Grcov report - direct_int

1

use conjure_cp::ast::{Atom, Expression as Expr, Literal};

2

use conjure_cp::ast::{SATIntEncoding, SymbolTable};

3

use conjure_cp::rule_engine::ApplicationError;

4

use conjure_cp::rule_engine::{

5

    ApplicationError::RuleNotApplicable, ApplicationResult, Reduction, register_rule,

6

};

7

8

use conjure_cp::ast::Metadata;

9

use conjure_cp::ast::Moo;

10

use conjure_cp::into_matrix_expr;

11

12

use super::boolean::{tseytin_and, tseytin_iff, tseytin_not, tseytin_or, tseytin_xor};

13

14

use conjure_cp::ast::CnfClause;

15

/// Converts an integer literal to SATInt form

16

///

17

/// ```text

18

///  3

19

///  ~~>

20

///  SATInt([true;int(1..), (3, 3)])

21

///

22

/// ```

23

#[register_rule(("SAT_Direct", 9500))]

24

419196

fn literal_sat_direct_int(expr: &Expr, _: &SymbolTable) -> ApplicationResult {

25

1410

    let value = {

26

13266

        if let Expr::Atomic(_, Atom::Literal(Literal::Int(value))) = expr {

27

1410

            *value

28

        } else {

29

417786

            return Err(RuleNotApplicable);

30

31

};

32

33

1410

    Ok(Reduction::pure(Expr::SATInt(

34

1410

        Metadata::new(),

35

1410

        SATIntEncoding::Direct,

36

1410

        Moo::new(into_matrix_expr!(vec![Expr::Atomic(

37

1410

            Metadata::new(),

38

1410

            Atom::Literal(Literal::Bool(true)),

39

1410

        )])),

40

1410

        (value, value),

41

1410

)))

42

419196

43

44

/// This function confirms that all of the input expressions are direct SATInts, and returns vectors for each input of their bits

45

/// This function also normalizes direct SATInt operands to a common value range by zero-padding.

46

20202

pub fn validate_direct_int_operands(

47

20202

    exprs: Vec<Expr>,

48

20202

) -> Result<(Vec<Vec<Expr>>, i32, i32), ApplicationError> {

49

    // TODO: In the future it may be possible to optimize operations between integers with different bit sizes

50

    // Collect inner bit vectors from each SATInt

51

52

    // Iterate over all inputs

53

    // Check they are direct and calulate a lower and upper bound

54

20202

    let mut global_min: i32 = i32::MAX;

55

20202

    let mut global_max: i32 = i32::MIN;

56

57

22866

    for operand in &exprs {

58

19842

        let Expr::SATInt(_, SATIntEncoding::Direct, _, (local_min, local_max)) = operand else {

59

18390

            return Err(RuleNotApplicable);

60

};

61

4476

        global_min = global_min.min(*local_min);

62

4476

        global_max = global_max.max(*local_max);

63

64

65

    // build out by iterating over each operand and expanding it to match the new bounds

66

67

1812

    let out: Vec<Vec<Expr>> = exprs

68

1812

        .into_iter()

69

3564

        .map(|expr| {

70

3564

            let Expr::SATInt(_, SATIntEncoding::Direct, inner, (local_min, local_max)) = expr

71

            else {

72

                return Err(RuleNotApplicable);

73

};

74

75

3564

            let Some(v) = inner.as_ref().clone().unwrap_list() else {

76

                return Err(RuleNotApplicable);

77

};

78

79

            // calulcate how many zeroes to prepend/append

80

3564

            let prefix_len = (local_min - global_min) as usize;

81

3564

            let postfix_len = (global_max - local_max) as usize;

82

83

3564

            let mut bits = Vec::with_capacity(v.len() + prefix_len + postfix_len);

84

85

            // add 0s to start

86

3564

            bits.extend(std::iter::repeat_n(

87

3564

                Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(false))),

88

3564

                prefix_len,

89

));

90

91

3564

            bits.extend(v);

92

93

            // add 0s to end

94

3564

            bits.extend(std::iter::repeat_n(

95

3564

                Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(false))),

96

3564

                postfix_len,

97

));

98

99

3564

            Ok(bits)

100

3564

})

101

1812

        .collect::<Result<_, _>>()?;

102

103

1812

    Ok((out, global_min, global_max))

104

20202

105

106

/// Converts a = expression between two direct SATInts to a boolean expression in cnf

107

///

108

/// ```text

109

/// SATInt(a) = SATInt(b) ~> Bool

110

/// ```

111

/// NOTE: This rule reduces to AND_i (a[i] ≡ b[i]) and does not enforce one-hotness.

112

#[register_rule(("SAT_Direct", 9100))]

113

135000

fn eq_sat_direct(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

114

    // TODO: this could be optimized by just going over the sections of both vectors where the ranges intersect

115

    // this does require enforcing structure separately

116

135000

    let Expr::Eq(_, lhs, rhs) = expr else {

117

133326

        return Err(RuleNotApplicable);

118

};

119

120

318

    let (binding, _, _) =

121

1674

        validate_direct_int_operands(vec![lhs.as_ref().clone(), rhs.as_ref().clone()])?;

122

318

    let [lhs_bits, rhs_bits] = binding.as_slice() else {

123

        return Err(RuleNotApplicable);

124

};

125

126

318

    let bit_count = lhs_bits.len();

127

128

318

    let mut output = true.into();

129

318

    let mut new_symbols = symbols.clone();

130

318

    let mut new_clauses = vec![];

131

    let mut comparison;

132

133

6612

    for i in 0..bit_count {

134

6612

        comparison = tseytin_iff(

135

6612

            lhs_bits[i].clone(),

136

6612

            rhs_bits[i].clone(),

137

6612

            &mut new_clauses,

138

6612

            &mut new_symbols,

139

6612

);

140

6612

        output = tseytin_and(

141

6612

            &vec![comparison, output],

142

6612

            &mut new_clauses,

143

6612

            &mut new_symbols,

144

6612

);

145

6612

146

147

318

    Ok(Reduction::cnf(output, new_clauses, new_symbols))

148

135000

149

150

/// Converts a != expression between two direct SATInts to a boolean expression in cnf

151

///

152

/// ```text

153

/// SATInt(a) != SATInt(b) ~> Bool

154

///

155

/// ```

156

///

157

/// True iff at least one value position differs.

158

#[register_rule(("SAT_Direct", 9100))]

159

135000

fn neq_sat_direct(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

160

135000

    let Expr::Neq(_, lhs, rhs) = expr else {

161

134526

        return Err(RuleNotApplicable);

162

};

163

164

150

    let (binding, _, _) =

165

474

        validate_direct_int_operands(vec![lhs.as_ref().clone(), rhs.as_ref().clone()])?;

166

150

    let [lhs_bits, rhs_bits] = binding.as_slice() else {

167

        return Err(RuleNotApplicable);

168

};

169

170

150

    let bit_count = lhs_bits.len();

171

172

150

    let mut output = false.into();

173

150

    let mut new_symbols = symbols.clone();

174

150

    let mut new_clauses = vec![];

175

    let mut comparison;

176

177

1158

    for i in 0..bit_count {

178

1158

        comparison = tseytin_xor(

179

1158

            lhs_bits[i].clone(),

180

1158

            rhs_bits[i].clone(),

181

1158

            &mut new_clauses,

182

1158

            &mut new_symbols,

183

1158

);

184

1158

        output = tseytin_or(

185

1158

            &vec![comparison, output],

186

1158

            &mut new_clauses,

187

1158

            &mut new_symbols,

188

1158

);

189

1158

190

191

150

    Ok(Reduction::cnf(output, new_clauses, new_symbols))

192

135000

193

194

/// Converts a </>/<=/>= expression between two direct SATInts to a boolean expression in cnf

195

///

196

/// ```text

197

/// SATInt(a) </>/<=/>= SATInt(b) ~> Bool

198

///

199

/// ```

200

/// Note: < and <= are rewritten by swapping operands to reuse lt logic.

201

#[register_rule(("SAT", 9100))]

202

342342

fn ineq_sat_direct(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

203

342342

    let (lhs, rhs, negate) = match expr {

204

        // A < B -> sat_direct_lt(A, B)

205

249

        Expr::Lt(_, x, y) => (x, y, false),

206

        // A > B -> sat_direct_lt(B, A)

207

333

        Expr::Gt(_, x, y) => (y, x, false),

208

        // A <= B -> NOT (B < A)

209

9492

        Expr::Leq(_, x, y) => (y, x, true),

210

        // A >= B -> NOT (A < B)

211

7908

        Expr::Geq(_, x, y) => (x, y, true),

212

324360

        _ => return Err(RuleNotApplicable),

213

};

214

215

1284

    let (binding, _, _) =

216

17982

        validate_direct_int_operands(vec![lhs.as_ref().clone(), rhs.as_ref().clone()])?;

217

1284

    let [lhs_bits, rhs_bits] = binding.as_slice() else {

218

        return Err(RuleNotApplicable);

219

};

220

221

1284

    let mut new_symbols = symbols.clone();

222

1284

    let mut new_clauses = vec![];

223

224

1284

    let mut output = sat_direct_lt(

225

1284

        lhs_bits.clone(),

226

1284

        rhs_bits.clone(),

227

1284

        &mut new_clauses,

228

1284

        &mut new_symbols,

229

);

230

231

1284

    if negate {

232

1236

        output = tseytin_not(output, &mut new_clauses, &mut new_symbols);

233

1236

234

235

1284

    Ok(Reduction::cnf(output, new_clauses, new_symbols))

236

342342

237

238

/// Encodes a < b for one-hot direct integers using prefix OR logic.

239

1284

fn sat_direct_lt(

240

1284

    a: Vec<Expr>,

241

1284

    b: Vec<Expr>,

242

1284

    clauses: &mut Vec<CnfClause>,

243

1284

    symbols: &mut SymbolTable,

244

1284

) -> Expr {

245

1284

    let mut b_or = Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(false)));

246

1284

    let mut cum_result = Expr::Atomic(Metadata::new(), Atom::Literal(Literal::Bool(false)));

247

248

13248

    for (a_i, b_i) in a.iter().zip(b.iter()) {

249

        // b_or is prefix_or of b up to index i: B_i = b_0 | ... | b_i

250

13248

        b_or = tseytin_or(&vec![b_or, b_i.clone()], clauses, symbols);

251

13248

252

        // a < b if there exists i such that a=i and b > i.

253

        // b > i is equivalent to NOT(B_i) assuming one-hotness.

254

13248

        let not_b_or = tseytin_not(b_or.clone(), clauses, symbols);

255

13248

        let a_i_and_not_b_i = tseytin_and(&vec![a_i.clone(), not_b_or], clauses, symbols);

256

13248

257

13248

        cum_result = tseytin_or(&vec![cum_result, a_i_and_not_b_i], clauses, symbols);

258

13248

259

260

1284

    cum_result

261

1284

262

263

/// Converts a - expression for a SATInt to a new SATInt

264

///

265

/// ```text

266

/// -SATInt(a) ~> SATInt(b)

267

///

268

/// ```

269

#[register_rule(("SAT_Direct", 9100))]

270

135000

fn neg_sat_direct(expr: &Expr, _: &SymbolTable) -> ApplicationResult {

271

135000

    let Expr::Neg(_, value) = expr else {

272

134928

        return Err(RuleNotApplicable);

273

};

274

275

72

    let (binding, old_min, old_max) = validate_direct_int_operands(vec![value.as_ref().clone()])?;

276

60

    let [val_bits] = binding.as_slice() else {

277

        return Err(RuleNotApplicable);

278

};

279

280

60

    let new_min = -old_max;

281

60

    let new_max = -old_min;

282

283

60

    let mut out = val_bits.clone();

284

60

    out.reverse();

285

286

60

    Ok(Reduction::pure(Expr::SATInt(

287

60

        Metadata::new(),

288

60

        SATIntEncoding::Direct,

289

60

        Moo::new(into_matrix_expr!(out)),

290

60

        (new_min, new_max),

291

60

)))

292

135000

293

294

13176

fn floor_div(a: i32, b: i32) -> i32 {

295

13176

    let (q, r) = (a / b, a % b);

296

13176

    if (r > 0 && b < 0) || (r < 0 && b > 0) {

297

4008

        q - 1

298

    } else {

299

9168

300

301

13176

302

303

/// Converts a / expression between two direct SATInts to a new direct SATInt

304

/// using the "lookup table" method.

305

///

306

/// ```text

307

/// SafeDiv(SATInt(a), SATInt(b)) ~> SATInt(c)

308

///

309

/// ```

310

#[register_rule(("SAT_Direct", 9100))]

311

135000

fn safediv_sat_direct(expr: &Expr, symbols: &SymbolTable) -> ApplicationResult {

312

135000

    let Expr::SafeDiv(_, numer_expr, denom_expr) = expr else {

313

134910

        return Err(RuleNotApplicable);

314

};

315

316

90

    let Expr::SATInt(_, SATIntEncoding::Direct, numer_inner, (numer_min, numer_max)) =

317

90

        numer_expr.as_ref()

318

    else {

319

        return Err(RuleNotApplicable);

320

};

321

90

    let Some(numer_bits) = numer_inner.as_ref().clone().unwrap_list() else {

322

        return Err(RuleNotApplicable);

323

};

324

325

90

    let Expr::SATInt(_, SATIntEncoding::Direct, denom_inner, (denom_min, denom_max)) =

326

90

        denom_expr.as_ref()

327

    else {

328

        return Err(RuleNotApplicable);

329

};

330

331

90

    let Some(denom_bits) = denom_inner.as_ref().clone().unwrap_list() else {

332

        return Err(RuleNotApplicable);

333

};

334

335

90

    let mut quot_min = i32::MAX;

336

90

    let mut quot_max = i32::MIN;

337

338

912

    for i in *numer_min..=*numer_max {

339

13956

        for j in *denom_min..=*denom_max {

340

13956

            let k = if j == 0 { 0 } else { i / j };

341

13956

            quot_min = quot_min.min(k);

342

13956

            quot_max = quot_max.max(k);

343

344

345

346

90

    let mut new_symbols = symbols.clone();

347

90

    let mut quot_bits = Vec::new();

348

349

    // generate boolean variables for all possible quotients

350

1002

    for _ in quot_min..=quot_max {

351

1002

        let decl = new_symbols.gensym(&conjure_cp::ast::Domain::bool());

352

1002

        quot_bits.push(Expr::Atomic(

353

1002

            Metadata::new(),

354

1002

            Atom::Reference(conjure_cp::ast::Reference::new(decl)),

355

1002

));

356

1002

357

358

90

    let mut new_clauses = vec![];

359

360

    // generate the lookup table clauses: (n_i AND d_j) => q_k

361

912

    for i in *numer_min..=*numer_max {

362

912

        let numer_bit = &numer_bits[(i - numer_min) as usize];

363

13956

        for j in *denom_min..=*denom_max {

364

13956

            let denom_bit = &denom_bits[(j - denom_min) as usize];

365

366

13956

            let k = if j == 0 { 0 } else { floor_div(i, j) };

367

368

13956

            let quot_bit = &quot_bits[(k - quot_min) as usize];

369

370

13956

            new_clauses.push(CnfClause::new(vec![

371

13956

                Expr::Not(Metadata::new(), Moo::new(numer_bit.clone())),

372

13956

                Expr::Not(Metadata::new(), Moo::new(denom_bit.clone())),

373

13956

                quot_bit.clone(),

374

            ]));

375

376

377

378

    // the quotient cannot take more than one value simultaneously.

379

1002

    for a in 0..quot_bits.len() {

380

9708

        for b in (a + 1)..quot_bits.len() {

381

9708

            new_clauses.push(CnfClause::new(vec![

382

9708

                Expr::Not(Metadata::new(), Moo::new(quot_bits[a].clone())),

383

9708

                Expr::Not(Metadata::new(), Moo::new(quot_bits[b].clone())),

384

9708

            ]));

385

9708

386

387

388

90

    let quot_int = Expr::SATInt(

389

90

        Metadata::new(),

390

90

        SATIntEncoding::Direct,

391

90

        Moo::new(into_matrix_expr!(quot_bits)),

392

90

        (quot_min, quot_max),

393

90

);

394

395

90

    Ok(Reduction::cnf(quot_int, new_clauses, new_symbols))

396

135000