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, key=Symbol.sortkey))
  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, dims):
 156         # use to remove certain variables
 157         islset = self._toislset(self.polyhedra, self.symbols)
 158         n = 0
 159         for index, symbol in reversed(list(enumerate(self.symbols))):
 160             if symbol in dims:
 161                 n += 1
 162             elif n > 0:
 163                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
 164                 n = 0
 165         if n > 0:
 166             islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
 167         dims = [symbol for symbol in self.symbols if symbol not in dims]
 168         return Domain._fromislset(islset, dims)
 169
 170     def sample(self):
 171         from .polyhedra import Polyhedron
 172         islset = self._toislset(self.polyhedra, self.symbols)
 173         islbset = libisl.isl_set_sample(islset)
 174         # next instruction should NOT be required
 175         islbset = libisl.isl_basic_set_finalize(islbset)
 176         return Polyhedron._fromislbasicset(islbset, self.symbols)
 177
 178     def intersection(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_intersect(islset1, islset2)
 186         return self._fromislset(islset1, symbols)
 187
 188     def __and__(self, other):
 189         return self.intersection(other)
 190
 191     def union(self, *others):
 192         if len(others) == 0:
 193             return self
 194         symbols = self._xsymbols((self,) + others)
 195         islset1 = self._toislset(self.polyhedra, symbols)
 196         for other in others:
 197             islset2 = other._toislset(other.polyhedra, symbols)
 198             islset1 = libisl.isl_set_union(islset1, islset2)
 199         return self._fromislset(islset1, symbols)
 200
 201     def __or__(self, other):
 202         return self.union(other)
 203
 204     def __add__(self, other):
 205         return self.union(other)
 206
 207     def difference(self, other):
 208         symbols = self._xsymbols([self, other])
 209         islset1 = self._toislset(self.polyhedra, symbols)
 210         islset2 = other._toislset(other.polyhedra, symbols)
 211         islset = libisl.isl_set_subtract(islset1, islset2)
 212         return self._fromislset(islset, symbols)
 213
 214     def __sub__(self, other):
 215         return self.difference(other)
 216
 217     def lexmin(self):
 218         islset = self._toislset(self.polyhedra, self.symbols)
 219         islset = libisl.isl_set_lexmin(islset)
 220         return self._fromislset(islset, self.symbols)
 221
 222     def lexmax(self):
 223         islset = self._toislset(self.polyhedra, self.symbols)
 224         islset = libisl.isl_set_lexmax(islset)
 225         return self._fromislset(islset, self.symbols)
 226
 227     def num_parameters(self):
 228         #could be useful with large, complicated polyhedrons
 229         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 230         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 231         return num
 232
 233     def involves_dims(self, dims):
 234         #could be useful with large, complicated polyhedrons
 235         islset = self._toislset(self.polyhedra, self.symbols)
 236         dims = sorted(dims)
 237         symbols = sorted(list(self.symbols))
 238         n = 0
 239         if len(dims)>0:
 240             for dim in dims:
 241                 if dim in symbols:
 242                     first = symbols.index(dims[0])
 243                     n +=1
 244                 else:
 245                     first = 0
 246         else:
 247             return False
 248         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 249         libisl.isl_set_free(islset)
 250         return value
 251
 252     @classmethod
 253     def _fromislset(cls, islset, symbols):
 254         from .polyhedra import Polyhedron
 255         islset = libisl.isl_set_remove_divs(islset)
 256         islbsets = isl_set_basic_sets(islset)
 257         libisl.isl_set_free(islset)
 258         polyhedra = []
 259         for islbset in islbsets:
 260             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 261             polyhedra.append(polyhedron)
 262         if len(polyhedra) == 0:
 263             from .polyhedra import Empty
 264             return Empty
 265         elif len(polyhedra) == 1:
 266             return polyhedra[0]
 267         else:
 268             self = object().__new__(Domain)
 269             self._polyhedra = tuple(polyhedra)
 270             self._symbols = cls._xsymbols(polyhedra)
 271             self._dimension = len(self._symbols)
 272             return self
 273
 274     def _toislset(cls, polyhedra, symbols):
 275         polyhedron = polyhedra[0]
 276         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 277             polyhedron.inequalities, symbols)
 278         islset1 = libisl.isl_set_from_basic_set(islbset)
 279         for polyhedron in polyhedra[1:]:
 280             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 281                 polyhedron.inequalities, symbols)
 282             islset2 = libisl.isl_set_from_basic_set(islbset)
 283             islset1 = libisl.isl_set_union(islset1, islset2)
 284         return islset1
 285
 286     @classmethod
 287     def _fromast(cls, node):
 288         from .polyhedra import Polyhedron
 289         if isinstance(node, ast.Module) and len(node.body) == 1:
 290             return cls._fromast(node.body[0])
 291         elif isinstance(node, ast.Expr):
 292             return cls._fromast(node.value)
 293         elif isinstance(node, ast.UnaryOp):
 294             domain = cls._fromast(node.operand)
 295             if isinstance(node.operand, ast.invert):
 296                 return Not(domain)
 297         elif isinstance(node, ast.BinOp):
 298             domain1 = cls._fromast(node.left)
 299             domain2 = cls._fromast(node.right)
 300             if isinstance(node.op, ast.BitAnd):
 301                 return And(domain1, domain2)
 302             elif isinstance(node.op, ast.BitOr):
 303                 return Or(domain1, domain2)
 304         elif isinstance(node, ast.Compare):
 305             equalities = []
 306             inequalities = []
 307             left = Expression._fromast(node.left)
 308             for i in range(len(node.ops)):
 309                 op = node.ops[i]
 310                 right = Expression._fromast(node.comparators[i])
 311                 if isinstance(op, ast.Lt):
 312                     inequalities.append(right - left - 1)
 313                 elif isinstance(op, ast.LtE):
 314                     inequalities.append(right - left)
 315                 elif isinstance(op, ast.Eq):
 316                     equalities.append(left - right)
 317                 elif isinstance(op, ast.GtE):
 318                     inequalities.append(left - right)
 319                 elif isinstance(op, ast.Gt):
 320                     inequalities.append(left - right - 1)
 321                 else:
 322                     break
 323                 left = right
 324             else:
 325                 return Polyhedron(equalities, inequalities)
 326         raise SyntaxError('invalid syntax')
 327
 328     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 329     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 330     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 331     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 332     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 333     _RE_NUM_VAR = Expression._RE_NUM_VAR
 334     _RE_OPERATORS = re.compile(r'(&|\||~)')
 335
 336     @classmethod
 337     def fromstring(cls, string):
 338         # remove curly brackets
 339         string = cls._RE_BRACES.sub(r'', string)
 340         # replace '=' by '=='
 341         string = cls._RE_EQ.sub(r'\1==\2', string)
 342         # replace 'and', 'or', 'not'
 343         string = cls._RE_AND.sub(r' & ', string)
 344         string = cls._RE_OR.sub(r' | ', string)
 345         string = cls._RE_NOT.sub(r' ~', string)
 346         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 347         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 348         # add parentheses to force precedence
 349         tokens = cls._RE_OPERATORS.split(string)
 350         for i, token in enumerate(tokens):
 351             if i % 2 == 0:
 352                 token = '({})'.format(token)
 353                 tokens[i] = token
 354         string = ''.join(tokens)
 355         tree = ast.parse(string, 'eval')
 356         return cls._fromast(tree)
 357
 358     def __repr__(self):
 359         assert len(self.polyhedra) >= 2
 360         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 361         return 'Or({})'.format(', '.join(strings))
 362
 363     @classmethod
 364     def fromsympy(cls, expr):
 365         import sympy
 366         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 367         funcmap = {
 368             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 369             sympy.Lt: Lt, sympy.Le: Le,
 370             sympy.Eq: Eq, sympy.Ne: Ne,
 371             sympy.Ge: Ge, sympy.Gt: Gt,
 372         }
 373         if expr.func in funcmap:
 374             args = [Domain.fromsympy(arg) for arg in expr.args]
 375             return funcmap[expr.func](*args)
 376         elif isinstance(expr, sympy.Expr):
 377             return Expression.fromsympy(expr)
 378         raise ValueError('non-domain expression: {!r}'.format(expr))
 379
 380     def tosympy(self):
 381         import sympy
 382         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 383         return sympy.Or(*polyhedra)
 384
 385
 386 def And(*domains):
 387     if len(domains) == 0:
 388         from .polyhedra import Universe
 389         return Universe
 390     else:
 391         return domains[0].intersection(*domains[1:])
 392
 393 def Or(*domains):
 394     if len(domains) == 0:
 395         from .polyhedra import Empty
 396         return Empty
 397     else:
 398         return domains[0].union(*domains[1:])
 399
 400 def Not(domain):
 401     return ~domain