Grcov report - integer

1

use conjure_cp::ast::{Expression as Expr, GroundDomain};

2

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

3

use conjure_cp::rule_engine::{

4

    ApplicationError, ApplicationError::RuleNotApplicable, ApplicationResult, Reduction,

5

    register_rule,

6

};

7

8

use conjure_cp::ast::Metadata;

9

use conjure_cp::ast::{Atom, Literal, Moo, Range};

10

use conjure_cp::into_matrix_expr;

11

12

use conjure_cp::{bug, essence_expr};

13

14

/// This function takes a target expression and a vector of ranges and creates an expression representing the ranges with the target expression as the subject

15

///

16

/// E.g. x : int(4), int(10..20), int(30..) ~~> Or(x=4, 10<=x<=20, x>=30)

17

438

fn int_domain_to_expr(subject: Expr, ranges: &Vec<Range<i32>>) -> Expr {

18

438

    let mut output = vec![];

19

20

438

    let value = Moo::new(subject);

21

22

498

    for range in ranges {

23

498

        match range {

24

81

            Range::Single(x) => output.push(essence_expr!(&value = &x)),

25

417

            Range::Bounded(x, y) => output.push(essence_expr!("&value >= &x /\\ &value <= &y")),

26

            _ => bug!("Unbounded domains not supported for SAT"),

27

28

29

30

438

    Expr::Or(Metadata::new(), Moo::new(into_matrix_expr!(output)))

31

438

32

33

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

34

/// This function also extends all vectors such that they have the same lengths

35

/// The vector lengths is either `n` for bit_count = Some(n), otherwise the length of the longest operand

36

2439

pub fn validate_log_int_operands(

37

2439

    exprs: Vec<Expr>,

38

2439

    bit_count: Option<u32>,

39

2439

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

40

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

41

    // Collect inner bit vectors from each SATInt

42

43

    // TODO: this file should be encoding agnostic so this needs to moved to the log_int_ops.rs file, do this once the direct ints have been merged to main though

44

2439

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

45

2439

        .into_iter()

46

4356

        .map(|expr| {

47

3636

            let Expr::SATInt(_, SATIntEncoding::Log, inner, _) = expr else {

48

720

                return Err(RuleNotApplicable);

49

};

50

3636

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

51

                return Err(RuleNotApplicable);

52

};

53

3636

            Ok(bits)

54

4356

})

55

2439

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

56

57

    // Determine target length

58

1719

    let max_len = bit_count

59

1719

        .map(|b| b as usize)

60

3276

        .unwrap_or_else(|| out.iter().map(|v| v.len()).max().unwrap_or(0));

61

62

    // Extend or crop each vector

63

3375

    for v in &mut out {

64

3375

        if v.len() < max_len {

65

            // pad with the last element

66

738

            if let Some(last) = v.last().cloned() {

67

738

                v.resize(max_len, last);

68

738

69

2637

        } else if v.len() > max_len {

70

            // crop extra elements

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            v.truncate(max_len);

72

2637

73

74

75

1719

    Ok(out)

76

2439

77

78

/// Converts an integer decision variable to SATInt form, creating a new representation of boolean variables if

79

/// one does not yet exist

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///

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/// ```text

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///  x

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///  ~~>

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///  SATInt([x#00, x#01, ...])

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///

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///  new variables:

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///  find x#00: bool

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///  find x#01: bool

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///  ...

90

///

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/// ```

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

93

315645

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

94

    // thing we are representing must be a reference

95

191571

    let Expr::Atomic(_, Atom::Reference(name)) = expr else {

96

136545

        return Err(RuleNotApplicable);

97

};

98

99

    // thing we are representing must be a variable

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    // symbols

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    //     .lookup(name)

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    //     .ok_or(RuleNotApplicable)?

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    //     .as_find()

104

    //     .ok_or(RuleNotApplicable)?;

105

106

    // thing we are representing must be an integer

107

179100

    let dom = name.resolved_domain().ok_or(RuleNotApplicable)?;

108

179100

    let GroundDomain::Int(ranges) = dom.as_ref() else {

109

178131

        return Err(RuleNotApplicable);

110

};

111

112

969

    let (min, max) = ranges

113

969

        .iter()

114

1059

        .fold((i32::MAX, i32::MIN), |(min_a, max_b), range| {

115

1059

116

1059

                min_a.min(*range.low().unwrap()),

117

1059

                max_b.max(*range.high().unwrap()),

118

1059

119

1059

});

120

121

969

    let mut symbols = symbols.clone();

122

123

969

    let new_name = &name.name().to_owned();

124

125

969

    let repr_exists = symbols

126

969

        .get_representation(new_name, &["sat_direct_int"])

127

969

        .is_some();

128

129

969

    let representation = symbols

130

969

        .get_or_add_representation(new_name, &["sat_direct_int"])

131

969

        .ok_or(RuleNotApplicable)?;

132

133

969

    let bits: Vec<Expr> = representation[0]

134

969

        .clone()

135

969

        .expression_down(&symbols)?

136

969

        .into_values()

137

969

        .collect();

138

139

969

    let cnf_int = Expr::SATInt(

140

969

        Metadata::new(),

141

969

        SATIntEncoding::Direct,

142

969

        Moo::new(into_matrix_expr!(bits.clone())),

143

969

        (min, max),

144

969

);

145

146

969

    if !repr_exists {

147

        // Domain constraint: the integer must take one of its valid values

148

483

        let constraints = vec![int_domain_to_expr(cnf_int.clone(), ranges)];

149

150

        // At-Most-One constraints: only one bit can be true.

151

483

        let mut clauses = vec![];

152

3708

        for i in 0..bits.len() {

153

37296

            for j in i + 1..bits.len() {

154

37296

                clauses.push(conjure_cp::ast::CnfClause::new(vec![

155

37296

                    Expr::Not(Metadata::new(), Moo::new(bits[i].clone())),

156

37296

                    Expr::Not(Metadata::new(), Moo::new(bits[j].clone())),

157

37296

                ]));

158

37296

159

160

161

483

        let mut reduction = Reduction::cnf(cnf_int, clauses, symbols);

162

483

        reduction.new_top = constraints;

163

483

        Ok(reduction)

164

    } else {

165

486

        Ok(Reduction::pure(cnf_int))

166

167

315645

168

169

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

170

144750

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

171

    // thing we are representing must be a reference

172

71304

    let Expr::Atomic(_, Atom::Reference(name)) = expr else {

173

80316

        return Err(RuleNotApplicable);

174

};

175

176

    // thing we are representing must be an integer

177

64434

    let dom = name.resolved_domain().ok_or(RuleNotApplicable)?;

178

64434

    let GroundDomain::Int(ranges) = dom.as_ref() else {

179

63756

        return Err(RuleNotApplicable);

180

};

181

182

678

    let (min, max) = ranges

183

678

        .iter()

184

678

        .fold((i32::MAX, i32::MIN), |(min_a, max_b), range| {

185

678

186

678

                min_a.min(*range.low().unwrap()),

187

678

                max_b.max(*range.high().unwrap()),

188

678

189

678

});

190

191

678

    let mut symbols = symbols.clone();

192

193

678

    let new_name = &name.name().to_owned();

194

195

678

    let repr_exists = symbols

196

678

        .get_representation(new_name, &["sat_order_int"])

197

678

        .is_some();

198

199

678

    let representation = symbols

200

678

        .get_or_add_representation(new_name, &["sat_order_int"])

201

678

        .ok_or(RuleNotApplicable)?;

202

203

678

    let bits: Vec<Expr> = representation[0]

204

678

        .clone()

205

678

        .expression_down(&symbols)?

206

678

        .into_values()

207

678

        .collect();

208

209

678

    let cnf_int = Expr::SATInt(

210

678

        Metadata::new(),

211

678

        SATIntEncoding::Order,

212

678

        Moo::new(into_matrix_expr!(bits.clone())),

213

678

        (min, max),

214

678

);

215

216

678

    if !repr_exists {

217

        // Domain constraint: the integer must take one of its valid values

218

318

        let constraints = vec![int_domain_to_expr(cnf_int.clone(), ranges)];

219

220

        // Ordering constraints: b_i -> b_{i-1} which is !b_i or b_{i-1}

221

318

        let mut clauses = vec![];

222

1071

        for i in 1..bits.len() {

223

1071

            clauses.push(conjure_cp::ast::CnfClause::new(vec![

224

1071

                Expr::Not(Metadata::new(), Moo::new(bits[i].clone())),

225

1071

                bits[i - 1].clone(),

226

1071

            ]));

227

1071

228

229

318

        if !bits.is_empty() {

230

            // Domain constraint: a >= min, which is b_min.

231

318

            clauses.push(conjure_cp::ast::CnfClause::new(vec![bits[0].clone()]));

232

318

233

234

318

        let mut reduction = Reduction::cnf(cnf_int, clauses, symbols);

235

318

        reduction.new_top = constraints;

236

318

        Ok(reduction)

237

    } else {

238

360

        Ok(Reduction::pure(cnf_int))

239

240

144750

241

242

/// Converts an integer decision variable to SATInt form (Log encoding)

243

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

244

373491

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

245

    // thing we are representing must be a reference

246

198288

    let Expr::Atomic(_, Atom::Reference(name)) = expr else {

247

218421

        return Err(RuleNotApplicable);

248

};

249

250

    // thing we are representing must be a variable

251

    // symbols

252

    //     .lookup(name)

253

    //     .ok_or(RuleNotApplicable)?

254

    //     .as_find()

255

    //     .ok_or(RuleNotApplicable)?;

256

257

    // thing we are representing must be an integer

258

155070

    let dom = name.resolved_domain().ok_or(RuleNotApplicable)?;

259

155070

    let GroundDomain::Int(ranges) = dom.as_ref() else {

260

154332

        return Err(RuleNotApplicable);

261

};

262

263

738

    let (min, max) = ranges

264

738

        .iter()

265

828

        .fold((i32::MAX, i32::MIN), |(min_a, max_b), range| {

266

828

267

828

                min_a.min(*range.low().unwrap()),

268

828

                max_b.max(*range.high().unwrap()),

269

828

270

828

});

271

272

738

    let mut symbols = symbols.clone();

273

274

738

    let new_name = &name.name().to_owned();

275

276

738

    let repr_exists = symbols

277

738

        .get_representation(new_name, &["sat_log_int"])

278

738

        .is_some();

279

280

738

    let representation = symbols

281

738

        .get_or_add_representation(new_name, &["sat_log_int"])

282

738

        .ok_or(RuleNotApplicable)?;

283

284

738

    let bits = representation[0]

285

738

        .clone()

286

738

        .expression_down(&symbols)?

287

738

        .into_values()

288

738

        .collect();

289

290

738

    let cnf_int = Expr::SATInt(

291

738

        Metadata::new(),

292

738

        SATIntEncoding::Log,

293

738

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

294

738

        (min, max),

295

738

);

296

297

738

    if !repr_exists {

298

        // add domain ranges as constraints if this is the first time the representation is added

299

513

        Ok(Reduction::new(

300

513

            cnf_int.clone(),

301

513

            vec![int_domain_to_expr(cnf_int, ranges)], // contains domain rules

302

513

            symbols,

303

513

))

304

    } else {

305

225

        Ok(Reduction::pure(cnf_int))

306

307

373491

308

309

/// Converts an integer literal to SATInt form

310

///

311

/// ```text

312

///  3

313

///  ~~>

314

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

315

///

316

/// ```

317

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

318

373491

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

319

1350

    let value = {

320

43218

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

321

1350

*v

322

        } else {

323

372141

            return Err(RuleNotApplicable);

324

325

};

326

    //TODO: Adding constant optimization to all int operations should hopefully make this rule redundant

327

328

1350

    let mut binary_encoding = vec![];

329

330

1350

    let bit_count = bit_magnitude(value);

331

332

1350

    let mut value_mut = value as u32;

333

334

4977

    for _ in 0..bit_count {

335

4977

        binary_encoding.push(Expr::Atomic(

336

4977

            Metadata::new(),

337

4977

            Atom::Literal(Literal::Bool((value_mut & 1) != 0)),

338

4977

));

339

4977

        value_mut >>= 1;

340

4977

341

342

1350

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

343

1350

        Metadata::new(),

344

1350

        SATIntEncoding::Log,

345

1350

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

346

1350

        (value, value),

347

1350

)))

348

373491

349

350

/// Determine the number of bits required to encode an i32 in 2s complement

351

1458

pub fn bit_magnitude(x: i32) -> usize {

352

1458

    if x >= 0 {

353

        // positive: bits = highest set bit + 1 sign bit

354

1305

        (1 + (32 - x.leading_zeros())).try_into().unwrap()

355

    } else {

356

        // negative: bits = highest set bit in magnitude

357

153

        (33 - (!x).leading_zeros()).try_into().unwrap()

358

359

1458

360

361

/// Given two vectors of expressions, extend the shorter one by repeating its last element until both are the same length

362

9

pub fn match_bits_length(a: Vec<Expr>, b: Vec<Expr>) -> (Vec<Expr>, Vec<Expr>) {

363

9

    let len_a = a.len();

364

9

    let len_b = b.len();

365

366

9

    if len_a < len_b {

367

        let last_a = a.last().cloned().unwrap();

368

        let mut a_extended = a;

369

        a_extended.resize(len_b, last_a);

370

        (a_extended, b)

371

9

    } else if len_b < len_a {

372

        let last_b = b.last().cloned().unwrap();

373

        let mut b_extended = b;

374

        b_extended.resize(len_a, last_b);

375

        (a, b_extended)

376

    } else {

377

9

        (a, b)

378

379

9