pypol/domains.py

   1 import ast
   2 import functools
   3 import re
   4
   5 from fractions import Fraction
   6
   7 from . import islhelper
   8 from .islhelper import mainctx, libisl, isl_set_basic_sets
   9 from .linexprs import Expression, Symbol
  10
  11
  12 __all__ = [
  13     'Domain',
  14     'And', 'Or', 'Not',
  15 ]
  16
  17
  18 @functools.total_ordering
  19 class Domain:
  20
  21     __slots__ = (
  22         '_polyhedra',
  23         '_symbols',
  24         '_dimension',
  25     )
  26
  27     def __new__(cls, *polyhedra):
  28         from .polyhedra import Polyhedron
  29         if len(polyhedra) == 1:
  30             polyhedron = polyhedra[0]
  31             if isinstance(polyhedron, str):
  32                 return cls.fromstring(polyhedron)
  33             elif isinstance(polyhedron, Polyhedron):
  34                 return polyhedron
  35             else:
  36                 raise TypeError('argument must be a string '
  37                     'or a Polyhedron instance')
  38         else:
  39             for polyhedron in polyhedra:
  40                 if not isinstance(polyhedron, Polyhedron):
  41                     raise TypeError('arguments must be Polyhedron instances')
  42             symbols = cls._xsymbols(polyhedra)
  43             islset = cls._toislset(polyhedra, symbols)
  44             return cls._fromislset(islset, symbols)
  45
  46     @classmethod
  47     def _xsymbols(cls, iterator):
  48         """
  49         Return the ordered tuple of symbols present in iterator.
  50         """
  51         symbols = set()
  52         for item in iterator:
  53             symbols.update(item.symbols)
  54         return tuple(sorted(symbols, key=Symbol.sortkey))
  55
  56     @property
  57     def polyhedra(self):
  58         return self._polyhedra
  59
  60     @property
  61     def symbols(self):
  62         return self._symbols
  63
  64     @property
  65     def dimension(self):
  66         return self._dimension
  67
  68     def disjoint(self):
  69         islset = self._toislset(self.polyhedra, self.symbols)
  70         islset = libisl.isl_set_make_disjoint(mainctx, islset)
  71         return self._fromislset(islset, self.symbols)
  72
  73     def isempty(self):
  74         islset = self._toislset(self.polyhedra, self.symbols)
  75         empty = bool(libisl.isl_set_is_empty(islset))
  76         libisl.isl_set_free(islset)
  77         return empty
  78
  79     def __bool__(self):
  80         return not self.isempty()
  81
  82     def isuniverse(self):
  83         islset = self._toislset(self.polyhedra, self.symbols)
  84         universe = bool(libisl.isl_set_plain_is_universe(islset))
  85         libisl.isl_set_free(islset)
  86         return universe
  87
  88     def isbounded(self):
  89         islset = self._toislset(self.polyhedra, self.symbols)
  90         bounded = bool(libisl.isl_set_is_bounded(islset))
  91         libisl.isl_set_free(islset)
  92         return bounded
  93
  94     def __eq__(self, other):
  95         symbols = self._xsymbols([self, other])
  96         islset1 = self._toislset(self.polyhedra, symbols)
  97         islset2 = other._toislset(other.polyhedra, symbols)
  98         equal = bool(libisl.isl_set_is_equal(islset1, islset2))
  99         libisl.isl_set_free(islset1)
 100         libisl.isl_set_free(islset2)
 101         return equal
 102
 103     def isdisjoint(self, other):
 104         symbols = self._xsymbols([self, other])
 105         islset1 = self._toislset(self.polyhedra, symbols)
 106         islset2 = self._toislset(other.polyhedra, symbols)
 107         equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
 108         libisl.isl_set_free(islset1)
 109         libisl.isl_set_free(islset2)
 110         return equal
 111
 112     def issubset(self, other):
 113         symbols = self._xsymbols([self, other])
 114         islset1 = self._toislset(self.polyhedra, symbols)
 115         islset2 = self._toislset(other.polyhedra, symbols)
 116         equal = bool(libisl.isl_set_is_subset(islset1, islset2))
 117         libisl.isl_set_free(islset1)
 118         libisl.isl_set_free(islset2)
 119         return equal
 120
 121     def __le__(self, other):
 122         return self.issubset(other)
 123
 124     def __lt__(self, other):
 125         symbols = self._xsymbols([self, other])
 126         islset1 = self._toislset(self.polyhedra, symbols)
 127         islset2 = self._toislset(other.polyhedra, symbols)
 128         equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
 129         libisl.isl_set_free(islset1)
 130         libisl.isl_set_free(islset2)
 131         return equal
 132
 133     def complement(self):
 134         islset = self._toislset(self.polyhedra, self.symbols)
 135         islset = libisl.isl_set_complement(islset)
 136         return self._fromislset(islset, self.symbols)
 137
 138     def __invert__(self):
 139         return self.complement()
 140
 141     def simplify(self):
 142         #does not change anything in any of the examples
 143         #isl seems to do this naturally
 144         islset = self._toislset(self.polyhedra, self.symbols)
 145         islset = libisl.isl_set_remove_redundancies(islset)
 146         return self._fromislset(islset, self.symbols)
 147
 148     def aspolyhedron(self):
 149         # several types of hull are available
 150         # polyhedral seems to be the more appropriate, to be checked
 151         from .polyhedra import Polyhedron
 152         islset = self._toislset(self.polyhedra, self.symbols)
 153         islbset = libisl.isl_set_polyhedral_hull(islset)
 154         return Polyhedron._fromislbasicset(islbset, self.symbols)
 155
 156     def project(self, dims):
 157         # use to remove certain variables
 158         islset = self._toislset(self.polyhedra, self.symbols)
 159         n = 0
 160         for index, symbol in reversed(list(enumerate(self.symbols))):
 161             if symbol in dims:
 162                 n += 1
 163             elif n > 0:
 164                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
 165                 n = 0
 166         if n > 0:
 167             islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
 168         dims = [symbol for symbol in self.symbols if symbol not in dims]
 169         return Domain._fromislset(islset, dims)
 170
 171     def sample(self):
 172         islset = self._toislset(self.polyhedra, self.symbols)
 173         islpoint = libisl.isl_set_sample_point(islset)
 174         if bool(libisl.isl_point_is_void(islpoint)):
 175             libisl.isl_point_free(islpoint)
 176             raise ValueError('domain must be non-empty')
 177         point = {}
 178         for index, symbol in enumerate(self.symbols):
 179             coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 180                 libisl.isl_dim_set, index)
 181             coordinate = islhelper.isl_val_to_int(coordinate)
 182             point[symbol] = coordinate
 183         libisl.isl_point_free(islpoint)
 184         return point
 185
 186     def intersection(self, *others):
 187         if len(others) == 0:
 188             return self
 189         symbols = self._xsymbols((self,) + others)
 190         islset1 = self._toislset(self.polyhedra, symbols)
 191         for other in others:
 192             islset2 = other._toislset(other.polyhedra, symbols)
 193             islset1 = libisl.isl_set_intersect(islset1, islset2)
 194         return self._fromislset(islset1, symbols)
 195
 196     def __and__(self, other):
 197         return self.intersection(other)
 198
 199     def union(self, *others):
 200         if len(others) == 0:
 201             return self
 202         symbols = self._xsymbols((self,) + others)
 203         islset1 = self._toislset(self.polyhedra, symbols)
 204         for other in others:
 205             islset2 = other._toislset(other.polyhedra, symbols)
 206             islset1 = libisl.isl_set_union(islset1, islset2)
 207         return self._fromislset(islset1, symbols)
 208
 209     def __or__(self, other):
 210         return self.union(other)
 211
 212     def __add__(self, other):
 213         return self.union(other)
 214
 215     def difference(self, other):
 216         symbols = self._xsymbols([self, other])
 217         islset1 = self._toislset(self.polyhedra, symbols)
 218         islset2 = other._toislset(other.polyhedra, symbols)
 219         islset = libisl.isl_set_subtract(islset1, islset2)
 220         return self._fromislset(islset, symbols)
 221
 222     def __sub__(self, other):
 223         return self.difference(other)
 224
 225     def lexmin(self):
 226         islset = self._toislset(self.polyhedra, self.symbols)
 227         islset = libisl.isl_set_lexmin(islset)
 228         return self._fromislset(islset, self.symbols)
 229
 230     def lexmax(self):
 231         islset = self._toislset(self.polyhedra, self.symbols)
 232         islset = libisl.isl_set_lexmax(islset)
 233         return self._fromislset(islset, self.symbols)
 234
 235     def num_parameters(self):
 236         #could be useful with large, complicated polyhedrons
 237         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 238         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 239         return num
 240
 241     def involves_dims(self, dims):
 242         #could be useful with large, complicated polyhedrons
 243         islset = self._toislset(self.polyhedra, self.symbols)
 244         dims = sorted(dims)
 245         symbols = sorted(list(self.symbols))
 246         n = 0
 247         if len(dims)>0:
 248             for dim in dims:
 249                 if dim in symbols:
 250                     first = symbols.index(dims[0])
 251                     n +=1
 252                 else:
 253                     first = 0
 254         else:
 255             return False
 256         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 257         libisl.isl_set_free(islset)
 258         return value
 259
 260     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 261
 262     def vertices(self):
 263         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 264         vertices = libisl.isl_basic_set_compute_vertices(islbset);
 265         vertices = islhelper.isl_vertices_vertices(vertices)
 266         points = []
 267         for vertex in vertices:
 268             expr = libisl.isl_vertex_get_expr(vertex);
 269             if islhelper.isl_version < '0.13':
 270                 string = islhelper.isl_set_to_str(expr)
 271                 print(string)
 272                 # to be continued...
 273             else:
 274                 # horrible hack, find a cleaner solution
 275                 string = islhelper.isl_multi_aff_to_str(expr)
 276                 matches = self._RE_COORDINATE.finditer(string)
 277                 point = {}
 278                 for symbol, match in zip(self.symbols, matches):
 279                     numerator = int(match.group('num'))
 280                     denominator = match.group('den')
 281                     denominator = 1 if denominator is None else int(denominator)
 282                     coordinate = Fraction(numerator, denominator)
 283                     point[symbol] = coordinate
 284                 points.append(point)
 285         return points
 286
 287     def points(self):
 288         if not self.isbounded():
 289             raise ValueError('domain must be bounded')
 290         from .polyhedra import Universe, Eq
 291         islset = self._toislset(self.polyhedra, self.symbols)
 292         islpoints = islhelper.isl_set_points(islset)
 293         points = []
 294         for islpoint in islpoints:
 295             point = {}
 296             for index, symbol in enumerate(self.symbols):
 297                 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 298                     libisl.isl_dim_set, index)
 299                 coordinate = islhelper.isl_val_to_int(coordinate)
 300                 point[symbol] = coordinate
 301             points.append(point)
 302         return points
 303
 304     def subs(self, symbol, expression=None):
 305         polyhedra = [polyhedron.subs(symbol, expression)
 306             for polyhedron in self.polyhedra]
 307         return Domain(*polyhedra)
 308
 309     @classmethod
 310     def _fromislset(cls, islset, symbols):
 311         from .polyhedra import Polyhedron
 312         islset = libisl.isl_set_remove_divs(islset)
 313         islbsets = isl_set_basic_sets(islset)
 314         libisl.isl_set_free(islset)
 315         polyhedra = []
 316         for islbset in islbsets:
 317             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 318             polyhedra.append(polyhedron)
 319         if len(polyhedra) == 0:
 320             from .polyhedra import Empty
 321             return Empty
 322         elif len(polyhedra) == 1:
 323             return polyhedra[0]
 324         else:
 325             self = object().__new__(Domain)
 326             self._polyhedra = tuple(polyhedra)
 327             self._symbols = cls._xsymbols(polyhedra)
 328             self._dimension = len(self._symbols)
 329             return self
 330
 331     @classmethod
 332     def _toislset(cls, polyhedra, symbols):
 333         polyhedron = polyhedra[0]
 334         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 335             polyhedron.inequalities, symbols)
 336         islset1 = libisl.isl_set_from_basic_set(islbset)
 337         for polyhedron in polyhedra[1:]:
 338             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 339                 polyhedron.inequalities, symbols)
 340             islset2 = libisl.isl_set_from_basic_set(islbset)
 341             islset1 = libisl.isl_set_union(islset1, islset2)
 342         return islset1
 343
 344     @classmethod
 345     def _fromast(cls, node):
 346         from .polyhedra import Polyhedron
 347         if isinstance(node, ast.Module) and len(node.body) == 1:
 348             return cls._fromast(node.body[0])
 349         elif isinstance(node, ast.Expr):
 350             return cls._fromast(node.value)
 351         elif isinstance(node, ast.UnaryOp):
 352             domain = cls._fromast(node.operand)
 353             if isinstance(node.operand, ast.invert):
 354                 return Not(domain)
 355         elif isinstance(node, ast.BinOp):
 356             domain1 = cls._fromast(node.left)
 357             domain2 = cls._fromast(node.right)
 358             if isinstance(node.op, ast.BitAnd):
 359                 return And(domain1, domain2)
 360             elif isinstance(node.op, ast.BitOr):
 361                 return Or(domain1, domain2)
 362         elif isinstance(node, ast.Compare):
 363             equalities = []
 364             inequalities = []
 365             left = Expression._fromast(node.left)
 366             for i in range(len(node.ops)):
 367                 op = node.ops[i]
 368                 right = Expression._fromast(node.comparators[i])
 369                 if isinstance(op, ast.Lt):
 370                     inequalities.append(right - left - 1)
 371                 elif isinstance(op, ast.LtE):
 372                     inequalities.append(right - left)
 373                 elif isinstance(op, ast.Eq):
 374                     equalities.append(left - right)
 375                 elif isinstance(op, ast.GtE):
 376                     inequalities.append(left - right)
 377                 elif isinstance(op, ast.Gt):
 378                     inequalities.append(left - right - 1)
 379                 else:
 380                     break
 381                 left = right
 382             else:
 383                 return Polyhedron(equalities, inequalities)
 384         raise SyntaxError('invalid syntax')
 385
 386     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 387     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 388     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 389     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 390     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 391     _RE_NUM_VAR = Expression._RE_NUM_VAR
 392     _RE_OPERATORS = re.compile(r'(&|\||~)')
 393
 394     @classmethod
 395     def fromstring(cls, string):
 396         # remove curly brackets
 397         string = cls._RE_BRACES.sub(r'', string)
 398         # replace '=' by '=='
 399         string = cls._RE_EQ.sub(r'\1==\2', string)
 400         # replace 'and', 'or', 'not'
 401         string = cls._RE_AND.sub(r' & ', string)
 402         string = cls._RE_OR.sub(r' | ', string)
 403         string = cls._RE_NOT.sub(r' ~', string)
 404         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 405         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 406         # add parentheses to force precedence
 407         tokens = cls._RE_OPERATORS.split(string)
 408         for i, token in enumerate(tokens):
 409             if i % 2 == 0:
 410                 token = '({})'.format(token)
 411                 tokens[i] = token
 412         string = ''.join(tokens)
 413         tree = ast.parse(string, 'eval')
 414         return cls._fromast(tree)
 415
 416     def __repr__(self):
 417         assert len(self.polyhedra) >= 2
 418         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 419         return 'Or({})'.format(', '.join(strings))
 420
 421     @classmethod
 422     def fromsympy(cls, expr):
 423         import sympy
 424         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 425         funcmap = {
 426             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 427             sympy.Lt: Lt, sympy.Le: Le,
 428             sympy.Eq: Eq, sympy.Ne: Ne,
 429             sympy.Ge: Ge, sympy.Gt: Gt,
 430         }
 431         if expr.func in funcmap:
 432             args = [Domain.fromsympy(arg) for arg in expr.args]
 433             return funcmap[expr.func](*args)
 434         elif isinstance(expr, sympy.Expr):
 435             return Expression.fromsympy(expr)
 436         raise ValueError('non-domain expression: {!r}'.format(expr))
 437
 438     def tosympy(self):
 439         import sympy
 440         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 441         return sympy.Or(*polyhedra)
 442
 443
 444 def And(*domains):
 445     if len(domains) == 0:
 446         from .polyhedra import Universe
 447         return Universe
 448     else:
 449         return domains[0].intersection(*domains[1:])
 450
 451 def Or(*domains):
 452     if len(domains) == 0:
 453         from .polyhedra import Empty
 454         return Empty
 455     else:
 456         return domains[0].union(*domains[1:])
 457
 458 def Not(domain):
 459     return ~domain