| 1 | package felix.optimizer; |
| 2 | |
| 3 | import java.util.ArrayList; |
| 4 | import java.util.HashMap; |
| 5 | import java.util.HashSet; |
| 6 | |
| 7 | import tuffy.mln.Literal; |
| 8 | import tuffy.mln.Predicate; |
| 9 | import tuffy.ra.Expression; |
| 10 | import tuffy.ra.Function; |
| 11 | |
| 12 | import org.apache.commons.math.optimization.GoalType; |
| 13 | import org.apache.commons.math.optimization.RealPointValuePair; |
| 14 | import org.apache.commons.math.optimization.linear.LinearConstraint; |
| 15 | import org.apache.commons.math.optimization.linear.LinearObjectiveFunction; |
| 16 | import org.apache.commons.math.optimization.linear.Relationship; |
| 17 | import org.apache.commons.math.optimization.linear.SimplexSolver; |
| 18 | |
| 19 | import felix.dstruct.FelixClause; |
| 20 | import felix.dstruct.FelixPredicate; |
| 21 | import felix.dstruct.StatOperator; |
| 22 | |
| 23 | //TODO: CURRENTLY SOLVED BY ROUND!!! |
| 24 | //TODO: MAYBE CHANGE TO HASH!!!!!! |
| 25 | |
| 26 | |
| 27 | /** |
| 28 | * An object of DataCracker1991 will try its best to discover opportunities |
| 29 | * of partitioning the data. |
| 30 | */ |
| 31 | public class DataCracker1991 { |
| 32 | |
| 33 | /** |
| 34 | * Map from variable ID to the signature of predicate's field. This ID is used |
| 35 | * in the ILP solver. |
| 36 | */ |
| 37 | public HashMap<Integer, String> varID2predField = new HashMap<Integer, String>(); |
| 38 | |
| 39 | /** |
| 40 | * Map from variable ID to the predicate. This ID is used |
| 41 | * in the ILP solver. |
| 42 | */ |
| 43 | public HashMap<Integer, FelixPredicate> varID2pred = new HashMap<Integer, FelixPredicate>(); |
| 44 | |
| 45 | /** |
| 46 | * Map from variable ID to predicate's field ID. This ID is used |
| 47 | * in the ILP solver. |
| 48 | */ |
| 49 | public HashMap<Integer, Integer> varID2field = new HashMap<Integer, Integer>(); |
| 50 | |
| 51 | /** |
| 52 | * The inverse map of {@link DataCracker1991#varID2predField}. |
| 53 | */ |
| 54 | public HashMap<String, Integer> predField2varID = new HashMap<String, Integer>(); |
| 55 | |
| 56 | /** |
| 57 | * The array that saves the solution of the ILP solver. |
| 58 | */ |
| 59 | double[] ss; |
| 60 | |
| 61 | /** |
| 62 | * Whether the recently processed operator is decomposable. |
| 63 | */ |
| 64 | boolean isDecomposable = false; |
| 65 | |
| 66 | /** |
| 67 | * Generate the signature of predicate's field. |
| 68 | * @param p |
| 69 | * @param fieldNum |
| 70 | * @return |
| 71 | */ |
| 72 | public String toCanonicalFieldName(FelixPredicate p, int fieldNum){ |
| 73 | return p.getName() + ":" + p.getArgs().get(fieldNum); |
| 74 | } |
| 75 | |
| 76 | /** |
| 77 | * Generate the signature of predicate's field. |
| 78 | * @param p |
| 79 | * @param fieldNum |
| 80 | * @return |
| 81 | */ |
| 82 | public String toCanonicalFieldName(Predicate p, int fieldNum){ |
| 83 | return p.getName() + ":" + p.getArgs().get(fieldNum); |
| 84 | } |
| 85 | |
| 86 | /** |
| 87 | * Decompose the data used by the given operator. |
| 88 | * @param op |
| 89 | */ |
| 90 | public void decompose(StatOperator op){ |
| 91 | |
| 92 | try{ |
| 93 | |
| 94 | // get all open predicates can be seperated |
| 95 | HashSet<FelixPredicate> openPredicates = op.outputPredicates; |
| 96 | |
| 97 | int ct = 0; |
| 98 | for(FelixPredicate p : openPredicates){ |
| 99 | for(int i=0;i<p.arity();i++){ |
| 100 | varID2predField.put(ct, toCanonicalFieldName(p, i)); |
| 101 | varID2pred.put(ct, p); |
| 102 | varID2field.put(ct, i); |
| 103 | predField2varID.put(toCanonicalFieldName(p, i), ct); |
| 104 | ct++; |
| 105 | } |
| 106 | } |
| 107 | |
| 108 | |
| 109 | double[] zeros = new double[ct]; |
| 110 | double[] ones = new double[ct]; |
| 111 | for(int i=0;i<ct;i++){ |
| 112 | zeros[i] = 0; |
| 113 | ones[i] = 1; |
| 114 | // System.out.println(i + "\t" + varID2predField.get(i)); |
| 115 | } |
| 116 | |
| 117 | // obj function :- 0x1 + 0x2 + ... + xn = 0 |
| 118 | LinearObjectiveFunction f = |
| 119 | new LinearObjectiveFunction(zeros, 0); |
| 120 | //LinearObjectiveFunction f = |
| 121 | // new LinearObjectiveFunction(ones, 0); |
| 122 | |
| 123 | ArrayList<LinearConstraint> constraints = new ArrayList<LinearConstraint>(); |
| 124 | |
| 125 | // constraint :- pi_1 + pi_2 + ... + pi_n >= 1 |
| 126 | constraints.add(new LinearConstraint(ones, Relationship.GEQ, 1)); |
| 127 | |
| 128 | |
| 129 | //TODO: Assume we know there are partitionings to some fields, |
| 130 | // how can we push them back to other operators? (e.g., date -> d |
| 131 | // throught aligned(.,.) relation). |
| 132 | |
| 133 | for(FelixClause c : op.allRelevantFelixClause){ |
| 134 | |
| 135 | // for each clause, generate constraints for the linear system. |
| 136 | ArrayList<Literal> allLiterals = c.getRegLiterals(); |
| 137 | |
| 138 | for(Literal l1 : allLiterals){ |
| 139 | for(Literal l2 : allLiterals){ |
| 140 | if(l1.equals(l2)){ |
| 141 | continue; |
| 142 | } |
| 143 | |
| 144 | if(op.outputPredicates.contains(l1.getPred()) == false || |
| 145 | op.outputPredicates.contains(l2.getPred()) == false){ |
| 146 | continue; |
| 147 | } |
| 148 | |
| 149 | //System.err.println(l1 + "\t" + l2); |
| 150 | |
| 151 | HashSet<String> allVars = new HashSet<String>(); |
| 152 | allVars.addAll(l1.getVars()); |
| 153 | allVars.addAll(l2.getVars()); |
| 154 | |
| 155 | for(String var : allVars){ |
| 156 | |
| 157 | HashSet<Integer> shouldBeOne = new HashSet<Integer>(); |
| 158 | HashSet<Integer> shouldBeNegOne = new HashSet<Integer>(); |
| 159 | |
| 160 | for(int i=0;i<l1.getVars().size();i++){ |
| 161 | if(var.equals(l1.getTerms().get(i).toString())){ |
| 162 | // System.out.print("+" + toCanonicalFieldName(l1.getPred(), i) + " "); |
| 163 | shouldBeOne.add(predField2varID.get(toCanonicalFieldName(l1.getPred(), i))); |
| 164 | } |
| 165 | } |
| 166 | |
| 167 | for(int i=0;i<l2.getVars().size();i++){ |
| 168 | if(var.equals(l2.getTerms().get(i).toString())){ |
| 169 | // System.out.print("-" + toCanonicalFieldName(l2.getPred(), i) + " "); |
| 170 | shouldBeNegOne.add(predField2varID.get(toCanonicalFieldName(l2.getPred(), i))); |
| 171 | } |
| 172 | } |
| 173 | |
| 174 | //System.out.println(); |
| 175 | |
| 176 | if(shouldBeOne.contains(null) || shouldBeNegOne.contains(null)){ |
| 177 | continue; |
| 178 | } |
| 179 | |
| 180 | double[] cons = new double[ct]; |
| 181 | int nOfPos = 0; |
| 182 | int nOfNeg = 0; |
| 183 | for(int i=0;i<ct;i++){ |
| 184 | cons[i] = 0; |
| 185 | if(shouldBeOne.contains(i)){ |
| 186 | cons[i] += 1; |
| 187 | nOfPos ++; |
| 188 | } |
| 189 | if(shouldBeNegOne.contains(i)){ |
| 190 | cons[i] += -1; |
| 191 | nOfNeg ++; |
| 192 | } |
| 193 | } |
| 194 | |
| 195 | // [# appearance] x_i_in_left * pi = x_i_in_right * pi |
| 196 | constraints.add(new LinearConstraint(cons, Relationship.EQ, 0)); |
| 197 | } |
| 198 | |
| 199 | |
| 200 | } |
| 201 | } |
| 202 | //System.out.println(c); |
| 203 | } |
| 204 | |
| 205 | RealPointValuePair solution = new |
| 206 | //SimplexSolver().optimize(f, constraints, |
| 207 | // GoalType.MAXIMIZE, false); |
| 208 | SimplexSolver().optimize(f, constraints, |
| 209 | GoalType.MAXIMIZE, false); |
| 210 | |
| 211 | // get the solution and translated them into |
| 212 | // integer form |
| 213 | double[] tmpss = solution.getPoint(); |
| 214 | ss = new double[tmpss.length]; |
| 215 | |
| 216 | double largest = Double.MIN_VALUE; |
| 217 | for(int i=0;i<tmpss.length;i++){ |
| 218 | if(tmpss[i] >= largest){ |
| 219 | largest = tmpss[i]; |
| 220 | } |
| 221 | } |
| 222 | |
| 223 | for(int i=0;i<ss.length;i++){ |
| 224 | ss[i] = tmpss[i]/largest; |
| 225 | } |
| 226 | |
| 227 | isDecomposable = true; |
| 228 | |
| 229 | }catch(Exception e){ |
| 230 | // e.printStackTrace(); |
| 231 | isDecomposable = false; |
| 232 | } |
| 233 | } |
| 234 | |
| 235 | /** |
| 236 | * Return the GCD of the given two numbers. |
| 237 | * @param a |
| 238 | * @param b |
| 239 | * @return |
| 240 | */ |
| 241 | int gcd2(int a, int b){ |
| 242 | if (b==0) return a; |
| 243 | return gcd2(b,a%b); |
| 244 | } |
| 245 | |
| 246 | /** |
| 247 | * Return the GCD of the given multiple numbers. |
| 248 | * @param numbers |
| 249 | * @return |
| 250 | */ |
| 251 | int gcd(int... numbers){ |
| 252 | if(numbers.length == 1){ |
| 253 | return numbers[0]; |
| 254 | } |
| 255 | int firstTwoGCD = gcd2(numbers[0], numbers[1]); |
| 256 | int[] newNumbers = new int[numbers.length - 1]; |
| 257 | for(int i = 2; i<numbers.length; i++){ |
| 258 | newNumbers[i-2] = numbers[i]; |
| 259 | } |
| 260 | newNumbers[newNumbers.length - 1] = firstTwoGCD; |
| 261 | return gcd(newNumbers); |
| 262 | } |
| 263 | |
| 264 | /** |
| 265 | * Given a clause appearing in the statOperator, return the appended expression |
| 266 | * to this clause to partition the data. |
| 267 | * @param fc |
| 268 | * @param _p if this value is not NULL and fc is NULL, generate a human-readable version for predicate _p |
| 269 | * @param base Number of partitions. |
| 270 | * @param nThread ID of the current partition. |
| 271 | * @param isSignature if this parameter is false, then it can be used as clause's constraints. |
| 272 | * @return |
| 273 | */ |
| 274 | public HashSet<Expression> getExpressions(FelixClause fc, Predicate _p, int base, int nThread, boolean isSignature){ |
| 275 | |
| 276 | HashSet<String> processedExpSignature = new HashSet<String>(); |
| 277 | HashSet<Expression> ret = new HashSet<Expression>(); |
| 278 | |
| 279 | if(fc != null){ |
| 280 | for(Literal l : fc.getRegLiterals()){ |
| 281 | |
| 282 | Predicate p = l.getPred(); |
| 283 | |
| 284 | Expression e = new Expression(Function.Eq); |
| 285 | |
| 286 | Expression emod = new Expression(Function.Modulo); |
| 287 | |
| 288 | Expression currentSumRoot = null; |
| 289 | |
| 290 | for(Integer fieldID : varID2pred.keySet()){ |
| 291 | |
| 292 | if(ss[fieldID] == 0){ |
| 293 | continue; |
| 294 | } |
| 295 | |
| 296 | if(!varID2pred.get(fieldID).equals(p)){ |
| 297 | continue; |
| 298 | } |
| 299 | |
| 300 | if(currentSumRoot == null){ |
| 301 | Expression etmp = new Expression(Function.Multiply); |
| 302 | if(isSignature == false){ |
| 303 | etmp.addArgument(l.getTerms().get(varID2field.get(fieldID)).isVariable() ? |
| 304 | Expression.exprVariableBinding(l.getTerms().get(varID2field.get(fieldID)).toString()) : |
| 305 | Expression.exprConstNum(l.getTerms().get(varID2field.get(fieldID)).constant() )); |
| 306 | }else{ |
| 307 | etmp.addArgument(Expression.exprVariableBinding(l.getPred().getArgs().get(varID2field.get(fieldID)).toString())); |
| 308 | } |
| 309 | etmp.addArgument(Expression.exprConstNum(ss[fieldID])); |
| 310 | |
| 311 | currentSumRoot = etmp; |
| 312 | }else{ |
| 313 | Expression etmp = new Expression(Function.Add); |
| 314 | etmp.addArgument(currentSumRoot); |
| 315 | |
| 316 | Expression etoadd = new Expression(Function.Multiply); |
| 317 | if(isSignature == false){ |
| 318 | etoadd.addArgument(l.getTerms().get(varID2field.get(fieldID)).isVariable() ? |
| 319 | Expression.exprVariableBinding(l.getTerms().get(varID2field.get(fieldID)).toString()) : |
| 320 | Expression.exprConstNum(l.getTerms().get(varID2field.get(fieldID)).constant() )); |
| 321 | }else{ |
| 322 | etoadd.addArgument(Expression.exprVariableBinding(l.getPred().getArgs().get(varID2field.get(fieldID)).toString())); |
| 323 | } |
| 324 | |
| 325 | etoadd.addArgument(Expression.exprConstNum(ss[fieldID])); |
| 326 | |
| 327 | etmp.addArgument(etoadd); |
| 328 | |
| 329 | currentSumRoot = etmp; |
| 330 | |
| 331 | } |
| 332 | } |
| 333 | |
| 334 | if(currentSumRoot != null){ |
| 335 | |
| 336 | Expression eround = new Expression(Function.Round); |
| 337 | eround.addArgument(currentSumRoot); |
| 338 | emod.addArgument(eround); |
| 339 | emod.addArgument(Expression.exprConstInteger(base)); |
| 340 | e.addArgument(emod); |
| 341 | e.addArgument(Expression.exprConstInteger(nThread)); |
| 342 | e.changeName = false; |
| 343 | |
| 344 | if(processedExpSignature.contains(e.toString())){ |
| 345 | continue; |
| 346 | } |
| 347 | |
| 348 | processedExpSignature.add(e.toString()); |
| 349 | ret.add(e); |
| 350 | |
| 351 | } |
| 352 | } |
| 353 | }else if(_p != null){ |
| 354 | |
| 355 | Expression e = new Expression(Function.Eq); |
| 356 | |
| 357 | Expression emod = new Expression(Function.Modulo); |
| 358 | |
| 359 | Expression currentSumRoot = null; |
| 360 | |
| 361 | for(Integer fieldID : varID2pred.keySet()){ |
| 362 | |
| 363 | if(ss[fieldID] == 0){ |
| 364 | continue; |
| 365 | } |
| 366 | |
| 367 | if(!varID2pred.get(fieldID).equals(_p)){ |
| 368 | continue; |
| 369 | } |
| 370 | |
| 371 | if(currentSumRoot == null){ |
| 372 | Expression etmp = new Expression(Function.Multiply); |
| 373 | if(isSignature == false){ |
| 374 | |
| 375 | }else{ |
| 376 | etmp.addArgument(Expression.exprVariableBinding(_p.getArgs().get(varID2field.get(fieldID)).toString())); |
| 377 | } |
| 378 | etmp.addArgument(Expression.exprConstNum(ss[fieldID])); |
| 379 | |
| 380 | currentSumRoot = etmp; |
| 381 | }else{ |
| 382 | Expression etmp = new Expression(Function.Add); |
| 383 | etmp.addArgument(currentSumRoot); |
| 384 | |
| 385 | Expression etoadd = new Expression(Function.Multiply); |
| 386 | if(isSignature == false){ |
| 387 | |
| 388 | }else{ |
| 389 | etoadd.addArgument(Expression.exprVariableBinding(_p.getArgs().get(varID2field.get(fieldID)).toString())); |
| 390 | } |
| 391 | |
| 392 | etoadd.addArgument(Expression.exprConstNum(ss[fieldID])); |
| 393 | |
| 394 | etmp.addArgument(etoadd); |
| 395 | |
| 396 | currentSumRoot = etmp; |
| 397 | |
| 398 | } |
| 399 | } |
| 400 | |
| 401 | if(currentSumRoot != null){ |
| 402 | |
| 403 | Expression eround = new Expression(Function.Round); |
| 404 | eround.addArgument(currentSumRoot); |
| 405 | emod.addArgument(eround); |
| 406 | emod.addArgument(Expression.exprConstInteger(base)); |
| 407 | e.addArgument(emod); |
| 408 | e.addArgument(Expression.exprConstInteger(nThread)); |
| 409 | e.changeName = false; |
| 410 | |
| 411 | processedExpSignature.add(e.toString()); |
| 412 | ret.add(e); |
| 413 | |
| 414 | } |
| 415 | } |
| 416 | return ret; |
| 417 | } |
| 418 | |
| 419 | } |
| 420 | |
| 421 | |
| 422 | |
| 423 | |
| 424 | |
| 425 | |