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 .coordinates import Point
  10 from .linexprs import Expression, Symbol
  11
  12
  13 __all__ = [
  14     'Domain',
  15     'And', 'Or', 'Not',
  16 ]
  17
  18
  19 @functools.total_ordering
  20 class Domain:
  21
  22     __slots__ = (
  23         '_polyhedra',
  24         '_symbols',
  25         '_dimension',
  26     )
  27
  28     def __new__(cls, *polyhedra):
  29         from .polyhedra import Polyhedron
  30         if len(polyhedra) == 1:
  31             polyhedron = polyhedra[0]
  32             if isinstance(polyhedron, str):
  33                 return cls.fromstring(polyhedron)
  34             elif isinstance(polyhedron, Polyhedron):
  35                 return polyhedron
  36             else:
  37                 raise TypeError('argument must be a string '
  38                     'or a Polyhedron instance')
  39         else:
  40             for polyhedron in polyhedra:
  41                 if not isinstance(polyhedron, Polyhedron):
  42                     raise TypeError('arguments must be Polyhedron instances')
  43             symbols = cls._xsymbols(polyhedra)
  44             islset = cls._toislset(polyhedra, symbols)
  45             return cls._fromislset(islset, symbols)
  46
  47     @classmethod
  48     def _xsymbols(cls, iterator):
  49         """
  50         Return the ordered tuple of symbols present in iterator.
  51         """
  52         symbols = set()
  53         for item in iterator:
  54             symbols.update(item.symbols)
  55         return tuple(sorted(symbols, key=Symbol.sortkey))
  56
  57     @property
  58     def polyhedra(self):
  59         return self._polyhedra
  60
  61     @property
  62     def symbols(self):
  63         return self._symbols
  64
  65     @property
  66     def dimension(self):
  67         return self._dimension
  68
  69     def disjoint(self):
  70         islset = self._toislset(self.polyhedra, self.symbols)
  71         islset = libisl.isl_set_make_disjoint(mainctx, islset)
  72         return self._fromislset(islset, self.symbols)
  73
  74     def isempty(self):
  75         islset = self._toislset(self.polyhedra, self.symbols)
  76         empty = bool(libisl.isl_set_is_empty(islset))
  77         libisl.isl_set_free(islset)
  78         return empty
  79
  80     def __bool__(self):
  81         return not self.isempty()
  82
  83     def isuniverse(self):
  84         islset = self._toislset(self.polyhedra, self.symbols)
  85         universe = bool(libisl.isl_set_plain_is_universe(islset))
  86         libisl.isl_set_free(islset)
  87         return universe
  88
  89     def isbounded(self):
  90         islset = self._toislset(self.polyhedra, self.symbols)
  91         bounded = bool(libisl.isl_set_is_bounded(islset))
  92         libisl.isl_set_free(islset)
  93         return bounded
  94
  95     def __eq__(self, other):
  96         symbols = self._xsymbols([self, other])
  97         islset1 = self._toislset(self.polyhedra, symbols)
  98         islset2 = other._toislset(other.polyhedra, symbols)
  99         equal = bool(libisl.isl_set_is_equal(islset1, islset2))
 100         libisl.isl_set_free(islset1)
 101         libisl.isl_set_free(islset2)
 102         return equal
 103
 104     def isdisjoint(self, other):
 105         symbols = self._xsymbols([self, other])
 106         islset1 = self._toislset(self.polyhedra, symbols)
 107         islset2 = self._toislset(other.polyhedra, symbols)
 108         equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
 109         libisl.isl_set_free(islset1)
 110         libisl.isl_set_free(islset2)
 111         return equal
 112
 113     def issubset(self, other):
 114         symbols = self._xsymbols([self, other])
 115         islset1 = self._toislset(self.polyhedra, symbols)
 116         islset2 = self._toislset(other.polyhedra, symbols)
 117         equal = bool(libisl.isl_set_is_subset(islset1, islset2))
 118         libisl.isl_set_free(islset1)
 119         libisl.isl_set_free(islset2)
 120         return equal
 121
 122     def __le__(self, other):
 123         return self.issubset(other)
 124
 125     def __lt__(self, other):
 126         symbols = self._xsymbols([self, other])
 127         islset1 = self._toislset(self.polyhedra, symbols)
 128         islset2 = self._toislset(other.polyhedra, symbols)
 129         equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
 130         libisl.isl_set_free(islset1)
 131         libisl.isl_set_free(islset2)
 132         return equal
 133
 134     def complement(self):
 135         islset = self._toislset(self.polyhedra, self.symbols)
 136         islset = libisl.isl_set_complement(islset)
 137         return self._fromislset(islset, self.symbols)
 138
 139     def __invert__(self):
 140         return self.complement()
 141
 142     def simplify(self):
 143         #does not change anything in any of the examples
 144         #isl seems to do this naturally
 145         islset = self._toislset(self.polyhedra, self.symbols)
 146         islset = libisl.isl_set_remove_redundancies(islset)
 147         return self._fromislset(islset, self.symbols)
 148
 149     def aspolyhedron(self):
 150         # several types of hull are available
 151         # polyhedral seems to be the more appropriate, to be checked
 152         from .polyhedra import Polyhedron
 153         islset = self._toislset(self.polyhedra, self.symbols)
 154         islbset = libisl.isl_set_polyhedral_hull(islset)
 155         return Polyhedron._fromislbasicset(islbset, self.symbols)
 156
 157     def project(self, dims):
 158         # use to remove certain variables
 159         islset = self._toislset(self.polyhedra, self.symbols)
 160         n = 0
 161         for index, symbol in reversed(list(enumerate(self.symbols))):
 162             if symbol in dims:
 163                 n += 1
 164             elif n > 0:
 165                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
 166                 n = 0
 167         if n > 0:
 168             islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
 169         dims = [symbol for symbol in self.symbols if symbol not in dims]
 170         return Domain._fromislset(islset, dims)
 171
 172     def sample(self):
 173         islset = self._toislset(self.polyhedra, self.symbols)
 174         islpoint = libisl.isl_set_sample_point(islset)
 175         if bool(libisl.isl_point_is_void(islpoint)):
 176             libisl.isl_point_free(islpoint)
 177             raise ValueError('domain must be non-empty')
 178         point = {}
 179         for index, symbol in enumerate(self.symbols):
 180             coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 181                 libisl.isl_dim_set, index)
 182             coordinate = islhelper.isl_val_to_int(coordinate)
 183             point[symbol] = coordinate
 184         libisl.isl_point_free(islpoint)
 185         return point
 186
 187     def intersection(self, *others):
 188         if len(others) == 0:
 189             return self
 190         symbols = self._xsymbols((self,) + others)
 191         islset1 = self._toislset(self.polyhedra, symbols)
 192         for other in others:
 193             islset2 = other._toislset(other.polyhedra, symbols)
 194             islset1 = libisl.isl_set_intersect(islset1, islset2)
 195         return self._fromislset(islset1, symbols)
 196
 197     def __and__(self, other):
 198         return self.intersection(other)
 199
 200     def union(self, *others):
 201         if len(others) == 0:
 202             return self
 203         symbols = self._xsymbols((self,) + others)
 204         islset1 = self._toislset(self.polyhedra, symbols)
 205         for other in others:
 206             islset2 = other._toislset(other.polyhedra, symbols)
 207             islset1 = libisl.isl_set_union(islset1, islset2)
 208         return self._fromislset(islset1, symbols)
 209
 210     def __or__(self, other):
 211         return self.union(other)
 212
 213     def __add__(self, other):
 214         return self.union(other)
 215
 216     def difference(self, other):
 217         symbols = self._xsymbols([self, other])
 218         islset1 = self._toislset(self.polyhedra, symbols)
 219         islset2 = other._toislset(other.polyhedra, symbols)
 220         islset = libisl.isl_set_subtract(islset1, islset2)
 221         return self._fromislset(islset, symbols)
 222
 223     def __sub__(self, other):
 224         return self.difference(other)
 225
 226     def lexmin(self):
 227         islset = self._toislset(self.polyhedra, self.symbols)
 228         islset = libisl.isl_set_lexmin(islset)
 229         return self._fromislset(islset, self.symbols)
 230
 231     def lexmax(self):
 232         islset = self._toislset(self.polyhedra, self.symbols)
 233         islset = libisl.isl_set_lexmax(islset)
 234         return self._fromislset(islset, self.symbols)
 235
 236     def num_parameters(self):
 237         #could be useful with large, complicated polyhedrons
 238         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 239         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 240         return num
 241
 242     def involves_dims(self, dims):
 243         #could be useful with large, complicated polyhedrons
 244         islset = self._toislset(self.polyhedra, self.symbols)
 245         dims = sorted(dims)
 246         symbols = sorted(list(self.symbols))
 247         n = 0
 248         if len(dims)>0:
 249             for dim in dims:
 250                 if dim in symbols:
 251                     first = symbols.index(dims[0])
 252                     n +=1
 253                 else:
 254                     first = 0
 255         else:
 256             return False
 257         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 258         libisl.isl_set_free(islset)
 259         return value
 260
 261     _RE_COORDINATE = re.compile(r'\((?P<num>\-?\d+)\)(/(?P<den>\d+))?')
 262
 263     def vertices(self):
 264         #returning list of verticies
 265         from .polyhedra import Polyhedron
 266         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 267         vertices = libisl.isl_basic_set_compute_vertices(islbset);
 268         vertices = islhelper.isl_vertices_vertices(vertices)
 269         points = []
 270         for vertex in vertices:
 271             expr = libisl.isl_vertex_get_expr(vertex)
 272             coordinates = []
 273             if islhelper.isl_version < '0.13':
 274                 constraints = islhelper.isl_basic_set_constraints(expr)
 275                 for constraint in constraints:
 276                     constant = libisl.isl_constraint_get_constant_val(constraint)
 277                     constant = islhelper.isl_val_to_int(constant)
 278                     for index, symbol in enumerate(self.symbols):
 279                         coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
 280                             libisl.isl_dim_set, index)
 281                         coefficient = islhelper.isl_val_to_int(coefficient)
 282                         if coefficient != 0:
 283                             coordinate = -Fraction(constant, coefficient)
 284                             coordinates.append((symbol, coordinate))
 285             else:
 286                 # horrible hack, find a cleaner solution
 287                 string = islhelper.isl_multi_aff_to_str(expr)
 288                 matches = self._RE_COORDINATE.finditer(string)
 289                 for symbol, match in zip(self.symbols, matches):
 290                     numerator = int(match.group('num'))
 291                     denominator = match.group('den')
 292                     denominator = 1 if denominator is None else int(denominator)
 293                     coordinate = Fraction(numerator, denominator)
 294                     coordinates.append((symbol, coordinate))
 295             points.append(Point(coordinates))
 296         return points
 297
 298     def points(self):
 299         if not self.isbounded():
 300             raise ValueError('domain must be bounded')
 301         from .polyhedra import Universe, Eq
 302         islset = self._toislset(self.polyhedra, self.symbols)
 303         islpoints = islhelper.isl_set_points(islset)
 304         points = []
 305         for islpoint in islpoints:
 306             coordinates = {}
 307             for index, symbol in enumerate(self.symbols):
 308                 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 309                     libisl.isl_dim_set, index)
 310                 coordinate = islhelper.isl_val_to_int(coordinate)
 311                 coordinates[symbol] = coordinate
 312             points.append(Point(coordinates))
 313         return points
 314
 315     def __contains__(self, point):
 316         for polyhedron in self.polyhedra:
 317             if point in polyhedron:
 318                 return True
 319         return False
 320
 321     def subs(self, symbol, expression=None):
 322         polyhedra = [polyhedron.subs(symbol, expression)
 323             for polyhedron in self.polyhedra]
 324         return Domain(*polyhedra)
 325
 326     @classmethod
 327     def _fromislset(cls, islset, symbols):
 328         from .polyhedra import Polyhedron
 329         islset = libisl.isl_set_remove_divs(islset)
 330         islbsets = isl_set_basic_sets(islset)
 331         libisl.isl_set_free(islset)
 332         polyhedra = []
 333         for islbset in islbsets:
 334             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 335             polyhedra.append(polyhedron)
 336         if len(polyhedra) == 0:
 337             from .polyhedra import Empty
 338             return Empty
 339         elif len(polyhedra) == 1:
 340             return polyhedra[0]
 341         else:
 342             self = object().__new__(Domain)
 343             self._polyhedra = tuple(polyhedra)
 344             self._symbols = cls._xsymbols(polyhedra)
 345             self._dimension = len(self._symbols)
 346             return self
 347
 348     @classmethod
 349     def _toislset(cls, polyhedra, symbols):
 350         polyhedron = polyhedra[0]
 351         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 352             polyhedron.inequalities, symbols)
 353         islset1 = libisl.isl_set_from_basic_set(islbset)
 354         for polyhedron in polyhedra[1:]:
 355             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 356                 polyhedron.inequalities, symbols)
 357             islset2 = libisl.isl_set_from_basic_set(islbset)
 358             islset1 = libisl.isl_set_union(islset1, islset2)
 359         return islset1
 360
 361     @classmethod
 362     def _fromast(cls, node):
 363         from .polyhedra import Polyhedron
 364         if isinstance(node, ast.Module) and len(node.body) == 1:
 365             return cls._fromast(node.body[0])
 366         elif isinstance(node, ast.Expr):
 367             return cls._fromast(node.value)
 368         elif isinstance(node, ast.UnaryOp):
 369             domain = cls._fromast(node.operand)
 370             if isinstance(node.operand, ast.invert):
 371                 return Not(domain)
 372         elif isinstance(node, ast.BinOp):
 373             domain1 = cls._fromast(node.left)
 374             domain2 = cls._fromast(node.right)
 375             if isinstance(node.op, ast.BitAnd):
 376                 return And(domain1, domain2)
 377             elif isinstance(node.op, ast.BitOr):
 378                 return Or(domain1, domain2)
 379         elif isinstance(node, ast.Compare):
 380             equalities = []
 381             inequalities = []
 382             left = Expression._fromast(node.left)
 383             for i in range(len(node.ops)):
 384                 op = node.ops[i]
 385                 right = Expression._fromast(node.comparators[i])
 386                 if isinstance(op, ast.Lt):
 387                     inequalities.append(right - left - 1)
 388                 elif isinstance(op, ast.LtE):
 389                     inequalities.append(right - left)
 390                 elif isinstance(op, ast.Eq):
 391                     equalities.append(left - right)
 392                 elif isinstance(op, ast.GtE):
 393                     inequalities.append(left - right)
 394                 elif isinstance(op, ast.Gt):
 395                     inequalities.append(left - right - 1)
 396                 else:
 397                     break
 398                 left = right
 399             else:
 400                 return Polyhedron(equalities, inequalities)
 401         raise SyntaxError('invalid syntax')
 402
 403     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 404     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 405     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 406     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 407     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 408     _RE_NUM_VAR = Expression._RE_NUM_VAR
 409     _RE_OPERATORS = re.compile(r'(&|\||~)')
 410
 411     @classmethod
 412     def fromstring(cls, string):
 413         # remove curly brackets
 414         string = cls._RE_BRACES.sub(r'', string)
 415         # replace '=' by '=='
 416         string = cls._RE_EQ.sub(r'\1==\2', string)
 417         # replace 'and', 'or', 'not'
 418         string = cls._RE_AND.sub(r' & ', string)
 419         string = cls._RE_OR.sub(r' | ', string)
 420         string = cls._RE_NOT.sub(r' ~', string)
 421         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 422         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 423         # add parentheses to force precedence
 424         tokens = cls._RE_OPERATORS.split(string)
 425         for i, token in enumerate(tokens):
 426             if i % 2 == 0:
 427                 token = '({})'.format(token)
 428                 tokens[i] = token
 429         string = ''.join(tokens)
 430         tree = ast.parse(string, 'eval')
 431         return cls._fromast(tree)
 432
 433     def __repr__(self):
 434         assert len(self.polyhedra) >= 2
 435         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 436         return 'Or({})'.format(', '.join(strings))
 437
 438     @classmethod
 439     def fromsympy(cls, expr):
 440         import sympy
 441         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 442         funcmap = {
 443             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 444             sympy.Lt: Lt, sympy.Le: Le,
 445             sympy.Eq: Eq, sympy.Ne: Ne,
 446             sympy.Ge: Ge, sympy.Gt: Gt,
 447         }
 448         if expr.func in funcmap:
 449             args = [Domain.fromsympy(arg) for arg in expr.args]
 450             return funcmap[expr.func](*args)
 451         elif isinstance(expr, sympy.Expr):
 452             return Expression.fromsympy(expr)
 453         raise ValueError('non-domain expression: {!r}'.format(expr))
 454
 455     def tosympy(self):
 456         import sympy
 457         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 458         return sympy.Or(*polyhedra)
 459
 460
 461 def And(*domains):
 462     if len(domains) == 0:
 463         from .polyhedra import Universe
 464         return Universe
 465     else:
 466         return domains[0].intersection(*domains[1:])
 467
 468 def Or(*domains):
 469     if len(domains) == 0:
 470         from .polyhedra import Empty
 471         return Empty
 472     else:
 473         return domains[0].union(*domains[1:])
 474
 475 def Not(domain):
 476     return ~domain