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         #returning list of verticies
 264         from .polyhedra import Polyhedron
 265         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 266         vertices = libisl.isl_basic_set_compute_vertices(islbset);
 267         vertices = islhelper.isl_vertices_vertices(vertices)
 268         points = []
 269         for vertex in vertices:
 270             expr = libisl.isl_vertex_get_expr(vertex)
 271             point = {}
 272             if islhelper.isl_version < '0.13':
 273                 constraints = islhelper.isl_basic_set_constraints(expr)
 274                 for constraint in constraints:
 275                     constant = libisl.isl_constraint_get_constant_val(constraint)
 276                     constant = islhelper.isl_val_to_int(constant)
 277                     for index, symbol in enumerate(self.symbols):
 278                         coefficient = libisl.isl_constraint_get_coefficient_val(constraint,
 279                             libisl.isl_dim_set, index)
 280                         coefficient = islhelper.isl_val_to_int(coefficient)
 281                         if coefficient != 0:
 282                             coordinate = -Fraction(constant, coefficient)
 283                             point[symbol]= coordinate
 284             else:
 285                 # horrible hack, find a cleaner solution
 286                 string = islhelper.isl_multi_aff_to_str(expr)
 287                 matches = self._RE_COORDINATE.finditer(string)
 288                 for symbol, match in zip(self.symbols, matches):
 289                     numerator = int(match.group('num'))
 290                     denominator = match.group('den')
 291                     denominator = 1 if denominator is None else int(denominator)
 292                     coordinate = Fraction(numerator, denominator)
 293                     point[symbol] = coordinate
 294             points.append(point)
 295         return points
 296
 297     def points(self):
 298         if not self.isbounded():
 299             raise ValueError('domain must be bounded')
 300         from .polyhedra import Universe, Eq
 301         islset = self._toislset(self.polyhedra, self.symbols)
 302         islpoints = islhelper.isl_set_points(islset)
 303         points = []
 304         for islpoint in islpoints:
 305             point = {}
 306             for index, symbol in enumerate(self.symbols):
 307                 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 308                     libisl.isl_dim_set, index)
 309                 coordinate = islhelper.isl_val_to_int(coordinate)
 310                 point[symbol] = coordinate
 311             points.append(point)
 312         return points
 313
 314     def subs(self, symbol, expression=None):
 315         polyhedra = [polyhedron.subs(symbol, expression)
 316             for polyhedron in self.polyhedra]
 317         return Domain(*polyhedra)
 318
 319     @classmethod
 320     def _fromislset(cls, islset, symbols):
 321         from .polyhedra import Polyhedron
 322         islset = libisl.isl_set_remove_divs(islset)
 323         islbsets = isl_set_basic_sets(islset)
 324         libisl.isl_set_free(islset)
 325         polyhedra = []
 326         for islbset in islbsets:
 327             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 328             polyhedra.append(polyhedron)
 329         if len(polyhedra) == 0:
 330             from .polyhedra import Empty
 331             return Empty
 332         elif len(polyhedra) == 1:
 333             return polyhedra[0]
 334         else:
 335             self = object().__new__(Domain)
 336             self._polyhedra = tuple(polyhedra)
 337             self._symbols = cls._xsymbols(polyhedra)
 338             self._dimension = len(self._symbols)
 339             return self
 340
 341     @classmethod
 342     def _toislset(cls, polyhedra, symbols):
 343         polyhedron = polyhedra[0]
 344         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 345             polyhedron.inequalities, symbols)
 346         islset1 = libisl.isl_set_from_basic_set(islbset)
 347         for polyhedron in polyhedra[1:]:
 348             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 349                 polyhedron.inequalities, symbols)
 350             islset2 = libisl.isl_set_from_basic_set(islbset)
 351             islset1 = libisl.isl_set_union(islset1, islset2)
 352         return islset1
 353
 354     @classmethod
 355     def _fromast(cls, node):
 356         from .polyhedra import Polyhedron
 357         if isinstance(node, ast.Module) and len(node.body) == 1:
 358             return cls._fromast(node.body[0])
 359         elif isinstance(node, ast.Expr):
 360             return cls._fromast(node.value)
 361         elif isinstance(node, ast.UnaryOp):
 362             domain = cls._fromast(node.operand)
 363             if isinstance(node.operand, ast.invert):
 364                 return Not(domain)
 365         elif isinstance(node, ast.BinOp):
 366             domain1 = cls._fromast(node.left)
 367             domain2 = cls._fromast(node.right)
 368             if isinstance(node.op, ast.BitAnd):
 369                 return And(domain1, domain2)
 370             elif isinstance(node.op, ast.BitOr):
 371                 return Or(domain1, domain2)
 372         elif isinstance(node, ast.Compare):
 373             equalities = []
 374             inequalities = []
 375             left = Expression._fromast(node.left)
 376             for i in range(len(node.ops)):
 377                 op = node.ops[i]
 378                 right = Expression._fromast(node.comparators[i])
 379                 if isinstance(op, ast.Lt):
 380                     inequalities.append(right - left - 1)
 381                 elif isinstance(op, ast.LtE):
 382                     inequalities.append(right - left)
 383                 elif isinstance(op, ast.Eq):
 384                     equalities.append(left - right)
 385                 elif isinstance(op, ast.GtE):
 386                     inequalities.append(left - right)
 387                 elif isinstance(op, ast.Gt):
 388                     inequalities.append(left - right - 1)
 389                 else:
 390                     break
 391                 left = right
 392             else:
 393                 return Polyhedron(equalities, inequalities)
 394         raise SyntaxError('invalid syntax')
 395
 396     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 397     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 398     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 399     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 400     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 401     _RE_NUM_VAR = Expression._RE_NUM_VAR
 402     _RE_OPERATORS = re.compile(r'(&|\||~)')
 403
 404     @classmethod
 405     def fromstring(cls, string):
 406         # remove curly brackets
 407         string = cls._RE_BRACES.sub(r'', string)
 408         # replace '=' by '=='
 409         string = cls._RE_EQ.sub(r'\1==\2', string)
 410         # replace 'and', 'or', 'not'
 411         string = cls._RE_AND.sub(r' & ', string)
 412         string = cls._RE_OR.sub(r' | ', string)
 413         string = cls._RE_NOT.sub(r' ~', string)
 414         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 415         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 416         # add parentheses to force precedence
 417         tokens = cls._RE_OPERATORS.split(string)
 418         for i, token in enumerate(tokens):
 419             if i % 2 == 0:
 420                 token = '({})'.format(token)
 421                 tokens[i] = token
 422         string = ''.join(tokens)
 423         tree = ast.parse(string, 'eval')
 424         return cls._fromast(tree)
 425
 426     def __repr__(self):
 427         assert len(self.polyhedra) >= 2
 428         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 429         return 'Or({})'.format(', '.join(strings))
 430
 431     @classmethod
 432     def fromsympy(cls, expr):
 433         import sympy
 434         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 435         funcmap = {
 436             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 437             sympy.Lt: Lt, sympy.Le: Le,
 438             sympy.Eq: Eq, sympy.Ne: Ne,
 439             sympy.Ge: Ge, sympy.Gt: Gt,
 440         }
 441         if expr.func in funcmap:
 442             args = [Domain.fromsympy(arg) for arg in expr.args]
 443             return funcmap[expr.func](*args)
 444         elif isinstance(expr, sympy.Expr):
 445             return Expression.fromsympy(expr)
 446         raise ValueError('non-domain expression: {!r}'.format(expr))
 447
 448     def tosympy(self):
 449         import sympy
 450         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 451         return sympy.Or(*polyhedra)
 452
 453
 454 def And(*domains):
 455     if len(domains) == 0:
 456         from .polyhedra import Universe
 457         return Universe
 458     else:
 459         return domains[0].intersection(*domains[1:])
 460
 461 def Or(*domains):
 462     if len(domains) == 0:
 463         from .polyhedra import Empty
 464         return Empty
 465     else:
 466         return domains[0].union(*domains[1:])
 467
 468 def Not(domain):
 469     return ~domain