forced_solution` - Fixed variable forces constraint on others
- `test_int_lin_ne_propagation` - Verify domain pruning works

**Edge Cases (3 tests):**
- `test_int_lin_ne_empty_array` - Empty sum ≠ 0 (unsatisfiable)
- `test_int_lin_ne_empty_array_satisfiable` - Empty sum ≠ 5 (satisfiable)
- `test_int_lin_ne_single_variable` - Single variable 3*x ≠ 9

**Advanced Tests (4 tests):**
- `test_int_lin_ne_large_coefficients` - Large coefficients 100*x + 50*y ≠ 250
- `test_int_lin_ne_combined_with_eq` - Combined with int_lin_eq
- `test_int_lin_ne_zero_coefficients` - Zero coefficients 2*x + 0*y + 3*z ≠ 11
- `test_int_lin_ne_unsatisfiable` - Verify unsatisfiable case detected

#### Test Results

```bash
cargo test --test test_int_lin_ne
```

**Output:**
```
running 13 tests
test test_int_lin_ne_basic ... ok
test test_int_lin_ne_with_coefficients ... ok
test test_int_lin_ne_negative_coefficients ... ok
test test_int_lin_ne_three_variables ... ok
test test_int_lin_ne_forced_solution ... ok
test test_int_lin_ne_propagation ... ok
test test_int_lin_ne_empty_array ... ok
test test_int_lin_ne_empty_array_satisfiable ... ok
test test_int_lin_ne_single_variable ... ok
test test_int_lin_ne_large_coefficients ... ok
test test_int_lin_ne_combined_with_eq ... ok
test test_int_lin_ne_zero_coefficients ... ok
test test_int_lin_ne_unsatisfiable ... ok

test result: ok. 13 passed; 0 failed; 0 ignored
```

**Status:** ✅ All 13 tests passing

---

## Integration with Existing Codebase

### Modified Files

**1. `src/model/constraints.rs`** (+~200 lines)

Added 7 new public methods:
- 6 float comparison reified methods (lines ~620-750)
- 1 integer linear not-equal method (lines ~732-790)

All methods fully documented with rustdoc comments and examples.

**2. `tests/test_float_comparison_reif.rs`** (NEW - ~450 lines)
- 16 comprehensive tests for float comparison reified constraints

**3. `tests/test_int_lin_ne.rs`** (NEW - ~280 lines)
- 13 comprehensive tests for int_lin_ne constraint

### Code Locations

**Float Comparison Reified (src/model/constraints.rs, lines ~620-750):**
```rust
impl Model {
    // ═══════════════════════════════════════════════════════════════════════
    // 🔢 Float Comparison Reified Constraints (FlatZinc Integration)
    // ═══════════════════════════════════════════════════════════════════════

    pub fn float_eq_reif(&mut self, x: VarId, y: VarId, b: VarId) {
        self.props.int_eq_reif(x, y, b);
    }

    pub fn float_ne_reif(&mut self, x: VarId, y: VarId, b: VarId) {
        self.props.int_ne_reif(x, y, b);
    }

    // ... (4 more methods)
}
```

**Integer Linear Not-Equal (src/model/constraints.rs, lines ~732-790):**
```rust
impl Model {
    pub fn int_lin_ne(&mut self, coefficients: &[i32], variables: &[VarId], constant: i32) {
        // Implementation...
    }
}
```

### Compatibility

**No Breaking Changes:**
- ✅ All existing tests still pass (237 library tests)
- ✅ No changes to existing APIs
- ✅ New methods are additive only
- ✅ `cargo check` confirms no regressions

---

## Use Cases

### Float Comparison Reified

**Use Case 1: Conditional Constraints**
```rust
// If temperature > 25.0, then cooling_power must be >= 80.0
let temp = model.float(0.0, 50.0);
let cooling = model.float(0.0, 100.0);
let needs_cooling = model.bool();

model.float_gt_reif(temp, model.float(25.0, 25.0), needs_cooling);
// Then use needs_cooling in conditional constraint
```

**Use Case 2: Counting Satisfying Conditions**
```rust
// Count how many values are above threshold
let values = vec![v1, v2, v3, v4, v5];
let threshold = model.float(10.0, 10.0);
let above_threshold_flags: Vec<VarId> = values
    .iter()
    .map(|&v| {
        let b = model.bool();
        model.float_gt_reif(v, threshold, b);
        b
    })
    .collect();

let count = model.sum(&above_threshold_flags);
// count tells us how many values > 10.0
```

**Use Case 3: Ordering Constraints**
```rust
// x < y < z with reification
let x = model.float(0.0, 10.0);
let y = model.float(0.0, 10.0);
let z = model.float(0.0, 10.0);
let b1 = model.bool();
let b2 = model.bool();

model.float_lt_reif(x, y, b1);
model.float_lt_reif(y, z, b2);
model.new(b1.eq(1));
model.new(b2.eq(1));
// Now x < y < z
```

### Integer Linear Not-Equal

**Use Case 1: Avoid Specific Sum**
```rust
// Resource allocation: total != 100 (must be under or over)
let cpu = model.int(0, 200);
let memory = model.int(0, 200);
let disk = model.int(0, 200);

model.int_lin_ne(&[1, 1, 1], &[cpu, memory, disk], 100);
```

**Use Case 2: Break Symmetry**
```rust
// Prevent symmetric solutions in scheduling
// worker1_hours + worker2_hours ≠ 16 (forces different schedules)
model.int_lin_ne(&[1, 1], &[worker1, worker2], 16);
```

**Use Case 3: Combine with Other Constraints**
```rust
// Budget must be between 90 and 110, but NOT exactly 100
model.int_lin_le(&[1, 1, 1], &[item1, item2, item3], 110);
model.int_lin_eq(&[1, 1, 1], &[item1, item2, item3], 90);
model.int_lin_ne(&[1, 1, 1], &[item1, item2, item3], 100);
```

---

## Summary

### Completion Status

✅ **Float Comparison Reified Constraints - COMPLETE**

| Method | Status | Tests |
|--------|--------|-------|
| `float_eq_reif` | ✅ Done | 3 tests |
| `float_ne_reif` | ✅ Done | 2 tests |
| `float_lt_reif` | ✅ Done | 3 tests |
| `float_le_reif` | ✅ Done | 2 tests |
| `float_gt_reif` | ✅ Done | 2 tests |
| `float_ge_reif` | ✅ Done | 2 tests |
| **Total** | **6/6** | **16 tests** |

✅ **Integer Linear Not-Equal - COMPLETE**

| Method | Status | Tests |
|--------|--------|-------|
| `int_lin_ne` | ✅ Done | 13 tests |

### Key Achievements

1. ✅ **Minimal implementation** - Only ~200 lines of code total
2. ✅ **Comprehensive testing** - 29 tests total (16 + 13), all passing
3. ✅ **Zero breaking changes** - All existing tests pass (237 library tests)
4. ✅ **FlatZinc compliant** - Direct builtin mapping for Zelen
5. ✅ **Well documented** - Inline rustdoc + this summary document

### FlatZinc Coverage Update

With these additions, **all major P1 FlatZinc features are now implemented:**

| Feature Category | Status | Methods | Tests |
|------------------|--------|---------|-------|
| Float Linear Constraints | ✅ Complete | 6 | 25+ |
| Float Comparison Reified | ✅ Complete | 6 | 16 |
| Integer Linear Constraints | ✅ Complete | 3 | 13+ |
| Array Float Constraints | ✅ Complete | 3 | 21 |
| Type Conversions | ✅ Complete | 4 | 31 |
| **Total P1 Features** | **✅ Complete** | **22** | **106+** |

---

## Verification

### Compilation Check
```bash
cargo check
# Result: ✅ Success (only pre-existing warnings)
```

### Test Results
```bash
# Float comparison reified tests
cargo test --test test_float_comparison_reif
# Result: ✅ 16/16 passed

# Integer linear not-equal tests
cargo test --test test_int_lin_ne
# Result: ✅ 13/13 passed

# All library tests (regression check)
cargo test --lib
# Result: ✅ 237/237 passed (1 ignored)
```

### Overall Status
✅ **All implementations complete, tested, and verified**

---

## References

- **FlatZinc Specification:** Sections 4.2.2 (Float Comparison Reified) and 4.2.3 (Linear Constraints)
- **Selen Version:** v0.9.1+
- **Implementation Date:** January 2025
- **Related Docs:**
  - `SELEN_MISSING_FEATURES.md` - Updated feature tracking
  - `tests/test_float_comparison_reif.rs` - Float reified test suite
  - `tests/test_int_lin_ne.rs` - Integer linear ne test suite
  - `src/model/constraints.rs` - Implementation

---

**Document Version:** 1.0  
**Implementation Status:** ✅ COMPLETE  
**Last Updated:** January 2025  
**Selen Version:** v0.9.1+
