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         #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         islset = self._toislset(self.polyhedra, self.symbols)
 158         # the trick is to walk symbols in reverse order, to avoid index updates
 159         for index, symbol in reversed(list(enumerate(self.symbols))):
 160             if symbol in symbols:
 161                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index, 1)
 162         # remaining symbols
 163         symbols = [symbol for symbol in self.symbols if symbol not in symbols]
 164         return Domain._fromislset(islset, symbols)
 165
 166     def sample(self):
 167         from .polyhedra import Polyhedron
 168         islset = self._toislset(self.polyhedra, self.symbols)
 169         islbset = libisl.isl_set_sample(islset)
 170         return Polyhedron._fromislbasicset(islbset, self.symbols)
 171
 172     def intersection(self, *others):
 173         if len(others) == 0:
 174             return self
 175         symbols = self._xsymbols((self,) + others)
 176         islset1 = self._toislset(self.polyhedra, symbols)
 177         for other in others:
 178             islset2 = other._toislset(other.polyhedra, symbols)
 179             islset1 = libisl.isl_set_intersect(islset1, islset2)
 180         return self._fromislset(islset1, symbols)
 181
 182     def __and__(self, other):
 183         return self.intersection(other)
 184
 185     def union(self, *others):
 186         if len(others) == 0:
 187             return self
 188         symbols = self._xsymbols((self,) + others)
 189         islset1 = self._toislset(self.polyhedra, symbols)
 190         for other in others:
 191             islset2 = other._toislset(other.polyhedra, symbols)
 192             islset1 = libisl.isl_set_union(islset1, islset2)
 193         return self._fromislset(islset1, symbols)
 194
 195     def __or__(self, other):
 196         return self.union(other)
 197
 198     def __add__(self, other):
 199         return self.union(other)
 200
 201     def difference(self, other):
 202         symbols = self._xsymbols([self, other])
 203         islset1 = self._toislset(self.polyhedra, symbols)
 204         islset2 = other._toislset(other.polyhedra, symbols)
 205         islset = libisl.isl_set_subtract(islset1, islset2)
 206         return self._fromislset(islset, symbols)
 207
 208     def __sub__(self, other):
 209         return self.difference(other)
 210
 211     def lexmin(self):
 212         islset = self._toislset(self.polyhedra, self.symbols)
 213         islset = libisl.isl_set_lexmin(islset)
 214         return self._fromislset(islset, self.symbols)
 215
 216     def lexmax(self):
 217         islset = self._toislset(self.polyhedra, self.symbols)
 218         islset = libisl.isl_set_lexmax(islset)
 219         return self._fromislset(islset, self.symbols)
 220
 221     @classmethod
 222     def _fromislset(cls, islset, symbols):
 223         from .polyhedra import Polyhedron
 224         islset = libisl.isl_set_remove_divs(islset)
 225         islbsets = isl_set_basic_sets(islset)
 226         libisl.isl_set_free(islset)
 227         polyhedra = []
 228         for islbset in islbsets:
 229             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 230             polyhedra.append(polyhedron)
 231         if len(polyhedra) == 0:
 232             from .polyhedra import Empty
 233             return Empty
 234         elif len(polyhedra) == 1:
 235             return polyhedra[0]
 236         else:
 237             self = object().__new__(Domain)
 238             self._polyhedra = tuple(polyhedra)
 239             self._symbols = cls._xsymbols(polyhedra)
 240             self._dimension = len(self._symbols)
 241             return self
 242
 243     def _toislset(cls, polyhedra, symbols):
 244         polyhedron = polyhedra[0]
 245         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 246             polyhedron.inequalities, symbols)
 247         islset1 = libisl.isl_set_from_basic_set(islbset)
 248         for polyhedron in polyhedra[1:]:
 249             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 250                 polyhedron.inequalities, symbols)
 251             islset2 = libisl.isl_set_from_basic_set(islbset)
 252             islset1 = libisl.isl_set_union(islset1, islset2)
 253         return islset1
 254
 255     @classmethod
 256     def _fromast(cls, node):
 257         from .polyhedra import Polyhedron
 258         if isinstance(node, ast.Module) and len(node.body) == 1:
 259             return cls._fromast(node.body[0])
 260         elif isinstance(node, ast.Expr):
 261             return cls._fromast(node.value)
 262         elif isinstance(node, ast.UnaryOp):
 263             domain = cls._fromast(node.operand)
 264             if isinstance(node.operand, ast.invert):
 265                 return Not(domain)
 266         elif isinstance(node, ast.BinOp):
 267             domain1 = cls._fromast(node.left)
 268             domain2 = cls._fromast(node.right)
 269             if isinstance(node.op, ast.BitAnd):
 270                 return And(domain1, domain2)
 271             elif isinstance(node.op, ast.BitOr):
 272                 return Or(domain1, domain2)
 273         elif isinstance(node, ast.Compare):
 274             equalities = []
 275             inequalities = []
 276             left = Expression._fromast(node.left)
 277             for i in range(len(node.ops)):
 278                 op = node.ops[i]
 279                 right = Expression._fromast(node.comparators[i])
 280                 if isinstance(op, ast.Lt):
 281                     inequalities.append(right - left - 1)
 282                 elif isinstance(op, ast.LtE):
 283                     inequalities.append(right - left)
 284                 elif isinstance(op, ast.Eq):
 285                     equalities.append(left - right)
 286                 elif isinstance(op, ast.GtE):
 287                     inequalities.append(left - right)
 288                 elif isinstance(op, ast.Gt):
 289                     inequalities.append(left - right - 1)
 290                 else:
 291                     break
 292                 left = right
 293             else:
 294                 return Polyhedron(equalities, inequalities)
 295         raise SyntaxError('invalid syntax')
 296
 297     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 298     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 299     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 300     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 301     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 302     _RE_NUM_VAR = Expression._RE_NUM_VAR
 303     _RE_OPERATORS = re.compile(r'(&|\||~)')
 304
 305     @classmethod
 306     def fromstring(cls, string):
 307         # remove curly brackets
 308         string = cls._RE_BRACES.sub(r'', string)
 309         # replace '=' by '=='
 310         string = cls._RE_EQ.sub(r'\1==\2', string)
 311         # replace 'and', 'or', 'not'
 312         string = cls._RE_AND.sub(r' & ', string)
 313         string = cls._RE_OR.sub(r' | ', string)
 314         string = cls._RE_NOT.sub(r' ~', string)
 315         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 316         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 317         # add parentheses to force precedence
 318         tokens = cls._RE_OPERATORS.split(string)
 319         for i, token in enumerate(tokens):
 320             if i % 2 == 0:
 321                 token = '({})'.format(token)
 322                 tokens[i] = token
 323         string = ''.join(tokens)
 324         tree = ast.parse(string, 'eval')
 325         return cls._fromast(tree)
 326
 327     def __repr__(self):
 328         assert len(self.polyhedra) >= 2
 329         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 330         return 'Or({})'.format(', '.join(strings))
 331
 332     @classmethod
 333     def fromsympy(cls, expr):
 334         raise NotImplementedError
 335
 336     def tosympy(self):
 337         raise NotImplementedError
 338
 339 def And(*domains):
 340     if len(domains) == 0:
 341         from .polyhedra import Universe
 342         return Universe
 343     else:
 344         return domains[0].intersection(*domains[1:])
 345
 346 def Or(*domains):
 347     if len(domains) == 0:
 348         from .polyhedra import Empty
 349         return Empty
 350     else:
 351         return domains[0].union(*domains[1:])
 352
 353 def Not(domain):
 354     return ~domain