pypol/domains.py

   1 import ast
   2 import functools
   3 import re
   4
   5 from . import islhelper
   6
   7 from .islhelper import mainctx, libisl, isl_set_basic_sets
   8 from .linexprs import Expression, Symbol
   9
  10
  11 __all__ = [
  12     'Domain',
  13     'And', 'Or', 'Not',
  14 ]
  15
  16
  17 @functools.total_ordering
  18 class Domain:
  19
  20     __slots__ = (
  21         '_polyhedra',
  22         '_symbols',
  23         '_dimension',
  24     )
  25
  26     def __new__(cls, *polyhedra):
  27         from .polyhedra import Polyhedron
  28         if len(polyhedra) == 1:
  29             polyhedron = polyhedra[0]
  30             if isinstance(polyhedron, str):
  31                 return cls.fromstring(polyhedron)
  32             elif isinstance(polyhedron, Polyhedron):
  33                 return polyhedron
  34             else:
  35                 raise TypeError('argument must be a string '
  36                     'or a Polyhedron instance')
  37         else:
  38             for polyhedron in polyhedra:
  39                 if not isinstance(polyhedron, Polyhedron):
  40                     raise TypeError('arguments must be Polyhedron instances')
  41             symbols = cls._xsymbols(polyhedra)
  42             islset = cls._toislset(polyhedra, symbols)
  43             return cls._fromislset(islset, symbols)
  44
  45     @classmethod
  46     def _xsymbols(cls, iterator):
  47         """
  48         Return the ordered tuple of symbols present in iterator.
  49         """
  50         symbols = set()
  51         for item in iterator:
  52             symbols.update(item.symbols)
  53         return tuple(sorted(symbols))
  54
  55     @property
  56     def polyhedra(self):
  57         return self._polyhedra
  58
  59     @property
  60     def symbols(self):
  61         return self._symbols
  62
  63     @property
  64     def dimension(self):
  65         return self._dimension
  66
  67     def disjoint(self):
  68         islset = self._toislset(self.polyhedra, self.symbols)
  69         islset = libisl.isl_set_make_disjoint(mainctx, islset)
  70         return self._fromislset(islset, self.symbols)
  71
  72     def isempty(self):
  73         islset = self._toislset(self.polyhedra, self.symbols)
  74         empty = bool(libisl.isl_set_is_empty(islset))
  75         libisl.isl_set_free(islset)
  76         return empty
  77
  78     def __bool__(self):
  79         return not self.isempty()
  80
  81     def isuniverse(self):
  82         islset = self._toislset(self.polyhedra, self.symbols)
  83         universe = bool(libisl.isl_set_plain_is_universe(islset))
  84         libisl.isl_set_free(islset)
  85         return universe
  86
  87     def isbounded(self):
  88         islset = self._toislset(self.polyhedra, self.symbols)
  89         bounded = bool(libisl.isl_set_is_bounded(islset))
  90         libisl.isl_set_free(islset)
  91         return bounded
  92
  93     def __eq__(self, other):
  94         symbols = self._xsymbols([self, other])
  95         islset1 = self._toislset(self.polyhedra, symbols)
  96         islset2 = other._toislset(other.polyhedra, symbols)
  97         equal = bool(libisl.isl_set_is_equal(islset1, islset2))
  98         libisl.isl_set_free(islset1)
  99         libisl.isl_set_free(islset2)
 100         return equal
 101
 102     def isdisjoint(self, other):
 103         symbols = self._xsymbols([self, other])
 104         islset1 = self._toislset(self.polyhedra, symbols)
 105         islset2 = self._toislset(other.polyhedra, symbols)
 106         equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
 107         libisl.isl_set_free(islset1)
 108         libisl.isl_set_free(islset2)
 109         return equal
 110
 111     def issubset(self, other):
 112         symbols = self._xsymbols([self, other])
 113         islset1 = self._toislset(self.polyhedra, symbols)
 114         islset2 = self._toislset(other.polyhedra, symbols)
 115         equal = bool(libisl.isl_set_is_subset(islset1, islset2))
 116         libisl.isl_set_free(islset1)
 117         libisl.isl_set_free(islset2)
 118         return equal
 119
 120     def __le__(self, other):
 121         return self.issubset(other)
 122
 123     def __lt__(self, other):
 124         symbols = self._xsymbols([self, other])
 125         islset1 = self._toislset(self.polyhedra, symbols)
 126         islset2 = self._toislset(other.polyhedra, symbols)
 127         equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
 128         libisl.isl_set_free(islset1)
 129         libisl.isl_set_free(islset2)
 130         return equal
 131
 132     def complement(self):
 133         islset = self._toislset(self.polyhedra, self.symbols)
 134         islset = libisl.isl_set_complement(islset)
 135         return self._fromislset(islset, self.symbols)
 136
 137     def __invert__(self):
 138         return self.complement()
 139
 140     def simplify(self):
 141         #does not change anything in any of the examples
 142         #isl seems to do this naturally
 143         islset = self._toislset(self.polyhedra, self.symbols)
 144         islset = libisl.isl_set_remove_redundancies(islset)
 145         return self._fromislset(islset, self.symbols)
 146
 147     def polyhedral_hull(self):
 148         # several types of hull are available
 149         # polyhedral seems to be the more appropriate, to be checked
 150         from .polyhedra import Polyhedron
 151         islset = self._toislset(self.polyhedra, self.symbols)
 152         islbset = libisl.isl_set_polyhedral_hull(islset)
 153         return Polyhedron._fromislbasicset(islbset, self.symbols)
 154
 155     def project_out(self, symbols):
 156         # use to remove certain variables
 157         if isinstance(symbols, str):
 158             symbols = symbols.replace(',', ' ').split()
 159         else:
 160             symbols = list(symbols)
 161             for i, symbol in enumerate(symbols):
 162                 if isinstance(symbol, Symbol):
 163                     symbols[i] = symbol.name
 164                 elif not isinstance(symbol, str):
 165                     raise TypeError('symbols must be strings or Symbol instances')
 166         islset = self._toislset(self.polyhedra, self.symbols)
 167         # the trick is to walk symbols in reverse order, to avoid index updates
 168         for index, symbol in reversed(list(enumerate(self.symbols))):
 169             if symbol in symbols:
 170                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index, 1)
 171         # remaining symbols
 172         symbols = [symbol for symbol in self.symbols if symbol not in symbols]
 173         return Domain._fromislset(islset, symbols)
 174
 175     def sample(self):
 176         from .polyhedra import Polyhedron
 177         islset = self._toislset(self.polyhedra, self.symbols)
 178         islbset = libisl.isl_set_sample(islset)
 179         return Polyhedron._fromislbasicset(islbset, self.symbols)
 180
 181     def intersection(self, *others):
 182         if len(others) == 0:
 183             return self
 184         symbols = self._xsymbols((self,) + others)
 185         islset1 = self._toislset(self.polyhedra, symbols)
 186         for other in others:
 187             islset2 = other._toislset(other.polyhedra, symbols)
 188             islset1 = libisl.isl_set_intersect(islset1, islset2)
 189         return self._fromislset(islset1, symbols)
 190
 191     def __and__(self, other):
 192         return self.intersection(other)
 193
 194     def union(self, *others):
 195         if len(others) == 0:
 196             return self
 197         symbols = self._xsymbols((self,) + others)
 198         islset1 = self._toislset(self.polyhedra, symbols)
 199         for other in others:
 200             islset2 = other._toislset(other.polyhedra, symbols)
 201             islset1 = libisl.isl_set_union(islset1, islset2)
 202         return self._fromislset(islset1, symbols)
 203
 204     def __or__(self, other):
 205         return self.union(other)
 206
 207     def __add__(self, other):
 208         return self.union(other)
 209
 210     def difference(self, other):
 211         symbols = self._xsymbols([self, other])
 212         islset1 = self._toislset(self.polyhedra, symbols)
 213         islset2 = other._toislset(other.polyhedra, symbols)
 214         islset = libisl.isl_set_subtract(islset1, islset2)
 215         return self._fromislset(islset, symbols)
 216
 217     def __sub__(self, other):
 218         return self.difference(other)
 219
 220     def lexmin(self):
 221         islset = self._toislset(self.polyhedra, self.symbols)
 222         islset = libisl.isl_set_lexmin(islset)
 223         return self._fromislset(islset, self.symbols)
 224
 225     def lexmax(self):
 226         islset = self._toislset(self.polyhedra, self.symbols)
 227         islset = libisl.isl_set_lexmax(islset)
 228         return self._fromislset(islset, self.symbols)
 229
 230     @classmethod
 231     def _fromislset(cls, islset, symbols):
 232         from .polyhedra import Polyhedron
 233         islset = libisl.isl_set_remove_divs(islset)
 234         islbsets = isl_set_basic_sets(islset)
 235         libisl.isl_set_free(islset)
 236         polyhedra = []
 237         for islbset in islbsets:
 238             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 239             polyhedra.append(polyhedron)
 240         if len(polyhedra) == 0:
 241             from .polyhedra import Empty
 242             return Empty
 243         elif len(polyhedra) == 1:
 244             return polyhedra[0]
 245         else:
 246             self = object().__new__(Domain)
 247             self._polyhedra = tuple(polyhedra)
 248             self._symbols = cls._xsymbols(polyhedra)
 249             self._dimension = len(self._symbols)
 250             return self
 251
 252     def _toislset(cls, polyhedra, symbols):
 253         polyhedron = polyhedra[0]
 254         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 255             polyhedron.inequalities, symbols)
 256         islset1 = libisl.isl_set_from_basic_set(islbset)
 257         for polyhedron in polyhedra[1:]:
 258             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 259                 polyhedron.inequalities, symbols)
 260             islset2 = libisl.isl_set_from_basic_set(islbset)
 261             islset1 = libisl.isl_set_union(islset1, islset2)
 262         return islset1
 263
 264     @classmethod
 265     def _fromast(cls, node):
 266         from .polyhedra import Polyhedron
 267         if isinstance(node, ast.Module) and len(node.body) == 1:
 268             return cls._fromast(node.body[0])
 269         elif isinstance(node, ast.Expr):
 270             return cls._fromast(node.value)
 271         elif isinstance(node, ast.UnaryOp):
 272             domain = cls._fromast(node.operand)
 273             if isinstance(node.operand, ast.invert):
 274                 return Not(domain)
 275         elif isinstance(node, ast.BinOp):
 276             domain1 = cls._fromast(node.left)
 277             domain2 = cls._fromast(node.right)
 278             if isinstance(node.op, ast.BitAnd):
 279                 return And(domain1, domain2)
 280             elif isinstance(node.op, ast.BitOr):
 281                 return Or(domain1, domain2)
 282         elif isinstance(node, ast.Compare):
 283             equalities = []
 284             inequalities = []
 285             left = Expression._fromast(node.left)
 286             for i in range(len(node.ops)):
 287                 op = node.ops[i]
 288                 right = Expression._fromast(node.comparators[i])
 289                 if isinstance(op, ast.Lt):
 290                     inequalities.append(right - left - 1)
 291                 elif isinstance(op, ast.LtE):
 292                     inequalities.append(right - left)
 293                 elif isinstance(op, ast.Eq):
 294                     equalities.append(left - right)
 295                 elif isinstance(op, ast.GtE):
 296                     inequalities.append(left - right)
 297                 elif isinstance(op, ast.Gt):
 298                     inequalities.append(left - right - 1)
 299                 else:
 300                     break
 301                 left = right
 302             else:
 303                 return Polyhedron(equalities, inequalities)
 304         raise SyntaxError('invalid syntax')
 305
 306     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 307     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 308     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 309     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 310     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 311     _RE_NUM_VAR = Expression._RE_NUM_VAR
 312     _RE_OPERATORS = re.compile(r'(&|\||~)')
 313
 314     @classmethod
 315     def fromstring(cls, string):
 316         # remove curly brackets
 317         string = cls._RE_BRACES.sub(r'', string)
 318         # replace '=' by '=='
 319         string = cls._RE_EQ.sub(r'\1==\2', string)
 320         # replace 'and', 'or', 'not'
 321         string = cls._RE_AND.sub(r' & ', string)
 322         string = cls._RE_OR.sub(r' | ', string)
 323         string = cls._RE_NOT.sub(r' ~', string)
 324         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 325         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 326         # add parentheses to force precedence
 327         tokens = cls._RE_OPERATORS.split(string)
 328         for i, token in enumerate(tokens):
 329             if i % 2 == 0:
 330                 token = '({})'.format(token)
 331                 tokens[i] = token
 332         string = ''.join(tokens)
 333         tree = ast.parse(string, 'eval')
 334         return cls._fromast(tree)
 335
 336     def __repr__(self):
 337         assert len(self.polyhedra) >= 2
 338         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 339         return 'Or({})'.format(', '.join(strings))
 340
 341     @classmethod
 342     def fromsympy(cls, expr):
 343         raise NotImplementedError
 344
 345     def tosympy(self):
 346         raise NotImplementedError
 347
 348 def And(*domains):
 349     if len(domains) == 0:
 350         from .polyhedra import Universe
 351         return Universe
 352     else:
 353         return domains[0].intersection(*domains[1:])
 354
 355 def Or(*domains):
 356     if len(domains) == 0:
 357         from .polyhedra import Empty
 358         return Empty
 359     else:
 360         return domains[0].union(*domains[1:])
 361
 362 def Not(domain):
 363     return ~domain