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
   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         # see isl_set_coalesce, isl_set_detect_equalities,
 142         # isl_set_remove_redundancies
 143         # which ones? in which order?
 144         raise NotImplementedError
 145
 146     def polyhedral_hull(self):
 147         # several types of hull are available
 148         # polyhedral seems to be the more appropriate, to be checked
 149         from .polyhedra import Polyhedron
 150         islset = self._toislset(self.polyhedra, self.symbols)
 151         islbset = libisl.isl_set_polyhedral_hull(islset)
 152         return Polyhedron._fromislbasicset(islbset, self.symbols)
 153
 154     def project(self, symbols):
 155         # not sure what isl_set_project_out actually does…
 156         # use isl_set_drop_constraints_involving_dims instead?
 157         raise NotImplementedError
 158
 159     def sample(self):
 160         from .polyhedra import Polyhedron
 161         islset = self._toislset(self.polyhedra, self.symbols)
 162         islbset = libisl.isl_set_sample(islset)
 163         return Polyhedron._fromislbasicset(islbset, self.symbols)
 164
 165     def intersection(self, *others):
 166         if len(others) == 0:
 167             return self
 168         symbols = self._xsymbols((self,) + others)
 169         islset1 = self._toislset(self.polyhedra, symbols)
 170         for other in others:
 171             islset2 = other._toislset(other.polyhedra, symbols)
 172             islset1 = libisl.isl_set_intersect(islset1, islset2)
 173         return self._fromislset(islset1, symbols)
 174
 175     def __and__(self, other):
 176         return self.intersection(other)
 177
 178     def union(self, *others):
 179         if len(others) == 0:
 180             return self
 181         symbols = self._xsymbols((self,) + others)
 182         islset1 = self._toislset(self.polyhedra, symbols)
 183         for other in others:
 184             islset2 = other._toislset(other.polyhedra, symbols)
 185             islset1 = libisl.isl_set_union(islset1, islset2)
 186         return self._fromislset(islset1, symbols)
 187
 188     def __or__(self, other):
 189         return self.union(other)
 190
 191     def __add__(self, other):
 192         return self.union(other)
 193
 194     def difference(self, other):
 195         symbols = self._xsymbols([self, other])
 196         islset1 = self._toislset(self.polyhedra, symbols)
 197         islset2 = other._toislset(other.polyhedra, symbols)
 198         islset = libisl.isl_set_subtract(islset1, islset2)
 199         return self._fromislset(islset, symbols)
 200
 201     def __sub__(self, other):
 202         return self.difference(other)
 203
 204     def lexmin(self):
 205         islset = self._toislset(self.polyhedra, self.symbols)
 206         islset = libisl.isl_set_lexmin(islset)
 207         return self._fromislset(islset, self.symbols)
 208
 209     def lexmax(self):
 210         islset = self._toislset(self.polyhedra, self.symbols)
 211         islset = libisl.isl_set_lexmax(islset)
 212         return self._fromislset(islset, self.symbols)
 213
 214     @classmethod
 215     def _fromislset(cls, islset, symbols):
 216         from .polyhedra import Polyhedron
 217         islset = libisl.isl_set_remove_divs(islset)
 218         islbsets = isl_set_basic_sets(islset)
 219         libisl.isl_set_free(islset)
 220         polyhedra = []
 221         for islbset in islbsets:
 222             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 223             polyhedra.append(polyhedron)
 224         if len(polyhedra) == 0:
 225             from .polyhedra import Empty
 226             return Empty
 227         elif len(polyhedra) == 1:
 228             return polyhedra[0]
 229         else:
 230             self = object().__new__(Domain)
 231             self._polyhedra = tuple(polyhedra)
 232             self._symbols = cls._xsymbols(polyhedra)
 233             self._dimension = len(self._symbols)
 234             return self
 235
 236     def _toislset(cls, polyhedra, symbols):
 237         polyhedron = polyhedra[0]
 238         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 239             polyhedron.inequalities, symbols)
 240         islset1 = libisl.isl_set_from_basic_set(islbset)
 241         for polyhedron in polyhedra[1:]:
 242             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 243                 polyhedron.inequalities, symbols)
 244             islset2 = libisl.isl_set_from_basic_set(islbset)
 245             islset1 = libisl.isl_set_union(islset1, islset2)
 246         return islset1
 247
 248     @classmethod
 249     def _fromast(cls, node):
 250         from .polyhedra import Polyhedron
 251         if isinstance(node, ast.Module) and len(node.body) == 1:
 252             return cls._fromast(node.body[0])
 253         elif isinstance(node, ast.Expr):
 254             return cls._fromast(node.value)
 255         elif isinstance(node, ast.UnaryOp):
 256             domain = cls._fromast(node.operand)
 257             if isinstance(node.operand, ast.invert):
 258                 return Not(domain)
 259         elif isinstance(node, ast.BinOp):
 260             domain1 = cls._fromast(node.left)
 261             domain2 = cls._fromast(node.right)
 262             if isinstance(node.op, ast.BitAnd):
 263                 return And(domain1, domain2)
 264             elif isinstance(node.op, ast.BitOr):
 265                 return Or(domain1, domain2)
 266         elif isinstance(node, ast.Compare):
 267             equalities = []
 268             inequalities = []
 269             left = Expression._fromast(node.left)
 270             for i in range(len(node.ops)):
 271                 op = node.ops[i]
 272                 right = Expression._fromast(node.comparators[i])
 273                 if isinstance(op, ast.Lt):
 274                     inequalities.append(right - left - 1)
 275                 elif isinstance(op, ast.LtE):
 276                     inequalities.append(right - left)
 277                 elif isinstance(op, ast.Eq):
 278                     equalities.append(left - right)
 279                 elif isinstance(op, ast.GtE):
 280                     inequalities.append(left - right)
 281                 elif isinstance(op, ast.Gt):
 282                     inequalities.append(left - right - 1)
 283                 else:
 284                     break
 285                 left = right
 286             else:
 287                 return Polyhedron(equalities, inequalities)
 288         raise SyntaxError('invalid syntax')
 289
 290     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 291     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 292     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 293     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 294     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 295     _RE_NUM_VAR = Expression._RE_NUM_VAR
 296     _RE_OPERATORS = re.compile(r'(&|\||~)')
 297
 298     @classmethod
 299     def fromstring(cls, string):
 300         # remove curly brackets
 301         string = cls._RE_BRACES.sub(r'', string)
 302         # replace '=' by '=='
 303         string = cls._RE_EQ.sub(r'\1==\2', string)
 304         # replace 'and', 'or', 'not'
 305         string = cls._RE_AND.sub(r' & ', string)
 306         string = cls._RE_OR.sub(r' | ', string)
 307         string = cls._RE_NOT.sub(r' ~', string)
 308         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 309         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 310         # add parentheses to force precedence
 311         tokens = cls._RE_OPERATORS.split(string)
 312         for i, token in enumerate(tokens):
 313             if i % 2 == 0:
 314                 token = '({})'.format(token)
 315                 tokens[i] = token
 316         string = ''.join(tokens)
 317         tree = ast.parse(string, 'eval')
 318         return cls._fromast(tree)
 319
 320     def __repr__(self):
 321         assert len(self.polyhedra) >= 2
 322         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 323         return 'Or({})'.format(', '.join(strings))
 324
 325     @classmethod
 326     def fromsympy(cls, expr):
 327         raise NotImplementedError
 328
 329     def tosympy(self):
 330         raise NotImplementedError
 331
 332
 333 def And(*domains):
 334     if len(domains) == 0:
 335         from .polyhedra import Universe
 336         return Universe
 337     else:
 338         return domains[0].intersection(*domains[1:])
 339
 340 def Or(*domains):
 341     if len(domains) == 0:
 342         from .polyhedra import Empty
 343         return Empty
 344     else:
 345         return domains[0].union(*domains[1:])
 346
 347 def Not(domain):
 348     return ~domain